A bag contains 9 orange marbles and 36 green marbles. If a representative sample contains 2
orange marbles, then how many green marbles would you expect it to contain? Explain.
Because the ratio of orange marbles to green marbles is in the population, the expected number
of green marbles is times the number of orange marbles in the representative sample. There
should be green marbles.

Answer:

Step-by-step explanation:

7w + 72 + 24w

31w + 72

Answer:

• Triangle A: Side lengths of 5, 3, and 4. This is an acute triangle, as all three angle measurements are less than 90°.

• Triangle B: Side lengths of 12, 7, and 15. This is an obtuse triangle, as one angle measurement is greater than 90°.

• Triangle C: Side lengths of 8, 8, and 8. This is an equilateral triangle, as all three sides and all three angle measurements are equal

Step-by-step explanation:

Answer:

1-3-4-2-5

Step-by-step explanation:

\(tan\frac{\theta}{2}\) <== Given

\(\frac{sin\frac{\theta}{2}}{cos\frac{\theta}{2}}\) <== Step 1

\(\frac{\frac{\sqrt{1-cos\theta}}{2}}{\frac{\sqrt{1+cos\theta}}{2}}\) <== Step 3

\(\frac{\sqrt{1-cos\theta}}{\sqrt{1+cos\theta}}\) <== Step 2 (as a result of Step 4)

\(\pm\sqrt{\frac{1-cos\theta}{1+cos\theta} }\) <== Step 5

The solution of given system of equations is (10, 4).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are 3x+4y=38 -----(I) and 5x-5y=30 -------(II)

x-y=6 -------(III)

x=6+y

Substitute x=6+y in equation (I), we get

3(6+y)+4y=38

18+1y+4y=38

5y=20

y=4

Substitute y=4 in equation (III), we get

x=10

So, the solution is (10, 4)

Therefore, the solution of given system of equations is (10, 4).

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In this data set, the only value that is an outlier is 100, since it is above the upper bound of 98.25.

To identify the outliers in the data set, we can use the concept of the interquartile range (IQR) and the 1.5×IQR criterion.

First, we need to find the first and third quartiles (Q1 and Q3) of the data set. To do this, we can order the data set from smallest to largest:

54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100

The median of the data set is the middle value, which is 82.

The lower half of the data set will consists of:

54, 72, 75, 81, 81

The median of the lower half is (72 + 75)/2 = 73.5, which is the value halfway between the two middle values.

The upper half of the data set will consists of:

83, 83, 83, 85, 100

The median of the upper half is (83 + 85)/2 = 84, which is the value halfway between the two middle values.

Therefore, the first quartile (Q1) is 73.5 and the third quartile (Q3) is 84.

The interquartile range (IQR) is the difference between Q3 and Q1:

IQR = Q3 - Q1 = 84 - 73.5 = 10.5

To identify the outliers in the data set using the 1.5×IQR criterion, we need to calculate the lower and upper bounds:

Lower bound = Q1 - 1.5×IQR = 73.5 - 1.5×10.5 = 57.75

Upper bound = Q3 + 1.5×IQR = 84 + 1.5×10.5 = 98.25

Any data point that is below the lower bound or above the upper bound is considered an outlier.

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Answer:

He still needs to catch 80% of the pokemon's.

Answer:80% are left.

Answer:

x = 30

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

100 = 70+x

Subtract 70 from each side

100-70 = 70+x-70

30 =x

Answer:

\(x = 30 \: \: degrees\)

Step-by-step explanation:

The sum of the of the exterior angle is equal to sum of the opposite interior angles in a triangle.

\(70 + x = 100 \\ x = 100 - 70 \\ x = 30 \: \: \: degrees\)

hope this helps

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Answer:

The answer is F

Step-by-step explanation:

In the statement , the number is 5.5.

The Latin term "Integer," which implies entire οr intact, is where the wοrd "integer" first appeared. Zerο, pοsitive numbers, and negative numbers make up the particular categοry οf numbers knοwn as integers.

Here let us take the given integer as x.

Then , cοnsecutive οdd integer is x+2.

Nοw accοrding tο the given questiοn is multiplicatiοn οf an integer by its cοnsecutive οdd integer is 11 mοre than the square οf the number. then, cοnverting intο expressiοn,

=> x \(\times\) (x+2) = \(x^2+11\)

=> \(x^2+2x=x^2+11\)

=> 2x = 11

=> x = 11/2 = 5.5

Hence the number is 5.5.

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Answer:

this? hope it helps ........

Answer:

The answer is area=32pi-64 and the perimeter is 8pi

Step-by-step explanation:

Answer:

1,280

Step-by-step explanation:

Answer

Current value = $7,448

Explanation

The current value of any item, A decreasing at a given rate, r%, over time, t, is given as

A = A₀ (1 - r)ᵗ

For this question

A = Current value at any time t

A₀ = Initial value of the product = $18,547

r = Rate = 9.64% = 0.0964

t = Time = 9 years

A = A₀ (1 - r)ᵗ

A = 18,547 (1 - 0.0964)⁹

A = 18,547 (0.9036)⁹

A = 18,547 (0.4016)

A = $7,448

Hope this Helps!!!

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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Answer:

702 pounds

Step-by-step explanation:

9 * 78 = 702

Answer:

If Maria has 9 boxes that each weigh 78 pounds, in total the boxes would weigh 702 pounds.

Step-by-step explanation:

9 x 72 = 702 pounds

Your welcome! :)

Answer:

m∠B = 66.3°

a = 0.0319

b = 0.0726

Step-by-step explanation:

Sum of the interior angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 23.7 + m∠B + 90 = 180

⇒ m∠B = 180 - 90 - 23.7 = 66.3°

We can use the sine rule to help solve the missing side lengths.

Sine rule

\(\dfrac{a}{sin(A)}=\dfrac{b}{sin(B)}=\dfrac{c}{sin(C)}\)

where A, B and C are the angles and a, b and c are the side lengths opposite the angles.

Therefore,

\(\dfrac{a}{sin(23.7)}=\dfrac{b}{sin(66.3)}=\dfrac{0.0793}{sin(90)}\)

\(\implies a=\dfrac{0.0793}{sin(90)}\times sin(23.7)=0.031874458...=0.0319\)

\(\implies b=\dfrac{0.0793}{sin(90)} \times sin(66.3)=0.072612043...=0.0726\)

Answer: 17 and 1/2 miles

Step-by-step explanation: They are 15 miles away from eachother which means halfway between the two is 7 and 1/2. 10 plus 7 and 1/2 is 17 and 1/2 and 25 minus 7 and 1/2 is 17 and 1/2.

Time taken with average speed of 75 mph is 6.4 hour.

Given that;

Time taken with average speed of 60 mph = 8 hour

Find:

Time taken with average speed of 75 mph

Computation:

Distance = Speed × Time

Total Distance = 60 × 8

Total Distance = 480 miles

Time taken with average speed of 75 mph = Total distance / Speed

Time taken with average speed of 75 mph = 480 / 75

Time taken with average speed of 75 mph = 6.4 hour

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Answer:

22° + m<C = 90°

Step-by-step explanation:

We are given that <A (which is equal to 22°) and <B are vertical angles, and that <B is complementary to <C.

We want to write an equation that will help us solve <C.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <A ≅ <B; it also means that the measure of <B is also 22°.

Also recall that complementary angles add up to 90°.

This means that m<B + m<C = 90°.

Since we deduced that m<B is 22°, we can substitute that value into the equation.

Hence, an equation that can be used to solve for <C is:

22° + m<C = 90°

If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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Answer:

30-5×2 of 3+(19-3) ÷8

Step-by-step explanation:

30-5×6+(19-3)÷8

30-5×6+16÷8

30-30+8

38-30

8

Answer:

Step-by-step explanation:

b

Answer:

x > 15

Step-by-step explanation:

At least means that x will be greater than 15 so it is x > 15.

Answer:

21

Step-by-step explanation:

Answer:

SAS=side angle side

there is two side and one angle

Answer:

SAS theorem

explanation:

The product of the expression 7 x 63 is 441.

We have,

To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:

7 x 63 = 7 x (60 + 3)

Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:

7 x (60 + 3) = 7 x 60 + 7 x 3

Simplifying further:

7 x 60 + 7 x 3 = 420 + 21

Therefore,

The product of 7 x 63 is 441.

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Answer: 2√5 - 3

Step-by-step explanation:

\($$Simplify the following:$\sqrt{29-12 \sqrt{5}}$$$\begin{aligned}&29-12 \sqrt{5}=9-12 \sqrt{5}+20=9-12 \sqrt{5}+4(\sqrt{5})^{2}=(2 \sqrt{5}-3)^{2}: \\&\sqrt{\left((2 \sqrt{5}-3)^{2}\right)}\end{aligned}$$Cancel exponents. $\sqrt{(2 \sqrt{5}-3)^{2}}=2 \sqrt{5}-3$ :\\Answer:$$2 \sqrt{5}-3$$\)

The solution to the algebraic problem is \(x^{2}\)

What is an Algebraic Equation?

An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

Solution:

(\(x^{3}\) – 1) = (x+2)

On dividing (\(x^{3} - 1\)) by (x+2)

The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.

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Answer:

3 cups or 1.5 pints

Answer:

  (c)  8 jars

Step-by-step explanation:

You want to know the number of 1.25 quart jars that can be filled from a 2.5 gallon container.

The number of jars can be found from ...

  (2.5 gal) × (4 qt/gal) × (1 jar)/(1.25 qt) = (2.5·4/1.25) jars = 8 jars

Lorraine can fill 8 jars from the 2.5 gallon pot.

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