Bivariate data for the quantitative variables xand y are given in the table below. These data are plotted in the scatter plot shown next to the table In the scatter plot; sketch an approximation of the least-squares regression line for the data.

Answer:

1/4 pound

Step-by-step explanation:

2 1/2 divided by 10

=

1/4

or

5/2 divided by 10

=

1/4

Answer: 1/4 lbs

Step-by-step explanation:

To find weight lost each day, you have to divide total weight lost 2 1/2 lbs by total number of days 10.

(2 1/2) / 10 = 5/2 * 1/0 = 1/4 lbs lost each day

The cost of 4 kilograms is £1.10, so Stuart has enough to buy it.

We can define the variables:

x = cost of a kg of onions.

y = cost of a kg of carrots.

We can write the system of equations.

2.5x + 2y = 2.36

3y = 1.74

Solving the second one we get:

y = 1.74/3 = 0.58

We can replace that in the other equation to get:

2.5x + 2*0.58 = 2.36

2.5x = 2.36 - 2*0.58

x = 0.6844/2.5 =0.274

Then the cost of 4 kg of onions is:

C = £0.274*4 = £1.10

And Stuart has 2 pounds, so he has enough.

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The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer: x2+17x+3

Step-by-step explanation:

2x2+7x−x2+10x+3

=2x2+7x+−x2+10x+3

Combine Like Terms:

=2x2+7x+−x2+10x+3

=(2x2+−x2)+(7x+10x)+(3)

=x2+17x+3

Answer:

2000

Step-by-step explanation:

Number of shares after split is 5/2 times the pre split value =800*5/2 = 2000

The value of x in each prism:

1) x = 5.47

2) x = 4.2

3) x = 2.1

Given,

Prisms of different shapes.

Now,

1)

Volume of cuboid = l * b *h

l = Length of cuboid

b = Breadth of cuboid

h = Height of cuboid

So,

256 = 3.8 * x * 12.3

x = 5.47

2)

Volume of triangular prism = 1/2 * s * h
s = 1/2* a * b

Substitute the values in the formula,

256 = 1/2 * x * 9.8 * 12.4

x = 4.2

3)

Volume of cylinder = π * r² * h

r = Radius of cylinder.

h = Height of cylinder.

Substitute the values,

256 = π * x² * 18.2

x = 2.1

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Answer:

12

Step-by-step explanation:

60 / 5 = 12

Answer:

12 please mark brainliest I really need it please

Answer:

C 3/2

Step-by-step explanation:

Since triangle PRQ is the original and is getting bigger proportionally (can tell by side lengths) you can eliminate options A and B since you have to multiply by a number/fraction greater than one since it's getting bigger. Then pick a side corresponding to another side of the other triangle. For example, the side length of PQ is 8. Side length P'Q' is 12. You will need to consider how you get from that 8 since it's the original to the 12. To do that you will need to multiply by 1.5 to get to 12. this is what it means by dilation. Since 3/2=1.5 that would be your answer.

Answer:

C 34 units

Step-by-step explanation:

I took the test.

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

The teacher can line up the students in 3991680 ways so that no two boys stand next to each other.

Given, A class has nine boys and eleven girls.

Any two boys will fight if they are next to each other.

Ways can the teacher line up the students so that no two boys stand next to each other:

The total number of students = 9 + 11 = 20.

To count the total number of arrangements such that no two boys stand next to each other, we will count the total number of arrangements of all students and then subtract the arrangements where two boys are together.

Let's take two cases :

1. Case 1: When a girl stands on both ends, there are 11 ways to do this.

After placing the girls, the number of possible ways to arrange boys in such a way that no two boys are standing next to each other can be calculated using the permutation formula.

(n - r + 1)P(r) = (9 - 1 + 1) P(9) = 9P9 = 9!

Thus, the total number of arrangements in this case = 11 × 9!

2.Case 2: When a boy stands on one end and a girl on the other, there are 2 ways to do this.

After placing the girl and boy, the number of possible ways to arrange boys in such a way that no two boys are standing next to each other can be calculated using the permutation formula.

