A teacher randomly chooses a two-person team from a group of four students. The first person chosen will
be the presenter and the second person will be the researcher. Two of the students, Amir and Aaron, are
boys. The other two students, Caitlin and Deniz, are girls. All the possible outcomes of the team selection
are listed below.
If we take outcomes 2, 3, 5, 6, 7, 8, 10, and 11 as a subset of the sample space, which of the statements
below describe this subset?

Answer:

Option C is the correct answer

Step-by-step explanation:

Let μ1 be the average flying speed of monarch butterflies and let μ2 be the average flying speed of swallowtail butterflies.

Also, let n1 be the sample size of monarch butterflies and let n2 be the sample size of swallowtail butterflies.

Thus, defining the hypothesis, we have;

Null hypothesis;H0: μ1 = μ2

Alternative hypothesis; H1: μ1 > μ2

In this case, the p-value = P_H0[t_(n1 + n2 - 2) ≥ t] where t is the test statistic based on tbe differences of sample mean,that follows t distribution with degrees of freedom (n1 + n2 - 2)

With respect to the question, the probability of the monarchs and swallowtails flying at the same speed is 0.072.

Thus,

P_H0[t_(n1 + n2 - 2) ≥ t] = 0.072

We can therefore conclude that in this case, the p-value is the probability of observing a difference equal to or greater than the sample difference under the null hypothesis which states that μ1 = μ2, which is 0.072

Thus, option C is the correct answer

Answer:

The correct option is;

b. The probability that monarchs and swallowtails fly at the same speed is 0.072

Step-by-step explanation:

The p- value indicates the probability of which the hypothesis tested, the null hypothesis is true and it is compared against a given confidence level. Whereby the p-value is more than the given confidence level then it indicates that the null hypothesis assumption is correct.

Therefore, whereby the null hypothesis tests proposes the equality of the two means, then at  a 5% confidence level or α = 0.05, whereby p-value = 0.072 > α = 0.05 we accept the null hypothesis and state that the probability that monarchs and swallowtails fly at the same speed is 0.072.

Answer:

About 374 people.

Step-by-step explanation:

[tex] \frac{11}{50} \times 1700 = 374[/tex]

Answer:

11 weeks

Step-by-step explanation:

25 divided by 5 = 5

So she saves 5 dollars a week meaning 5 x 11 = 55

Answer:

10 weeks and 5 days

Step-by-step explanation:

5 weeks is 25 ->

10 weeks is 50->

she gets 1.4 a day ->

1.4 times 3 days is4.2 so you would use 5 days ->

so it would be 10 weeks and 5 days

Answer: 2e +24 which equals 130.477527766

:)

Answer:

1e+24

Step-by-step explanation:

The probability of drawing a red marble first and a yellow marble second is 5/21.

To find the probability that the first marble drawn is red and the second one is yellow, we need to consider the total number of marbles and the number of red and yellow marbles in the bag.

Since we are drawing without replacement, the probabilities are dependent.

The probability of drawing a red marble on the first draw is 5/7. After the first marble is drawn, there are now 4 red marbles and 2 yellow marbles left in the bag. The probability of drawing a yellow marble on the second draw is 2/6.

Therefore, the probability of drawing a red marble first and a yellow marble second is (5/7) × (2/6) = 10/42 = 5/21.

Final answer:

The probability of drawing a red marble first and then a yellow marble from a bag with 2 yellow marbles and 5 red marbles is calculated by multiplying the probability of each event, giving a final answer of 5/21.

Explanation:

The calculation of the probability that the first marble is red and the second one is yellow when two marbles are drawn without replacement from a bag containing 2 yellow marbles and 5 red marbles involves step-by-step conditional probabilities.

Step 1: Calculate the probability of drawing a red marble first. Since there are 5 red marbles out of a total of 7 marbles, the probability is 5/7.

Step 2: Now that a red marble has been drawn and not replaced, there are 1 yellow marble less and 1 red marble less in the bag, making a total of 6 marbles. The probability of then drawing a yellow marble is 2/6, or 1/3.

