Deloitte employment survey asked sample of human resource executives how their company planned to change its workforce over the next 12 months_ categorical response variable showed three options: The company plans to hire and add to the number of employees the company plans no change in the number of emplovees_ or the company plans to lay off and reduce the number of emplovees_ Another categorical variable indicated if the company was private public Sample data for 168 companies are summarized as follows Company Employment Plan Private Public Add Employees No Change Lay Off Employees Conduct test of independence to determine if the employment plan for the next 12 months is independent of the type of company At a 05 level of significance_ Compute the value of the x? test statistic (to 2 decimals). 8.73 The p-value petween 01 and .025 What is your conclusion? Conclude the employment plan not independent of the type of company. Discuss any differences in the employment plans for private and public companies Over the next 12 months_ Private companies are more likely to add employees Public companies are more likely to lay off employees_ of private companies plan on adding employees_ 34.9 % of public companies plan on adding off employees. (to decimal)
As per the chi square test, the variable are dependent to each other.
What is meant by chi-square test?
In math, the chi square test refer a statistical test used to compare observed results with expected results.
From the table in the question; we can see the changes in employees adding, shedding, or not changing their staffing.
Converting the table to chi- squared using the relation.
Here the observed frequency is = 44 and the expected frequency is = 34.8
And the Number Change 0.1421 0.0079 0.15
=> Lay Off 4.8286 2.4083 7.2369
=> Total = 14.657
Therefore, the total chi-square = 14.657;
In order to find the value for p; we need to determine the degree of freedom
=> df = (2-1)(3-1)
Then the result to a degree of freedom of 2
Here from the chi square chart at the chi-square is 14.657 and degree of freedom is 2 ; the p value is between 0.1 and 0.005. Since this makes p-value less than 0.05.
Therefore, the variables are dependent.
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line m and point p are graphed on the coordinate grid below. which equation represents a line that passes through point p and is parallel to line m?
The equation of the graphed on the coordinate grid parallel to line M y = x and passing through the point P(4, -7) is equal to y = x - 11.
As given in the question,
Equation of the line M is given by :
y = x
Slope of the line M by comparing it with standard equation of the line with slope m is given by :
y = mx + c
Equation of the line M is y = x
Here m = 1
Slope of the required line is m₁ = 1 as it is parallel to line M
Equation of the required line which passes through ( x₁ , y₁) = ( 4, -7) with slope m₁ = 1 is given by:
y - y₁ = m₁( x - x₁)
⇒ y + 7 = 1( x - 4)
⇒ y= x - 4 -7
⇒ y= x - 11
Therefore, the equation of the required line which is parallel to line M and passing through point P is equal to y = x - 11.
Line M is graphed on the coordinate grid. y = x. Which equation can be used to represent a line parallel to M passing through the point P(4, -7)?
A. x = 4 B. x = -7 C. y = -7 D. y = 4
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An electronics store receives a shipment of 30 graphing calculators, including 7 that are defective. Four of the calculators are selected to be sent to a local high school. How many of these selections will contain no defective calculators?
Based on probability, three of the four selected calculators will contain no defective.
What is the probability?Probability refers to the likelihood or chance that an expected outcome occurs in the midst of many possible outcomes or events.
Probability is zero when uncertain and one when 100% certain. Otherwise, probability lies between zero and one, which yields a fractional value denoted by decimals, percentages, or fractions.
The number of shipped graphing calculators = 30
The number of defective calculators = 7
The probability of defective calculators = 0.233 (7/30)
The probability of no defective calculators = 0.767 (1- 0.233)
The number of calculators to be sent to a high school = 4
The number of these that will contain no defective calculators = 3.068 (4 x 0.767)
= 3
Thus, the local high school will probably receive 3 non-defective units.
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An SRS of size 26 is drawn from a population that has a normal distribution. The sample has a mean of 143.5 and a standard deviation of 4. Give the standard error of the mean:
An SRS of size 26 is drawn from a population that has a Normal distribution, the standard error of the mean is 0.7844..
The standard error of the mean, or simply standard error, indicates how much the population mean can differ from the sample mean. It indicates how much the sample mean would change if the survey were repeated with new samples from a single population. It is calculated by dividing the standard deviation by the square root of the sample size.
We have given that,
SRS size , n = 26
The distribution is normal distribution,
Mean, u = 143.5
Standard deviations, sd = 4
standard error of the mean = sd/√n
= 4√26 = 0.7844
Hence, the standard error of mean is 0.7844..
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a market research firm is studying the effects of price and type of packaging on sales of a particular product. twenty-seven stores with shoppers of similar characteristics will be used in the study. the nine combinations of three price levels and three packaging types are the treatments of interest. total sales of the product over a seven-week period will be recorded. which of the following describes the best design to use for the study?
The market research can increase the precision of the result of the study by using a randomized block design RBD.
The best design the market research company should use for the study is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combination
Reason:
The given parameters are;
The study = The effect of price and type of packaging
Number of stores in the study = 27 stores
Characteristics of the shoppers in the stores = Similar
Number of packaging type = 3 (three)
Number of price levels = 3 (three)
The number of pair combinations = ⁶₂C - (3, pairs of the same packaging +
3, pairs of the same prices) = 9
Required:
The best design to use for the study
Solution:
Given that the shoppers at each store are similar, in order to differentiate and show the effect of the price and package combination, it is possible to group the treatment into groups having a particular characteristics, while ensuring that the other available treatments are assigned to each member within a group at least once.
The above design of the study is known as a randomized block design,
Therefore the correct option is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combinations.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The value of x that will make the two given solids similar is: d. x = 31.
What are Similar Solids?Similar solids are solids that are scale copy of each other, that is, either of the solids can produce the other when enlarged by a scale factor to get the dimension of the other solid.
Therefore, if two solids are similar, their corresponding linear dimensions would have an equal ratio, or they would be proportional.
Applying the definition of similar solids, the equation below would be created in order to determine the value of x:
x/15.5 = 29/14.5
Cross multiply:
14.5x = 15.5 × 29
14.5x = 449.5
14.5x/14.5 = 449.5/14.5
x = 31
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The wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into a farmer's lake. The function N defined by 600t +500 Ne)represents the approximate number of fish in the lake as a tunction of time (n years) Which ome f he olowin N(t)0.5+1 describes how the number of fish in the lake changes over time? O The number of fish gets larger each year, but does not exceed 1200. OThe number of fish gets smaller every year but does not get smaller then 1200. O The number of fish gets arger each year, but does not exceed 600. O The number of fish gets larger each year, but does not exceed 500. O The number of fish gets smaller every year, but does not get smaller than 500.
This steady-state number of fish is ... 1200 - 1058 = 142 . . . . below the original carrying capacity
The differential equation is modified by adding a -100 fish per year constant term:
(dN)/(dt) = (0.4)/(1200)N(1200-N) -50
The steady-state value of the fish population will be when N reaches the value that makes dN/dt = 0.
(0.4/1200)(N)(1200-N) -50 = 0
N(N-1200) = -(50)(1200)/0.4) . . . . rewrite so N^2 has a positive coefficient
N^2 -1200N + 600^2 = -150,000 +600^2 . . . . complete the square
(N -600)^2 = 210,000 . . . . . simplify
N = 600 + √210,000 ≈ 1058
This steady-state number of fish is ...
1200 - 1058 = 142 . . . . below the original carrying capacity
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The quadratic equation y = - 1612 +40t +2 represents the height of a projectile, y ,in feet, at a particular time, 1, in seconds. For what interval or intervals of time will the projectile be above 18 feet?
The interval of time after solving the inequality -16[tex]t^{2}[/tex] + 40t + 2 > 18 is 0.5 < t < 2
What are inequalities?Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.
How to solve an inequality?We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).
