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The linear regression that predicts the offspring is The regression equation is y = 0.2134x + 0.513  and the box plot of the data is illustrated below.

The term called box plot is defined as a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

Here we have know that a scatter plot showing the relationship between father and offspring telomere length.

Then the box plot of the data is plotted as follows.

=> 0.281, 0.301, 0.282, 0.425, 0.463, 0.514, 0.506, 0.535, 0.556, 0.59, 0.49, 0.435, 0.482, 0.504, 0.524, 0.487, 0.554, 0.588, 0.631, 0.664, 0.698, 0.513

Then the linear regression is written as

=> y = 0.2134x + 0.513

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Answer:

0.1

Step-by-step explanation:

Answer:

Cos B = 4/5

Step-by-step explanation:

From the question given above, the following data were obtained:

Sine B = 3/5

Cos B =?

Recall:

Sine B = Opposite / Hypothenus

Sine B = 3/5

Therefore,

Opposite = 3

Hypothenus = 5

Next, we shall determine the Adjacent. This can be obtained as follow:

Opposite = 3

Hypothenus = 5

Adjacent =?

Hypo² = Adj² + Opp²

5² = Adj² + 3²

25 = Adj² + 9

Collect like terms

Adj² = 25 – 9

Adj² = 16

Take the square root of both side

Adj = √16

Adjacent = 4

Finally, we shall determine Cos B. This can be obtained as follow:

Hypothenus = 5

Adjacent = 4

Cos B =?

Cos B = Adjacent / Hypothenus

Cos B = 4/5

Answer:

 1.75 ton·miles = 18,480,000 ft·lb

Step-by-step explanation:

You want to know the work done by a freight train locomotive as it pulls cars with a force of 7 tons over a distance of 1/4 mile.

Work is the product of force and distance:

  W = Fd

  W = (7 t)(1/4 mi) = 7/4 t·mi

In foot·pounds, this is ...

  1.75 t·m × 2000 lb/t × 5280 ft/mi = 18,480,000 ft·lb

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

simplify the expression the answer would be 65.

Step-by-step explanation:

hope this helps.

Answer:

65

Step-by-step explanation:

I used a calculator if I used my brain it would be wrong.

Answer:

A

Step-by-step explanation:

V = π r² h           Given d = 7 so the radius (r) = 3.5

577 = 3.14 (3.5)²h

577 = 38.465h

577/38.465 = h

15.00064 = h

15 cm ≈ h

Answer:

The correct answer is A,B,D

Answer:

1 - (1.021)^(1/12) ≈ 0.17 %

Step-by-step explanation:

In the given expression 3.50 is the initial value (cost per pound at the time of the first recording) and (1.021)^t is the increase factor for a given time difference since first recording (in years).

Putting \(t := {\frac{1}{12}}\) into that expression yields the increase factor per month and subtracting it from 1 yields the “rate” notation which is just the part that was “added” to the initial amount.

Bonus: \(p(u) = 3.50 \cdot (1.021)^\frac{s}{12} \approx 3.50 \cdot (1.0017)^s\) is the cost function for a given time \(s := 12 t\) in months.

Note that this approach gives you an increase rate based on an average month length. It doesn’t consider that a real month has different amount of days. For example “s = 3” means “3/12 of a year”, or “1/4 of a year” as opposed to something like “June 13 till September 13”.

Answer:

(1.002)12t.

Step-by-step explanation:

he expression, (1.021)t, reveals the rate of increase for the cost of a pound of strawberries per year.

In order to reveal the monthly rate of increase, rewrite the expression in terms of months. Since there are 12 months in a year, raise the growth factor for the year to the power in order to find the growth factor for the month. To keep this expression equivalent to the given expression, the exponent outside the parentheses needs to change to 12t.

Therefore, the expression that reveals the monthly rate of increase for the cost of a pound of strawberries is (1.002)12t.

The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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Answer:

Step-by-step explanation:

Some qucik lil definitions of these words

Coefficient - A multiplicative factor in some term of a polynomial, a series, or any expression.

Constant - A value that is unchanging.

Term - A  single mathematical expression.

Variable - A letter used to represent an unknown.

When an inequality is multiplied or divided by a negative number, the inequality sign will flip, meaning it will change its direction. For example, if you have a > b and you multiply or divide both sides by a negative number, the inequality will become a < b. This is because the relationship between the values reverses when multiplied or divided by a negative number.

Explanation:

When an inequality is multiplied or divided by a negative number, the direction of the inequality sign is flipped. This is because multiplication or division by a negative number, results in a reversal of the order of the numbers on the number line.

To see why this happens, consider the following example:

Suppose we have the inequality x < 5. If we multiply both sides of this inequality by -1, we get -x > -5. Notice that we have flipped the inequality sign from "<" to ">". This is because multiplying by -1 changes the sign of x to its opposite, and also changes the sign of 5 to its opposite, resulting in a reversal of the order of the numbers on the number line.

Similarly, if we divide both sides of the inequality x > 3 by -2, we get (-1/2)x < (-3/2). Here, we have again flipped the inequality sign from ">" to "<". This is because dividing by a negative number also changes the order of the numbers on the number line.

In general, if we have an inequality of the form a < b or a > b, where a and b are real numbers, and we multiply or divide both sides by a negative number, we obtain:

If we multiply by a negative number, the inequality sign is flipped. For example, if a < b and c < 0, then ac > bc.

If we divide by a negative number, the inequality sign is also flipped. For example, if a > b and c < 0, then a/c < b/c.

Therefore, it is important to be mindful of the signs of the numbers involved when performing operations on inequalities. If we multiply or divide by a negative number, we must flip the direction of the inequality sign accordingly.

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The scale factor of figure A to figure B is 5/2

A scale factor can be defined as the ratio of the scale difference between  a given original shape and a new shape.

It is seen as a number from which the size of a dimensional shape or figure can be transformed with respect to its original size or magnitude.

It is also described as the ratio between corresponding measurements of an object and a representation of that object.

The formula for scale factor is expressed as;

Scale factor = Dimension of the new shape ÷ Dimension of the original shape

This is so for the downgrading of a shape

Now, we have;

Scale factor = Adjacent of the triangle A/adjacent of triangle B

Scale factor = 10/ 4

Reduce to simply forms

Scale factor = 5/ 2

Hence, the scale factor is 5/2

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Answer:

Total consumer spending is 160

Step-by-step explanation:

Here , we are interested in calculating the total consumer spending.

In a long run perfect competition market, price interest with MC and minimum point of AC

Hence , P = AC

this means that Q = 40,000/P = 40,000/150 = 266.67 which is approximately 267 potatoes will be consumed

The total consumer spending is thus 267 * 0.6 = 160

Answer:

It's the first one.

Step-by-step explanation:

Using the formula, Total Cost = Purchase Price + Sales Tax,

Let x be the sales tax

$21.56 = $19.99 + x

At this point, it's very easy to do this. To find x, you subtract $19.99 from the total cost or $21.56.

$21.56 - $19.99 = $1.57 hence the sales tax is $1.57.

How can we check our answer?

If you aren't sure if you are correct, just add the purchase price with the sales tax.

$19.99 + $1.57 = x

$19.99 +$1.57 = $21.56

It is the same as the Total Cost so $1.57 is your correct answer.

It asks for the rate, not the sales tax. Continuing with this, to find the rate, you do Sales Tax/Purchase Price = Rate of Sales Tax/100%

1.57/19.99 = x/100%

Cross multiply: 19.99*x = 1.57*100

19.99*x = 157

Then, do

19.99*x/19.99 = 157/19.99 which is equal to 7.85392696%, round that to 7.85%

So the rate of the sales tax is 7.85%

Answer:

12x^3 + 19x^2 + x - 5

Step-by-step explanation:

To solve this, I set up the problem like this:

(3x^2 + x - 1)(4x + 5)

Now, just distribute everything from the first set of ( ) to the second set of ( ). Here's what you should have when you do that:

12x^3 + 15x^2 + 4x^2 + 5x - 4x - 5

Now, you would just combine like terms, which would get you to the final answer.

Hope this helps!

12x³ + 19x² + x -5

Polynomials are expressions that have multiple terms.

Breaking Apart Polynomials

When multiplying by a polynomial, we can break apart one of the polynomials, and multiply by each term individually. This means to multiply 3x² + x - 1 by 4x + 5, we can break apart the binomial into its separate terms. Instead of trying to multiply everything at once, we can multiply the trinomial by 4x and then multiply the trinomial by 5. Finally, add together the 2 products for the final answer.

Multiplying Polynomials

First, let's multiply the trinomial by 4x.

To find the product, multiply each term of the trinomial by 4x, then add them back together.

So, the first product is 12x³ + 4x²- 4x. Next, let's multiply 5(3x² + x - 1) the same way.

This means that the second product is 15x² + 5x - 5. Finally, let's add the 2 products together.

Then, simplify the expression.

This gives us our final answer. The product of 3x² + x - 1 and 4x + 5 is 12x³ + 19x² + x - 5.

It will take 3 hours to bake 3 pans of baked macaroni if the oven can only bake one pan of baked macaroni for 1 hour.

If Jeanna's oven can only bake one pan of baked macaroni for 1 hour, then it will take 3 hours to bake 3 pans of baked macaroni. This is because the time it takes to bake the pans is directly proportional to the number of pans being baked. Therefore, if it takes 1 hour to bake 1 pan, it will take 3 hours to bake 3 pans. So, the answer is 3 hours.

It is important to note that the number of pans Jeanna wishes to bake, which is 34 pans, is irrelevant to the question. The question only asks for the time it will take to bake 3 pans of baked macaroni, so the number of pans Jeanna wishes to bake does not affect the answer.

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Answer:

56.2

Explanation:

There is a way to remember the ways to solve for right triangles, SOH CAH TOA which stands for each of the ways to solve for angles or sides:

Sine: Opposite over Hypotenuse

Cosine: Adjacent over Hypotenuse

Tangent: Opposite over Adjacent

In this case, with the information we have, we would use tangent since we have both the opposite side, b, and the adjacent side, a.

It would be the inverse of tangent (tan⁻¹) since you are solving for the angle and not a side.

You would use a calculator to solve this, by dividing b by a.

tan⁻¹(b/a)

tan⁻¹(46.7/31.3) = 56.1686012868

Round to the nearest tenth = 56.2

*Make sure your calculator is in degrees mode or it will give you an incorrect result.

Answer: D

Step-by-step explanation:

If sinA = 3/8, the value of cosec A - sec A is (72√55 - 440)/495

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

If sin A = 3/8

and SinA = opp/ hyp

opp = 3 and hyp = 8

using Pythagoras theorem

8² = 3²+adj²

adj = √ 8²-3²

adj = √64-9

adj = √55

cos A = √55/8

sec A = 1/CosA = 8/√55

cosec A = 1/sinA = 8/3

cosec A-sec A = 8/ √55 - 8/3

= (24-8√55)/3√55

= (72√55 - 440)/495

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Answer:

Choice B.

Explanation:

The side length is the distance between the vertices of the triangle given.

Answer:

a rotation 90˚ clockwise and then a reflection across the y-axis

Step-by-step explanation:

I'm doing the test right now

Function 1 has a greater slope than Function 2, and the answer is Function 1.

Function 1 is defined by the equation y = \(\frac{5}{4}r - 1\).

Function 2 is defined by line p, which is shown on the graph.

The problem asks which function has a greater slope.

The slope of a line is calculated by the ratio of the difference between the vertical axis values and the difference between the horizontal axis values.

This is shown in the formula:

slope = rise/run.

Here, rise refers to the vertical difference and run refers to the horizontal difference.

This means that the slope of a line measures how steeply the line is increasing or decreasing.

Function 1: y = \(\frac{5}{4}r - 1\)

Here, the equation of Function 1 is given as y = \(\frac{5}{4}\)r - 1.

From this equation, we can see that the slope of Function 1 is equal to \(\frac{5}{4}\).

Therefore, the slope of Function 1 is 1.25.Function 2: Line pNext, we need to determine the slope of line p, which represents Function 2.

To do this, we can use two points on the line.

From the graph, we can see that the line passes through the point (0, -2) and the point (4, 1).

The rise of this line is equal to 1 - (-2) = 3, while the run is equal to 4 - 0 = 4.

Thus, the slope of line p is equal to 3/4.

Therefore, the slope of Function 2 is 0.75.

Comparing the slopes, we can see that Function 1 has a greater slope than Function 2.

Specifically, the slope of Function 1 is 1.25, while the slope of Function 2 is 0.75.

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Answer:

d. Jordan needs 1 and one-half cups of diced chicken for 3 salads

Step-by-step explanation:

cups of chicken are shown on the y axis, number of salads is shown on the x axes. For 3 salads you need 1.5 cups of chicken.

Answer:

the answer i d

Step-by-step explanation:

Answer:

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The maximum point of a function found by solving f'(x) = 0

1.Y(x) = 900, if x ≤ 30

2.900 - 40(x - 30), if x > 30

3.T(x) = x × Y(x)

4.dT/dx = 900, if x < 30

5.2100x - 40x² if x > 30

6.The derivative dT/dx equals zero at x = 52.5, but it is not valid in the given context.

7.The maximum yield occurs at x = 30 trees per acre, with a maximum yield of 27,000 peaches per acre.

8.T(x) is differentiable at x = 30.

To find the function that describes the per-tree yield, Y, in terms of x, use the given information:

If there are 30 or fewer trees planted per acre (x ≤ 30), the per-tree yield is 900 peaches per tree.

If there are more than 30 trees planted per acre (x > 30), the per-tree yield decreases by 40 peaches for every extra tree planted beyond 30.

The function Y(x) as follows:

Y(x) = 900, if x ≤ 30

Y(x) = 900 - 40(x - 30), if x > 30

find the total yield per acre, T, that results from planting x trees per acre. The total yield is simply the per-tree yield (Y) multiplied by the number of trees per acre (x):

T(x) = x × Y(x)

differentiate T with respect to x (dT/dx) to find where the maximum yield occurs.

dT/dx = d/dx (x × Y(x))

dT/dx = d/dx (x × (900 - 40(x - 30)))

To find if this derivative ever equals zero, it to zero and solve for x:

0 = 900 - 40(x - 30)

40(x - 30) = 900

x - 30 = 22.5

x = 52.5

So, the derivative dT/dx equals zero at x = 52.5. However, we need to check whether this value is valid for our function. Recall that if x > 30, the per-tree yield decreases by 40 peaches for every extra tree planted beyond 30. Therefore, planting 52.5 trees per acre would result in a negative per-tree yield, which is not physically meaningful in this context. Thus, the maximum yield occurs at the critical point within the valid domain, which is x = 30.

Now, let's find the maximum value of the yield at x = 30:

T(30) = 30 ×Y(30) = 30 × 900 = 27,000 peaches per acre

The optimal value of x that maximizes the yield is 30 trees per acre, and the maximum yield is 27,000 peaches per acre.

Finally, let's determine if T(x) is differentiable when x equals 30. Since T(x) is a piecewise function, we need to check if the left and right-hand derivatives at x = 30 are the same.

Left-hand derivative (x < 30):

dT/dx = d/dx (x × 900) = 900

Right-hand derivative (x > 30):

dT/dx = d/dx (x × (900 - 40(x - 30))) = d/dx (x × (900 - 40x + 1200)) = d/dx (2100x - 40x²)

Now, evaluate the right-hand derivative at x = 30:

dT/dx = 2100(30) - 40(30)² = 63,000 - 36,000 = 27,000

Since the left-hand derivative and the right-hand derivative at x = 30 are equal (both are 27,000), T(x) is differentiable at x = 30.

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Answer:

840

Step-by-step explanation:

840&*67---***&%%%%%:

3.864×10⁵ is the product of 840 and 4.6×10² in scientific notation

Multiplication is a method of finding the product of two or more numbers

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

We need to find the product of 840 and 4.6×10²

Eight hundred forty into four point six into ten to the power of two.

840× 4.6×10²

3864×10^2

Divide and multiply by 1000

3.864×10^5

Hence 3.864×10⁵ is the product of 840 and 4.6×10²

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I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Answer:

Step-by-step explanation:

Answer:

M = 61

nm = 31

kn = 45

L = 119

Step-by-step explanation:

its a parallelogram so everything is obvious

Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

In plan A,

    Plans for saving = $500

  Amount of saving each week = $20

∴ Number of weeks needed to make goal = (500 ÷ 20) (by using division)

                                                                       = 25

In plan B,

    Plans for saving = $500

   Amount of saving each week = $30

∴ Number of weeks needed to make goal = (500 ÷ 30) (by using division)

                                                                       = 17

In plan C,

    Plans for saving = $500

   Amount of saving each week = $40

∴ Number of weeks needed to make goal = (500 ÷ 40) (by using division)

                                                                       = 13

In plan D,

    Plans for saving = $500

   Amount of saving each week = $50

∴ Number of weeks needed to make goal = (500 ÷ 50) (by using division)

                                                                       = 10

So, Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

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