(n - r + 1)P(r) = (9 - 1)P(8) = 8P8 = 8!

Thus, the total number of arrangements in this case = 2 × 8!

Thus, the total number of arrangements in which no two boys stand next to each other is = (11 × 9!) + (2 × 8!)

= 11 × 362880 + 2 × 40320= 3991680.

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The data suggests a direct relationship between force and distance in the spring experiment.

Based on the given data, as the force increases (4 N, 8 N, 12 N, 16 N, 20 N), the distance the spring stretches also increases (10.0 cm, 20.0 cm, 30.0 cm, 40.0 cm, 50.0 cm). This indicates a direct relationship between force and distance. In other words, as the force applied to the spring increases, the amount by which the spring stretches also increases.

To describe this relationship quantitatively, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement or stretch of the spring from its equilibrium position. Mathematically, Hooke's Law is expressed as F = k * x, where F is the force applied to the spring, k is the spring constant, and x is the displacement from the equilibrium position.

In the given data, the force (F) corresponds to the weight applied to the spring, and the distance (d) corresponds to the displacement. Therefore, the variation model that describes the relationship between force and distance in this experiment is F = k * d, where k represents the spring constant specific to the spring being used.

By analyzing the data and applying Hooke's Law, we can conclude that the force and distance have a direct relationship, and the variation model F = k * d represents this relationship.

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Answer:

3/8 gallon

Step-by-step explanation:

They drink 1/2 of their milk at breakfast => it means they drank 1/2 of 3/4 gallon of milk.

So, they drank : 3/4 x 1/2 = 3/8 gallon of milk.

I'll do parts (a) through (c) to get you started

(a) False. The explanatory variable is always along the x axis, and the response variable is along the y axis. The response variable reacts to whatever the input explanatory variable is, hence the name "response".

---------

(b) True. If all data lie along a single straight line with nonzero slope, then either r = -1 or r = 1. If we have all data points on a line with some negative slope, then r = -1. If the regression slope is positive, then r = 1. Either way, it will lead to r^2 = 1 because (1)^2 = 1 and (-1)^2 = 1. In other words, there are two solutions to r^2 = 1 and they are r = -1 or r = 1. In the case of r = -1, we say the data has perfect negative linear correlation. With r = 1, the data has perfect positive linear correlation.

---------

(c) True. If r > 0, then we have some level of positive correlation which means the regression slope is positive in some way. If r < 0, then the regression slope is negative in some way. That must mean r = 0 leads to the regression slope having a flat horizontal line. This could mean one of two things: i) The points are all on or near the same curve such as a parabola, ii) The points are completely randomly scattered about. If case (i) happens, then it's better to use nonlinear regression instead of linear regression.

Answer:

\(y = 0.5x + 5\)

Step-by-step explanation:

(Given in the attachment)

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Answer:

x=4

Step-by-step explanation:

(whole secant) x (external part) =   (whole secant) x (external part)

(6+x) * 6 =(5+x+3) *5

(6+x) * 6 =(x+8) *5

Distribute

36+6x = 5x+40

Subtract 5x from each side

36+6x-5x = 5x-5x+40

36+x = 40

Subtract 36 from each side

36+x-36 = 40-36

x = 4

Answer:

Step-by-step explanation:

42)1.50/6=0.25

43)3/2=1.5

44)1x2=2

Answer:

42.) $0.25 per banana.

43.) 1.5 cakes per hour.

44.) 2 pounds of food per hour.

Step-by-step explanation:

42.)

\(\frac{Cost}{Amount}=\frac{1.50}{6}=0.25\)

43.)

\(\frac{Amount}{Time}=\frac{3}{2}=1.5\)

44.)

\(\frac{Amount}{Time}=\frac{1}{0.5}=2\)

R(80) = 2240, C(80) = 174, and P(80) = 2066.

To find the function P(x), we need to substitute R(x) and C(x) in the expression for total profit:

P(x) = R(x) - C(x)

= (60x - 0.4x^2) - (2x + 14)

= 58x - 0.4x^2 - 14

Therefore, the function for total profit is P(x) = 58x - 0.4x^2 - 14.

To find R(80), we substitute x = 80 in the expression for total revenue:

R(80) = 60(80) - 0.4(80)^2

= 4800 - 2560

= 2240

To find C(80), we substitute x = 80 in the expression for total cost:

C(80) = 2(80) + 14

= 160 + 14

= 174

To find P(80), we substitute x = 80 in the expression for total profit:

P(80) = 58(80) - 0.4(80)^2 - 14

= 4640 - 2560 - 14

= 2066

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Answer:

-20

Step-by-step explanation:

First thing you do is set up your equation:

y-17= -37

+17   +17        Next you add 17 to both sides

-------------        Follow your integer rules

y= -20

We can check this by putting it back into the solution

-20-17= -37  Integer Rules

                     You use KCC aka Keep Change Change

= -20+ -17= -37

Answer:

Step-by-step explanations:

Therefore, the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2).

To show that the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2), we can use the concept of the Intermediate Value Theorem and Rolle's Theorem.

Let's assume that the equation has two distinct roots, denoted as a and b, in the interval (-2, 2). Without loss of generality, we assume a < b.

Since the function is continuous on the closed interval [-2, 2] and differentiable on the open interval (-2, 2), we can apply Rolle's Theorem. According to Rolle's Theorem, there exists a point c in the open interval (a, b) such that the derivative of the function at c is zero.

Consider the derivative of the function f(x) = x^3 - 15x + c:

f'(x) = 3x^2 - 15

Setting f'(c) = 0, we have:

3c^2 - 15 = 0

c^2 - 5 = 0

c^2 = 5

Taking the square root of both sides, we get:

c = ±√5

Now, let's consider the function values at the endpoints of the interval (-2, 2):

f(-2) = (-2)^3 - 15(-2) + c = -8 + 30 + c = 22 + c

f(2) = (2)^3 - 15(2) + c = 8 - 30 + c = -22 + c

If c = √5, then f(-2) = 22 + √5 and f(2) = -22 + √5.

If c = -√5, then f(-2) = 22 - √5 and f(2) = -22 - √5.

In either case, the function values at the endpoints have different signs. This implies that there exists at least one value, say k, in the interval (-2, 2) such that f(k) = 0, according to the Intermediate Value Theorem.

However, we assumed at the beginning that there are two distinct roots in the interval (-2, 2), denoted as a and b. This contradicts our finding that there is at most one root in the interval. Hence, our assumption of having two distinct roots is false.

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Step-by-step explanation:

the answer is 2.50+1.50+733=737

Answer: 5:1

Step-by-step explanation:

american : asian

45 : 9

5 : 1

There are 7 people in Mr. Wilson's class, as Zach is the second person and Mary is the seventh person.

To calculate the total number of people in the class, we can use the formula 2x = 7, where x is the total number of people. Solving for x, we get x = 7.

To determine the number of people in Mr. Wilson's class, we can use the formula for the number of people in a circle, which is N = 2(n-1), where n is the number of people standing opposite each other in the circle. In this case, n is 2 (Zach and Mary). Therefore, N = 2(2-1) = 2 people. However, since there are 7 people in total in the circle, we can conclude that the number of people in Mr. Wilson's class is 7. To explain further, based on the given information, we can say that Zach is the second person, which means there are 2 people before him in the circle. Therefore, there are 7 people in Mr. Wilson's class. To further explain, we can break down the equation as follows: The person opposite of Zach is the seventh person, or 7th, so we can say that 7 is equal to the number of people in the class multiplied by 2, or 2x. Then, solving for x, we get x = 7. This means that the total number of people in the class is 7.

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Answer: This kind of property is the multiplicative property of 0.

Answer:

The answer should be muiltpication Property

Step-by-step explanation:

Since its dealing with multipication of the number 0 then its multipication property if not then it might be associative property. Let me know if this helps