Calculations:
Normal pop has mean of 20.0
standard deviation = 4.0
XNN(20.0, 4.0)
a).
[tex]z=\frac{x-h}{z}[/tex]
[tex]=\frac{25-20}{4.0} =\frac{5}{4} =1.25[/tex]
Z = 1.25
b).
The proportion between 20 and 25 is P(20 <x<25.0)
[tex]=p(\frac{20-20}{4} < z < \frac{25-0}{4} )[/tex]
[tex]=P(0 < z < 1.25)[/tex]
[tex]=P(Z < 1.25)-P(z < 0)[/tex]
[tex]=0.8944-0.5000[/tex]
P(20 < x < 25)=0.3944
c).
The proportion value is less than 18 when
[tex]P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}[/tex]
[tex]=P(z < \frac{-2}{4})[/tex]
[tex]=P(z < -0.5)[/tex]
P(x<18) = 0.3085
Which sentence from the source best supports the reason "recreational sports are valuable because youth need to exercise daily"? 1 2 3 4
The sentence that best supports the reason for youth recreational sports is (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day.
What are recreational sports?Recreational sports are competitive physical games played for fun and physical exercise with friends or as part of extra-curricular activities.
They do not involve professional sports persons.
Question Completion:Read this source of information. (1) American youth have school commitments and extracurricular activities. (2) Many also enjoy leisure activities, such as reading and playing video games. (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day. (4) The specific amount of activity needed for a healthy lifestyle depends on daily caloric intake.
Thus, the sentence that best supports the reason for youth recreational sports is Sentence 3.
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Answer:
ez 3
Step-by-step explanation:
1. (y + x) = 4; use x = 2 and y = 2
2. x + y ÷ 6; use x = 5 and y = 6
3. y(x + 5); use x = 1 and y = 4
4. q-m+q; use m = 3 and q = 6
Step-by-step explanation:
1-)2+2=4
2-)5+6÷6=6
3-)4(1+5)=24
4-)6-3+6=9
The equation 5x2 30x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 5x2 30x 15 = 0 step 1 ✔ step 2 5(x2 6x 9) 15 − 45 = 0 step 3 5(x 3)2 − 30 = 0 5(x2 30x ___) 15 ___ = 0 5(x2 30x ___) − 15 ___ = 0 5(x2 6x ___) − 15 ___ = 0 5(x2 6x ___) 15 ___ = 0
The missing step in making the equation in vertex form is option D which is
[tex]5(x^{2} +[/tex]6x____)+15.
Given Equation [tex]5x^{2} +30x+15=0[/tex]
Parabola in vertex form. Equation is a relationship between two or more variables which is expressed in equal to form. It is solved to find the variables.
To express the equation of a parabola in vertex form we must complete squares. The equation is given as
[tex]5x^{2} +30x+15=0[/tex]
The first step is to factor 5 and leave space to complete the third term in the parenthesis, along with a space outside it to compensate. This should look like
([tex]5(x^{2} +6x............)+15..........=0[/tex]
Those spaces need to be filled out like shown in the step 2. Thus the correct step is D.
Hence the correct step in vertex form is D which is
[tex]5(x^{2} +6x[/tex]___-)+15____=0.
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15 people were asked to measure their pulse rates after completing a 3 km run. The sample data are given below and are assumed to be normally distributed. Use a TI-83, TI-83 plus, or TI-84 calculator to construct a 98% confidence interval for the mean of the population. Round your answers to two decimal places and use increasing order.
Using the t-distribution, the 98% confidence interval for the mean of the population is (99.21, 110.79).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Researching the problem on the internet, the data-set is given as follows:
104, 102, 103, 105, 125, 106, 107, 110, 110, 95, 108, 86, 112, 101, 101.
The parameters are given as follows:
[tex]\overline{x} = 105, s = 8.54, n = 15[/tex].
The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 15- 1 = 14 df, is t = 2.6245.
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 105 - 2.6245\frac{8.54}{\sqrt{15}} = 99.21[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 105 + 2.6245\frac{8.54}{\sqrt{15}} = 110.79[/tex]
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what is the range of f(x)=3^x
Answer: [tex]f(x) > 0[/tex]
Step-by-step explanation:
The range of all exponential functions without a vertical shift is the set of positive real numbers.
The blue truck from old time is part to the right truck from hit road a green truck from super suppliers is part to the right of all time the white truck from Joe's hardware is part to the left of hit road how many trucks are between the Joe's hardware truck in a super supplier's truck
There are 2 trucks are between Joe's hardware truck in a super supplier's truck.
What is the reasoning?The reasoning is the capacity to make logical judgments based on newly available or previously known information.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
The blue truck from the old time is part to the right truck from hit road the green truck from super suppliers is part to the right of all time.
According to the information provided, there are only two trucks between the Super Suppliers truck and the Joe's Hardware truck.
Joe's Hardware is essentially on the left and Super Suppliers is on the right, with 2 trucks in between.
Thus, there are 2 trucks are between Joe's hardware truck in a super supplier's truck.
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If the width of the dining room table is w feet, and the length is 3w - 2 feet, write an
algebraic expression that represents the perimeter of the table.
Answer:
2(w)+2(3w-2), or, 8w-4Step-by-step explanation:
The formula for finding the perimeter is 2w+2L (2*width + 2*length)
So, since we know the width is "w" and the length is "3w-2", we can just substitute those into the equation.
2(w)+2(3w-2)
From there, if needed, you can simplify to:
2w + 6w-4
Add like terms:
8w - 4
Hope that helps.
Here's my work, is it right?
SA=2πr^2+2πrh
r=3.6cm
h=21.9cm
2π(3.6)^2+2π(3.6)(21.9)
=576.7964cm^2
Answer:
no
Step-by-step explanation:
there are somethings you need to know. The given height is the combined height of the cylinder and hemisphere. but we need to use the height of cylinder in the formula so we subtract the original height by radius.
Next thing is that the formula 2πrh is for C.S.A of the cylinder but we need the base area as well for surface area of this combined solid. So we add base area (i.e πr²) to 2πrh.
A ride-sharing company charges $6 per mile plus a $10 surcharge during peak hours. Suppose Manish’s ride during peak hours costs $22. To determine how many miles he traveled during this ride, solve for x in the following equation: 6x + 10 = 22
Answer:
2 miles
Step-by-step explanation:
6X + 10 = 22
X = (22-10)/6 = 12/6 = 2 miles
A summer camp cookout is planned for the campers and their families. there is room for 450 people. each adult costs $7, and each camper costs $4. there is a maximum budget of $1,150. write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers. x y ≤ 1,150 7x 4y ≤ 450 x y ≤ 450 7x 4y ≤ 1,150 x y ≤ 1,150 4x 7y ≤ 450 x y ≤ 450 4x 7y ≤ 1,150
Hence, the required inequality is x+y≤4, 7x+4y≤1150
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to solve?Let x be the number of adults and y be the number of campers.
There are rooms for 450 people, so
x+y≤450.
Each adult costs $7, then x adults cost $7x.
Each camper costs $4, then y campers cost $4y.
There is a maximum budget of $1,150, so
7x+4y≤1,150
Hence, you get the system of two inequalities:
x+y≤4
7x+4y≤1150
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Answer:
x + y [tex]\leq[/tex] 450
7x + 4y [tex]\leq[/tex] 1,150
Step-by-step explanation:
X and Y is the amount of people it can fit.
7 and 4 is the amount of money for each person.
7x is the amount per adult, 4y is the amount per camper.
Hope this helps.
The surface area of a cone with radius r units and slant height s units is shown below:
30 points
Surface area = 3.14(rs + r2)
Part A: If r = 3 units and s = 5 units, write an expression that can be used to calculate the surface area of the cone. (4 points)
Part B: What is the surface area of the cone? Show your work. (6 points)
Step-by-step explanation:
part A:
[tex]Area_{_{surface}}=3.14*(3*5+3^2);[/tex]
part B:
[tex]Area_{_{surface}}=3.14*(15+9)=3.14*24=75.36[units^2].[/tex]
I need help please. Trying to get my HS diploma. I did not graduate :(
Which of the following is the graph of f(x)+1?
The graph of f(x) + 1 is the graph in the option C.
Which is the graph of f(x) + 1?
For a given function f(x), a vertical translation is written as:
g(x) = f(x) + N
If N > 0, then the translation is upwards.If N < 0, then the translation is downwards.Here we have g(x) = f(x) + 1, so we have a translation of 1 unit upwards, the graph of f(x) + 1 is the graph of f(x) but translated one unit upwards.
From that, we conclude that the correct option is C.
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Dwight Donovan, the president of Finch Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of five years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $103,000 and for Project B are $41,000. The annual expected cash inflows are $34,441 for Project A and $12,522 for Project B. Both investments are expected to provide cash flow benefits for the next five years. Finch Enterprises’ desired rate of return is 8 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.)
1. The computation of the net present value of each project is as follows:
Project A Project B
NPV $36,523 $9,000
2. Based on the net present value approach, Project A should be adopted, instead of Project B.
What is the net present value?The net present value is the difference between the costs and the annual cash inflows discounted to their present values.
Data and Calculations:Project A Project B
Initial costs $103,000 $41,000
Annual cash inflows $34,441 $12,522
Project live 5 years 5 years
Rate of return 8% 8%
Annuity factor 3.993 3.993
PV of cash inflows $139,523 $50,000
NPV $36,523 $9,000
Question Completion:1. Compute the net present value of each project.
2. Which project should be adopted based on the net present value approach?
Thus, based on the net present value approach, Project A should be adopted.
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In a biology class, the final grade is based on several things; a lab score, scores on two major tests, ad score on the final exam. There are 100 points availablefor each score. However, the lab score is worth 25% of the total grade, each major test is worth 22.5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam.
Which of the following models the context "A plumber who charges $50 for a
house call and $85 per hour"?
Answer:
a. y = 85x + 50
Step-by-step explanation:
a. y = 85x + 50
Solve for x. Round to the nearest tenth, if necessary.
K
Answer:
0.5
Step-by-step explanation:
The sides opposite and adjacent to the given angle are shown in this right triangle. The relation between them is given by the tangent trig function:
Tan = Opposite/Adjacent
tan(63°) = 1/x
Solve for xWe can multiply this equation by x/tan(63°) to find the value of x:
x = 1/tan(63°) ≈ 1/1.96261 ≈ 0.509525
The length x is about 0.5 units.
What is the least
common multiple of 12 and 16?
Answer: 48
Explanation: 16 x 3 = 48, 12 x 4 = 48
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.Find the probability that the person has an IQ score between 92 and 108.
Using the normal distribution, it is found that there is a 0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 100, \sigma = 15[/tex].
The probability that the person has an IQ score between 92 and 108 is the p-value of Z when X = 108 subtracted by the p-value of Z when X = 92, hence:
X = 108:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{108 - 100}{15}[/tex]
Z = 0.53
Z = 0.53 has a p-value of 0.7019.
X = 92:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 100}{15}[/tex]
Z = -0.53
Z = -0.53 has a p-value of 0.2981.
0.7019 - 0.2981 = 0.4038.
0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
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What is the number of Power set of A show step by step? A = {a,b, {a}, 3, {3}}.
By "number of Power set of A" I wonder if you mean the cardinality of the power set.
For any finite set with [tex]n[/tex] elements, its power set contains [tex]2^n[/tex] elements.
Here [tex]|A| = 5[/tex], so the power set will contain [tex]|\mathcal P(A)| = 2^5 = \boxed{32}[/tex] elements.
Recall that the power set is the set of all subsets of a given set
• subsets of [tex]A[/tex] of size 0 (1):
[tex]\emptyset[/tex]
• subsets of size 1 (5):
[tex]\{a\}\\ \{b\}\\ \{\{a\}\}\\ \{3\}\\ \{\{3\}\}[/tex]
• subsets of size 2 (10):
[tex]\{a,b\}\\ \{a,\{a\}\}\\ \{a, 3\}\\ \{a, \{3\}\}\\ \{b,\{a\}\}\\ \{b,3\}\\ \{b,\{3\}\}\\ \{\{a\},3\}\\ \{\{a\}, \{3\}\}\\ \{3,\{3\}\}[/tex]
• subsets of size 3 (10):
[tex]\{a,b,\{a\}\}\\ \{a,b,3\}\\ \{a,b,\{3\}\}\\ \{a,\{a\},3\}\\ \{a,\{a\},\{3\}\} \\ \{a,3,\{3\}\}\\ \{b,\{a\},3\}\\ \{b,\{a\},\{3\}\}\\ \{\{a\},3,\{3\}\}[/tex]
• subsets of size 4 (5):
[tex]\{a,b,\{a\},3\}\\ \{a,b\{a\},\{3\}\}\\ \{a,b,3,\{3\}\}\\ \{a,\{a\},3,\{3\}\}\\ \{b,\{a\},3,\{3\}\}[/tex]
• subsets of size 5 (1):
[tex]\{a,b,\{a\},3,\{3\}\}[/tex]
QUICK PLEASE. George invested $1000 for 4 years. If the investments earned 5.5% compounded weekly, how many compounding period would occur and what is the interest rate?
The number of compounding period is 52.
The interest rate is 0.11%.
What is the compounding period and interest rate?The compounding period is the number of times the investment would earn a compound interest in a year. Because interest is compounded weekly, the compounding period would be equivalent to the number of weeks in a year. This is 52.
Interest rate = yearly interest / compounding period
5.5 / 52 = 0.11%
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A cyclist rides her bike at a rate of 9 kilometers per hour. What is this rate in kilometers per minute? How many kilometers will the cyclist travel in 15 minutes? Do not round your answers.
The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
60 km/h = 1 km/min
Hence:
9 km/h = 9 km/h * (1 km/min) / ( 60 km/h) = 0.15 km/min
In 15 minutes, distance = 0.15 km/min * 15 min = 2.25 km
The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.
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What is the base of the expression ? 3 11 12 21
Answer:
[tex]11[/tex]
[tex]a {}^{b} [/tex]
a is the base and b is the exponent.
Step-by-step explanation:
HOPE THIS HELPS.
Which expressions are equivalent to √1,120y? Select three options.
√√2-2-2-2-5-7-y-y
√2² √2² √2² √5² √7²√√
√2² √2² √2. √5.17.√7.SY
02.2.y√2-5-7-y
4y√70y
The expression that is equivalent to √1,120y is: 4√70y.
What are Equivalent Expressions?Expressions are said to be equivalent when the value of one is the same as the value of the other when evaluated or simplified.
Given the expression, √1,120y, we can simplify as shown below:
√(16 × 70 × y)
= 4√70y
Thus, 4√70y is equivalent to √1,120y .
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The graph of the exponential function with base, e, has a_______ at _______ Its domain is _______ Its range is _____
The graph of the exponential function in discuss whose base is; e would have a y-intercept t at point (0, 1), with a domain as the set of all real numbers and its range as the set of all positive numbers.
What is the description of the graph of an exponential functions whose base is e?It follows from the task content that the function in discuss can be written as;
y = e^x.
Consequently, the y-intercept of the graph which corresponds to x= 0 is; (0, 1).
The domain and range of the graph as with other exponential functions are therefore given as the set of all real numbers and all real positive numbers respectively.
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Use the Empirical Rule to determine the percentage of candies with weights between 0.7 and 0.98 gram. Hint: x=0.84
Using the Empirical Rule, it is found that 95% of the candies have weights between 0.7 and 0.98 gram.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Researching this problem on the internet, we have that:
The mean is of 0.84.The standard deviation is of 0.07.Then 95% of the candies have weights between 0.7 and 0.98 gram, as:
0.7 = 0.84 - 2 x 0.07.0.98 = 0.84 + 2 x 0.07.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Please answer this question
Answer: B
Step-by-step explanation:
The factors of 1 are [tex]\pm 1[/tex]
The factors of 20 are [tex]\pm \{1, 2, 4, 5, 10, 20\}[/tex].
By the rational root theorem, we see that the answer is B.
I need help with this question I got 1 as an answer but it’s saying it’s wrong
log 4 (x³ +255) = 4
Answer:
see image
Step-by-step explanation:
I did two different problems depending on whether the 4 beside the log is a base or not.
If the log IS the base, I got x = 1 as you did. But if the 4 is not the base then there is no base written and that means the base is 10.
For log problems that have log on one side of the equation only, then a good strategy is to change the equation from logarithmic form to exponential form. See image for work. Hope this helps.
Find the mean of the list of data 43,69, 48,37,85,57,95,102
WHAT IS THE VALUE OF THE EXPRESSION 8 MORE THEN 3 TIMES THE DIFFRENCE OF 4 AND A NUMBER WHEN N=3
The value of the expression as described in the task content is; 11.
What is the value of the expression?The expression as described in the task content is; 3(4 - N) +8.
However, the value of N in this scenario is; 3.
Therefore, the value of.the expression is;
3(4 - 3) +8
= 3(1) + 8
= 3+8
= 11.
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Identity the x-intercept of the liner equation 3x + y -9=0
Answer:
The x intercept is 3
(3,0)
Step-by-step explanation:
3x+y -9 =0
To find the x intercept, set y=9 and solve for x.
3x+0-9=0
3x -9=0
Add 9 to each side
3x-9+9=9
3x =9
Divide by 3
3x/3 = 9/3
x =3
The x intercept is 3
(3,0)