-16[tex]t^{2}[/tex] + 40t -16 > 0
Dividing the equation by 8,
-2[tex]t^{2}[/tex] + 5t - 2 > 0
Rearrange gives,
2[tex]t^{2}[/tex] - 5t + 2 < 0
Using middle term breaking,
(2t-1)(t-2) < 0
Hence, the interval is 0.5 < t < 2
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differentiate of the following w.r.t.
give me this answer i mark u brainlist
Answer:
[tex]\frac{dy}{dx}=\frac{4}{3}x^{1/3}+e^x +\cos x[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx} x^{4/3}=\frac{4}{3}x^{1/3} \\ \\ \frac{d}{dx} e^x=e^x \\ \\ \frac{d}{dx} \sin x=\cos x \\ \\ \therefore \frac{dy}{dx}=\frac{4}{3}x^{1/3}+e^x +\cos x[/tex]
Compared to the parent function f(x)=x², the function g(x) has been horizontally shrunk by a factor of 1/3 and then vertically stretched by a factor of 4 .
Which is g(x) ?
(A) g(x)=3(1/4x)²
(B) g(x)=3(4 x)²
(c) g(x)=4(1/3x)²
(D) g(x)=4(3 x)²
If the parent function f(x) = x² is horizontally shrunk by factor of 1/3 ad vertically stretch by factor of 4 then g(c) will be g(x) = 4(1/3x)² , the correct option is (c) .
In the question ,
it is given that ,
the parent function is ⇒ f(x) = x² ;
the graph is horizontally shrunk by a factor of 1/3 that means
the function will become (1/3x)² .
next the function is then vertically stretch by a factor of 4 ,that means
then the function becomes g(x) = 4(1/3x)².
Therefore , the correct option is g(x) = 4(1/3x)² .
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Consider The Following Problem: Min - X1 + X2 S.T. X1 + X3 – 2xı = 0 (X1, X2) E X Where X Is The Convex Combination Of The Points (-1,0), (0,1) (1,0), (0,-1). a. find the optimal solution graphically b. Do the frizt john or KTT condition hold the optimal solution in part (a)? if not explain in the term of the theorem 4.3.2.and 4.3.7 in the textbook.
The objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, satisfies the KKT condition.
To find the optimal solution graphically, first plot the points (-1,0), (0,1), (1,0), and (0,-1) on the coordinate plane. These points form a square. The objective function for this problem is to minimize -x1 + x2. So we need to find the point on the square that is as low as possible on the y-axis (because the y-axis represents x2).
The constraint in question is x1 + x3 - 2x1 = 0, which can be rewritten as x3 = 2x1. Since x1 and x3 are variables, this represents a line on the coordinate plane. You can draw this line by selecting two points on this line and connecting them with a line. For example, you can select points (-1, -2) and (1, 2). These points lie on the line x3 = 2x1 and the connecting lines are plotted in the coordinate plane.
We can find the best solution by finding the point on the square that is the lowest possible on the straight line of y-axis and x3 = 2x1. The point that satisfies both of these conditions is the point (0,-1). This is the best solution for your problem.
To answer the second part of the question we need to determine whether the Fritz-John condition or the KKT condition is the optimal solution. The Fritz-John condition is an optimality requirement involving an objective function and problem constraints. A KKT condition is a necessary and sufficient condition for optimality that includes an objective function, a constraint, and a multiplier associated with the constraint.
The Fritz-John condition is not considered optimal for this problem. This is because the optimal solution does not satisfy the condition x1 + x3 – 2x1 = 0. The point (0,-1) does not satisfy the condition because it is not on the line x3 = 2x1.
KKT conditions are considered to be the best solution. This is because the point (0,-1) is a legal point (it lies on the square representing the legal region) and the global minimum of the objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, which satisfies the KKT condition.
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2. To help pay for college, you worked part-time at a local restaurant, earning $25,000 in
wages and tips. Using the FICA table on your formula sheet, calculate the FICA taxes for
you to pay.
FICA=
Ir part-time at a local supermarket. The job pays $8.80-
40% of his gross pay
Answer:
8584946569585889594934u
Is the following information a statistic or a parameter?
You have surveyed a group of 35 randomly selected peers to inquire how many cell phones they owned in their life and found that the most common answer was 4 cell phones.
Statistic
Parameter
It is based on a sample and provides information about the sample based on a survey of 35 samples, this four cell phone is a statistic, so the response is a statistic.
When looking at populations, the term "median" is a significant and frequently used statistic. Most of the time, it's used to represent a set of numbers.
We sort the population numbers to find the one in the middle to find the median. It differs from the mean and can sometimes be more useful than the mean, such as when there are outliers that could have an excessive impact on the mean. We should take the average of the two values in the middle if the number of values is even.
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Mrs. Parker earns a 8.5% commission on her total sales. Last month, she had sales of $53,910. How much commission did Mrs. Parker earn last month
The commission earn by Mrs. Parker earn last month is $ 4,582.35
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
What is the formula's percentage?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
Given that:
Total sales = $53,910
Commission = 8.5%
Commission in cash = 53910 * 0.085 = 4,582.35
Hence commission earn by Mrs. Parker earn last month is $ 4,582.35
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to determine that a item is not in an unordered array of 100 items, how many values must linear search examine on average? a) 7 b) 10 c) 100
To determine that an item is not in an unordered array of 100 items, total numbers of values which have to linear search examine on average is 100. The correct answer is C.
What is Linear Search?Linear Search is described as a sequential search algorithm which starts at one end and goes through each element of a list until the needed element is found, otherwise the search continues till the end of the data set. This is the simplest searching algorithm.
Starting at the beginning of the data set, each item of data is examined until a match is made. Once the item is found, the search ends.
Hence, in this case, since there are 100 items, then there will be 100 numbers of values.
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The number t is rational and positive. Which statement about ग/t is true?
The number π/t is an irrational and positive number.
What are rational and irrational numbers?The rational numbers are composed by the set of all numbers that can be represented by fractions, such as whole numbers, terminating decimals, or repeating decimals.
The irrational numbers, conversely, are composed by the set of numbers that cannot be represented by fractions, such as non-exact roots and non-terminating decimals.
The number π is defined as follows:
π = 3.1415...
Which is a non-terminating decimal, hence it is an irrational number.
When an irrational number is divided by a rational number, as is the case in this problem, the result is irrational.
π is a positive number, just like t, hence the quotient is also a positive number.
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Kehlani launches a toy rocket from a platform. The height of the rocket in feet is given by h= -16t^2 + 72t + 144 where t represents the time in seconds after launch. How long is the rocket in the air?
Answer:
6 seconds--------------------------------
Rocket is in the air until it hits the ground.
Therefore we need to find the value of t when h = 0.
- 16t² + 72t + 144 = 02t² - 9t - 18 = 0 2t² - 12t + 3t - 18 = 02t(t - 6) + 3(t - 6) = 0(t - 6)(2t + 3) = 0t - 6 = 0 or 2t + 3 = 0t = 6 or t = - 3/2 (discarded as negative)The rocket is in the air for 6 seconds.
Answer:
6 seconds
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+72t+144[/tex]
where:
h is the height of the rocket.t is the time (in seconds) after launch.To find how long the rocket is in the air, find the positive value of t when h(t)=0.
[tex]\implies -16t^2+72t+144=0[/tex]
[tex]\implies -8(2t^2-9t-18)=0[/tex]
[tex]\implies 2t^2-9t-18=0[/tex]
[tex]\implies 2t^2+3t-12t-18=0[/tex]
[tex]\implies t(2t+3)-6(2t+3)=0[/tex]
[tex]\implies (t-6)(2t+3)=0[/tex]
Apply the zero-product property:
[tex]t-6=0 \implies t=6[/tex]
[tex]2t+3=0 \implies t=-\dfrac{3}{2}[/tex]
Therefore, as t > 0, the rocket is in the air for 6 seconds.
Write a congruence statement for the triangles. Then identify all pairs of congruent corresponding paris.
∠Q≅ ?
∠R≅ ?
∠P≅ ?
PQ≅ ?
QR≅ ?
The ΔPQR and ΔCBA are congruent using ( SAS , AAA , ASA) properties
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.
