Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length.
A least-squares regression on the data he collected produces the equation
ŷ =37.67+33.18x
where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94.
Construct a 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places.
Lower limit: ____ Upper limit: ____

Answer: 11/14 (eleven over fourteen)

Step-by-step explanation:

Answer: The equation that has the same solution as the given equation is −1 − 22 ⁢ n = −20 ⁢ n − 9. This can be seen by solving both equations for n.

To solve the given equation − 5 ⁢ n + 31 = − 14 ⁢ n − 5 for n, we can start by adding 5n to both sides to obtain 31 = − 9 ⁢ n − 5. Then, we can add 9n and 5 to both sides to obtain n = −1.

To solve the equation −1 − 22 ⁢ n = −20 ⁢ n − 9 for n, we can start by adding 22n to both sides to obtain −1 = −20 ⁢ n − 9. Then, we can add 20n and 9 to both sides to obtain n = −1.

Since both equations have the same solution for n (namely, n = −1), they have the same solution. Note that the other equations listed in the question do not have the same solution as the given equation. For example, the equation 1 = 0.75 ⁢ n + 3.25 has the solution n = −4, while the equation 3 − 6 ⁢ n + 3 ⁢ n = − 3 + 4 − 4 ⁢ n has the solution n = 1/5. These solutions are different from the solution n = −1 of the given equation, so these equations do not have the same solution as the given equation.

Answer:

11/4n+2=-3+ 3/2n

Step-by-step explanation:

The required supply function is p = 3q - 300 and the required demand function is p = -3q + 1110. The equilibrium quantity is 235 and the equilibrium price is $405.

a) Find an equation for the supply function's price p as a function of q as follows.

Let p = mq + b be the required linear supply function.

From the given information, the supply function passes through points (125, 75) and (150,150).

Find the slope m using the points (125, 75) and (150,150) as shown below.

m = (p2-p1)/(q2-q1)

m = (150-75)/ (150-125) = 75/25 = 3

Now find the value of b using the point (125, 75) and slope m = 3 as follows.

p = mq + b

75 = 3(125) + b

b = - 375 + 75 = -300

Therefore, the required supply function is p = 3q - 300.

b) Find an equation for the demand function's price p as a function of q as follows.

Let p = mq + b be the required linear supply function.

From the given information, the demand function passes through points (355, 45) and (330,120).

Find the slope m using the points (355, 45) and (330,120) as shown below.

m = (p2-p1)/(q2-q1)

m = (120-45)/ (330-355) = 75/-25 = -3

Now find the value of b using the point (355, 45) and slope m = -3 as follows.

p = mq + b

45 = -3(355) + b

b = 1065 + 45 = 1110

Therefore, the required demand function is p = -3q + 1110.

Find the equilibrium quantity and equilibrium price as follows.

In order to find the equilibrium quantity, equate the demand function and supply function and solve the equation solve for q as shown below as p is common.

3q - 300 = -3q + 1110

=> 6q = 1410

=> q = 235

Thus, the equilibrium quantity is 235.

Find the equilibrium price by substituting q = 235 in p = 3q -300.

p = 3 x 235 - 300

p = 705 -300 = 405

Hence, the equilibrium price is $405.

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Answer:

I cant see numbers sorry. post question again

The question is unclear.

The point of intersection is (0, -4).

What is the point of intersection?

In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.

Here, we have

Given: f(x) = -x -4, g(x) -5x -4

The lines intersect where f(x) = g(x)

f(x) = g(x)

- x - 4 = -5x - 4

-x +5x = -4 +4

4x = 0

x = 0

Now, we put the value of x in f(x) and we get

f(0) = - 0 - 4

f(0) = -4

Hence, the point of intersection is (0, -4).

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A translation 3 units left and 2 units up best describes the graph of  f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x

How to solve this problem?

f(x) = log2(x + 3) + 2 (given)

g(x) = log2x (given)

We need to describe the best statement for the graph

The graph is shown in the image

The following steps are shown to describe the graph.

The general equation of f(x) = log2(x-h)+k

When h > 0 (positive)

The graph of the base of the function shift to the right

When  h < 0 (Negative)

The graph of the base function shifts to the left.

When k > 0 (Positive)

The graph of the base function shifts upward.

When k < 0 (Negative)

The graph of the base function shifts downward

Here h = 3 , k = 2

Hence , a translation 3 units left and 2 units up describes the graph.

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Answer:

A

Step-by-step explanation:

Blue = River Y

Red = River Z

River Y equation: y = 18

River Z equation: y = 10 + 2x

Graph A represents this system of equations.

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Applying the triangle midsegment theorem, the measure of AC is: 32 units.

Since DE is a midsegment of triangle ABC, the triangle midsegment theorem therefore states that the length of DE is half of the length of the third side of the triangle, AC.