Step 3: To find the combined probability of both events happening in sequence (a red marble first, then a yellow marble), multiply the individual probabilities: (5/7) * (1/3).

The final answer is therefore (5/7) * (1/3) = 5/21.

Answer:

Step-by-step explanation:

You want the volume of a medicine capsule and the mass of active ingredient if the capsule is a cylinder 4 mm in diameter and 5.6 mm long, capped on either end by a hemisphere, and the active ingredient has a density of 0.7 mg/mm³.

The volume of a cylinder is given by ...

  V = πr²h

and the volume of a sphere is given by ...

  V = 4/3πr³

The two hemispheres have a total volume equal to that of a sphere, and the radii of the cylinder and sphere are the same. This means the volume of the capsule can be found as ...

  V = πr²h +4/3πr³

  V = πr²(h +4/3r)

The radius is half the diameter, so we have ...

  V = π(2 mm)²(5.6 mm +4/3(2 mm)) ≈ 103.882 mm³

The volume of the capsule is about 103.9 mm³.

Multiplying the volume by the density gives the mass of active ingredient:

  m = ρV

  m = (0.7 mg/mm³)·(103.882 mm³) ≈ 72.72 mg

There are about 72.7 mg of active medication in one capsule.

Answer:

14

Step-by-step explanation:

it's going up by 2 everytime so you just take away 2

Answer:-5

Step-by-step explanation:

It’s just how it is -5

The coordinate of S' is (1, -5) if the triangle in the diagram is translated 3 units right and 4 units down.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Let point is (-2, -1)

Now,

Translated 3 units right, the x-coordinate of the point = -2 + 3 = 1

Translated 4 units down, the y-coordinate of the point = -1 - 4 = -5

The coordinate of S' is (1, -5)

Thus, the coordinate of S' is (1, -5) if the triangle in the diagram is translated 3 units right and 4 units down.

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Answer: 18°

Step-by-step explanation:

From the question, Miles hs a piece of paper that is 1/4 of a large circle and he cuts the paper into five equal parts from the center of the circle.

The total angle of a circle is 360°. Since Miles caught 1/4 of the circle, this means that he'll have an angle of : 360° × 1/4 = 90°.

Then, he now cuts the paper into five equal parts. This means that we divide 90° by 5 which will give:

= 90° ÷ 5

= 18°

The angle measure of each part is 18°.

Answer:

18°

Step-by-step explanation:

Extracting the key information from the question:

*** Miles has paper that is 1/4 of a large circle.

*** He cut this paper into five equal parts.

*** We are required to calculate the angle measure of each part.

The sum of the angles in a circle is 360°. So I miles has 1/4 of a large circle, it means that the sum of the angles of this paper should be a quarter of 360°

= 1/4 × 360°

= 90°

Again, since he cuts the paper into five equal parts, we will find the angle measure of each part by dividing 90° by 5.

The angle measure of each

= 1/5 × 90°

= 18°

Therefore, each of the five parts of paper had an angle of 18°

Answer:

4 or 3/2

Step-by-step explanation:

The given equation is 3(x - 4) (2x - 3) =0

When we have 0 on the right hand side of given equation , we can compare two factors with 0 .

we can do this by :

(3×x - 3×4) (2x-3)=0

(3x-12)(2x-3)=0

either , (3x-12)=0

or,3x = 12

or, x = 12/3

or ,x = 4

now , comparing other factor:

(2x -3) =0

or, 2x = 3

or ,x=3/2

Answer:

  B) Circle F is shown. A line segment goes from one point to another point on the circle and goes through point F. It has a length of 20.

Step-by-step explanation:

A segment that goes through the center of the circle and that has its ends on the circle is a diameter. The radius is half the length of the diameter.

A chord through the center of circle F with a length of 20 units means circle F has a radius of 10 units.

Final answer:

Option B is the correct answer because it describes a line segment that passes through the center and is 20 units long, indicating it's a diameter; hence the radius is half of that, which is 10 units.

