1. What is the shape of the distribution below?
(a) The distribution is symmetrical
(b) The distribution is not symmetrical

Answer:

C 84.2-79.2/SQRoot(10.2^2/50  + of of 6.8^2/30)

​

Step-by-step explanation:

Final answer:

To determine if there is a significant difference in lifespan between men who are distance runners and those who are not, a two-sample t-test test statistic is calculated as approximately 1.051 using the provided sample means, standard deviations, and sample sizes.

Explanation:

To determine if men who are distance runners live significantly longer, on average, than men who are not distance runners, we would use a two-sample t-test statistic. The test statistic formula for a two-sample t-test is:

t = (x1 - x2) / [tex]\sqrt{(s1^2/n1 + s2^2/n2)[/tex]

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes of the two groups.

In this case, the mean age at death for men who are distance runners is 84.2, the standard deviation is 10.2, and the sample size is 50 (n1 = 50). The mean age at death for men who are not distance runners is 79.2, the standard deviation is 6.8, and the sample size is 30 (n2 = 30).

Plugging the values into the formula, we calculate the test statistic as follows:

t = (84.2 - 79.2) / [tex]\sqrt{(10.2^2/50 + 6.8^2/30)[/tex]

t = 2.0 / [tex]\sqrt{((104.04/50) + (46.24/30))[/tex]

t = 2.0 / [tex]\sqrt{(2.0808 + 1.5413)[/tex]

t = 2.0 / √3.6221

t ≈ 2.0 / 1.9032

t ≈ 1.051

This is the test statistic that you would use to determine whether there is a significant difference in lifespan between the two groups.

To find the span of the bridge, or the length of its minor axis, we use the equation for an ellipse with the given dimensions and solve for 'b'. Then, we multiply 'b' by 2 to find the total span.

To determine the span of the bridge, or the length of its minor axis, we know that the top of the arch (which coincides with the semi-major axis) is 35 feet above the ground and the height is 15 feet above the ground at a distance of 27 feet from the center. The equation for an ellipse with a vertical major axis is:

where 'a' is the semi-major axis and 'b' is the semi-minor axis. Since the total height is 35 feet, the semi-major axis, 'a', is 35/2 = 17.5 feet. The distance of 27 feet from the center to the point where the height is 15 feet can be plugged into the equation with 'y' being the remaining height from that point to the top of the arch:

Upon calculating and rearranging the terms, we have:

Rounding 'b', the semi-minor axis, to two decimal places will give us the span of the bridge which is twice 'b' because it's a complete minor axis.

To find the span of the bridge (the length of its minor axis), we first need to determine the equation of the ellipse.

The standard equation of an ellipse with the center at the origin and the major axis along the x-axis is:

[tex]\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \][/tex]

Where \( a \) is the semi-major axis (half of the major axis) and [tex]\( b \)[/tex] is the semi-minor axis (half of the minor axis).

Given that the top of the arch is 35 feet above the ground (the major axis) and the height 27 feet from the center is to be 15 feet above the ground, we can set up the following system of equations:

1. When [tex]\( y = 0 \)[/tex] (ground level), [tex]\( x = a \)[/tex]

2. When [tex]\( y = 27 \)[/tex] (height above the center), [tex]\( x = 15 \)[/tex]

Using these conditions, we can solve for [tex]\( a \) and \( b \):[/tex]

[tex]1. \( \frac{a^2}{a^2} + \frac{0}{b^2} = 1 \)2. \( \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \)[/tex]

Solving equation 1 for[tex]\( a \):[/tex]

[tex]\[ \frac{a^2}{a^2} = 1 \]\[ a = a \][/tex]

Solving equation 2 for [tex]\( b \):[/tex]

[tex]\[ \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \]\[ \frac{225}{a^2} + \frac{729}{b^2} = 1 \]\[ \frac{729}{b^2} = 1 - \frac{225}{a^2} \]\[ b^2 = \frac{729a^2}{a^2 - 225} \]\[ b = \sqrt{\frac{729a^2}{a^2 - 225}} \][/tex]

We already know that [tex]\( a = 35 \)[/tex](since it's the distance from the center to the top of the arch).

[tex]\[ b = \sqrt{\frac{729 \times 35^2}{35^2 - 225}} \][/tex]

Now we can calculate [tex]\( b \):[/tex]

[tex]\[ b = \sqrt{\frac{729 \times 1225}{1225 - 225}} \]\[ b = \sqrt{\frac{893025}{1000}} \]\[ b ≈ \sqrt{893.025} \]\[ b ≈ 29.88 \][/tex]

So, the span of the bridge (the length of its minor axis) should be approximately 29.88 feet, rounded to two decimal places.

Answer:

To find the radius diameter circumference and area, The area of a circle =  π x radius^2, Circumference of a circle = π x diameter, Remember that the diameter = 2 x radius.

Step-by-step explanation:

Answer:

41.9 cubic feet

Step-by-step explanation:

The formula for the volume of a cone is

V = 1/3πr^2h, where r=radius and h=height.

Diameter = 2*radius, so our radius is 4 ft. Plug these values in:

V = 1/3πr^2h

   = 1/3π4^2 * 2.5

   = 40π/3 cubic feet = about 41.9 cubic feet

The volume of a right circular cone with a height of 2.5 ft and a base diameter of 8 ft is approximately 41.9 cubic feet when rounded to the nearest tenth.

To find the volume of a right circular cone, we'll use the formula for the volume of a cone: V = (1/3) π r^2 h. First, we need to find the radius of the cone's base. Since the diameter is given as 8 ft, the radius (r) is half that value, so r = 4 ft.

The volume (V) is then calculated as follows:

Rounding to the nearest tenth, the volume is approximately 41.9 cubic feet.

Answer: Yes.

Step-by-step explanation: It is very rare, but is indeed possible.

Answer:

c

Step-by-step explanation:

The graph represents the solution set is attached.

The value of x is 0 and y is 3.

Given that,

Equation; [tex]-x + 2y = 6 \ and \ 4x + y = 3[/tex].

We have to determine,

Which graph represents the solution set to this system of equations?

According to the question,

Equation; [tex]-x + 2y = 6 \ and \ 4x + y = 3[/tex].

Solving both the equation,

From equation 1,

[tex]-x+2y =6\\\\2y = x+6\\\\y= \dfrac{x+6}{2}[/tex]

Substitute the value of y in equation 2,

[tex]4x+y = 3\\\\4x + \dfrac{x+6}{2} = 3\\\\\dfrac{8x+x+6} {2}= 3\\\\{9x+6} = 3\times 2\\\\9x + 6 = 6\\\\ 9x = 6-6\\\\9x =0\\\\x = \dfrac{0}{9}\\\\x = 0[/tex]

And the value of y is,

[tex]-x+2y = 6\\\\-0+2y = 6\\\\2y = 6\\\\y = \dfrac{6}{2}\\\\y = 3[/tex]

Hence, The value of x is 0 and y is 3.

For more details refer to the link given below.

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Answer:

.15 kilometers or 150 meters

Step-by-step explanation:

Answer:

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

Step-by-step explanation:

Mean SAT scores = 1026

Standard Deviation = 209

Mean ACT score = 20.8

Standard Deviation = 4.8

We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.

The formula to calculate the z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.

z-score for junior scoring 860 in SAT exam will be:

[tex]z=\frac{860-1026}{209}=-7.59[/tex]

z-score for junior scoring 16 in ACT exam will be:

[tex]z=\frac{16-20.8}{4.8}=-1[/tex]

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

Steps to solve:

f(x) = 3x+5/x; x = 2

~Substitute

f(2) = 3(2)+5/2

~Simplify

f(2) = 6+5/2

~Add

f(2) = 11/2

~Simplify

f(2) = 5.5

Best of Luck!

Answer:

discriminant

Step-by-step explanation:

Discriminant is the expression under the radical in a quadratic equation formula that indicates the nature of the solutions real or complex, rational or irrational , single or double root in other words

A discriminant can be said to be used to indicate the nature of the result that a quadratic equation when solved will yield and this can be : rational or irrational , complex or real, single or double roots. and it also indicates by how many  it would be  

Answer:

38

Step-by-step explanation:

Answer:

38 packs

Step-by-step explanation:

I don’t know about the first one the second one if it starts from the origin the point represents that it an proportional 3 is when they start together by seeing if it is x and y I don’t know if it is right

Answer:

Since both equations are equal to y, we can set them equal to each other.

y =-3x +8

y = -5x -2

-3x +8 = -5x -2

Solve for x.To do this, we need to get x by itself. First, move all the numbers to one side of the equation, and all the variables to the other.

-3x +8 = -5x -2

Add 5x to both sides

-3x+5x +8=-5x+5x -2

2x+8=-2

Subtract 8 from both sides

2x+8-8 = -2-8

2x=-10

Now, all the numbers are on one side, with the variables on the other. x is not by itself, it is being multiplied by 2. To undo this, divide both sides by 2

2x/2= -10/2

x= -5

Now, to find y, substitute -5 in for x in one of the equations.

y = -5x -2

y= -5(-5) -2

y=25-2

y=23

Put the solution into (x,y)

The solution is (-5, 23)

Answer:

36 minutes when both pipes are working together

Step-by-step explanation:

capacity of tank = 5400 liters

Pipe A flow per mint. = 5400/90 = 60 liters per mint.

Pipe B flow per mint. = 5400/60 = 90 liters per mint.

Flow of A + B per mint. 60 + 90 = 150 liter per mint.

Therefore, 5400 / 150 = 36 minutes to fill the tank

Answer:

he started fishing by 5:10pm

Step-by-step explanation:

just subtract 1:30 from 6:40

We have been given that square ABCD has a side length of 4 inches. The square is dilated by a scale factor of 4 to form square A'B'C'D'. We are asked to find the side length of square A'B'C'D'.

We know that when scale factor is greater than 1, then the resulting figure would be an enlargement.

To find the side length of new square after dilation, we will multiply the original side by scale factor.

[tex]\text{New side length}=\text{Original side}\times \text{Scale factor}[/tex]

[tex]\text{New side length}=\text{4 inches}\times 4[/tex]

[tex]\text{New side length}=16\text{ inches}[/tex]

Therefore, the side length of square A'B'C'D' would be 16 inches.

Answer:

36 units

Step-by-step explanation:

Split the parallelogram into 3 shapes. Two right triangles and one rectangle.

Find the length of all the sides.

Triangle one:                                                 Triangle two:

Leg 1: 8                         a^2+b^2=c^2            Leg 1: 8                  a^2+b^2=c^2

Leg 2: 6                      8^2 + 6^2 = c^2         Leg 2: 6                  8^2 + 6^2 = c^2

Hypotenuse: ?             64 + 36 = c^2           Hypotenuse: ?           64 + 36 = c^2

                                        100=c^2                                                      100=c^2

                                         c=10                                                               c=10

Hypotenuse One: 10 units

Hypotenuse Two: 10 units

Base One Length: 8 units

Base Two Length: 8 units

Add all these numbers up and your answer would be 36 units.

You have not given the data for which you like to find the median.

I will however explain how you can find the median of a given set of data, and you can apply the same method to your problem.

Step-by-step explanation:

Median, just like it sounds, is simply the middle value of a given set of data.

Given a set of numbers:

a, b, c, d, e, ..., z.

To find the median, first,

- Arrange the numbers a, b, c, d, e, ..., ..., z in an ascending or descending order.

- Count the whole numbers, if it is odd, you have a middle number, and that is the median.

If it is even, you have two middle numbers, then the median will be the addition of those two numbers divided by two.

Example: To find the median of

4, 5, 2, 1, 2, 6, 7, 3, 5.

First, we arrange in ascending:

1, 2, 2, 3, 4, 5, 5, 6, 7

Next, we locate the middle number(s), which is 4.

The MEDIAN is 4 .

Example 2: To find the median of

9, 4, 5, 2, 1, 2, 6, 7, 3, 5.

First, we arrange in ascending:

1, 2, 2, 3, 4, 5, 5, 6, 7, 9

Next, we locate the middle number(2), which are 4 and 5.

The median = (4 + 5)/2

= 9/2

= 4.5

The MEDIAN is 4.5.

Answer:

B

Step-by-step explanation

a squared plus b squared equals c squared.

16 plus 144 equal 160.

now square 160

Answer:

9 inches

Step-by-step explanation:

Volume is the product of cross sectional area and height.

V=Ah

Where A is area of base and h is height

Given that the base is square, the area of square is given by A=b*b

Xonsidering that the area is given as 81 square inches then

b*b=81

b is the square root of 81 which is +9 or -9

Since base must be positive interger, then base is 9 inches

The zeros of the function [tex]G(r) = r^2 - 6r - 5[/tex]5 are r = 11 and r = -5.

To find the zeros of the function [tex]G(r) = r^2 - 6r - 55[/tex], we set G(r) equal to zero and solve for r:

Now, we can use the quadratic formula to solve for r:

r = [-b ± √[tex](b^2 - 4ac)[/tex]] / 2a

where a, b, and c are the coefficients of the quadratic equation [tex](r^2 - 6r - 55 = 0)[/tex].

In this case, a = 1, b = -6, and c = -55. Let's substitute these values into the formula:

r = [-( -6) ± √[tex]((-6)^2 - 4 * 1 * (-55))[/tex]] / 2 * 1

r = [6 ± √(36 + 220)] / 2

r = [6 ± √256] / 2

Now, let's consider the two possible solutions:

1) r = [6 + √256] / 2

r = [6 + 16] / 2

r = 22 / 2

r = 11

2) r = [6 - √256] / 2

r = [6 - 16] / 2

r = -10 / 2

r = -5

So, the zeros of the function  are r = 11 and r = -5.

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Answer:

x=13 y=18

Step-by-step explanation:

The value of x and y from the given triangle are 13 and 13√2 respectively.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, Adjacent is 13 units, opposite side is x units and hypotenuse id y units.

We know that tanθ=Opposite/Adjacent and cosθ=Adjacent/Hypotenuse

tan45°=x/13

1=x/13

x=13 units

cos45°=13/y

1/√2=13/y

y=13√2

Therefore, the value of x and y from the given triangle are 13 and 13√2 respectively.

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Answer:

  y +3 = -6(x +9)

Step-by-step explanation:

The point-slope form of the equation of a line is ...

  y -k = m(x -h)

for a line with slope m through point (h, k).

You want the line with slope -6 through point (-9, -3), so its equation is ...

  y -(-3) = -6(x -(-9))

  y +3 = -6(x +9) . . . . . matches the last choice

Answer:

3/26

Step-by-step explanation:

The face cards are: Jack, Queen, and King. There are only three face cards for each of the 4 suits.

Among the 4 suits, two of them are red: diamonds and hearts. And, each of these two has 3 faces. That means that in a deck of 52 cards, there are 2 * 3 = 6 cards that are both red cards and face cards.

Probability is (# times specific event can occur) / (# times any general event will occur).

Here, the specific event is drawing a card that is both red and a face card (of which there are 6 ways), and the general event is drawing a card (of which there are 52 ways):

P(draw a card that is both red and a face card) = 6/52 = 3/26

Answer:

3/26

Step-by-step explanation:

In a deck of 52 cards, there are two red suits: Diamonds and Hearts

There are 6 red face cards:

2 red King

2 red Queen

2 red Jack

P(red face card) = 6/52 = 3/26

Answer:

Coordinate plane

Step-by-step explanation:

The two dimensional plane made up by the intersection of a vertical (y-axis) and a horizontal (x-axis) perpendicular lines that cross each other once at the zero point mark known as the origin is called the Cartesian plane or coordinate plane. The origin is labeled letter O with coordinates 0,0

The Cartesian plane is used to plot graph lines and points so as to present algebraic ideas in a visual form and to form as well as interpret ideas in algebra.

Answer:

69

Step-by-step explanation:

The solution is,  138 divided by 2 is 69.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

138 divided by 2

i.e. 138/2

= 69

Hence, The solution is,  138 divided by 2 is 69.

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Answer:

Answer is below

Step-by-step explanation:

Charles is wrong because 3 doesn't represent exponential decay. This is because 3 is greater than 1, so it represents exponential growth. If the number was less than 1, then it would represent exponential decay.

If this answer is correct, please make me Brainliest!

The correct answer is Charles should represent as  Exponential growth instead of exponential decay

Here f(x) = 3 where 3 is greater than 1

so, It is exponential growth instead of exponential decay

Hence , Charles made an error of exponential decay instead of exponential growth.

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Answer:

c. -1/2x + y = -10

Step-by-step explanation:

[tex] - \frac{1}{2} x + y = - 10 \\ y = \frac{1}{2} x - 10[/tex]

Changing the order of the equation, you can verify the coefficient of x is the same when y is isolated.

In slope-intercept form, the coefficient of x, or the m in y=mx+b, is the slope or gradient.

After converting each given equation to the slope-intercept form, it is clear that both the original equation Y=1/2x-10 and the option c, -1/2x + y = -10, have the same slope of 1/2.

To determine which equation has the same slope as Y=1/2x-10, we rewrite each given equation in slope-intercept form (y = mx + b), where m represents the slope.

Based on this analysis, the equations y = 1/2x - 10 and -1/2x + y = -10 both have the same slope of 1/2. Therefore, the correct answer is option c.

Answer:

20

Step-by-step explanation:

If she has 68 lollipops, and she had 8 remaining, we should subtract the two.

68 - 8 = 60

So now we know she gave away 60 lollipops in total.

We know she gave 3 to each of her friends, so we would divide 60 by 3.

60/3 = 20

So she has 20 friends.