Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it

The number of ways can the committee be organized will be 2220075. Then the correct option is 3.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

The prom committee is made up of 8 boys and girls.

If there are 12 boys and 15 girls in the group to pick the committee from.

Then the number of ways can the committee be organized will be

Then the number of ways is given by the combination formula. Then we have

Number of ways = ¹²C₀ x ¹⁵C₈ + ¹²C₁ x ¹⁵C₇ + ¹²C₂ x ¹⁵C₆ + ¹²C₃ x ¹⁵C₅ + ¹²C₄ x ¹⁵C₄ + ¹²C₅ x ¹⁵C₃ + ¹²C₆ x ¹⁵C₂ + ¹²C₇ x ¹⁵C₁ +¹²C₈ x ¹⁵C₀

Number of ways = 6435 + 77220 + 330330 + 660660 + 675675 + 360360 + 97020 + 11880 + 495

Number of ways = 2220075

Thus, the correct option is 3.

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Answer:

[tex]\displaystyle\frac{5}{36}[/tex]

Step-by-step explanation:

Probability is used to find how likely an outcome is to happen. Probability can be expressed as a fraction with the total outcomes as the denominator and the number of successful outcomes (what you want to happen) as the numerator.

Sample Size

The sample size is the number of possible outcomes. In this case, the sample size will be the total number of coins. To find the sample size we need to add together all of the coins.

This means that the sample size is 12. For this type of probability, the sample size will serve as the denominator for each probability.

Replacement

In the question, it is stated that coins are replaced. This means that the sample size will not change at any point. So, the denominator will be the same for every probability.

Creating Probability Fractions

We are looking for the probability of getting a quarter and nickel, so we need to find the fractions that represent both situations.

First, let's find the quarter. As stated in the first paragraph, the number of successful outcomes is the numerator. There are 4 quarters, so 4 is the number of successful outcomes. Therefore, 4 will be the numerator. Then, 12 will be the denominator because 12 is the sample size.

Next, we need to find the probability of a nickel. Since there are 5 nickels, there are 5 successful outcomes. Then, the sample size is still 12 because there is replacement.

Complex Probability

Now we have the probability of both a quarter and nickel alone. However, this question asks about the probability of both, so this is an example of complex probability. To find complex probability, you have to multiply each probability together.

To reach the final answer we have to simplify the answer.

This means that the probability of pulling a quarter and then a nickel is 5/36.

The area of the lawn is 2.5 times greater than the area of the garden.

Heron's formula for finding the area of a triangle in terms of the lengths of its sides.

In symbols, if a, b, and c are the lengths of the sides: Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.

Given vertices W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) of a backyard,

We have to find distances WX, XY, YZ, ZW and XZ:

1. WX= √(-100+100)²+(0+70)²

=√0+4900

=70

2. XY= √(0+100)²+(0-0)²

=100 units.

3. YZ= √(-60-0)²+(-70-0)²

=√3600+4900

= √8500= 10√85

4. ZW= √(-60+100)²+(-70+70)²

=√40²+0

=40 units

5. XZ= √(-60+100)²+(-70+0)²

=√40²+70²

=√6500=10√65

Then:

1. the area of WXZ

[tex]\sqrt{(70+40+10\sqrt{65}) /2 * ({70+40+10\sqrt{65}) /2 -70* {(70+40+10\sqrt{65}) /2 -40[/tex]*[tex]\sqrt{(70+40+10\sqrt{65}) /2 -10\sqrt{65}[/tex]

=1400 feet²

Area of XYZ= [tex]\sqrt{(100+10\sqrt{65}+10\sqrt{85}) /2 * (100+10\sqrt{65}+10\sqrt{85}) /2 -100* {(100+10\sqrt{85}+10\sqrt{65}) /2[/tex]-[tex]\sqrt{-10\sqrt{85}*(10+10\sqrt{85} +10\sqrt{65}) /2 -10\sqrt{65}[/tex]

=3500 feet²

Then, ar(WXZ)/ ar (XYZ)= 3500/1400=2.5 times.

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multiply the height x the length x the width to find the volume of a room (or another 3d object)

Answer:

Hi,

Step-by-step explanation:

directrix: x=-8

focus=(8,0)

[tex]x=\dfrac{(y-0)^2}{2*(8+8)}+\dfrac{8-8}{2}\\\\\boxed{x=\dfrac{y^2}{32}}[/tex]

Applying the Pythagorean theorem and the trigonometric ratios, the perimeter of triangle ABC is: 68.8 units.

The perimeter of a triangle = sum of its 3 sides.

Given the following:

Use the Pythagorean theorem to find AD considering triangle ADB as a right triangle:

AD = √(15² - 9²)

AD = 12 units

Use the trigonometric ratios to find DC and AC:

sin 30 = AD/AC

sin 30 = 12/AC

AC = 12/sin 30

AC = 24 units

tan 30 = AD/DC

tan 30 = 12/DC

DC = 12/tan 30

DC ≈ 20.8 units

BC = BD + DC = 9 + 20.8

BC = 29.8 units.

Perimeter of triangle ABC = BC + AB + AC

Perimeter of triangle ABC = 29.8 + 15 + 24

Perimeter of triangle ABC = 68.8 units.

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The total amount Sam will pay in all will be $2,400,000

From the question, we are to determine the interest Sam pays in all

Using the simple interest formula,

I = PRT

From the given information,

P = $2,000,000

R = 5% = 0.05

T = 4

Putting the parameters into the formula,

I = $2000000 × 0.05 × 4

I = $400000

The interest Sam will pay is $400,000

The total amount Sam will pay in all will be $2,000,000 + $400,000

= $2,400,000

Hence, the total amount Sam will pay in all will be $2,400,000

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Answer:

Step-by-step explanation:400000

Answer:

  ∠AXB or ∠PXQ or ∠AXQ or ∠PXB or ...

Step-by-step explanation:

A vertical angle is formed from the rays that are opposite the rays that form the original angle.

__

The rays forming angle CXD are rays XC and XD. The ray opposite XC will have end point X, and can be named by either of the two points shown on the ray: A or P. That is, rays XA and XP are opposite ray XC.

Similarly, rays XB and XQ are opposite ray XD.

The vertical angle can be named using either of the first pair of opposite rays with either of the second pair:

  ∠AXB, ∠PXB, ∠AXQ, ∠PXQ

Of course, the ray names can be reversed in the angle names:

  ∠BXA, ∠BXP, ∠QXA, ∠QXP

Altogether, there are 8 ways to name the vertical angle to ∠CXD.

Answer:

-17, -10, -6, -5, 3, 8 only change is between 3 and 8

Answer:

[tex]y = \frac{7}{2} [/tex]

Step-by-step explanation:

[tex]3y + 7 = 5y \\ 7 = 5y - 3y \\ 7 = 2y \\ \frac{7}{2} = y \\ y = \frac{7}{2} [/tex]

Sometimes. p ⇒ q is true if both p and q are true, or whenever p is false.

Always. ¬ p ⇒ ¬q is true if ¬p and ¬q are both true (which means p and q are both false), or whenever ¬p is false (p is true).

By using any two of the points in the table, we will see that the slope is -2.

A general linear relationship is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if the line passes through (x₁, y₁) and (x₂, y₂), the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we can use the first two points on the table:

(-4, 11) and (2, -1), so the slope is:

[tex]a = \frac{11 - (-1)}{-4 - 2} = 12/-6 = -2[/tex]

Then the slope of the line is -2.

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Step-by-step explanation:

$79.99 - $64.99 = $15

(79.99 - 64.99)/|79.99| =15

15/79.99 =

15 ÷ 79.99 =

15 ÷ 79.99 × 100/100 =

(15 × 100 ÷ 79.99)/100 =

(1,500 ÷ 79.99)/100

≈18.752344043005/100 =

18.752344043005% ≈18.75%;

Answer:

by solving the divisions

Step-by-step explanation:

8/9 ÷ 3/10 = 8/9 × 10/3 = 80/27 = 2.96.

now from the solutions you can get the least to greatest

1.40 , 2.96, 5.28 and 23.75

After getting answer in decimal form change it to fraction like how they set the question

Answer:

a= 2x-3 b= 2x+5

ab= (2x-3)(2x+5)

= 2x*2x+ 2x*5- 3*2x- 3*5

= 4x+ 10x- 6x- 15

= 14x- 6x- 15

= 8x -15

x= 2

= 8(2)- 15

= 16-15

= 1

Answer:

1029 minutes or 17.15 hours

Step-by-step explanation:

25+0.06M=86.74

0.06M=61.74

M=61.74/0.06=1029

The mean, median, standard deviation, and interquartile range for each data set is given below.

When arranged from lowest to highest, the IQR represents the central 50% of values.

Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).

These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.

Using the statistical tool, the following were arrived at:

Using the statistical tool, the following were arrived at:

See the respective Histograms attached.

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Answer:

C.

Step-by-step explanation:

9+ 15+ 17+ 18+6+ 20+ 8+ 5+ 18+ 18+ 10+ 5+ 14+ 12+ 10+ 7=192

192/16=12

Hope this helps!

If not, I am sorry.

Using the distance formula, the length of WX is approximately: 8.5.

Distance formula is, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the endpoints:

W(5,-3) = (x1, y1)

X(-1,-9) = (x2, y2)

Plug in the values:

WX = √[(−1−5)² + (−9−(−3))²

WX = √[(−6)² + (−6)²]

WX = √72

WX ≈ 8.5

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Answer:

6 2 with the little check mark line in the midddle

Step-by-step explanation:

Answer:

step1:add 3y to both sides

step2:add 4 to both sides

step3:multiply both sides by(1/5)

14/15

Step-by-step explanation:

Answer:

h = -5

Step-by-step explanation:

1) Subtract 7th from both sides

6h = 7h + 5

6h - 7h= 7h + 5 - 7h

2) Simplify

- Combine like terms

6h - 7h = 7h + 5 - 7h

-h = 7h + 5 - 7h

- Combine like terms

-h = 7h + 5 - 7h

-h = 5

3) Divide both sides by the same factor

-h = 5

-h/-1 = 5/-1

4) Simplify

Cancel terms that are in both the numerator and denominator

h/-1 = 5/-1

h = 5/-1

Divide the numbers

h = 5/-1

h = -5

Answer:

The answer is H=-5

Step-by-step explanation:

The probability that you pull a card from a standard deck of 52 and then pull a second card without replacing the first card is 2%

The given parameters are:

Cards = 52

Face card = 12

Ace = 4

The probability of selecting a face card is:

P(Face card) = 12/52

Now, there are 51 cards.

The probability of selecting an ace is:

P(Ace) = 4/51

The required probability is:

P = 12/52 * 4/51

Evaluate

P = 0.0181

Express as percentage

P = 1.81%

Approximate

P = 2%

Hence, the probability is 2%

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Answer:

B. x = 5/2

Step-by-step explanation:

-2x+14+ 10x=34

-2x+10x=34-14

8x=20

x=20/8 =5/2

Answer:

Yes they are.

Step-by-step explanation:

By simply moving 2x from the LHS to the RHS we'll get it's equivalent to be 3x.

i.e 5x - 2x = 3x

Answer:

Step-by-step explanation:

Remark

x/(x+1) - 1/2 = -1 /(x + 1) is the equation to be solved. Add 1/(x + 1 to both sides

x/(x+1) + 1/(x+1) - 1/2 = -1/(x + 1) + 1/(x + 1)              Combine

x/(x+1) + 1/(x + 1) - 1/2 = 0                                      Combine x/(x+1) + 1/(x+1)

(x + 1)/(x + 1) - 1/2 = 0                                            Cancel (x+1)/(x+1) = 1

1 - 1/2 = 0                                                              No solution

Answer: No solution

[tex]sin60 = \frac{opp}{hyp} \\ sin60 = \frac{y}{12 } \\ \frac{ \sqrt{3} }{2} = \frac{y}{12} \\ 2y= 12 \sqrt{3} \\ y = 6 \sqrt{3} [/tex]

[tex]cos60 = \frac{adj}{hyp} \\ cos60 = \frac{x}{12} \\ \frac{1}{2} = \frac{x}{12 } \\ 2x = 12 \\ x = 6[/tex]

Hope it helps

Please give brainliest

Answer:

first multiply numbrrs3*2=6ab

Answer:

A=πr^2

Step-by-step explanation:

A=π*r^2

Where, A is area of circle

r is radius of circle

π is constant

.

Hope it's help and I think I have give brainleist answer

Answer:

πr^2

Step-by-step explanation:

it's just πr^2.

easy

Answer:

1. 4/12, 3/9, 2/6, 5/15

2. 4/8, 8/16, 6/12

3. 2/8, 4/16, 3/12

4. 6/8, 9/12, 4/16

Step-by-step explanation:

I'm assuming your question is about all 4 problems shown so I'll explain how to solve all of them.

1. The question is asking you to find an equivalent fraction to 1/3. The easiest way to do this is to reduce all of the options given.

To reduce fractions, first determine if the numerator and denominator share any factors. If they do, divide both terms by the shared factors until you no longer get whole numbers.

Step 1: reduce answer choices

6/16 = 3/8 (done by dividing both terms by 2)

4/10 = 2/5 (divide both by 2)

3/8 = 3/8 (fully reduced)

2/5 = 2/5 (fully reduced)

4/12 = 1/3 (divide both by 4)

5/10 = 1/2 (divide both by 5)

1/2 = 1/2 (fully reduced)

3/9 = 1/3 (divide both by 3)

2/6 = 1/3 (divide both by 2)

5/15 = 1/3 (divide both by 5)

3/8 = 3/8 (fully reduced)

3/4 = 3/4 (fully reduced)

2. This question is solved the same way as question 1.

Step 1: reduce answer choices

2/5 = 2/5

6/9 = 2/3

4/8 = 1/2

3/9 = 1/3

8/16 = 1/2

8/10 = 4/5

7/12 = 7/12

6/12 = 1/2

3. This question is solved the same way as questions 1 and 2.

Step 1: reduce answer choices

3/8 = 3/8

2/8 = 1/4

4/9 = 4/9

2/7 = 2/7

4/16 = 1/4

10/14 = 5/7

6/9 = 2/3

3/12 = 1/4

4. This question is solved the same way as questions 1, 2, and 3.

Step 1: reduce answer choices

6/8 = 3/4

4/9 = 4/9

4/6 = 2/3

9/12 = 3/4

10/12 = 5/6

6/9 = 2/3

12/16 = 3/4

7/9 =7/9

The x-intercept is (1, 0) and (-0.5, 0).

The correct option is (a)

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Given function is:

f(x)= [tex]-2x^{2}+x+1[/tex]

So, The graph of this equation is attaches below.

The x- intercepts of this graph

[tex]\mathrm{X\:Intercepts}:\:\left(-\frac{1}{2},\:0\right),\:\left(1,\:0\right)[/tex]

or

X intercepts: (1, 0) and (-0.5, 0)

Hence, the x-intercept is (1, 0) and (-0.5, 0).

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