Which of the following statements concerning the linear correlation coefficient are​ true? ​I: If the linear correlation coefficient for two variables is​ zero, then there is no relationship between the variables. ​II: If the slope of the regression line is​ negative, then the linear correlation coefficient is negative. ​III: The value of the linear correlation coefficient always lies betweenminus1 and 1. ​IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of minus0.82.

Answer:

A

Step-by-step explanation:

The first "circle" is the "domain", which is the set of x values of the function.

The second "circle" is the "range", which is the set of y values of the function.

The range is 4, 7, 9. There are a few x values that match to same y-values but the range is basically the three numbers, 4, 7, and 9.

Option A, {4,7,9} is the correct answer.

[tex] - {x}^{2} - 4x + 15 \\ = - {x}^{2} - 4x - 4 + 15 + 4 \\ = - ( {x}^{2} + 4x + 4) + 19 \\ = \underbrace{- {(x + 2)}^{2}}_{ \leqslant 0} + 19 \\ \Rightarrow - {(x + 2)}^{2} + 19 \leqslant 19 \\ \Rightarrow Maximum \: value \: is \: 19 \: as \: x=-2

[/tex]

Answer:

The correct answer option is 48.

Step-by-step explanation:

In the given experiment, three events take place which include rolling a die, flipping a coin and spinning a spinner.

The possible outcomes of each of these events are as follows:

Rolling a die - 6

Flipping a coin - 2

Spinning a spinner - 4

Therefore, by multiplying their possible outcomes, we can find the number of elements in the sample space of this environment.

Number of elements = 6 × 2 × 4 = 48

Answer:

2+2 is 4

Step-by-step explanation:

Answer:

im doing just find what about you mate

Step-by-step explanation:the answer  is 4

Solving the system of equation, we get Option (C) (2,-1).

The equations given are 2x - y = 5 and 3x + 2y = 4.

To find the point which solves the two equation, we have to satisfy the given x and y coordinates of the point on the given two equations.

Checking all the other Options, it does not satisfies except Option (C).

Checking the point (2,-1) on the first equation 2x - y = 5 , we get 5 in the left hand side of the equation.

Again checking the point (2,-1) on the second equation 3x + 2y = 4 , we get 4 in the left hand side of the equation.

Therefore the coordinates (2,-1) (Option C) satisfies both the equation which is the required solution.

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They need about 9 vans.

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

 xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

  the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ [tex](\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=[/tex]

 ( [tex]\frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0[/tex]

* Lets open the bracket

∴ [tex]\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0[/tex]

* Lets add the like terms

∴ [tex]\frac{-4xy}{2}-16=0[/tex]

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

Answer:

a. hyperbola;

Looks like the limit is

[tex]\displaystyle\lim_{x\to\pi/2^+}\frac{\cos x}{1-\sin x}[/tex]

which yields an indeterminate form [tex]\dfrac00[/tex]. Rewriting as

[tex]\dfrac{\cos x(1+\sinx)}{(1-\sin x)(1+\sin x)}=\dfrac{\cos x(1+\sin x)}{1-\sin^2x}=\dfrac{1+\sin x}{\cos x}[/tex]

we see the numerator approaches 1 + 1 = 2, while the denominator approaches 0. Since [tex]\cos x<0[/tex] for [tex]x[/tex] near [tex]\dfrac\pi2[/tex] with [tex]x>\dfrac\pi2[/tex], the limit is [tex]-\infty[/tex].

Answer:

B

Step-by-step explanation:

The exponential function is the function of the form

[tex]y=a\cdot b^x,[/tex]

where [tex]b[/tex] is the base and [tex]a[/tex] is the initial value.

The function [tex]y=x^2[/tex] is the quadratic function, which cannot be represented as [tex]y=a\cdot b^x.[/tex] Thus, this function is not exponential.

Answer:

The answer is B.

Step-by-step explanation:

I think it’s Cnincouod be wrong

Answer:

The correct answer is false.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If y = 2x + 1, then dy/dt = 2(dx/dt).

If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x.  y = 81.

(a) if dx/dt = 3, find dy/dt when x = 4:

       Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.

(b) if dy/dt = 2, find dx/dt when x = 40:

        Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.

First, you differentiate the given function. Next, apply the chain rule which states dy/dt = dy/dx * dx/dt. Substitute the known values to find dy/dt. For the second part, rearrange the chain rule to find dx/dt = dy/dt / dy/dx and substitute the known values.

This question deals with the basic application of the chain rule in differentiation. The given function is y = 2x + 1, where both y and x are functions of t. You are supposed to determine dy/dt and dx/dt.

(a) First, differentiate y = 2x + 1 with respect to x to obtain dy/dx = 2. According to the chain rule in calculus, dy/dt = dy/dx * dx/dt. Substituting the known values from the question, we have dy/dt = 2 * 3 = 6 when x = 4.

(b) For dy/dt = 2, you need to rearrange dy/dt = dy/dx * dx/dt to find dx/dt = dy/dt / dy/dx. As dy/dx = 2, you can evaluate dx/dt = 2 / 2 = 1 when x = 40.

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Answer:

155 lbs.

Step-by-step explanation:

69.75 g of protein divided by 0.45= 155

Answer: He weighs 155 lbs.

Step-by-step explanation:

Since we have given that

Amount of protein he used = 69.75 g

Factor = 0.45

We need to find the weight of an individual.

So, Weight of an individual is given by

[tex]Weight\times factor=Protein\\\\Weight=\dfrac{Protein}{Factor}[/tex]

[tex]=\dfrac{69.75}{0.45}\\\\=155\ lbs[/tex]

Hence, he weighs 155 lbs.

The mode is the number that appears most often.

Looking at the chart, there are two 1's on the right side, so the mode would be 31

Answer:13

Step-by-step explanation:you have to divide it  

The area of a sector is found using the formula :

Area = πr^2(angle/360)

R is given as 6 meters and the angle is given as 78 degrees.

Area = π * 6^2 * (78/360)

Area = π * 36 * 0.21666

Area = π * 7.8

Area = 7.8π square meters. ( Exact area in terms of PI)

or using 3.14 for PI: Area = 24.492 square meters.

Round the decimal area as needed.

The product of (3x - 7y)^2 is found by squaring the binomial using the FOIL method, which leads to 9x^2 - 42xy + 49y^2.

To find the product of (3x \\- 7y)^2, you must square the binomial. This means you will multiply the binomial by itself. When you square a binomial, you use the FOIL method (First, Outer, Inner, Last) to multiply the terms.

First: (3x)(3x) = 9x^2
Outer: (3x)(-7y) = -21xy
Inner: (-7y)(3x) = -21xy
Last: (-7y)(-7y) = 49y^2

Combine like terms (the Outer and Inner terms in this case).

9x^2 - 21xy - 21xy + 49y^2 = 9x^2 - 42xy + 49y^2

Thus, the product of (3x - 7y)^2 is 9x^2 - 42xy + 49y^2.

The volume of a sphere with a radius of 4 centimeters is calculated using the formula V = (4/3)πr³. Substituting 4 cm for the radius and 3.14 for π, the volume is approximately 268 cubic centimeters.

To calculate the volume of a sphere with a given radius, you can use the formula V = (4/3)πr³, where V represents the volume and r is the radius. In our case, the radius is 4 centimeters. Substituting the values into the formula gives us V = (4/3) * 3.14 * (4 cm)³.

Performing the calculation: V = (4/3) * 3.14 * 64 cm³ = 267.94666666666666 cm³. Therefore, the volume of the sphere is approximately 268 cm³ when rounded to a whole number.

Answer: [tex]b=10^3[/tex]

Step-by-step explanation:

You know that there are 10 blueberries in each muffin. There are 10 muffins in each box and the total number of boxes is 10.

Then, to calculate the total number of blueberries, you need to multiply the total number of boxes by the number of muffins in each box and multiply this by the number of blueberries in each muffin.

Let be "b" the total number of blueberries. Then:

[tex]b=10*10*10[/tex]

By the Product of powers property:

[tex]a^m*a^n=a^{(m+n)}[/tex]

Then you can write the expression:

[tex]b=10^3[/tex]

To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, calculate the sample mean and standard deviation, determine the critical t-value, and use the confidence interval formula to find the range.

To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, we first calculate the sample mean and the sample standard deviation. The sample mean is the average of the seven data points (40, 30, 28, 22, 36, 16, and 50), which is 32. The sample standard deviation is the measure of variability in the data, which is calculated to be approximately 12.11.

Next, we determine the critical t-value for a 90% confidence interval with 6 degrees of freedom (7 data points minus 1). We can find this value in the t-distribution table or use statistical software, and it is approximately 1.943.

Finally, we can calculate the confidence interval using the formula: Confidence interval = sample mean ± (t-value * standard deviation / square root of sample size). Plugging in the values, we get the confidence interval as (23.52, 40.48). Therefore, we can be 90% confident that the average number of customers who visit the salon on weekdays falls within this range.

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Answer:

Step-by-step explanation:

[tex]x^2-2x+17=0\qquad\text{subtract 17 from both sides}\\\\x^2-2x=-17\\\\x^2-2(x)(1)=-17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2(x)(1)+1^2=-17+1^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-1)^2=-17+1\\\\(x-1)^2=-16<0\Rightarrow\boxed{\text{NO REAL SOLUTION}}\ because\ x^2\geq0\\\\\text{In the set of complex numbers}\\\\i=\sqrt{-1}\\\\(x-1)^2=-16\iff x-1=\pm\sqrt{-16}\\\\x-1=-\sqrt{(16)(-1)}\ \vee\ x-1=\sqrt{(16)(-1)}\\\\x-1=-\sqrt{16}\cdot\sqrt{-1}\ \vee\ x-1=\sqrt{16}\cdot\sqrt{-1)[/tex]

[tex]x-1=-4i\ \vee\ x-1=4i\qquad\text{add 1 to both sides}\\\\x=1-4i\ \vee\ x=1+4i[/tex]

Answer:

72 voters

Step-by-step explanation:

Total surveyed members: 40

Total members with a yes vote: 12

Percentage of the voters (voting yes): [tex]\frac{12}{40} * 100 = 30%[/tex]

From analysis, it is observed that 30% of the voters are expected to vote yes in a sample.

Therefore, the number of voters expected to vote yes out of 240 are: 30% of 240

=> [tex]\frac{30}{100} * 240 = 72[/tex]

Answer:

72 voters

Step-by-step explanation:

Answer:

6.25 m²

Step-by-step explanation:

The area of the small mural is 1.5 times greater than that of the small mural.

That means the area of the large mural is 2.5 times the area of the small mural.

Area = 2.5 × 2.5 m² = 6.25 m²

The area of the large mural is 6.25 m².

Answer:

48 miles

Step-by-step explanation:

Answer:

Option b

Step-by-step explanation:

The equation [tex]4x ^ 2 + 5y ^ 2 = 20[/tex] has center in (0,0).

But the transformation [tex]T(5, -6)[/tex] shifts the center of the equation to the point (5, -6).

Therefore, when applying [tex]T(5, -6)[/tex] we will have the following equation translated.

[tex]4(x-5) ^ 2 + 5(y - (-6)) ^ 2 = 20[/tex].

Simplifying we have:

[tex]4(x-5) ^ 2 + 5(y + 6) ^ 2 = 20[/tex]

Now we expand [tex](x-5) ^ 2[/tex] and [tex](y + 6) ^ 2[/tex]

[tex]4(x ^ 2 -10x +25) + 5(y ^ 2 + 12y +36) = 20\\\\4x ^ 2 -40x + 100 + 5y ^ 2 + 60y + 180 = 20\\\\4x ^ 2 + 5y ^ 2 -40x + 60y +260 = 0[/tex]

The equation of a circle has the form

[tex]h(x-a) ^ 2 + q(y-b) ^ 2 = r[/tex]

For h = 1 and q = 1.

If [tex]h \neq 1[/tex] and [tex]q\neq 1[/tex] then the graph becomes an ellipse.

In this problem h = 4 and q = 5 therefore the figure is an ellipse

[tex]\displaystyle\\6<\sqrt[3]{x}<7~~~\Big|^3\\\\6^3<\Big(\sqrt[3]{x}\Big)^3<7^3\\\\216<x<343\\\\\boxed{x\in\{217,~218,~219,~220,~\cdots~,~340,~341,~342\}}[/tex]

.

Answer:

Step-by-step explanation:

The value would be 6.5

Answer:

The shape of the mat is a square

Step-by-step explanation:

we know that

The area of the rectangle (An Olympic floor exercise mat) is equal to

[tex]A=LW[/tex]

we have that

[tex]A=144\ ft^{2}[/tex]

[tex]L=12\ ft[/tex]

substitute the values and solve for W

[tex]144=12W[/tex]

[tex]W=144/12=12\ ft[/tex]

so

The length is equal to the width

therefore

The shape of the mat is a square

Answer:

2nd graph

Step-by-step explanation:

Exponential increase will be a graph that increase all throughout and the rate of increase "increases" with age.

The 2nd graph is correct because it shown "increase" as well as "exponential" increase (the rate of increase increases).

Answer: 2nd graph

Your answer is going to be the second graph