= Mean and median of a data set The 6 students in Mrs. Barnes' class were asked how many minutes it takes them to get to school in the morning. Here is what they answered: 5. 13. 13.6.8.11 Find the mean and median travel times for these students. If necessary, round your answers to the nearest tenth.

Answer:

The researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program

Step-by-step explanation:

Here, we want to state what the conclusion of the researcher should be:

From the last part of the question, we can see that the test statistic is greater than the critical value

So what do we do in a case like this?

We can see that the researcher is trying to see if there is a correlation between hours worked out and the number of pounds lost over a specific period of time.

Now, let us form the null hypothesis;

The null hypothesis here H0 is that we do not have a correlation between number of hours spent working out and the amount of pounds lost

The alternative hypothesis here H1 is that there is a correlation between the number of hours spent working out and the amount of pounds lost

Since we have the value of the test statistic greater than the critical value, we reject the null hypothesis and accept the alternative hypothesis

So therefore, the researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program

Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

Answer:

answer =-1.

Step-by-step explanation:

(i)write the question nicely again.

(ii) substitute the ltter with the value that is given.

(iii)u gonna use BEDMAS RULE TO SOLVE.

The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.

What is a triangle?

A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.

To start, let's graph the triangle to get a better understanding of the problem:

(0,3)   *

       |\

       | \

       |  \

       |   \

       |    \

(0,0)   *-----*-----> x

        (5,0)

The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.

The area of a semicircle is πr²/2, so the volume of this slice is:

V(x) = π * (3/10 * x)² / 2 * dx

To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:

V = ∫₀₅ π * (3/10 * x)² / 2 dx

V = π/20 * ∫₀₅ x² dx

V = π/20 * [x³/3] from 0 to 5

V = π/20 * (5³/3)

V = π/4 * (25/3)

V = 25π/12

Therefore, the volume of the solid is 25π/12 cubic units.

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Answer:

220 miles

Step-by-step explanation:

.18m + 11d = 61.60

d = 2

.18m + 22 = 61.60

Subtract 22 from both sides

.18m = 39.60

Divide both sides by .18

m = 220

Answer:

Step-by-step explanation:

4 : 2

8 : 4

12 : 6

16:8

The ratio in the form of n: 1 will be 2: 1.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The ratio is given below.

⇒ 4: 2

Simplify the ratio in the form of n: 1, then we have

⇒ 4: 2

⇒ 2: 1

The ratio in the form of n: 1 will be 2: 1.

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The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = \(πr^2\), where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = \(πr^2\)

A ≈ 3.14 × \((2^2)\)

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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Answer:

81.5% of 1-mile long roadways with potholes numbering between 22 and 52

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 42, standard deviation of 10.

The normal distribution is symmetric, so 50% of the measures are below the mean and 50% are above the mean

Approximate percentage of 1-mile long roadways with potholes numbering between 22 and 52:

22 = 42 - 2*10

So 22 is two standard deviations below the mean. Of the 50% of the measures that are below the mean, 95% are between two standard deviations below the mean(22) and the mean(42).

52 = 42 + 10

So 42 is one standard deviation above the mean. Of the 50% of the measures that are above the mean, 60% are between the mean(42) and one standard deviation above the mean(52).

In the desired interval, the percentage is:

\(P = 0.5*0.95 + 0.5*0.68 = 0.815\)

81.5% of 1-mile long roadways with potholes numbering between 22 and 52

The incorrect statement is the reflection is over x-axis.

Given that an image has been reflected to form another image, we need to find the incorrect statement from the given options,

A reflection is known as a flip.

A reflection is a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

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The incorrect statement is the reflection is over x-axis.

Given that,

an image has been reflected to form another image, we need to find the incorrect statement from the given options,

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

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Renee’s layaway fee is $15.95, her down payment is $31.90, and her weekly payments are $7.98 each.

We are given that;

Combined price of the items = $318.95

Layaway fee=5%

Down payment=10%

Now,

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The layaway fee by multiplying the item price by 5%. The formula is: layaway fee=item price×0.05

The down payment by multiplying the item price by 10%. The formula is: down payment=item price×0.1

Calculate the weekly payment by multiplying the item price by 15% and dividing it by 6. The formula is: weekly payment=6item price×0.15​

Plugging in the given values and simplify the expressions. Here are the calculations:

layaway fee=318.95×0.05=15.95

down payment=318.95×0.1=31.90

weekly payment=6318.95×0.15​=7.98

Therefore, by percentage the answer will be $15.95, $31.90, and $7.98

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Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

Step-by-step explanation:

Given the coordinates F(b+1, a+2, M(3,5) and G(2a, 3b+3), if M is the midpoint of F and G then, to get the value of a and b we will use the formula for calculating the midpoint a shown;

M(X, Y) = (x₁+x₂/2, y₁+y₂/2)

X = x₁+x₂/2 and  Y = y₁+y₂/2

From the given coordinates x₁ = b+1, y₁ = a+2, x₂ = 2a, y₂ = 3b+3, X = 3 and Y = 5

Substituting the given parameters into the formula, we can get the value of a and b as shown;

3 = b+1+2a/2

6 = 2a+b+1

2a+b = 5 ............... 1

Similarly, for the Y coordinate;

5 = a+2+3b+3/2

10 =  a+2+3b+3

a+3b = 10-2-3

a+3b = 5 ........ 2

Solving equation 1 and 2 simulatneously using elimination method

2a+b = 5 ............... 1 * 1

a+3b = 5 ........ 2 * 2

---------------------------------------------------------

2a+b = 5 ...........3

2a +6b = 10.......... 4

subtract 3 from 4

b - 6b = 5-10

-5b = -5

b = -5/-5

b = 1

substitute b =1 into equation 2 to get a;

a + 3b = 5

a + 3(1) = 5

a = 5-3

a = 2

From the calculation above it is seen that the value of variable a can be determined and it is equivalent to 2

Answer:

To determine the value of​ a, set up and solve a system of equations in two variables. The value of a is 2

Step-by-step explanation:

Answer:

5 for 12.50

Step-by-step explanation:

i think this is better because when you find the cost per ticket on this deal (divide 12.5 by 5), you get 2.5 dollars per ticket. the other deal was 8 for 20.16. when dividing 20.16 by 8, you get 2.52 per ticket.

overall, you end up paying less because 12.50 is obviously less than 20.16 and also the cost per ticket is just a little lower, 2.5 instead of 2.52.

Answer:

  -6

Step-by-step explanation:

A suitable calculator can find this for you directly.

-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:

  ∛(-216) = -∛216 = -6

__

Additional comment

Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.

The second attachment shows a calculator capable of finding the complex roots as well as the real one.

Answer:

69

Step-by-step explanation:

Step-by-step explanation:

9×5= 45

45+120+1000+23+600+200+32 = 2020

Answer:

2020

Step-by-step explanation:

9+9+9+9+9+120+1000+23+600+200+32

= 2020

The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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Answer:

C  

Step-by-step explanation:

because if u add them together you get the answer

Answer:

The third one is correct

Step-by-step explanation:

Answer:

Joe Biden

Step-by-step explanation:

Answer:

I think the games r 50$ a piece a d the controllers r 81$

The number of games are 60.25 and number of controllers are 40.5.

Two or more expressions with an Equal sign is called as Equation.

Given that Joel wanted to buy some games and controllers for his Playstation 4.

Let x be number of games and y be the number of controllers.

Joel bugs 2 games and 3 controllers for $242

2x+3y=242..(1)

Omar bought 4 games and 1 controller for $281.50.

4x+y=281.5...(2)

Multiply equation 1 with 2.

4x+6y=484..(3)

Subtract 3 from equation 2.

4x+y-4x-6y=281.5-484

-5y=-202.5

Divide both sides by 5

y=40.5

Now plug in y value in equation 1

2x+3(40.5)=242

2x+121.5=242

2x=242-121.5

2x=120.5

Divide both sides by 2

x=60.25

Hence, the number of games are 60.25 and number of controllers are 40.5.

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To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

It is B I think

Step-by-step explanation:

D is incorrect

The functions are illustrations of trigonometry ratios

\(\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}\)

\(\mathbf{sin\theta = \sqrt{1 - (15/25)}}\)

Take LCM

\(\mathbf{sin\theta = \sqrt{\frac{10}{25}}}\)

\(\mathbf{sin\theta = \frac{\sqrt{10}}{5}}\)

\(\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}\)

\(\mathbf{Hypotenuse^2 = 10 + 4}\)

\(\mathbf{Hypotenuse^2 = 14}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{14}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}\)

\(\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}\)

The sine of the angles is:

\(\mathbf{sin \theta = \frac{1}{csc\theta}}\)

So, we have:

\(\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}\)

\(\mathbf{sin \theta = \frac{3}{\sqrt{15}}}\)

Rationalize

\(\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}\)

\(\mathbf{sin \theta = \frac{\sqrt{15}}{5}}\)

\(\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}\)

\(\mathbf{sin\theta = \sqrt{(1 - 9/6)}}\)

\(\mathbf{sin\theta = \sqrt{( - 3/6)}}\)

The sine of the angle does not have a real value

\(\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}\)

Start by calculating the tangent of the angle

\(\mathbf{tan\theta = \frac{1}{cot\theta}}\)

So, we have:

\(\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}\)

\(\mathbf{tan\theta = \frac{2}{\sqrt 6}}\)

Rationalize

\(\mathbf{tan\theta = \frac{2\sqrt 6}{6}}\)

\(\mathbf{tan\theta = \frac{\sqrt 6}{3}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}\)

\(\mathbf{Hypotenuse^2 = 6 + 9}\)

\(\mathbf{Hypotenuse^2 = 15}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{15}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}\)

Rewrite as:

\(\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}\)

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Answer:

Step-by-step explanation:

A)\((tanx-4)(9sin^2x-1)=0\\\\\\\)

\(9sin^2x-1=0\\\\sin^2x=\frac{1}{9} sinx=\frac{1}{3}\) or \(sinx=\frac{-1}{3}\)

OR    \(tanx=4\\\)

B)

\(3sin2x=3.2.sinx.cosx\\\\6.sinx.cosx-4.sinx= 2sinx.(3cosx-2)=0\\\\3.cosx=2 cosx=\frac{2}{3}\)

Answer:

The slope of these coordinates is 0.

It is a horizontal line.

Step-by-step explanation: