Bone strength, gives the bone strengths of the dominant and the nondominant arms for 15 men who were controls in a study.

ID Group NonDom Dom
1 Control 15.7 16.3
2 Control 25.2 26.9
3 Control 17.9 18.7
4 Control 19.1 22.0
5 Control 12.0 14.8
6 Control 20.0 19.8
7 Control 12.3 13.1
8 Control 14.4 17.5
9 Control 15.9 20.1
10 Control 13.7 18.7
11 Control 17.7 18.7
12 Control 15.5 15.2
13 Control 14.4 16.2
14 Control 14.1 15.0
15 Control 12.3 12.9

a. Plot the data. Use the bone strength in the nondominant arm as the explanatory variable and bone strength in the dominant arm as the response variable.
b. The least-squares regression line for these data is dominant = 2.74 + (0.936 × nondominant) Add this line to your plot.
c. Use the scatterplot (a graphical summary), with the least-squares line (a graphical display of a numerical summary) to write a short paragraph describing this relationship.

Answer:

$5.99 per can of gas

Step-by-step explanation:

$23.96 divided by 4 = $5.99

This means that each can of gas is $5.99.

Answer:

$95.84

Step-by-step explanation:

Each can of Fuel is $23.96 and you want to find out How much she payed for 4. So all you have to do is multiply the given cost($23.96) by the amount of fuel cans(4). 23.96 times 4 give you the answer $95.84.

The y-intercept is -6, when the coordinate is -3,-3 and the slope is -1

More specifically, it is defined as the ratio of the change in the y-coordinate (vertical) to the change in the x-coordinate (horizontal) between any two points on the line or surface.

The slope of a line is often denoted by the letter "m" and can be calculated using the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

A positive slope indicates that the line is rising from left to right, while a negative slope indicates that the line is falling from left to right. A slope of zero indicates that the line is horizontal.

The slope of a surface can be calculated using partial derivatives. The slope of a surface at a point is the slope of the tangent plane at that point.

Slope is an important concept in mathematics, physics, and engineering, and is used to calculate rates of change, velocities, and accelerations, and to model relationships between variables. It is also used in a variety of practical applications, such as in construction and surveying, where it is necessary to determine the slope of the land.

To find the equation of the line when the coordinate is (-3, -3) and the slope is -1, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is the given point. Plugging in the values, we get:

y - (-3) = -1(x - (-3))

y + 3 = -x - 3

y = -x - 6

The y-intercept is the point where the line intersects the y-axis, which occurs when x = 0. Plugging in x = 0 into the equation, we get:

y = -0 - 6

y = -6

Therefore, the y-intercept is -6.

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The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.

The formula to find the slope between two coordinates is expressed as:

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope of each line above the x-axis are:

Slope 1 = (5 - 0)/(5 - 8)

Slope 1 = -1.7

Slope 2 = (5 - 5)/(5 - (-2))

Slope 2 = 0

Slope 3 = (5 - 0)/(-2 - (-5))

Slope 3 = 5/3 = 1.7

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Answer: x=14 y=10

Step-by-step explanation:

Answer:

24x-40

Step-by-step explanation:

you use the distributive property to distribute 8 to 3x and -5

3x(8)= 24x   and    -5(8)= -40

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad \qquad \stackrel{slope}{m}\implies 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{5}(x-\stackrel{x_1}{(-2)})\implies y-4=5(x+2)\)

Answer: 4,582,656

Step-by-step explanation:

A coin is tossed 4 times,

2^4 outcomes: 16

and then a standard six-sided die is rolled 3 times, 6^3

216 outcomes:

and finally, a group of two cards is drawn from a standard deck of 52 cards without replacements

It says a “group”, so, I guess the order doesn’t matter… So it is “52 choose 2”

52*51/ (2*1) = 26*51

how many different outcomes are possible?

16*216*26*51 = 4,582,656

Answer:

\(distance = \sqrt{ {( - 3 - 3)}^{2} + {( - 1 - ( - 9))}^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} \\ = 10 \: units\)

Using sine law to solve the triangle will give m∠C = 72.1°, m∠B = 72.9°, AB = 28.1 units

The sine law shows the relationship between the sides and angles of a triangle.

Sine law can be written as:

a/sin A = b/sin B = c/sin C

Given: the triangle ABC and A = 34°, a = 16.5, b = 28.2

Using Sine law:

a/sin A = b/sin B

16.5/sin34° = 28.2/sin B

sin B =  (28.2 × sin34°)/16.5

sin B = 0.956

B = sin⁻¹(0.956)

B = 72.9°

Thus, m∠B = 72.9°

C = 180 - 34° - 72.9° = 72.1°

Thus, m∠C = 72.1°

a/sin A = c/sin C

16.5/sin34° = c/sin 72.1°

c = (16.5 × sin 72.1°) / sin34°

c = 28.1 units

Since c = AB

Thus, AB = 28.1 units

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Convert them all into decimals. Percent is just 0.--, and the fraction you can calculate out which gives: 0.625=5/8,0.64=64%

5/8

64%

0.65

The dimensions of the room are approximately 5.87 meters by 7.63 meters.

Let's assume the width of the room is "x" meters.

According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.

Perimeter = 2(length + width)

Substituting the values we know:

27 = 2(1.3x + x)

Simplifying:

27 = 2(2.3x)

27 = 4.6x

Dividing both sides by 4.6:

x = 27 / 4.6

x ≈ 5.87

The width of the room is approximately 5.87 meters.

To find the length, we can multiply the width by 1.3:

Length = 1.3 * 5.87 ≈ 7.63

The length of the room is approximately 7.63 meters.

Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.

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The X variables have an overall correlation of 0. VIF, or Variance Inflationary Factor, measures the

Regression analysis's level of multicollinearity is gauged by a variance inflation factor, or VIF. When several independent variables in some kind of a model with multiple regression correlate with one another, this is known as multicollinearity. The regression findings may be significantly impacted by this.

Greater correlation between the variable and other variables is indicated by a higher value. With values of Ten or more being considered very high, values greater than 4 or 5 are occasionally considered to be moderate to high.

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Answer:

Answer is [A]

Step-by-step explanation:

Arc length = 2πr × (θ/360) where θ is the angle of sector which is p in the question and the radius is still the symbol R

Answer:

t=3/2p

Step-by-step explanation:

We can see the linear pattern between t and p as

p/t = 2/3=4/6=6/9 etc... So t/p=1/(2/3) =3/2 and therefore t=3/2p

Slope

Equation

Or

Answer:

B

Step-by-step explanation:

If the diameter of sphere B is 42, that means the radius is half, so it is 21.

The question is asking what multiplied by 24 is 21, or 21 divided by 24. 21/24 can be simplified to 7/8.

Answer:

Step-by-step explanation:

use an ASA triangle  with law of sine

since we know that 180 = 20 +45 + C   .. solve for C = 115°

now use  law of sines    c/ sin(C) = b/sin(B) .. and solve for b

Sin(20)*100/sin(115) = b

b = 37.73774 ft

that's the hypotenuse of the 45 triangle

SOH CAH TOA   to remember how trig functions fit

use b*Cos(45) = adj

26.6846 = adj

The bird is 26.7 ft. from the ground

The average T2, T7, T6, T4, and T10 in Processor 1

T8, T9, T3, T1, and T5 on Processor 2.

Work on tasks t2, t7, t6, t4, and t10 will be done by processor 1. The first task to be finished is task t2, followed by tasks t7, t6, t4, and lastly t10. Work on tasks t8, t9, t3, t1, and t5 will be done by processor 2. The first work to be finished is task t8, followed by t9, t3, t1, and ultimately t5. In order to finish the job quickly, both processors will cooperate, with Processor 1 concentrating on the early tasks and Processor 2 concentrating on the later duties. This guarantees that the project is finished on schedule and that all the tasks are carried out in the proper order.

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Answer:

Step-by-step explanation:

                                                   error

Answer:

x ≈ 75.2

Step-by-step explanation:

using the tangent ratio in the right triangle

tan62° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{40}\) ( multiply both sides by 40 )

40 × tan62° = x , then

x ≈ 75.2 ( to the nearest tenth )

Answer:

500

Step-by-step explanation:

65 is 13% of 500

500 x .13= 65

Catie will have to babysit for more than 7 hours to make a profit which has been obtained from the inequality 5 + 3x > 26.

What is an inequality?

An inequality is an algebraic inequality that has one or more unknown values (often referred to as unknowns) in addition to some known information and two members related by one of the following signs >, <, ≤ and ≥.

We are given that Catie spent $26 to make signs to advertise and charges an initial fee of $5 and then $3 for each hour of service.

Let the number of hours be 'x'.

Now, in order to make profit, we get the inequality as

5 + 3x > 26

Now, on solving the inequality, we get

⇒ 3x > 21

⇒ x > 7

From the solution, we interpret that for making profit, she will have to babysit for more than 7 hours.

Hence, Catie will have to babysit for more than 7 hours to make a profit.

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The original principal was RM 200 when rate of interest was 5% p.a. for 180 days amounted to RM205.

What is Simple interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.

Given, time period = 180 days.

Time ( T) in years = 180/365 year

Amount (A) = RM 205

Rate of interest (R) = 5% p.a. = 0.05

The formula to calculate amount (A) with respect to principal (P) is:

A = P(1+RT)

⇒ 205 = P(1 + 0.05*180/365)

⇒ 205 = P(1.025)

⇒ P = 205/1.025

⇒ P = 200

Hence, principal comes out as RM200.

The original principal was RM 200 when rate of interest was 5% p.a. for 180 days amounted to RM205.

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Using Simple Interest, The original principal was RM 200 when rate of interest was 5% p.a. for 180 days amounted to RM205.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.

Given, time period = 180 days.

Time ( T) in years = 180/365 year

Amount (A) = RM 205

Rate of interest (R) = 5% p.a. = 0.05

The formula to calculate amount (A) with respect to principal (P) is:

A = P(1+RT)

⇒ 205 = P(1 + 0.05*180/365)

⇒ 205 = P(1.025)

⇒ P = 205/1.025

⇒ P = 200

Hence, principal comes out as RM200.

The original principal was RM 200 when rate of interest was 5% p.a. for 180 days amounted to RM205.

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Answer:

55

Step-by-step explanation:

Remark

This is a really good question to know the answer to. <PRQ = 1/2 POQ (the central angle. )

The central angle for this question is 110o. So any angle that has its vertex on the circumference is 1/2 110 = 55. The central angle and the angle on the circumference must be related as they are as this question is. (Both are on the same side of PQ which is not drawn but you can draw it).

The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

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ANSWER

17

EXPLANATION

We wamt to find the value of x in the figure.

To do that, we have to apply Pythagorean theorem:

Therefore, we have that:

That is the answer.

The expression that describe the end behavior of the expression f(x)= (3.25)^x + 6 is The curve begins infinitely close to the line y equals 6 in the second quadrant.

The behavior of the graph of a function at its "ends" on the x-axis is referred to as the end behavior of a function, f.

For example, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞), the end behavior of a function explains the trend of the graph.

The graph of the function is attached and from the graph it shows that the graph continued to tend towards towards line y = 6

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Answer:

\((f-g)(x) = 2x^2+ 6x-5\)

Step-by-step explanation:

Given

\(f(x) = 3x^2 + 4x - 2\)

\(g(x) = x^2 - 2x + 3\)

Required

Find \((f-g)(x)\)

In functions:

\((f-g)(x) = f(x) - g(x)\)

Substitute values for f(x) and g(x)

\((f-g)(x) = 3x^2 + 4x - 2 - (x^2 - 2x + 3)\)

Open bracket

\((f-g)(x) = 3x^2 + 4x - 2 - x^2 + 2x - 3\)

Collect Like Terms

\((f-g)(x) = 3x^2 - x^2+ 4x + 2x- 2 - 3\)

\((f-g)(x) = 2x^2+ 6x-5\)

The experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

The experimental probability of the next train to pull into Lakeside Station being full can be calculated by dividing the number of times a full train occurred by the total number of trains observed.

Given that out of the last 20 trains, 14 were full, we can express the experimental probability as a fraction:

P(full) = Number of full trains / Total number of trains observed

P(full) = 14 / 20

Simplifying the fraction, we get:

P(full) = 7 / 10

Therefore, the experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

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Answer:

ok so get ready

Step-by-step explanation:

it would be 70 degrees because 180-(22*5)=70 and the equation to find an angle like this would be 180-(length of ladder * how far the ladder is from the house)= the angle of the ladders elevation.