According to the question,
We have to identify all the pairs of congruent
In ΔPQR and ΔCBA,
If we look the figure
(1) ∠Q ≅ ∠B
(2) ∠R ≅ ∠A
(3) ∠P ≅ ∠C
(4) PQ ≅ CB
(5) QR ≅BA
Therefore , All three angles are equal and all three sides
hence , ΔPQR ≅ ΔCBA by using AAA or ASA or SAS properties
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Please help me with the attached question on linear function. Thank you.
The number of lattice points in the first quadrant of the graph is equal to five (5).
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
What is a lattice point?In Mathematics, a lattice point can be defined as a point on a graph whose ordered pair (x and y coordinates) are both positive and whole numbers.
By critically observing the graph of the function 3x + 4y = 59, we can reasonably infer and logically deduce that the number of lattice points in the first quadrant (where the ordered pair are both positive) are five (5).
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researchers are testing a new diagnostic tool designed to identify a certain condition. the null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. for the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective. which of the following should the researchers do to avoid the more consequential error?
Based on the null hypotheses, the type of error is Decrease the significance level to decrease the probability of Type I error.
What does null hypotheses means?
In math, null hypotheses refers a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations.
Here we have give that researchers are testing a new diagnostic tool designed to identify a certain condition. the null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. for the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective.
And we need to find in which of the following should the researchers do to avoid the more consequential error.
According to the given question, the null hypothesis is that the new diagnostic tool is not effective in detecting the condition.
Here the more consequential error described is that the diagnostic tool is not effective, but the significance test indicated that it is effective. This is a type I error.
And in Hypothesis testing, a type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.
Therefore, it involves saying there is significant evidence to show that the new diagnostic tool is effective in detecting the condition when in reality, it isn't.
When the level of significance (α) of a hypothesis test directly gives the probability of a type I error. So, by setting it lower, we reduce the chances of a type I error.
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which of the variables listed above would best be displayed graphically using a bar graph? mark all that apply. group of answer choices number of minutes of exposure to secondhand smoke per day currently diagnosed with asthma race years of education gender
The two possible variables design are; "COHORT STUDY" and "CROSS-SECTIONAL STUDY".
Cohort study design is an observational study in which people who receives a particular treatment or are under a particular condition, are been observed and studied. This type of research model also allows a researcher to compare people affected by a condition to people unaffected by the same conditions.
The investigator is likely to use the cohort design because it will help in studying the children that are always exposed to smoke, and to observe the affected and unaffected children.
The CROSS-SECTIONAL design is an observational study in which a specific population are studied at a particular time. This type of research allows the researcher to study the difference in that population at a time interval.
This study design is likely to be used by the investigator, because it will help the investigator to determine the amount of secondhand smoke each child inhale at a particular time. It will also help the investigator to know the outcome of each child after 5years
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If Aarón has 4 times as many dimes as quarters and they have a combined value of 520 cents, how many of each coin does he have?
Aaron has 32 dimes and 8 quarters
How to determine the number of each coin?From the question, we have the following parameters that can be used in our computation:
Worth of coins = 520 cents
Type of coins = Dimes and quarters
Four times as many dimes as quarters
Represent the dimes with d and the quarters with q
So, we have the following representation
d = 4q
When the dimes and quarters are converted to dollars, we have the following representations
Dimes = $0.10
Quarters = $0.25
So, we have the following representation
0.10d + 0.25q = 5.20
Recall that
d = 4q
So, we have
0.10 * 4q + 0.25q = 5.20
Evaluate the products
0.65q = 5.20
Divide both sides by 0.65
q = 8
Recall that
d = 4q
So, we have
d = 4 * 8
Evaluate
d = 32
Hence, the number of dimes is 32
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To create a chocolate blend chocolate in two concentrations 61% cocoa and 51% cocoa are combined together if 18 ounces of the 61% chocolate is used
Answer:
To create a chocolate blend using 61% cocoa and 51% cocoa, 18 ounces of the 61% chocolate and an appropriate amount of the 51% cocoa are combined together. The exact amount of 51% cocoa required will depend on the desired concentration of the final blend.