Given the following:

DE = 9x - 20

AC = 5x + 12

Find the value of x by creating an equation to solve:

DE = 1/2(AC) [based on the triangle midsegment theorem]

Substitute:

9x - 20 = 1/2(5x + 12)

Solve for x:

2(9x - 20) = 5x + 12

18x - 40 = 5x + 12

18x - 5x = 40 + 12

13x = 52

Divide both sides by 13

13x/13 = 52/13 [division property of equality]

x = 4

AC = 5x + 12

Plug in the value of x

AC = 5(4) + 12

AC = 32 units.

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The two inequalities that describe the total cost and no. of guests are

18a + 9c ≤ 2475 and

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let 'a' be the no. of adults and 'c' be the no. of children.

The expense for this event must not exceed $2,475.00.

Therefore, 18a + 9c ≤ 2475...(i)

The venue can hold no more than 150 guests.

Therefore, a + c ≤ 150...(ii)

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10 inches is the scale factor from the drawing to the actual billboard

A scale factor is a ratio of change from a drawing to real life. Typically, a scale factor is unit-less; a scale factor of 48 (or 1:48) is saying that for one unit on the page, it represents 48 of the same units in real life.

A scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Scale drawings show an image either reduced or enlarged in size. The change between the original and the scaled drawing is generally represented by two numbers separated by a colon, like 10:1 (read as “ten to one”).

The difference between the ratio numbers represents the factor by which the scaled image is enlarged or reduced. So for a 10:1 scale ratio, a 1 inch (2.5 cm) drawing will be 10 inches (25 cm) in real life.

Methods are as follows :

Changing Scale Digitally-

Scan the image or snap a pic of it with your phone.

Insert the image into a suitable program or app.

Navigate to the image layout options.

Adjust the height and width under the “Scale” heading.

Save the scaled image and you’re done.

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The correct option is B (f-g)(y)=8 y²-y+3

What exactly are function and example?

A rule is something that produces one output from one input, such as a function. Alex Federspiel was the source of the image. As an illustration, consider the equation y=x2. For every x input, there is only one y output. The fact that x is the input value leads us to say that y is a function of x.

Which four sorts of functions are there?

The classification of various types of functions can be done using four primary categories. All functions are based on the element: one to one, many to one, onto, one to one, and into.

Given that:

f(y)=5 y²-2y+1

g(y)=-3y²-y-2

(f-g)(y) = 8y²-y+3

Option b is correct

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The difference of the given polynomials 8x³+5x+6 and 2x²+3x is 8x³-2x²+2x+6. So, the correct answer is D.

To subtract polynomials from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.

Given that, 8x³+5x+6-(2x²+3x)

Group the like terms are perform the addition or subtraction

= 8x³+5x+6-2x²-3x

= 8x³+(5x-3x)-2x²+6 (Here, like terms are 5x and 3x)

= 8x³+2x-2x²+6

= 8x³-2x²+2x+6

So, the standard form of obtained polynomial is 8x³-2x²+2x+6.

The polynomials difference is 8x³-2x²+2x+6. Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Which polynomial represents the difference below?

8x³ + 5x+6-(2x² + 3x)

A. 10x+ 8x² +6

B. -2x² + 8x³ + 8x+6

C. 6x¹⁰+2x+6

D. -2x²+ 8x³+2x+6

The linear inequality x < - 3 is represented on the number line below

An Inequality represents the mathematical expression that shows both sides are not equal. When the relationship makes a non-equal comparison between two expressions or two numbers, then it is known as inequality. In this case, the equal sign in the expression is represented by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).

The inequality given is;

-2x + 0.25 > 6.25

-2x > 6.25 - 0.25

-2x > 6.0

Divide both sides by coefficient of x

x < -3

Placing this on a number line, we would have;

Kindly find the attached graph below

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There is an attachment that includes the graph for the inequality 8x + 5y 100.

How do you calculate the scenario's graph?

The parameters are as follows, taken from the query:

The customer's purchase must not exceed $100.

Each bath towel costs $8.

Each hand towel costs $5.

Inequality among the available combinations is another factor that we have.

8x + 5y ≤ 100

like that

x is the quantity of bath towels, while y is the quantity of hand towels.

Plotting the inequality's graph is the following step.

A graphing tool can be used for this.

In order to attach the graph, we enter the inequality in the graphing tool.

Keep in mind that the inequality is provided as

8x + 5y ≤ 100

See the inequality graph in the attached. 8x + 5y ≤ 100

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Answer:

x=9

Step-by-step explanation:

these 2 angles are supplementary angles meaning added together they will equal 180 degrees

so we can add them together and set it equal to 180

(8x-3)+(16x-33)=180

combine like terms

(8x+16x)+(-3-33)=180

24x-36=180

     +36. +36

24x=216

/24.  /24

x=9

hopes this helps

Resulting box has the greatest volume for the values  (25 ± 5√7)/6 .

This is a problem that can be solved using derivatives , maxima & minima and common logic.

Hence , going by logic :

Creating a flap of 'a' inches in width, the base of the box will be

 (10 - 2a) by (15 - 2a)

and the depth of the box will be the width of the fold-up flap: a.

Then the volume of the box is

 v = [tex]a(10 -2a)(15 -2a) = 150a -50a^2 +4a^3[/tex]

Using the derivative of the volume will be zero at the maximum volume.

 0 = [tex]dv/da = 150 -100a +12a^2[/tex]

This has roots at

 a = (100 ±√(100² - 4(12)(150)))/(2·12)

 a = (100 ± √2800)/24 = (25 ± 5√7)/6

Only the smaller of these solutions gives a maximum volume.

You should cut (5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.

Similarly , replacing the values of 10 by A and 15 by B , a generalized solution can be formed .

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The equation of the line that has the slope of 7/3 is:  y = (7/3) x - 27/49

Finding the slope and y-intercept is necessary to express the equation of a graphed line in y-intercept (y=mx+c) form, which can then be used to get the equation of the line. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.

Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

Given that,

slope (m) = 7/3

Putting (7,-9) into the equation: y =mx+c

or, -9 = (7/3) × (7) + c

or, -9 = 49 /3 + c

or, c = (-9) × (3/49)

or, c = -27/49

Thus, the equation becomes:

or, y = (7/3) x + -27/49

or, y = (7/3) x - 27/49

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Answer:

gh(b)

Step-by-step explanation:

Answer:

shifted to the right

Step-by-step explanation:

Each kit will have 3 bags of marshmallows and 4 boxes of toothpicks

From the question, we have the following parameters that can be used in our computation:

The number of bags of marshmallows in each kit is calculated as

Bags = Bags of marshmallows/Greatest number of identical kits

Bags = 36/12

Bags = 3

The number of boxes of toothpicks in each kit is calculated as

Boxes = boxes of toothpicks/Greatest number of identical kits

Boxes = 48/12

Boxes = 4

hence, the bags are 3 and the boxes are 4

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The polynomials using synthetic division is [tex]2 y+4+\frac{5}{y+3}[/tex].

What is polynomials?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x^2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

[tex]\frac{\left(2 y^2+10 y+17\right)}{(y+3)}$$[/tex]

[tex]$$\begin{aligned}& \text { Divide } \frac{2 y^2+10 y+17}{y+3}: \frac{2 y^2+10 y+17}{y+3}=2 y+\frac{4 y+17}{y+3} \\& =2 y+\frac{4 y+17}{y+3}\end{aligned}$$[/tex]

Divide [tex]$\frac{4 y+17}{y+3}: \quad \frac{4 y+17}{y+3}=4+\frac{5}{y+3}$[/tex]

[tex]=2 y+4+\frac{5}{y+3}[/tex]

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Answer:

$22.50

Step-by-step explanation:

Using the given formula, we have been able to prove that; the expected value of the students' score is 18 correct responses

1) Let X denote the number of correct guesses, assuming that a student guesses randomly among the five options of all 25 questions. Then X has a binomial probability distribution with;

n = 25

p = 1/5 = 0.2

2) Let Y denote the number of correct responses on the seven questions for which the student guesses randomly from among the five options. Then Y has a binomial probability distribution with n = 7 and p = 0.20. Then the expected value of Y is;

E(Y) = np = 7(0.2) = 1.4

Using the scoring formula given, we have;

Score = (18 + Y) - 0.25(7 - Y) + 0(0)

= 16.25 + 12Y

The expected value of the students' score is;

E(16.25 + 12Y) = 16.25 + 12(1.4)

= 18 correct responses.

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Answer:

-2

Step-by-step explanation:

The line appears to cross through (2,3) and (4,-1)

You can subtract the x values and y values to determine the difference:

[tex]2 - 4= - 2 \\ 3 - ( - 1) = 4[/tex]

These can be used as the y and x values in y over x to find the slope:

[tex] \frac{4}{ - 2} = - 2[/tex]

The slope is -2

If a store decides to spend $1500 on Sunday TV ads for all-terrain tires, we can predict that 95% of the values for the revenue in those weeks from the sale of these will be between $21863.59 and $25617.41.

A company can use regression analysis to determine statistical relationships between the total sales of its products and the costs associated with promotions and advertising. The outcomes of these analyses can then be used to determine how best to allocate spending funds among, say, various products or sales regions.

n = 41

df = n - 2

df = 41 - 2 = 39

SSₓₓ = (n - 1)S²ₓ

SSₓₓ = (41 - 1) * (400)²

SSₓₓ = 6400000

y = 15531.3086 + 5.4728 * x

If, x = 1500 then:

y = 15531.3086 + 5.4728 * 1500

y = 23740.51

Prediction range of y at 95% = [tex]y + t_{\frac{0.05}{2},39 } * S_{e} * \sqrt{1 + \frac{1}{n} + \frac{(x - x_{1} )^{2}}{SS_{xx} } }[/tex]

Prediction range of y at 95% = [tex]23740.51 + 2.022691 * 915.247 * \sqrt{1 + \frac{1}{41} + \frac{(1500 - 1700)^{2} }{6400000}[/tex]

Prediction range of y at 95% = (2186.1 , 25619.92)

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Answer:

The approximate error of weight is 6.241 - 6 = 0.241 lbs

The approximate error of the given weight is 0.241 lbs

The approximate error of weight is the difference between the claimed weight and the actual weight, which is:

Approximate error = Actual weight - Claimed weight

As per the question, we have

Actual weight =  6.241 lbs

Claimed weight = 6 lbs

Substitute the values in the formula and we get:

Approximate error = 6.241 lbs - 6 lbs

Approximate error = 0.241 lbs

Therefore, the approximate error of weight is 0.241 lbs.

This means that the claimed weight is off by 0.241 lbs, which could be significant depending on the context.

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The sequence of transformations that maps ∆ABC to ∆A'B'C' include the following: D. (T(0, -4) о r(90°, 0)(∆ABC)

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle ABC (∆ABC), the coordinates of the vertices of the image (∆A′B′C′) are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (5, 5) → Ordered pair A' = (-5, 5)

Ordered pair B = (1, 3) → Ordered pair B' = (-3, 1)

Ordered pair C = (2, 1) → Ordered pair C' = (-1, 2)

Next, we would translate the vertices of the image (∆A′B′C′) 0 units to the right and 4 units downward as follows;

Ordered pair A' = (-5, 5) → (-5 + 0, 5 - 4) = (-5, 1)

Ordered pair B' = (-3, 1) → (-3 + 0, 1 - 4) = (-3, -3)

Ordered pair C' = (-1, 2) → (-1 + 0, 2 - 4) = (-1, -2)

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The solution is D = 200 feet

The diameter of the circular store is = 200 feet

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the diameter of the circle be represented as = D

Let the radius of the circular store be = r

D = 2r

Now , the area of the circular store be = A

The value of A = 31,415 feet²

The area of the circular store is given by the formula

Area of the circle = πr²

Substituting the values in the equation , we get

31415 = 3.1415 x r²

Divide by 3.1415 on both sides of the equation , we get

r² = 10000

Taking square roots on both sides of the equation , we get

r = 100 feet

Now , the diameter of the store = 2 x radius of the store

Diameter of the store D = 2 x 100 feet

Therefore , diameter of the store D = 200 feet

Hence , The diameter of the circular store is = 200 feet

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The area of the surface formed by revolving the polar equation over the given interval about the given line , r = 4cosθ is 16π .

Polar coordinate system is a two dimensional coordinates system like Cartesian system with the variables r, θ ( polar coordinates) and axis called polar axis . Consider the polar equation

r = 4cosθ --(1) ; 0≤θ ≤π/2

The axis of a rotation is in polar axis.

We know that, the surface area about θ = π/2 is

S = 2π ∫(r sinθ√(r² + (dr/dθ)²) dθ with limits

so, differenatiate equation (1) with respect to θ we get , dr/dθ = - 4 sinθ

Now, S =2π₀∫ˣ [4cosθsinθ√(4²cos²θ + (-4 sinθ)²)]dθ where x = π/2

S = 2π ₀∫ˣ[ 4cosθsinθ√(4²cos²θ + 4²sin²θ)]dθ

S = 2π₀∫ˣ [ 4cosθsinθ√4²(cos²θ+sin²θ)]dθ

S = 2π ₀∫ˣ [ 16cosθsinθ√(cos²θ+sin²θ)]dθ

S = 32π ₀∫ˣ [cosθ sinθ √1 ]dθ

S = (32π/2) ₀∫ˣ 2cosθsinθdθ

S = (16π) ₀∫ˣ sin2θdθ

S = 16π ₀[- cos2θ/2]ˣ

putting the upper limit θ = x = π/2 and lower limit θ = 0

S = (- 16π/2) [ cos2 (π/2) - cos2(0)]

S = (- 8π )[ cosπ - cos0° ] = - 8π[ - 1 - 1]

S = 16π

Hence, surface area is 16π .

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Complete question :

Find the area of the surface formed by revolving the polar equation over the given interval about the given line_ Polar Equation r = 2 cosQ

Interval 0 < Q <π/ 2 Axis of Revolution Polar axis.