Grace is having trouble deciding what to order for dessert. The options are 4 different flavors of ice cream, 3 different flavors of cake, or 2 different flavors pie. If she were to choose one item at random, what is the probability that she will choose a cake?

Answers

Answer 1

Answer: The probability that she would choose cake is 0.33 (or 33%)

Step-by-step explanation: The number of all possible outcomes is given as follows;

4 (ice cream) + 3(cake) + 2(pie), that is 4 + 3 + 2 = 9  

This means there is a possibility of 9 different outcomes if she decided to choose her dessert at random.

However, there are 3 flavors of cake available which means the possibility of choosing cake is 3.

Therefore the probability that she will choose a cake is give as,

P(Cake) = Number of required outcomes/Number of all possible outcomes

P(Cake) = 3/9

P(Cake) = 1/3 or 0.33

Therefore the probability that she would choose cake is 0.33 or 33%


Related Questions

what is the solution of the system equations y =-3x +8 y = -5x -2

Answers

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)

. Hernandez bought 18 pens for her class. Highlighters cost $3 each, and gel pens cost $2.50 each. She spent a total of $50. Use a system of equations to find the number of highlighters and gel pens Mrs. Hernandez bought. Enter your answers in the boxes.

Answers

Before we solve for anything, let's assign variables for highlighters and gel pens. Highlighters can be 'h,' and gel pens can be 'g'.

We can make two equations from what we've been given so far. Since we know that Hernandez bought 18 pens, we know that:

h + g = 18

And since we know the cost of an individual gel pen and highlighter as well as the total price, we can make another equation:

3h + 2.50g = 50

We can simplify the first equation by keeping only one variable on one side:

h + g = 18
h = 18 - g

Now that we have a value for h, we can assign it to the second equation:

3h + 2.50g = 50
3(18 - g) + 2.50g = 50
54 - 3g + 2.50g = 50

Simplify:
-0.50g = -4
0.5g = 4
5g = 40
g = 8

Put this value into the equation we made earlier:

h = 18 - g
h = 18 - 8
h = 10

Hernandez bought 10 highlighters and 8 gel pens.

An arch for a bridge over a highway is in the form of a semi ellipse. The top of the arch is 35 feet above ground​ (the major​ axis). What should the span of the bridge be​ (the length of its minor​ axis) if the height 27 feet from the center is to be 15 feet above​ ground? Round to two decimal places

Answers

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:

(x^2/b^2) + (y^2/a^2) = 1

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:

(27^2/b^2) + ((35-15)^2/(17.5)^2) = 1
(27^2/b^2) + (20^2/17.5^2) = 1
(27^2/b^2) + (400/306.25) = 1

Upon calculating and rearranging the terms, we have:

b^2 = 27^2 / (1 - 400/306.25)
b^2 = 729 / (306.25 - 400) / 306.25
calculate b^2
calculate b

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.

What is the perimeter of the parallelogram?

Answers

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.

Teresa is maintaining a camp fire. She has kept the fire steadily burning for 4 hours with 6 logs. She wants to know how many logs she needs to keep the fire burning for 18 hours.
Select the equations Teresa can use, and determine the number of logs she needs to maintain the fire for 18 hours. Select all that apply.

x/6=4/18

x/18=6/4

x/4=18/6

4/6=18

Answers

Answer:

X/18=6/4

Step-by-step explanation:

4hrs=6 logs

18hrs=x

4x=18×6

Which can also be written as

[tex] \frac{x}{18 } = \frac{6}{4} [/tex]

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Answers

Answer:

x=4.36

this is rounded

Step-by-step explanation:

a^2 + b^2 = c^2

A^2 + 9^2 = 10^2

a^2 + 81 = 100

Then subtract 81 from each side

a^2 = 19

then you have to square root 19 and you get

x=4.3588989

Brainliest?

4. Find the value of each variable. (x and y) *
45°

Answers

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.

What are trigonometric ratios?

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.

Learn more about the trigonometric ratios here:

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Which of the following has the same slope as the equation Y=1/2x-10?

a
1/2x - y = 10
b
-x + 3y = 12
c
-1/2x + y = -10
d
-2x + y = -6

Answers

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.

Final answer:

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.

Explanation:

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.

1/2x - y = 10 can be rewritten as y = 1/2x - 10, which has a slope of 1/2.-x + 3y = 12 can be rewritten as y = 1/3x + 4, so the slope is 1/3.-1/2x + y = -10 can be rewritten as y = 1/2x - 10, which has a slope of 1/2.-2x + y = -6 can be rewritten as y = 2x - 6, indicating a slope of 2.

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.

It is POSSIBLE to toss a coin 20 times and have it land tails-up all 20 times.

Answers

Answer: Yes.

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

Find the volume of a right circular cone that has a height of 2.5 ft and a base with a diameter of 8 ft. Round your answer to the nearest tenth of a cubic foot.

Answers

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:

V = (1/3) πr^2 hV = (1/3) × π× (4 ft)^2 × 2.5 ftV = (1/3) × π× 16 ft^2 × 2.5 ftV = (1/3) × π× 40 ft^3V ≈ (1/3) × 3.1416 × 40 ft^3V ≈ 41.887 ft^3

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

An aquarium tank can hold 5400 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 90 minutes. The second pipe can fill the tank in 60 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Answers

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

g(r) = r^2 – 6r – 55
1) What are the zeros of the function?

Answers

(r-11)(r+5)=0
Zeros= 11 & -5

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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This is a plane with two axes as a frame of reference. The x axis is a horizontal line and the y axis is perpendicular to it the intersection of the two axes is called the origin

Answers

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.

The volume of a gift box is 972 in³. The height of the gift box is 12 inches and the area of the base is 81 in². If the base shape is a square, what is the length of each side of the square base? *

Answers

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

Confession under the radical in the quadratic formula that indicates the nature of the solutions real or complex rational or irrational single or double route is what

Answers

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  

In circle Z, what is m∠2?

Answers

Answer:

In a circle, interior angles that are not inscribed or central can be found using the formula < = larger arc + smaller arc / 2. So, in order to find <2, the formula would be <2 = 147 + 133 / 2, so 140.

Answer:

m < 2 is 140

Step-by-step explanation:

Error Analysis- Charles claimed the function
f(x) = (3) represents exponential decay.
Explain the error Charles made.

Answers

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

What are exponential growth and exponential decay?Exponential growth  : In a function [tex]f (x) =b^{x}[/tex] where b is always greater than 1 is known as exponential growthExponential Decay :In a function [tex]f (x) =b^{x}[/tex] where b is always less than 1 is known as 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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Simplify the expression.
7x2 + 3 - 5(x2 - 4)

Answers

Final answer:

To simplify the expression, distribute the 5 to both terms inside the parentheses, combine like terms, and obtain the simplified expression 2x^2 + 23.

Explanation:

To simplify the expression 7x2 + 3 - 5(x2 - 4), we can distribute the 5 to both terms inside the parentheses:

7x2 + 3 - 5x2 + 20

Combining like terms:

2x2 + 23

So, the simplified expression is 2x2 + 23.

Consider a standard deck of 52 playing cards with 4 suits.
What is the probability of randomly drawing 1 card that is both a red card and a face card?
(Remember that face cards are jacks, queens, and kings.)
Enter your answer as a fraction in simplest form, using the / symbol, like this: 5/14

Answers

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

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'. What is the side length of square A'B'C'D' ? Type a number for your answer.

Answers

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.

Find the hypotenuse,c, of the triangle!

Answers

Answer:

B

Step-by-step explanation

a squared plus b squared equals c squared.

16 plus 144 equal 160.

now square 160

Jazmine won 68 lollipops playing basketball at her school's game night. Later, she gave three to each of her friends. She only has 8 remaining. How many friends does she have.

Answers

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.

Construct a consistent and independent system of equations that has ( − 1 , − 4 ) as its solution. Use x and y as your variables, and put your equations in the form A x + B y = C with A ≠ 0 and B ≠ 0 using the four answer boxes below. Note that there are many possible correct answers.

Answers

Final answer:

To create a consistent and independent system of equations with the solution (-1, -4), we generate two linear equations: 2x - 3y = 10 and 5x + 4y = -21, both of which are satisfied by the given solution.

Explanation:

To construct an independent and consistent system of equations that has the solution (-1, -4), we can create two distinct linear equations where the point (-1, -4) satisfies both.

As an example, we choose two arbitrary linear equations, ensuring that they are not multiples of each other, and that they are satisfied by x = -1 and y = -4.

The general form of a linear equation is Ax + By = C.

For our first equation, we could have 2x - 3y = 2(-1) - 3(-4) = 10. To ensure the second equation is not a multiple of the first, we could choose 5x + 4y = 5(-1) + 4(-4) = -21.

The system of equations would then be:

2x - 3y = 105x + 4y = -21

Recognizing Components of Cylinders
What solid will be produced if rectangle ABCD is
rotated around line m? Assume that the line bisects
both sides it intersects. What will the dimensions of the
three-dimensional solid be?
A
6 in.
6 in.
B
O
rectangular prism; length = 12 in.; width = 6 in.;
height = 5 in
triangular prism; length = 12 in.; width = 6 in.;
height = 5 in.
5 in.
O
O cylinder, radius = 12 in.; height = 5 in.
O cylinder; radius = 6 in.; height = 5 in.
es

Answers

Answer:

Cylinder: Radius: 6 in, height: 6 in

Step-by-step explanation:

See the attached image for a visual explanation!

Translate the following statement into a mathematical equation:

Six, plus four times a number, is eighteen.
(6 + 4) n = 18
4 n + 18 = 6
6 + 4 n = 18
6 + 4 + n = 18

Correct answer will get brainliest!!!

Answers

Answer:

I think it is the third:

6 + 4 n = 18

I reckon it would be C.. if you usually have a number beside a letter it usually means multiply them together (I think)
6 + 4 n = 18
(I think n = 3. 4 x 3 = 12. 12 + 6 = 18)

Answer for me please

Answers

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

The correct answer is bottles of olive oil

What is the median number of guest for each holiday

Answers

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.

SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores.

Answers

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.

A psychological study found that men who were distance runners lived, on average, five years longer than those who were not distance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years. Which of the following is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners?

Answers

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.

Which graph represents the solution set to this system of equations? –x + 2y = 6 and 4x + y = 3

Answers

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.

rainly.com/question/16208461

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