Step-by-step explanation:
a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week, t(t). the function t(t) can be expressed as t(t)
a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week is C(T) = $730 + $25T
R(T) = $35T
T = 193 transact
C = cost ; R = revenue ; T = number of transactions
Amount paid per transaction = $25
Cost keeping office open = $730
Amount collected on each transaction = $35
(a) Find a formula that gives C as a function of T.
C(T) = Cost of keeping office open + (cost per transaction × number of transactions)
C(T) = $730 + $25T
(b) Find a formula that gives R as a function of T.
R(T) = (Amount collected per transaction * number of transactions)
R(T) = $35T
(c) Find the number of daily transactions that are needed to make the revenue $1200 more than the cost.
R = C + 1200
Substitute the value of R and C into the equation:
35T = 730 + 25T + 1200
35T - 25T = 730 + 1200
10T = 1930
T = 1930 / 10
T = 193 transactions
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In addition to planning the move, which other factors do you need to consider when preparing to move gondolas?
The factors that you need to consider when preparing to move gondolas are:
Height
width
length
color.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity
In choosing gondola one need to look at some factor in decisions such as height.
Know that it is good to consider the construction material and also the center wall configuration for its building also.
The factors that you need to consider when preparing to move gondolas are:
Height
width
length
color.
Hence, Height, width, length and color are the other factors we need to consider while moving Gondola.
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a woman deposits 100 eur in her daughter's bank account on her first birthday. on every subsequent birthday, she deposits 10 eur more than she deposited the previous year, so on her second birthday, she deposits 110 eur, and on her third birthday she deposits 120 eur.
At the end of her daughter's 10th birthday, the woman has deposited a total of 310 eur. On her first birthday, a woman transfers 100 euros into her daughter's bank account. every birthday after that.
On the daughter's 1st birthday:
100 eur deposit
On the daughter's 2nd birthday:
100 eur (previous year) + 10 eur (increase) = 110 eur deposit
On the daughter's 3rd birthday:
110 eur (previous year) + 10 eur (increase) = 120 eur deposit
On the daughter's 4th birthday:
120 eur (previous year) + 10 eur (increase) = 130 eur deposit
On the daughter's 5th birthday:
130 eur (previous year) + 10 eur (increase) = 140 eur deposit
On the daughter's 6th birthday:
140 eur (previous year) + 10 eur (increase) = 150 eur deposit
On the daughter's 7th birthday:
150 eur (previous year) + 10 eur (increase) = 160 eur deposit
On the daughter's 8th birthday:
160 eur (previous year) + 10 eur (increase) = 170 eur deposit
On the daughter's 9th birthday:
170 eur (previous year) + 10 eur (increase) = 180 eur deposit
On the daughter's 10th birthday:
180 eur (previous year) + 10 eur (increase) = 190 eur deposit
Total deposited over 10 years:
100 eur (1st birthday) + 110 eur (2nd birthday) + 120 eur (3rd birthday) + 130 eur (4th birthday) + 140 eur (5th birthday) + 150 eur (6th birthday) + 160 eur (7th birthday) + 170 eur (8th birthday) + 180 eur (9th birthday) + 190 eur (10th birthday) = 1,100 eur
Total deposited over 10 years: 1,100 eur - 100 eur (1st birthday deposit) = 1,000 eur
Total deposited over 10 years: 1,000 eur / 10 years = 100 eur per year
Total deposited over 10 years: 100 eur x 10 years = 1,000 eur
Total deposited over 10 years: 1,000 eur + 100 eur (1st birthday deposit) = 1,100 eur
Total deposited over 10
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Carissa skis along a circular ski trail with a radius 1.3 km long. Carissa starts at the 3-o'clock position of the trail (the East-side) and travels in the CCW direction. Which of the following expressions represents Carissa's distance to the right of the center of the skitrail in km, h, in terms of the number of km that Carissa has traveled since she started skiing.d? Oh 1.3 cos(d+ 1.3) Oh = 1.3 cos(1.3. d) h = 1.3 cos d 1.3 Oh = 1.3 cos(d) OhCOS 1.3 Submit Question 16. Points possible: 4
The expressions that represents Carissa's distance to the right of the center of the skitrail, i.e, h in terms of the number of times Carissa has traveled since she started skiing,d is h = 1.3 cos( d/1.3). So, correct answer is option (c).
We have, Carissa skis along a circular ski trail. Radius of circle , r = 1.3 km
Carissa starts at the 3-o'clock position of the trail travels in the counter clockwise direction. let "d" km be total distance that Carissa has traveled since she started skiing and "h" km be Carissa's distance to the right of the center of the skitrail in km.
We have to wright an expressions for "h" in terms of d . Here, we see an sector is formed with one side length is r and arc's distance is d km . Let θ be angle formed by this sector . Using the sector formula,
θ = arc length /radius of circle
=> θ = d/r = d/1.3 --(1)
Also, ∆ formed here , h = r cos θ
=> h = 1.3 cos( d/1.3)
Hence, the required expression is h=1.3 cos( d/1.3).
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Complete question:
Carissa skis along a circular ski trail with a radius 1.3 km long. Carissa starts at the 3-o'clock position of the trail (the East-side) and travels in the CCW direction. Which of the following expressions represents Carissa's distance to the right of the center of the skitrail in km, h, in terms of the number of km that Carissa has traveled since she started skiing.d?
a)h 1.3 cos(d+ 1.3)
b) h = 1.3 cos(1.3/d)
c)h = 1.3 cos (d /1.3 )
d)h = 1.3 cos(d)
e) h = COS( 1.3 )
Submit Question 16. Points possible:
Two times the sum of a number and nine is 24. What is the number?
Answer: The number is 3
Step-by-step explanation:
2(x+9)=24
x+9=12
x=3
The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, . . . (where F0 0).
(a) Give the recursive definition for the sequence.
(b) Write out the first few terms of the sequence of partial sums: 0, 0 + 1, 0 + 1 + 1,. . .
(c) Give a closed formula for the sequence of partial sums in terms of Fn (for example, you might say F0 + F1 + · · · + Fn 3F 2 n−1 + n, although that is definitely not correct).
(Discrete Mathematics)
The Fibonacci sequence is the sequence in which the numbers are written such that each succeeding number is sum of two preceding numbers.
The Fibonacci sequence is defined recursively as follows:
F0 = 0
F1 = 1
For n > 1, Fn = Fn-1 + Fn-2
(b) The sequence of partial sums is:
S0 = 0
S1 = 0 + 1 = 1
S2 = 0 + 1 + 1 = 2
S3 = 0 + 1 + 1 + 2 = 4
S4 = 0 + 1 + 1 + 2 + 3 = 7
S5 = 0 + 1 + 1 + 2 + 3 + 5 = 12
(c) A closed formula for the sequence of partial sums in terms of Fn is not possible, since the sequence of partial sums depends on the values of all previous terms in the Fibonacci sequence. However, it is possible to express the nth term of the sequence of partial sums, Sn, in terms of the nth term of the Fibonacci sequence, Fn, using the following formula:
Sn = F0 + F1 + ... + Fn = (F0 + F1) + (F1 + F2) + ... + (Fn-1 + Fn) = F1 + F2 + ... + Fn + F0 + F1 + ... + Fn-1 = 2Sn-1 - Fn + F0
This formula can be derived by considering the previous term in the sequence of partial sums and adding the current term of the Fibonacci sequence to it.
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12 Express this in scientific notation: (1.33) (13 × 10³)
1.729 × 10⁰
B) 1.729 x 108
C) 17.29 x 10⁹
D) 17.29 x 108
The given expression can be written in scientific notation as 1.729 x 10⁹.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
Given is to express the given expression in scientific notation.
The given expression is -
(1.33) (13 × 10⁸)
Solving further -
1.33 x 13 x 10⁸
17.29 x 10⁸
1.729 x 10⁹
Therefore, the given expression can be written in scientific notation as 1.729 x 10⁹.
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