Explanation:

To determine which circle has a radius of 10 units, we need to recall that the radius is a straight line from the center of the circle to a point on its boundary. Two radii lined up end-to-end across a circle form a diameter. Therefore, a diameter is twice the length of the radius.

Option A describes a line segment of length 10, but we cannot confirm if it's a radius or a diameter without additional information.

Option B describes a line segment that goes through the center point F and is 20 units long, indicating it's a diameter. Since the diameter is twice the radius, a circle with a diameter of 20 units has a radius of 10 units.

Option C, like option A, cannot be confirmed without additional information about the line segment's relation to the center of the circle.

Option D also describes a line segment of 20 units, but again, without confirmation that it's a diameter, we cannot be sure.

Therefore, the correct answer is Option B, where the circle's diameter is explicitly mentioned to be 20 units, meaning the radius is 10 units.

Answer:

[tex]1 \frac{2}{5} hours[/tex]

Step-by-step explanation:

LeRoy practiced for 1 2/5 hours today.

To find how long LeRoy practiced today, we need to determine half of his usual practice time of 2 4/5 hours. To do this, we divide 2 4/5 by 2. If we simplify the fraction, we get 14/5. Dividing 14/5 by 2, we get 7/5 or 1 2/5 hours. Therefore, LeRoy practiced for 1 2/5 hours today.

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Answer:

£8.10

Step-by-step explanation:

Since we have to convert Euro to pound we will first find value of one euro in terms of pound.

Given

£3 = €4

=> £3/4 = €1

=> €10.80 = £3/4 * 10.80  ---->multiplying both side by 10.80 as we have have to find value of €10.80  in pounds

= > €10.80 = £8.10

Answer:

£8.10

Step-by-step explanation:

Given,

£3 = €4

Dividing both side by four

€1 = £0.75

We have to convert €10.80 to pounds

Multiplying 10.80 both side

€10.80 = £0.75 x 10.80

€10.80 =£8.10

Hence,  €10.80 is equal to £8.10.

Given:

Given that the triangular prism with height 10 inches.

The side lengths of the base of the triangle are 12 inches, 13 inches and 5 inches.

We need to determine the surface area of the prism.

Surface area of the prism:

The surface area of the prism can be determined using the formula,

[tex]SA=bh+(s_1+s_2+s_3)H[/tex]

where b is the base and h is the height of the triangle.

s₁, s₂, s₃ are the side lengths of the triangle and

H is the height of the prism.

Substituting b = 12, h = 5, s₁ = 12, s₂ = 5, s₃ = 13 and H = 10 in the above formula, we get;

[tex]SA=(12)(5)+(12+5+13)(10)[/tex]

[tex]SA=60+(30)(10)[/tex]

[tex]SA=60+300[/tex]

[tex]SA=360 \ in^2[/tex]

Thus, the surface area of the triangular prism is 360 square inches.

Hence, Option b is the correct answer.

Answer:

360 sq in

Step-by-step explanation:

i did it trust me

Answer:

6 times

Step-by-step explanation:

In order to figure out how many times a number goes into another number we need to divide the numbers:

88/14 ≅ 6.29

Since the answer is 6.29 then 14 fits into 88, 6 full times

Answer:

Step-by-step explanation:

Exact Form:

x=5,−32

Decimal Form:

x=5,−1.5

Mixed Number Form:

x=5,−112

                      ( I tried... )

Answer:

444444

Step-by-step explanation:

Answer:

444,444

Step-by-step explanation:

You would estimate first look at the 100's place 3+2=5 so we already have 500 so we know that the sumis greater than 500 because is you at 61+83 with 500 its a larger number than just 500

Final answer:

To see if 361 + 283 is greater than 500, round each number to the nearest hundred and add them. The rounded sum of 400 + 300 = 700 is clearly greater than 500, thus the actual sum must also be greater than 500.

Explanation:

To determine if the sum of 361 + 283 is greater than 500 without actually adding the numbers together, you can use estimation. You can round each number to its nearest hundred to make the math easier. 361 can be rounded to 400 and 283 can be rounded to 300. When you add these rounded numbers together, 400 + 300 = 700, which is clearly greater than 500. Since rounding each number up only increases the sum, the actual sum of 361 + 283 must also be greater than 500.

This concept is based on the understanding that the rules of mathematics are universally valid, as addition is commutative (A+B=B+A).

Answer:

$12.25

Step-by-step explanation:

2.5 yards of fabric * $4.90 per yard of fabric = $12.25. Hope this helps!

Final answer:

Aisha pays $12.25 for the 2.5 yards of fabric she buys.

Explanation:

The total amount of fabric Aisha buys is 2.5 yards.

To find the total cost, multiply the number of yards by the cost per yard. For Aisha, this would be 2.5 yards x $4.90/yard = $12.25.

Answer:

log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x

Step-by-step explanation:

Given:

log Subscript 2 Baseline 9 x cubed?

Required:

Find the equivalent of the above expression.

First, we need to represent it mathematically;

log Subscript 2 Baseline 9 x cubed = [tex]log_{2} 9x^{3}[/tex]

From Laws of logarithm  

[tex]log_{x} AB = log_{x} (A* B)\\log_{x} AB = log_{x}A + log_{x}B[/tex]

Note how the expression is split into two

We'll apply the same logic above, here

First, is to simplify the mathematical expression;

[tex]log_{2} 9x^{3} = log_{2} (9 * x^{3})[/tex]

Then we split into two

[tex]log_{2} 9x^{3} = log_{2}(9) + log_{2}(x^{3})[/tex]

[tex]log_{2} 9x^{3} = log_{2}(3^2) + log_{2}(x^{3})[/tex]

Also from laws of logarithm,

[tex]log_{m}A^{n} = nlog_{m}A[/tex]

We'll apply this law on [tex]log_{2}(x^{3})[/tex] and [tex]log_{2}(3^{2})[/tex]

[tex]log_{2}x^{3} = 3log_{2}x[/tex]

[tex]log_{2}(3^2) = 2log_{2}3[/tex]

So, [tex]log_{2} 9x^{3} = log_{2}(9) + log_{2}(x^{3})[/tex] becomes

[tex]log_{2} 9x^{3} = 2log_{2}3 + 3log_{2}x[/tex]

log Subscript 2 Baseline 9 x cubed is equivalent to [tex]2log_{2}3 + 3log_{2}x[/tex]

[tex]2log_{2}3[/tex] can be represented as 2 log subscript 2 Baseline 3

and

[tex]3log_{2}x[/tex] can be represented as 3 log subscript 2 Baseline x

Hence, log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x

Answer:

a) log2 9x^3

Step-by-step explanation:

got it right on edg

The price of adult ticket is $ 13and child ticket is $12.Hope this will help u.....

For given equation x^2+6x-15=0, value of x is [tex]-3\pm 2 \sqrt{6}[/tex]

The "solutions" of an equation are referred to as the roots of the equation. Solutions are the numbers that, once the variable has been solved, are equal to it. We can use the discriminant formula to obtain the roots of quadratic equations.

The given equation [tex]x^2+6x-15=0\\[/tex] can be solved using discriminant method.

[tex]d=b^2 -4ac\\[/tex].......................1

[tex]x=-b\pm\sqrt{d}/2a[/tex].....................2

To calculate d,

Substitute a=1,b=6,c=-15 in eq 1.

[tex]d=6^2-4\times 1\times -15\\ d=96[/tex]

[tex]x=-6\pm \sqrt{96}/2\\x=-3\pm 2\sqrt6[/tex]

Thus, value of x is  [tex]-3\pm 2 \sqrt{6}[/tex]

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Final answer:

x = -3 ±√24.

Explanation:

To solve the quadratic equation x²+6x-15=0 by completing the square, follow these steps:

First, move the constant term to the other side of the equation:

x² + 6x = 15.

Add the square of half the coefficient of x to both sides to complete the square: (6/2)² = 9, so add 9 to both sides resulting in x² + 6x + 9 = 24.

Now the equation is a perfect square on the left side:

(x+3)² = 24.

Take the square root of both sides to solve for x:

x+3 = ±√24.

Subtract 3 from both sides to find the values of x:

x = -3 ±√24.

Final answer:

The submarine will travel approximately 1532 feet horizontally as it dives down at an angle of depression of 40 degrees to a depth of 2000 feet, using the cosine trigonometric function to calculate this distance.

Explanation:

The student's question involves finding the horizontal distance a submarine will travel as it dives at a given angle of depression. When solving problems like this, we can use trigonometric functions, specifically the cosine function, because the horizontal distance is the adjacent side of a right-angled triangle, with the angle of depression being one of the angles, and the depth of the dive being the opposite side.

Now calculate the horizontal distance: x = 2000 * 0.766, which gives us x ≈ 1532 feet.

Therefore, the horizontal distance traveled by the submarine when it finished its dive is approximately 1532 feet.

Answer:

Positive

Step-by-step explanation: When you look at a graph you always look at it like your reading a book. So you read it from left to right and if you read the line shown it is going up meaning it is positive.

Hope this helps :)

Answer:

3.33 can i have brainliest

Step-by-step explanation:

5/3 = 1.6666666666...

1.6666666666..... X 2 = 3.333333.....

The angles are 150°, 108°, 90°, and 12°.

In a literal sense, corresponding means pairwise angles. Like the right corner angles of two triangles etc. But usually, we take them as:

For two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles. They are of the same measurement.

Suppose for example, that 10 people choose city A as a destination.

To calculate its corresponding angle, we have to use the following proportion, 60 people represent the whole circle, is 360°, then 10 people are represented by:

France:

25/60 × 360 = 150°

Spain:

18/60 × 360 = 108°

Greece:

15/60 × 360 = 90°

Other:

2/60 × 360 = 12°

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Answer: BC = 15

Step-by-step explanation:

Since the triangles are congruent, that means they are the same. So side AB = side EF. Since we know side FD is 15, that means side BC= 15

Final answer:

To find BC when given triangles ABC and DEF are congruent and the perimeter of DEF is 38, subtract the summed lengths of DE and EF from 38 to get the length of DF, which will be equal to BC.

Explanation:

If you are given that triangle ABC is congruent to triangle DEF and the perimeter of DEF is 38 units, to find the length of side BC, we need to first establish that corresponding sides of congruent triangles are equal in length. This means that each side of triangle ABC corresponds and is equal to a side of triangle DEF. Therefore, if you are given the lengths of sides DE and EF, you subtract their sum from the total perimeter of triangle DEF to find the length of side DF. Since triangle ABC is congruent to triangle DEF, BC is equal to DF. Thus, the length of side BC in triangle ABC can be calculated.

For example, if DE is 10 units and EF is 12 units, then:

The amount owed after 9 years on a $2000 loan compounded semiannually at an 18% interest rate is approximately $8599.63.

When we need to find the amount owed after 9 years on a $2000 loan compounded semiannually at an 18% interest rate, we use the formula for compound interest:

A = P (1 + r/n)^(nt)

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount ($2000).

r is the annual interest rate (18% or 0.18).

n is the number of times the interest is compounded per year (2 for semiannual).

t is the time the money is invested for, in years (9 years).

Substituting the values into the formula, we have:

A = 2000 (1 + 0.18/2)^(2*9)

A = 2000 (1 + 0.09)^(18)

A = 2000 (1.09)^18

Calculating this expression gives us the amount owed after 9 years. Do not round any intermediate computations, and round your answer to the nearest cent.

The calculation is as follows:

A = $2000 * (1.09)^18

A ≈ $2000 * 4.299816955

A ≈ $8599.63

Therefore, the amount owed after 9 years would be approximately $8599.63.

Answer: 774.86 or 775

Step-by-step explanation:

Answer:

755

Step-by-step explanation: