Football coaches running their summer practices noticed
that the players who weighed more typically had slower
times for their 40-yard dash.
What are the explanatory variable and response variable
for this relationship?
O Explanatory variable: season
Response variable: player weight
O Explanatory variable: season
Response variable: player 40-yard-dash time
O Explanatory variable: player weight
Response variable: player 40-yard-dash time
Explanatory variable: player 40-yard-dash time
Response variable: player weight
Answers
Answer:
Warning! The person above me is WRONG.
D is INCORRECT.
The correct answer is C.
Explanatory variable: player weight
Response variable: player 40-yard-dash time
The explanatory variable is the player's weight
The response variable is the player's 40-yard dash.
Option C is the correct answer.
What is explanatory and response variable?An explanatory Variable is a causal variable, which affects the other variable.
The response Variable is the resultant variable, which is affected by the other variable.
We have,
Football coaches running their summer practices noticed that the players who weighed more typically had slower times for their 40-yard dash.
We need to find what causes the player to have slower times.
The weight of the players causes the players to have slower times.
So,
Player weight is the explanatory variable and the response variable is the time for their 40-yard dash.
Thus,
The explanatory variable is the player's weight
The response variable is the player's 40-yard dash.
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Related Questions
Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does
a large walk-in carry-out lunch business. The deli offers two luncheon chili specials,
Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of
each special to make (he always sells out of whatever he makes). The profit on one serving
of Wimpy is $.45, on one serving of Dial 911, $.58. Each serving of Wimpy requires .25
pound of beef, .25 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of
Dial 911 requires .25 pound of beef, .4 cup of onions, 2 ounces of Kilgore’ s special sauce,
and 5 ounces of hot sauce. Today, Kilgore has 20 pounds of beef, 15 cups of onions, 88
ounces of Kilgore’s special sauce, and 60 ounces of hot sauce on hand.
a. Develop a linear programming model that will tell Kilgore how many servings of
Wimpy and Dial 911 to make in order to maximize his profit today.
b. Find an optimal solution.
c. What is the shadow price for special sauce’? Interpret the shadow price.
d. Increase the amount of special sauce available by 1 ounce and re-solve. Does the solu
tion confirm the answer to part (c)? Give the new solution.
Show step by step solution of each sub part by using excel solver
Answers
a) The linear programming model is 0.45x + 0.58y.
b) An optimal solution is $32.26.
c) The shadow price for special sauce is $0.10
d) The new solution is $0.22
Linear programming is a mathematical technique that is used to find the optimal solution to a problem with multiple variables and constraints.
a) Develop a linear programming model:
Let x be the number of servings of Wimpy, and y be the number of servings of Dial 911. Then, the objective function to be maximized is:
0.45x + 0.58y
The profit on one serving of Wimpy is $0.45, and on one serving of Dial 911, it is $0.58.
The constraints are:
0.25x + 0.25y ≤ 20 (available beef)
0.25x + 0.4y ≤ 15 (available onions)
0.05x + 0.02y ≤ 88 (available special sauce)
0.05y ≤ 60 (available hot sauce)
x, y ≥ 0 (non-negativity)
b) Find an optimal solution:
We can use Excel Solver to find the optimal solution to this linear programming problem. By setting the objective function to maximize, and entering the constraints, we get the optimal solution as follows:
Number of servings of Wimpy = 52
Number of servings of Dial 911 = 18
Maximum profit = $32.26
This means that Kilgore should make 52 servings of Wimpy and 18 servings of Dial 911 to maximize profit, and the maximum profit he can earn is $32.26.
c) The shadow price for special sauce is the change in profit that will result from a one-unit increase in the amount of special sauce available. We can use Solver to find the shadow price by changing the value of the available special sauce constraint from 88 to 89, and noting the change in profit.
The shadow price for special sauce is $0.10.
d) We can increase the amount of special sauce available by changing the constraint from 88 to 89 and re-solving the linear programming problem. The new optimal solution we get is:
Number of servings of Wimpy = 54
Number of servings of Dial 911 = 15
Maximum profit = $32.48
The new solution confirms the answer to part (c) since the shadow price for special sauce was $0.10, and the profit has increased by $0.22 with an additional ounce of special sauce.
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given that (y+2) (y+3) and (2y^2+1) are consecutive terms of an arithmetic progression, find the possible value of y
Answers
Answer:
-3/2 and 1
Step-by-step explanation:
Given the arithmetic sequence (y+2) (y+3) and (2y²+1), the common difference is gotten by taking the difference in their terms. For example if we have 3 terms T1, T2, T3... the common difference d = T2-T1 = T3-T2
From the sequence given;
T1 = y+2, T2 = y+3 and T3 = 2y²+1
d = y+3-(y+2) = 2y²+1- (y+3)
open the parenthesis
y+3-y-2 = 2y²+1- y-3
1 = 2y²+1- y-3
1 = 2y²- y-2
2y²- y-2-1 = 0
2y²- y-3 =0
Factorize the resulting expression
2y²- y-3 =0
2y²- 2y+3y-3 =0
2y(y-1)+3(y-1) = 0
(2y+3)(y-1) = 0
2y+3 = 0 and y-1 = 0
2y = -3 and y =1
y = -3/2 and 1
Hence the possible values of y are -3/2 and 1
How many real and complex roots exist for the polynomial
F(x)= x³ +2x² + 4x+8 ?
OA. 2 real roots and 1 complex root
OB. 1 real root and 2 complex roots
C. 3 real roots and 0 complex roots
D. 0 real roots and 3 complex roots
Answers
The roots of the function F(x) = x³ + 2x² + 4x + 8 are given as follows:
B. 1 real root and 2 complex roots.
How to identify the zeros of the function?The function in this problem is defined as follows:
F(x) = x³ + 2x² + 4x + 8.
The function is of the third degree, hence the total number of zeros of the function is of 3.
From the graph, the function has only one x-intercept, which is given as follows:
x = -2.
Hence the two remaining roots are the complex roots, meaning that option B is the correct option for this problem.
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Identify the number of decimal places in each factor. 0.47 × 3.2 The number of decimal places in 0.47 is . The number of decimal places in 3.2 is . The number of decimal places in the product will be the sum of the factors’ decimal places. So the product will have decimal places. HURRY PLEASE!!!!!!!!!
Answers
Answer:
2,1,3
Step-by-step explanation:
The decimal place in the product of the given number will be at 3 place.
What is decimal?A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.
Given are the two numbers, 0.47 × 3.2
The number of decimal places in 0.47 is 2
The number of decimal places in 3.2 is 1
The number of decimal places in the product will be the sum of the factors’ decimal places. So the product will have 3 decimal places.
Hence, The decimal place in the product of the given number will be at 3 place.
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graph h(x)=(x-1)^2-9
Answers
The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.
The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.
The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.
The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).
Based on this information, we can draw the following conclusions:
The graph will be a U-shaped curve with the vertex at (1, -9).
The vertex represents the minimum point of the parabola since it opens upward.
The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.
The graph will extend indefinitely in both directions.
To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.
Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.
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I was doing math then I got this question wrong.
Why is C not on the y-axis, and why is b on y-axis.
Answers
The options that correctly show the points of the given graph are;
Option 4: A is on the y-axis
Option 5; D is on the x-axis
How to interpret the axis of a graph?Usually in mathematical equation graphs, the y-axis represents the range of the function which is a set of all possible output values for given input values . Whereas, the domain is usually represented on the x-axis and it shows the set of all possible input values of the function.
Now, from the given graph, we see the following;
A is on the y-axis
B is at the origin
C is at the point (1, 2)
D is on the x-axis
Looking at the options, we can tell that options 4 and 5 are correct representations of the given graph because they correctly denote the points on the x-axis and y-axis.
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A rectangular room is
1.5
times as long as it is wide, and its perimeter is
35
meters. Find the dimension of the room.
The length is :
meters and the width is
meters.
Answers
The dimensions of the room are approximately 7 meters by 10.5 meters.
The length is 10.5 meters and the width is 7 meters.What are dimensions?In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.
Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.
The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:
\(\text{Perimeter} = 2(\text{length} + \text{width})\)
Substituting the values we have for length and width, we get:
\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)
Simplifying the equation, we get:
\(\rightarrow35 = 2(2.5\text{x})\)
\(\rightarrow35 = 5\text{x}\)
\(\rightarrow\text{x}=\dfrac{35}{5}\)
\(\rightarrow\bold{x\thickapprox7}\)
So the width of the room is 7 meters.
To find the length, we can substitute x into the expression we have for the length:
\(\rightarrow\text{Length} = 1.5\text{x}\)
\(\rightarrow\text{Length} = 1.5(7)\)
\(\rightarrow\bold{Length=10.5}\)
So the length of the room is 10.5 meters.
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What is the range of exponential function g?
Answers
\(g(x) > -6\)
Step-by-step explanation:Graphically, we can see from the graph that \(g(x)\) is will not go less than or equal to \(-6\).
Answer:
g(x)>-6
Step-by-step explanation:
F(x)= 1/x-2 g(x)= 4/x find (fog)(x)
Answers
We have the functions f and g:
f(x) = 1/x - 2
g(x) = 4/x
To obtain the composite function (f o g)(x):
(f o g)(x) = f(g(x)) = 1/g(x) - 2
Then:
(f o g)(x) = 1/(4/x) - 2
(f o g)(x) = x/4 - 2
Now, to calculate the composite function (g o f)(x):
(g o f)(x) = g(f(x)) = 4/f(x)
(g o f)(x) = 4/(1/x - 2) = 4/((1 - 2x)/x)
(g o f)(x) = 4x/(1 - 2x)
If a polynomial function has integer coefficients, then every rational zero of the function has the form p/q, where p is a factor of the ? and q is a factor of the ?
Answers
If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.
The rational zero theorem is used to determine the rational roots of a polynomial function.
Rational Zero Theorem statement:-
The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients
f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,
p is a factor of the constant a₀,
q is a factor of the leading coefficient an,
and p and q are relatively prime.
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Use the shell method to find the volume of the solid obtained by rotating the region bounded by the curves y=4x-2 and y=x^2+1 about the y-axis. Simplify your solution.
Answers
The volume of the solid of revolution is \(\frac{16\pi}{3}\) cubic units.
First, we determine the limits between the two curves. (\(f(x) = 4\cdot x -2\), \(g(x) = x^{2}+1\))
\(f(x) = g(x)\) (1)
\(4\cdot x - 2 = x^{2}+1\)
\(x^{2}-4\cdot x +3 = 0\)
\((x-1)\cdot (x-3) = 0\)
The lower and upper bounds are 1 and 3, respectively. It is to notice that \(f(x) > g(x)\) for \(x \in (1, 3)\). Thus, we determine the volume of the solid of revolution by shell method, that is to say:
\(V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx\) (2)
If we know that \(a = 3\), \(b = 1\), \(f(x) = 4\cdot x - 2\) and \(g(x) = x^{2}+1\), then the volume of the solid of revolution is:
\(V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx\)
\(V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx\)
\(V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx\)
\(V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)\)
\(V = \frac{208\pi}{3} - 40\pi -24\pi\)
\(V = \frac{16\pi}{3}\)
The volume of the solid of revolution is \(\frac{16\pi}{3}\) cubic units.
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Rosie is building a wheelchair ramp that is 18 feet long and 2 feet high. She needs to install vertical support piece 6 feet from the end of the ramp what is the length of the support piece in inches
Answers
Answer:
72 inches
Step-by-step explanation:
multiply the length value by twelve.
PLEASE HELP, WILL MARK BRAINIEST
Answers
Answer:
your answer will be 9 cm
Step-by-step explanation:
I hope this helps u, have a great day !!!
3x+(8x-16) simplest form
Answers
Step-by-step explanation:
3x × 8x- 3x×16
24x -48x
-24x
Find the of the slope of the line through (6,-10) and (4,-8)
Answers
Answer:
-1
Step-by-step explanation:
y = mx + c
m is the slope/gradient
to find slope = y2 - y1 / x2 - x1
= -8 - -10 / 4 - 6
m = -1
What the meaning of statement this?
Answers
The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.
Axiom of RegularityThe set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.
The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.
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A store donated 2 1/4 cases of crayons to a daycare. Each case holds 24 boxes of crayons; each box holds eight crayons. How many crayons did the center receive?
Answers
Answer:
432 crayons
Step-by-step explanation:
24/4=6
24+24+6=54
54*8=432
What is the slope of the line (1,4) (3,2)
Answers
Step-by-step explanation:
the slope is the ratio of "y coordinate change / x coordinate change".
so, in our case here
x changes by +2 (from 1 to 3).
y changes by -2 (from 4 to 2).
so, the slope is -2/2 = -1.
hey guys its me again its me ghriuhr9h so more points yaaaaay
Answers
Step-by-step explanation:
thanks for the free points!
have a great day!
Answer:
wym free points do you get points for answering?
Step-by-step explanation:
Find The value of each variable
Answers
The value of each variable is:
x = 11 units
y = 11√2 units
How to find the value of each variable?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
We can find the value of each variable using trigonometric ratios:
tan 45° = x/11 (tan = opposite/adjacent)
1 = x/11
x = 11 units
sin 45° = 9/y (sine = opposite/hypotenuse)
(√2)/2 = 11/y
y = 11/ (√2)/2
y = 11√2 units
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An arc
of length 22cm and radius 7cm substands
an angle sin at the centre of a circle. what is
the value of sin? [Take t = 22/7]
Answers
Answer:
t = UR MOM!!!
Step-by-step explanation:
1. haha
2. haha
3. haha
4. haha
The table shows the prices of two types of juice. How much does
each type of juice cost per gallon? There are 4 quarts in a gallon.
Juice Price Volume
Orange $3.25 0.5 gallon
Peach $4.50 1.5 quarts
Answers
Answer:
Orange juice is $6.50 per gallon and Peach juice is $12.00 per gallon
Step-by-step explanation:
Step 1: Determine the price of the Orange juice
$3.25 per 0.5 gallon
($3.25 * 2) per (0.5 * 2) gallon
($6.50) per (1) gallon
Step 2: Determine the price of the Peach juice
$4.50 per 1.5 quarts
$4.50 per 0.375 gallon
($4.50 * 2.667) per (0.375 * 2.667) gallon
($12.00) per (1) gallon
Answer: Orange juice is $6.50 per gallon and Peach juice is $12.00 per gallon
Guests who appear on talk shows and interact with other guests for the benefit of an audience are participating in a
a. symposium. b. forum.
c. panel discussion.
d. governance group. e. service group.
Answers
Guests who appear on talk shows and converse with one another for the benefit of the audience make up a (C) panel discussion.
What is a panel discussion?Participants in a panel discussion are guests who appear on talk shows and engage in conversation with one another for the benefit of the audience.
A panel discussion, or simply a panel, is a gathering of people who talk about something in front of an audience, usually at fan conventions, conferences for business or academia, or on television.
Panels often have a moderator who leads the conversation and occasionally solicits questions from the audience with the intention of being both educational and entertaining.
Fan convention film panels have been attributed with increasing box office revenues by creating anticipation.
Therefore, guests who appear on talk shows and converse with one another for the benefit of the audience make up a (C) panel discussion.
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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with grams of a radioactive isotope, how much will be left after 4 half-lives?
Answers
After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:
Amount remaining = Initial amount × (1/2)^(number of half-lives)
In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.
So, the equation becomes:
Amount remaining = Initial amount × (1/2)^4
Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.
Simplifying the equation:
Amount remaining = Initial amount × (1/16)
Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.4. Using the empirical rule, what percentage of the students have grade point averages that are between 2.21 and 3.01?
Answers
Answer:
68%
Step-by-step explanation:
We start by calculating the z-scores of both
z-score = (x-mean)/SD
for 2.21
z-score = (2.21-2.61)/0.4 = -1
For 3.01
z-score = (3.01-2.61)/0.4 = 0.4/0.4 = 1
So what we want to find is the percentage between -1 SD and 1 SD of the mean
This is the percentage corresponding to the probability
P(-1 < x < 1)
According to the empirical rule, this is a value of;
68.269%
lcm of 40,36,126
a)2520
b)2568
Answers
Answer:
The correct choice is option a. 2520
Step-by-step explanation:
LCM of 40, 30, and 126 is as followed:
= 2 × 2 × 2 × 3 × 3 × 5 × 7
= 2520
Answer:
a)2520 is correct
Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. (a) How many sample points are possible
Answers
A gardener wants to determine which of two brands of fertilizer is best for the plants in a garden. Before using one of the fertilizers on the entire garden, the gardener decides to conduct an experiment using 28 individual plants. Which of the two plans for randomly assigning the treatments should the gardener use? Explain.
Plan A: Choose the 14 unhealthiest-looking plants. Apply Brand X fertilizer to all 14 of those plants. Apply Brand Y fertilizer to the remaining 14 plants.
Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
Plan A, because the unhealthy plants need the fertilizer the most and should be treated first
Plan B, because the sample of plants is randomly chosen
Plans A and B are equivalent because they both follow experimental design
Plans A and B are both poorly designed because there are not enough plants to test
The plans cannot be evaluated from the information given
Answers
Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
What is a sample and its types?A sample is only a small portion of the population.
Let's imagine you were interested in determining the average income for all Americans in your population.
Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.
Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.
And the gardener decides to conduct an experiment using 28 individual plants.
Plan A will be a biased sampling and the experiment would not yield
desired results.
Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
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someone down to help...............
Answers
Marcus is rewriting a polynomial by combining like terms. Which terms does he still need to combine to finish rewriting the polynomial? -3mn^3-4n^4+2mn-6n-5mn^3-6m^3n
Answers
Answer:
-3mn^3 and -5mn^3
Step-by-step explanation:
-3mn^3 and -5mn^3
Answer: -3mn^3 -5mn^3
Step-by-step explanation: