A group of middle and high school students are surveyed as to their breakfast preferences. The results are shown below.
Eat Breakfast
Skip Breakfast
Middle Schooler
40
14
High Schooler
12
24
Total
52
38
What is the probability a randomly selected student eats breakfast?
What is the probability a randomly selected student is a middle schooler?
What is the probability a randomly selected student is either a high schooler OR eats breakfast?
What is the probability a randomly selected student is a high schooler AND eats breakfast?
What is the probability a randomly selected student is a high schooler, given that they eat breakfast?
What is the probability a randomly selected student eats breakfast given the student is a high schooler?
Total
54
36
90

By finding the proportional relation between x and y, we will see that when x = 16, we have y = 32.

If y varies directly with x, then we can write the relation as:

y = k*x

Where k is the constant of proportionality.

First, we know that when x = 4, we have y = 8, replacing that we get:

8 = k*4

Solving for k, we get:

k = 8/4 = 2.

Then the relation between x and y is:

y = 2*x

When x = 16, we have:

y = 2*16 = 32

Then the correct option is a.

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Answer:

a=

b=8

Step-by-step explanation:

20-5=15 (admittance fee)

15-3=12 (food and drink)

12÷1.5=8 rides because 1.50 is price for every ride

The income that's made based on the equation when 1 comb is sold is $0.5.

From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.

Therefore, the income by selling 1 comb will be:

y = 1/2

y = $0.5

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The ratio in the form of 1 :n is 1:300.

Ratio of two number A and B is the comparison of A with respect to B and when two ratios are equal they are said to be in proportion.

It is given that a ratio is

6mm : 180cm

It has to be simplified in the form of

1:n

1 cm = 10mm

therefore

180 cm = 1800 mm

6mm:180cm = 6/ 1800

= 1/300

Therefore the ratio in the form of 1 :n is 1:300.

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Answer:  p = 2 3/7

Step-by-step explanation:

7p+13 = 30

7p = 17

p = 17/7

p = 2 3/7

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

The value of p as a fraction in its simplest form is 17/7

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example:

1/2, 1/3 is a fraction.

2/4 is a fraction but we can simplify further since there is a common factor of 2 with 2 and 4.

2/4 = 1/2 is a fraction.

4/16 = 4/(4x4) = 1/4 is a fraction.

We have,

7p + 13 = 30

Solve for p.

Subtract 13 on both sides.

7p + 13 - 13 = 30 -13

7p = 17

Divide both sides by 7.

p = 17/7

We can not further simplify the fraction as there are no common factors between 17 and 7.

Thus,

The value of p as a fraction in its simplest form is 17/7

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Answer:

yes of course it was a question about the same as you can use it for a while now I am with you forever

Answer:

5/6

Step-by-step explanation:

i'm not rly confident,, but i used a calculator and solved it,,

so im sry if im wrong. Good luck!!

Answer:

$113.64

Step-by-step explanation:

0.88 x $113.636364 = 100 euros

= $113.64

(Hope this helps ^-^)

The answer is f of 5 = negative 1. The correct answer is option B

The complete graph is attached with the answer below.

Graphing functions is drawing the curve that represents the function on the coordinate plane. If a curve (graph) represents a function, then every point on the curve satisfies the function equation.

We can see in the graph that the point (5, -1) is on the f(x). Hence, the answer is f of 5 = negative 1.

Therefore answer is f of 5 = negative 1. The correct answer is option B

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Answer:

The answer is f of 5 = negative 1.

Step-by-step explanation:

Edge

[tex]\text{L.H.S}\\\\=\begin{vmatrix} 1 & bc& b+c\\ 1 & ca& c+a\\ 1 &ab&a+b\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & bc& b+c-(a+b+c)\\ 1 & ca& c+a-(a+b+c)\\ 1 &ab&a+b-(a+b+c)\end{vmatrix}~~~~~~~~~~~~~~~;c_3\rightarrow c_3 -(a+b+c)c_1\\\\\\=\begin{vmatrix} 1 & bc& -a\\ 1 & ca& -b\\ 1 &ab&-c\end{vmatrix}\\\\\\=\dfrac 1{abc}\begin{vmatrix} a & abc& -a^2\\ b & abc& -b^2\\ c &abc&-c^2\end{vmatrix}\\\\\\=-\dfrac {abc}{abc}\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\[/tex]

[tex]=-1\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\\\\\=-1 \times -1 \begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & a& a^2\\ 1 & b& b^2\\ 1 &c&c^2\end{vmatrix}\\\\\\=\text{R.H.S}\\\\\text{Showed.}[/tex]

Changing the confidence level from 95% to 90% will make the necessary sample size decrease if the margin of error stays the same.

From the question, we understand that the confidence level decreases from 95% to 90%

When the confidence level decreases, the sample size increases because the standard error increases

Hence, the statement that completes the blank is decrease

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Answer:

ehhhh probably C cuz it makes more sense

Answer:

its 150

Step-by-step explanation:

the "ten" is 5 to round it it will have to be the number to the right, which is 0 if its below 4 its changed to 0 and nothing happens to the ten

Answer:

32 sq inches

Step-by-step explanation:

Answer:

two groups

Step-by-step explanation:

you just divide the six students into two groups of two

Answer:

230??

Step-by-step explanation:

If C =270°

And b=40°

270-40= 230

Actually belive the one on top

Answer:

C

Step-by-step explanation:

The y-intercept if the graph is 2 and the slope is 2 so the rule is y=2x+2

Answer: y > -1/2x + 2

Step-by-step explanation: first, in order to find the inequalities you should find the gradient by choosing two points from the line and you should you the formula m=y2-y1/x2-x1 to find the gradient.

Next, you should find the y-intercept in order to complete the inequality it can be easily found as the y-intercept is the place where the line crosses the y axis

Then you create your equation { y = -1/2x + 2 } and then if above the line is shaded then it is {> greater than} and if below the line is shaded then it should be {< less than}

(so you should replace the equation with the lesser or greater sign according to the way the graph is shaded)

Answer:

25

Step-by-step explanation:

35 days is 5 weeks , 7 days is 1 week

Answer:

the top of the ladder is approx 8.485 meters off the ground

written explanation included

Step-by-step explanation:

I should probably write this out in one note but bear with me, please.

Assuming the ground and the wall meet at a 90° angle

therefore the angles of the triangle formed are 90°, 30°, and 60°

Answer:

[tex]\normalsize \textsf{$x = -\dfrac{8}{3}$}[/tex]

Step-by-step explanation:

Given: [tex]\normalsize \textsf{$3(2x - 9) - 4(3x + 4) = 2(x - 12) + \dfrac{7}{3}$}[/tex]

1. Distribute

For 3:

[tex]\normalsize \textsf{$3(2x - 9)$}\\\normalsize \textsf{$3(2x) + 3(- 9)$}\\\normalsize \boxed{\textsf{$6x -27$}}\\[/tex]

For -4:

[tex]\normalsize \textsf{$-4(3x + 4)$}\\\normalsize \textsf{$-4(3x) + -4(4)$}\\\normalsize \boxed{\textsf{$-12x -16$}}\\[/tex]

For 2:

[tex]\normalsize \textsf{$2(x - 12)$}\\\normalsize \textsf{$2(x) + 2(-12)$}\\\normalsize \boxed{\textsf{$2x -24$}}\\[/tex]

Now we have: [tex]\normalsize \textsf{$6x - 27 - 12x -16 = 2x-24 + \dfrac{7}{3}$}[/tex]

2. Combine like terms:

[tex]\normalsize \textsf{$-6x -43 = 2x -\dfrac{72}{3} + \dfrac{7}{3}$}\\\\\normalsize \textsf{$-6x -43 = 2x -\dfrac{65}{3}$}\\\\[/tex]

3. Subtract 2x from both sides:

[tex]\normalsize \textsf{$-6x-2x -43 = 2x -2x -\dfrac{65}{3}$}\\\\\normalsize \textsf{$-8x -43 = -\dfrac{65}{3}$}\\\\[/tex]

4. Add 43 to both sides:

[tex]\normalsize \textsf{$-8x -43 +43 = -\dfrac{65}{3} + 43$}\\\\\normalsize \textsf{$-8x = -\dfrac{65}{3} + \dfrac{129}{3}$}\\\\\normalsize \textsf{$-8x = \dfrac{64}{3}$}[/tex]

5. Divide both sides by -8

[tex]\normalsize \textsf{$-8x = \dfrac{64}{3}$}\\\\\normalsize \textsf{$-8x \div 8 = \dfrac{64}{3} \div -\dfrac{8}{1}$}\\\\\normalsize \boxed{\textsf{$x = -\dfrac{8}{3}$}}[/tex]

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Formulate

Based on the given conditions, formulate:

78 - (-14)

Calculate

78 - (-14)

Determine the sign

78 +14

Calculate

92

SO THE ANSWER IS 92

Answer:

3/2,6

Step-by-step explanation:

Answer:

answer is 6/4 because 18/6=3,12/4=3 so,

Answer:

Part A)

[tex]\displaystyle z_6 = 9609600000x^{10}[/tex]

Part B)

[tex]z_4 = 10500 x^9[/tex]

Step-by-step explanation:

Recall the binomial expansion theorem:

[tex]\displaystyle (x+y)^n = \sum_{k=0}^{n}{n \choose k} x^{n-k} y^k[/tex]

Part A)

Our expression is equivalent to:

[tex]\displaystyle (2x+5)^{15} = \sum_{k = 0}^{15} {15 \choose k} (2x)^{15-k}\cdot 5^k[/tex]

To find the sixth term, let k  = 5. Therefore, the sixth term is:

[tex]\displaystyle \begin{aligned} z_6 &= {15\choose 5} (2x)^{15-5}\cdot 5^5 \\ \\ & = {15\choose 5}x^{10} \cdot (2)^{10}\cdot 5^5 \\ \\ &= 9609600000x^{10}\end{aligned}[/tex]

Part B)

Likewise:

[tex]\displaystyle \begin{aligned} \left(x^2 + \frac{5}{x}\right)^9 = \sum_{k=0}^9 {9\choose k}(x^2)^{9-k}\left(\frac{5}{x}\right)^{k}\end{aligned}[/tex]

To find the fourth term, let k = 3. Therefore, the fourth term is:

[tex]\displaystyle \begin{aligned} z_4 & = {9\choose 3}\left(x^2\right)^{9-3} \left(\frac{5}{x}\right)^{3} \\ \\ & = {9\choose 3}x^{12} \cdot \frac{5^3}{x^3} \\ \\ & = 10500x^9\end{aligned}[/tex]

Answer:

Karen expects the vehicle to depreciate by 600 each year.

Step-by-step explanation:

Given:

- initial value: 4400

- salvage value: 800

- another six years

It is expected to depreciate from 4400 to 800 in 6 years.

The depreciation per year is the ratio

depreciation per year = (total depreciation) / (number of years)

Total depreciation is the change in value, so the depreciation per year is

 (4400 - 800)/6 = 600

The sample space S =  {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}

It is defined as the space in which all possible outcomes are represented in a list form for a particular event.

We have:

A number cube with faces labeled from 1 to 6 will be rolled once.

Let S is the sample space:

As we know, the sample space is the set of all possible outcomes:

S = {1, 2, 3, 4, 5, 6}

The total number of outcomes:

n(S) = 6

The outcomes for the event of rolling the number 2.

E = {2}

n(E) = 1

Thus, the sample space S =  {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}

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The length of major arc ACD in the circle with center D is given as (325/36)π feet

An equation is an expression that shows the relationship between two or more numbers and variables.

The length of major arc ACD = [(360 - 35) / 360) * 2π(10/2) = (325/36)π feet

The length of major arc ACD in the circle with center D is given as (325/36)π feet

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