The different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour include 11 cups of 1/4 or 3.67 cups of 3/4.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4-cup measuring cup and a 3/4-cup measuring cup that you can use.
The combination will be:.
= 2 3/4 ÷ 1/4.
= 11
The second combination will be:
= 2 3/4 ÷ 3/4
= 3.67
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In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference in two population means. Are the conditions for use of a T-model met?
1. In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
2. In a random sample of 50 university students (37 females and 13 males), the distribution of time spent at university recreational facilities is strongly skewed to the right for females but not strongly skewed for males. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
3. In a study of 100 brother-sister sibling pairs at the university, the distribution of time spent at university recreational facilities for the 100 males is compared to the 100 females; both distributions are fairly normal.
In the following first scenario the conditions for the t-test is not met for the difference in populations mean so the hypothesis test cannot be done.
1)The distribution of time spent at university recreational facilities is considerably skewed to the right in a random sample of 100 university students.
The variable is X, which stands for time spent at the university's leisure facilities.
Because the variable "time" is at least ordinal, this criterion is satisfied.
The sample was drawn at random, hence this requirement is met.
The data is heavily skewed to the right, the normal distribution is symmetrical, and this data set is highly unlikely to have a normal distribution.
2)The distribution of time spent at university recreational facilities is highly skewed to the right for females but not strongly skewed for males in a random sample of 50 university students (37 females and 13 males).
In this scenario, you have two groups of interest, and the variable X: Time spent at the university recreational facilities will be measured for each group.
Because the variable "time" is at least ordinal, this criterion is satisfied.
The samples "male students" and "female students" were randomly taken so this condition tests.
You have two populations of interest in this case. Male university students and female university students are divided into two groups. To use the t-test, both populations must be normal.
The distribution for the females has strongly skewed to the males have a somewhat skewed distribution.
If the distribution of females is substantially skewed, it is impossible for it to be normal.
In this case, a t-test is not appropriate.
3)Because the experimental units are dependent, this is a "paired sample" situation. (Consider the sibling pair's relationship; if they get along well, it is more likely that they will spend time together in the recreational facilities; if their relationship is not so good, it is more likely that the presence of one of the siblings in the facilities will cause the other to spend less time there.)
X will be the variable measured for each member of the "sibling pair": Time spent at university recreational facilities, and the research variable in this case, will be defined by the difference in times measured for both siblings.
The normality condition checks.
so the t-test in this scenario can be applied.
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Please Help
Have a close look at the diagram below. What is the probability of selecting the following marbles in order: red - blue - blue - blue ? Show your work and explain your thinking.
The probability of selecting the following marbles in order: red - blue - blue - blue will be 3 / 40.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
From the diagram Illustrated, it should be noted that that there are 2 blue balls and 3 red balls. The total number of balls will be 5.
The probability of selecting the following marbles in order: red - blue - blue - blue will be:
= 3/5 × 2/4 × 1/4 × 0/3
= 6 / 80
= 3 / 40
The probability is 3 / 40.
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Researchers in the Hopkins Forest (see Problem 7-16 from) also count the number of maple trees (genus
acer) in plots throughout the forest. The following is a histogram of the number of live maples in 1002 plots
sampled over the past 20 years. The average number of maples per plot was 19.86 trees with a standard
deviation of 23.65 trees.
a). If we took the mean of a sample of eight plots, what would be the standard error of the
mean?
b). Using the central limit theorem, what is the probability that the mean of the eight would be
within 1 standard error of the mean?
c). Why might you think that the probability that you calculated in (b) might not be very
accurate?
collect at least 50 observations from a data source of your choice. the observations you collect may be discrete data or continuous data but cannot be categorical in nature. you can generate or collect the observations yourselves, but you may not use mass emailing to the class to do so. you can obtain the data from internet sites, but you must include where you collected the data from as a reference
The discrete data can be number of legs, number of teeth.
The continuous data can be the length of tail, and the height of dog.
Consider the provided information.
The discrete data is a data whose value is obtained by counting and they can be described by an integer value.
So, the discrete data can be number of legs, number of teeth.
A continuous data is a variable whose value is obtained by measuring.
The continuous data can be the length of tail, and the height of dog.
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A manufacturer of floor mops would like her product to last 700 hours, on the average. She hopes the mean number of hours is not a lot less than 700 (people will not continue to buy her product) or a lot more than 700 (people would seldom have to buy the product). However, the manufacturer has reason to believe the mean may have changed. A random sample of 48 items shows that sample mean = 675 and sample standard deviation = 77 hours. Use the significance level α=.05. What is the appropriate test to perform? Regarding the hypothesis testing in question 1, what is the rejection region? Regarding the hypothesis testing in question 1, what is the p-value of the test? Round your answer to four decimal places Regarding the hypothesis testing in question 1, what is your conlusion?
The appropriate test to perform is one sample t test
The rejection reason is t statistic less than -2.012 or t statistic more than -2.012
The p value of the test is 0.0292
Firstly,
As the population standard deviation is unknown and the sample size is more than 30, it is appropriate to use one sample t test for this hypothesis testing
Testing if the mean is changed from 700 levels or not
Null and alternate hypothesis are 700
Degree of freedom,
n-1
= 48-1
= 47
Using alpha level 0.05 and t critical table, we found the following two critical values
t critical values= -2.012 and 2.012
So, the rejection reason is t statistic less than -2.012 or t statistic more than -2.012
Now,
Population means = 700 hours
Sample mean = 675 hours
n = 48
So,
Test statistic= (mean-alternate hypothesis)/(s/√n)
= (675-700)/ (77/√48)
=-25/11.1140
= -2.249
Degree of freedom = n-1
= 48-1
= 47
With t distribution table for -2.249 and 47 degrees of freedom obtain p value of 0.0292
So, pvalue= 0.0292
Reject null hypothesis since the p value is less than alpha level
So, we conclude that the mean has changed from 700 hours
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Indicate whether a binomial distribution is a reasonable probability model for the random variable X. give your reasons in each case.
joey buys a virginia lottery ticket every week. x is the number of times in a year that he wins a prize.
The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.
How to identify binomial distribution model?The conditions for binomial distribution are;
1: The number of observations n must be fixed.
2: Each observation must be independent.
3: Each observation must represent one of two outcomes ("success" or "failure").
4: The probability of "success" p must be the same for each outcome.
Now, we are given the statement;
Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.
From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.
Secondly, we can say that there could be success by winning a price or failure by not winning the price.
Each weekly observation is independent.
The probability is the same for each outcome.
Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.
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An organization needs to reach out to a specific target audience, and has decided that it wants to use social media advertising to do so. It wants to buy specific keywords to accurately target the audience who would want to see these ads. The aim is to get a high effective exposure rate and engagement rate without invading consumer privacy. Which of the following advertising revenue models would best suit the organizations' needs? a. Bidding for ad words b. Pay-per-click c. I-Traffic Index d. Pop-under ads e. Bidding for ad space
The advertising revenue model that would best suit the organization needs is Bidding for ad words.
Given that,
A company has made the decision to employ social media advertising to connect with a certain target population in order to accomplish this. To precisely target the demographic that would be interested in seeing these ads, it wants to purchase a set of keywords. The objective is to increase consumer involvement and exposure rates without violating their privacy.
The Organization investing to buy specific keywords for advertising, when someone searches for some words in a social media search engine, the search engine queries it's users looking for the keyword matches in it's ad group thus displaying the most relevant ad aiming for more exposure.
Therefore, bidding for ad words is the advertising income strategy that would best meet the organization's needs.
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In a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.
How many were in math only?
How many were not majoring in computer science?
How many were not math or computer science?
Answer:
How many were in math only?7
How many were not majoring in computer science?9
How many were not math or computer science?2
Step-by-step explanation:
Total students 25
-math major 13
-Science major 10
_______________
2 not majoring in math or CS majors
math major 13 -6 dual majors = 7 major in math only
math major 7+ not math or CS 2 = 9 not majoring in CS
nikki williams wishes to evaluate the risk and return behaviors associated with various combinations of assets x and y
Nikki can use modern portfolio theory to assess the risk and return behaviors associated with different combinations of assets X and Y.
Modern portfolio theory involves calculating the expected return and risk of a portfolio of assets by analyzing the correlations between the assets. It also looks at the diversification benefits of combining different assets and the impact of adding riskier assets to a portfolio. By quantifying the risk and return behaviors of different portfolios, Nikki can make informed decisions about which portfolios are most suitable for her.Modern portfolio theory is used to assess the risk and return behaviors of different combinations of assets X and Y. It considers correlations between the assets, the diversification benefits of combining them, and the impact of adding riskier assets. By quantifying the risk and return behaviors, Nikki can make informed decisions about which portfolios are most suitable for her.
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An evergreen nursery usually sells certain shrub after 6 years of growth and shaping: The growth rate during those 6 years is approximated by dh/dt = 1.2t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t = 0). (a) Find the height after years h(t) (b) How tall are the shrubs when they are sold? cm
(a) After t years, the height is 18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. If $6000 is invested at 4% interest, compounded annually, then after n years the investment is worth an = 6000(1.04) dollars. Exercise (a) Find the first five terms of the sequence {an}. Step 1 For an = 6000(1.04)", we have a = 6000(1.04) 6240 6240.00 and a2 = 6000(1.04) = 6489.6 6489.60 Step 2 Rounding answers to two decimal places, we similarly have a3 = 6749.184 ,24 = 7019.151 ,ag = 7299.197 X Submit Skip_(you cannot come back) Exercise (b) Is the sequence convergent or divergent? Step 1 Since 1.04 is greater than 1, we have the following. (If an answer does not exist, enter DNE.) lim (1.04)" = 6000n + 1 6000n n00 x Submit Skip (you cannot come back)
As per question and the information provided we can compute the solution for both exercises as follows:
Investments are defined as assets bought or invested in with the goal of increasing wealth and setting aside funds from salary or capital gains. The main goal of an investment is to generate additional revenue or to make money on the investment over a certain amount of time.
Exercise (a)
The sequence "an "'s" first five terms are:
[tex]a1 = 6000(1.04) = 6240 [/tex]
[tex]a2 = 6000(1.04) ^2 = 6489.6 [/tex]
[tex]a3 = 6000(1.04)^3 = 6749.184 [/tex]
[tex]a4 = 6000(1.04) ^4 = 7019.151 [/tex]
[tex]a5 = 6000(1.04)^5 = 7299.197[/tex]
Exercise (b)
Because infinity, which is not a finite number, serves as the series's limit as n approaches infinity, the sequence is divergent.
[tex]an = 6000(1.04)^n [/tex]
that is the formula for the nth term of the sequence. As n rises, the value of
[tex](1.04)^n[/tex]
it grows steadily larger, which causes a to grow steadily larger until it approaches infinity. The sequence "an" diverges as a result.
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The given point is reflected across the line indicated. Find the coordinates of the image.
R across y = -2
If the given point R is reflected across the line y = -2, the image is
(Type an ordered pair.)
The function g(x) is graphed below. According to the graph, what is the
value of g(4)?
Answer:
6
Step-by-step explanation:
g(4) tells us that we need to look for the y coordinate when g(x) reaches 4 on the x axis.
6 is the answer
An article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations. Ethnicity: African, American, Asian, Caucasian, Hispanic Frequency: 69, 11, 330, 8, In a recent census, the proportions for these four ethnic groups are 0.177.0.020, 0.734, and 0.069, respectively. Does the data suggest that the proportions in commercials are different from the census proportions? Carry out a test of appropriate hypotheses using a significance level of 0.01. (Let P, PPs, and be the population proportions of the four ethnic groups (African American, Asian, Caucasian, and Hispanic respectively) appearing in commercials on Philadelphia television stations.) State the appropriate hypotheses. o H0: P1 = 0.165, P2 = 0.026, P3 = 0.789, P4 = 0.019 Ha: at least one P1 ≠ P10o H0: P1 = 0.069, P2 = 0.011, P3 = 0.330, P4 = 0. 008Ha: at least one P1 ≠ P10o H0: P1 = 0. 177, P2 = 0.020, P3 = 0.734, P4 = 0.069Ha: at least one P1 ≠ P10o H0: P1 = P2 = P3 = P4 = 0.250Ha at least one p1 ≠ 0.25 Calculate the test statistic (Round your answer to two decimal places.)x^2 = ______
When comparing the proportions of ethnic groups represented in television commercials on Philadelphia stations to census data, we can use a chi-squared test to see if there is a difference.
Suitable hypotheses for this test include the following: H0: P1 = 0.165, P2 = 0.026, P3 = 0.789, and P4 = 0.019 Ha: at least one P1 to P10, where P1, P2, P3, and P4 represent the proportions of the four main ethnic groups—African, Asian, Caucasian, and Hispanic—in the population.
The test statistic cannot be calculated until we get the predicted frequencies for each group under the null hypothesis. Given that N is the total number of observations and E I is the expected frequency for group I, E I = N * P I provides the expected frequency for each group.
the population percentage for group I is P i.
These equations allow us to determine the anticipated frequencies in the following ways:
E 1 = 69 * 0.165 = 11.485
E 2 = 11 * 0.026 = 0.286
E 3 = 330 * 0.789 = 261.67
E 4 = 8 * 0.019 = 0.152
After that, the chi-squared test statistic is calculated as follows: x2 = ∑_(i=1)4 [(O i - E i)2 / E i], where O i is the observed frequency for group I and E i is the anticipated frequency for group i.
The numbers for the observed and anticipated frequencies are substituted to produce the following equation: x2 = (69 - 11.485)2 / 11.485 + (11 - 0.286)2 / 0.286 + (330 - 261.67)2 / 261.67 + (8 - 0.152)2 / 0.152
= 57.015^2
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Hey WRLD... 999
Match each polynomial with its factorization. Type the number of the corresponding polynomial on the line of it’s factorization on the right.
1.
x2 – 2x – 48
_____ (x + 2)(9 – x)
2.
-3x2 + 14x - 8
____ (2 – 3x)(x – 4)
3.
X2 – 10x – 25
_____ (x + 6) (x – 8)
4.
-x2+7x+18
____ 3(x – 7) (x + 7)
5.
X4 – 16
_____ (x – 5)2
6.
3x2 – 147
_____ ( x – 2)( x + 2)( x2 + 4)
Each equation is expressed and mentioned in its factorized form are given above.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given are the polynomials along with their factorized forms.
The polynomials along with their correct factorized forms are as follows -
x² - 2x - 48 → (x + 6) (x – 8)-3x² + 14x - 8 → (2 – 3x)(x – 4)x² – 10x + 25 → (x - 5)²- x² + 7x + 18 → (x + 2)(9 – x)x⁴ - 16 → (x – 2)(x + 2)(x² + 4)3x² – 147 → 3(x – 7) (x + 7)Therefore, each equation is expressed and mentioned in its factorized form are given above.
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Arianys invested $61,000 in an account paying an interest rate of 7% compounded
continuously. Yusuf invested $61,000 in an account paying an interest rate of 7%
compounded monthly. After 14 years, how much more money would Yusuf have in
his account than Arianys, to the nearest dollar?
Given the above information the amount Yusuf would have more in his account than Arianys is $9,929,539.57
How to calculate compound interest?You should be aware that compound interest is sum of money that accrues on the capital over a stated period of time.
The given parameters are:
Arianys investment = $61,000, interest rate 7% compounded continuously
Yusufs investment = $61,000, rate 7% compounded monthly
number of years each 14 years
Arianys investment
Compound interest = [tex]P(1+r)^{t}[/tex] - 1
Applying the figures we have
CI= 61000(1+0.07)¹⁴ - 1
=61000(1.07)¹⁴ -1
CI=$96,290.58
For Yusuf investment
CI=[tex]P(1+\frac{r}{n})^{nt} - 1[/tex]
Applying the figures we have
Ci=61000(1+0.0121)²⁹⁶⁸ -1
Compound Interest = 61000(1.0058)¹⁶⁸ - 1
Simplifying this we have
61000(164.36)
CI=$10,025,830.12
Therefore the amount in Yusufs account more than Arianys account is $(10,025,830.12-96,290.58)
Amount = $9,929,539.57
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What number is 0.1 less than 15.2?
Answer:
15.1
Step-by-step explanation:
A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33
The 95% confidence interval for this situation is (0.95, 9.71).
What is the Standard deviation?
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.
The formula for Confidence Interval for Population Mean When Population Standard deviation is known
[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]
α for 95% confidence level = (100-95)/100 =0.05
[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025
[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96
σ = 20
95% Confidence Interval for Population Mean When Population Standard deviation is known
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
a.
n=70 ; [tex]\overline{x}=27[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
27 ± 1.96 × (20/√70)
= 27 + 1.96 x 2.3905
= 27 + 4.6853 = (22.31.31.69)
(22.31, 31.69)
b.
n=150 ; [tex]\overline{x}=115[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 115 + 1.96 x
= 115 +1.96 x 1.633 = 115 + 3.2007 = (111.8, 118.2)
(111.8, 118.2)
c.
n=80 , [tex]\overline{x}=18[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 18 + 1.96 x 2.2361 = 18 + 4.3827 = (13.62.22.38) V8018+
(13.62, 22.38)
d.
n=80, [tex]\overline{x}=5.33[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 5.33 1.96 x 2.2361 = 5.33 4.3827 = (0.95, 9.71)
(0.95, 9.71)
e.
No. Since Sample sizes are large [tex](n\small \geq30)[/tex] and randomly selected from the target population, the condition guarantees that the sampling distribution of [tex]\overline{x}[/tex] is approximately normal.
Hence, the 95% confidence interval for this situation is (0.95, 9.71).
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2. Use the product rule (and chain rule) to find the derivative of the following
(a) y = x²(3x + 4)²
(b) y = (1+x²) (2 - x²³)³
(c) y = (2+√)(x+3)²
(d) y = (2x² + 1)(x5 +3)4
The derivative of the following are:
(a) 36x³ + 72x² + 32x
(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)
(c) -1/2√x(x+3)² + 2(x+3)(2+√x)
(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³
What is a derivative?
The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
Here, we have
Given
(a) y = x²(3x + 4)²
Derivative with respect to x and we get
dy/dx = 2x(3x + 4)² + x²(18x + 24)
dy/dx = 36x³ + 72x² + 32x
(b) y = (1+x²) (2 - x²³)³
Derivative with respect to x and we get
dy/dx = 2x(2 - x²³)³ + (1+x²)(-23x²²)3(2 - x²³)²
dy/dx = 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)
(c) y = (2+√x)(x+3)²
Derivative with respect to x and we get
dy/dx = -1/2√x(x+3)² + (2+√x)2(x+3)
dy/dx = -1/2√x(x+3)² + 2(x+3)(2+√x)
(d) y = (2x² + 1)(x⁵ +3)⁴
Derivative with respect to x and we get
dy/dx = 4x(x⁵ +3)⁴ + (2x² + 1)4(x⁵ +3)³(5x⁴)
dy/dx = 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³
Hence, the derivative of the following are:
(a) 36x³ + 72x² + 32x
(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)
(c) -1/2√x(x+3)² + 2(x+3)(2+√x)
(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³
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Brainly please don't delete my question it's not even breaking your guideline I even checked I just need my questions answered!
Answer:
Hey
you are correct
18x – 40
Step-by-step explanation:
2( x + 4 (2x – 5) )
= 2( x + 8x – 20)
= 2x + 16x – 40
= 18x – 40
Dont forget to rate the answer as brainliest
Have a good day
Answer: 18x-40
Step-by-step explanation: First, you have to isolate the 2, so now it would look like this:
=(2)(x+4(2x−5))
Now, You have to isolate the x, along with the 2 again, so it would look like this:
=(2)(x)+(2)(4(2x−5))
Now, you would combine the like terms of 2x & x, and all the numbers that don't have a variable, so it would look like this:
2x+16x−40
Now, finally, we can combine 2x + 16x, because they are like terms, so that is how we get 18x - 40
I hoped this helped friend!
-Shining Dream
Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting. Unfortunately, it only took him 1 12
hours to melt.
Percent error is a way to describe error, expressed as a percentage of the actual amount. What is the percentage error in this situation?
The percentage error in this situation will be 33%.
How to calculate the percentage?It's important to note that Percent error is a way to describe error, expressed as a percentage of the actual amount.
Since Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting but it only took him 1 1/2 hours to melt. The percentage error in this situation will be:
= (2 - 1 1/2) / 1 1/2 × 100
= 1/2 ÷ 1 1/2 × 100
= 1/3 × 100
= 33.33%
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HII EVERYONE can you help me and this problem TYSM
10) There is no solution to given the simultaneous equations
11) There is no solution to given the simultaneous equations
15) There is no solution to given the simultaneous equations
How to solve the system of simultaneous equations?10) We are given the simultaneous equations as;
y = -6x - 8
y = -6x + 8
Plug -6x + 8 for y in eq 1 to get;
-6x + 8 = -6x - 8
Since the coefficient of the variable on both sides are equal, then there is no solution to the simultaneous equation.
11) We are given the simultaneous equations as;
3x - y = 6
-3x + y = -6
Add eq 1 to eq 2 to get;
0 = 0
Thus, there is no solution to the simultaneous linear equations.
12) We are given the simultaneous equations as;
9x - 15y = 24 ------(1)
6x - 10y = -16 ------(2)
Multiply eq 2 by 1.5 and eq 1 by 1 to get;
9x - 15y = 24 ------(3)
9x - 15y = -24 -----(4)
When we subtract eq 3 from eq 4, we get;
0 = -48
Thus, no solution exists.
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sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants she packed. The total number of pairs of pants and shirts was 16
Answer:
She packed 6 pairs of pants and 10 shirts.
Step-by-step explanation:
Say the number of pants is x. Then, the number of pants is 2x-2. Now you have the equation:
x+ (2x-2)=16
Solving this equation gives x=6.
Therefore, she packed 6 pairs of pants and 10 shirts.
Claim: all natural numbers are either even or odd. Proof: By induction. Base case:0 is even, since 0 = 2.0. Now suppose that n - 1 is either even or odd, and we must show that n is either even or odd. Case 1: If n - 1 is even, then n - 1 = 2k for some k, so n = 2k + 1, showing n must be odd. Case 2: If n - 1 is odd, thenn - 1 = 2k +1 for some k, so n = 2k + 2 = 2(k+1), showing n must be even. Is this proof correct?
• Yes • No
No. The proof is wrong.
Here we are asked to prove all Natural numbers are either even or odd.
Natural numbers start from 1 to infinity.
Hence to prove by mathematical induction, we need to take the base case to be n = 1.
here, 1 = 2X0 + 1, therefore 1 is odd
Then we need to assume that for any integer m < n, m is either even or odd.
Now n > 1
Therefore,
n -1 > 0
Hence n - 1 will be a natural number.
Hence by our earlier assumption where any number smaller than is either even or odd
n - 1 has to be either even or odd.
case 1
here n - 1 is odd
if n - 1 is odd then
n-1 + 1 is a sum of two odd numbers, hence n is even
Case 2- If n - 1 is even
then, n-1 + 1 is a sum of an even and n odd number hence n is odd
Therefore n will either be even or odd.
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Diana
averages 6 mph walking
to school. Averaging 35 mph on
the way back home by car, she
takes 3/4 hour less time.
How far is the school
from her home?
The school is 5.43 miles from Diana's house. This is evaluated by using the speed-distance-time relationship.
What is the relation between the speed-distance-time?The ratio of distance to time gives speed to an object.
I.e., S = D/T or D = ST ot T = D/S
Calculation:It is given that,
Diana walks to her school at a speed of 6 mph.
So, the time taken for her to walk is t1 = d/6 hours
Diana returns home by car at a speed of 35 mph.
So, the time taken for her to return by car is t2 = d/35 hours
But it is given that, she takes 3/4 hours less time for returning by car.
Thus, we can write t2 = t1 - 3/4
⇒ d/35 = d/6 - 3/4
⇒ 3/4 = d/6 - d/35 = d(1/6 - 1/35)
⇒ 3/4 = d(29/210)
⇒ d = (3 × 210)/(4 × 29) = 5.431 miles
On rounding the obtained value to the nearest hundredths is 5.43 miles.
Thus, the distance between Diana's home and her school is 5.43 miles.
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elementary surveying two ridges b and c forms a valley having a at the bottom part in between the ridges. elevation difference between b nad c is 111..356 m. observing at point a, the angle of elevation is
the difference of elevation between a and b.Let AB = x, tan 36 = x/111.356 ,x = 111.356 tan 36= 64.39 m and Difference in elevation = 64.39m
We are given that two ridges B and C form a valley with a point A at the bottom part with an elevation difference of 111.356m between the ridges and and angle of elevation of 36 degrees at point A. To find the difference of elevation between A and B, we use the formula of tangent which is tan θ = Opposite/Adjacent. We substitute the values and solve for x, which is the elevation difference between A and B. So the difference in elevation between A and B is 64.39m.
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The least expensive
buttons cost
$0.28 each. Yellow bought all of
the buttons she could for $1.40 and
wore them proudly.
The number of buttons that she can wear proudly will be 5.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another.
As per the given,
Cost of one button = $0.28
The cost of buttons that she can wear = $1.40
A number of buttons = $1.40/$0.28 = 5
Hence "She will be able to wear five buttons with pride.".
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Test of Independence 6. Are the factors that contribute to a person's wellbeing, (ie: Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status. See the chart. Marital married Widowed/divorced totals 42 132 49 Factors contribution to a 50 33 110 person's wellbeing. 21 25 58 100 300 a. a. b. b. C. C. d. d. e. e. status single Friendship 41 and social life Job or 27 primary activity Health and physical condition totals 80 120 State the null and alternative hypothesis State the observed values State the expected values Give the p-value Give a conclusion for the hypothesis test. 12
The conclusion of the hypothesis test is 0.342112
What is meant by hypothesis?
In statistics, hypothesis means an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
Here we have given that the factors that contribute to a person's wellbeing, That is Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status.
And we need to find the null and alternative hypothesis and the conclusion of the hypothesis test.
As per the given table of data we have to calculated the p value in order to find the null and alternative hypothesis,
For that we gathered the value of the following,
Number of samples = 9
Then the mean value of data = 83.63
And the standard deviation of the data = 80.475
Then the p - value is calculated as,
p-value ≈ 0.342112
This decision is made at significance level α = 0.05.
Therefore, the result is not statistically significant: there is not enough evidence to reject the null hypothesis.
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A local university offers a review course for those who are planning to take the GRE exam. Thirty
percent of the people who took the exam had attended the university's GRE review course. The results
of the test showed that 60% of those who attended the review passed the exam, while among those who
did not attend the course, only 20% passed the exam. An individual has passed the exam. Knowing this,
what is the probability that he attended the review course?
The probability that an individual attended the course given he passed
is 37.5%.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
We know the probability of A given B is P(A/B) = P(A∩B)/P(B).
Let, The number of students be 100.
Given, Thirty percent of the people who took the exam had attended the university's GRE review course which is 30 and hence 70 people did not attend the review course.
60% of those who attended the review passed the exam,
= (60/100)×30.
= 18 people.
20% who passed the exam did not attend the review course.
= (20/100)×70.
= 14.
So, The no. of people who passed is (18 + 14)/100 = 32/100 = 0.32.
The probability that a student passed and taken the course is (18/30)×(14/70) = 0.12.
Therefore, Given that he passed, the likelihood that someone took the course is = (0.12/0.32) = 0.375 Or 37.5%.
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Krystal is considering job offers from two companies. Company A offered her a starting salary of $45,000 with a $2100 raise at the end of each year. Company B offered her a starting salary of $45,000 with a 4.2% raise at the end of each year. Let f(t) represent Carissa's salary at Company At years after accepting a position at Company A, and let g(t) represent Carissa's salary at Company B t years after accepting a position at Company B. a. Find a function formula for f. b. Find a function formula for g. c. If Carissa was expecting to work for 5 years before going back to school, which company do you think she should work for? Use your functions to justify your answer. I d. If Carissa was expecting to work for 10 years before going back to school, which company do you think she should work for? Use your functions to justify your answer.
The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.
Given that,
Krystal is weighing two job offers from various organizations. She received a $45,000 beginning salary from Company A, with annual raises of $2100. Company B gave her a $45,000 beginning salary with an annual rise of 4.2%. Let f(t) stand for Carissa's pay at the company. Let g(t) stand in for Carissa's pay at Company B at Years after Accepting a Position at Company B, and at Years after Accepting a Position at Company A.
We have to find the function formula for f and g.
We know that,
Company A has
f(t) = $45000+$2100t
And
Company B has
g(t) = $45000(1+0.042) to the power of t.
Therefore, The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.
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