smplify the following algebraic expression: 6(2y + 8) - 2(3y - 2)

Answer:

Step-by-step explanation:

The system of equations (a) is the correct one for this situation.  We must now solve this system for x and y, which are the unit costs.

Multiplying the 2nd equation by (-3/2) yields -12x - 18y = -168.

Now eliminate x by combining the two equations

12x + 5 y = 116

-12x  -18y  = - 168

-------------------------

         -13y = -52, or y = 4.

If y = 4 then 12x + 5y = 116, or

                    12x  +5(4) = 116, or

                     12x  +  20  =  116, or

                      12x       = 96, or x = 8

Roller pens are $8/dozen and ball point pens are $4 per dozen.

I think it’s A:

Cause it is what it is

Answer:

They arrive on Monday, December 13th

Step-by-step explanation:

First, we know that this family must drive a total of 2,142 miles.

They average 50 miles per hour and drive 6 hours each day, thus we can see that they drive (50)(6)=300 miles per day.

Now, to know how many days it will take them to drive the total of 2,142 miles we are going to divide the total amount of miles between the number of miles driven per day:

2,142÷300= 7.14

Thus, it takes them 7.14 days to drive 2,142 miles.

If we round this (since the number is greater than 7 this would mean it takes them more than 7 days and they would stop at 7 for the day) to the next digit, we would have that it will take them 8 days to get to San Francisco.

Thus, since they start on December 6th (day 1), December 7th would be day 2 and following this pattern we would have that the eighth day would be December 13th.

Now, since the days repeat every 7 days and we now that December 6th was monday, we would have that the day they arrive to San Francisco (December 13th) is monday too.

Answer:

x=0, y=2

Step-by-step explanation:

3x+4y=8

x+2y=4

Multiply the second equation by 2:

2x+4y=8

Subract it from the first equation:

x=0

y=2

Hope this helps!

Answer:

You usually wouldn't divide lengths

Step-by-step explanation:

Answer:

[tex]X \sim N(99,4)[/tex]  

Where [tex]\mu=99[/tex] and [tex]\sigma=4[/tex]

We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:

[tex] X = \mu -3\sigma[/tex]

And replacing we got:

[tex] X = 99 -3*4 = 87[/tex]

So then the Annie's score would be 87

Step-by-step explanation:

Let X the random variable that represent the test scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(99,4)[/tex]  

Where [tex]\mu=99[/tex] and [tex]\sigma=4[/tex]

We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:

[tex] X = \mu -3\sigma[/tex]

And replacing we got:

[tex] X = 99 -3*4 = 87[/tex]

So then the Annie's score would be 87

Answer: 87

Step-by-step explanation:

We can work backwards using the z-score formula to find the x-value. The problem gives us the values for z, μ and σ. So, let's substitute these numbers back into the formula:

z−3−1287=x−μσ=x−994=x−99=x

We can think of this conceptually as well. We know that the z-score is −3, which tells us that x is three standard deviations to the left of the mean, 99. So we can think of the distance between 99 and the x-value as (3)(4)=12. So Annie's score is 99−12=87.

Answer:

a=12

Step-by-step explanation:

if a=6b

and b=2

a=2×6

a=12

Answer:

A. $130.50

B. 150%

C. 50%

Step-by-step explanation:

First, find 50% of 87 and add it to find the new price.

87 x 0.5 = 43.5

87 + 43.5 = 130.5

Then, find the percent by doing 130.5 ÷ 87, which is 150%

Calculate the percent increase by doing (130.5-87) ÷ 87, which is 50%

Answer:

see below

Step-by-step explanation:

First find the markup

87* 50%

87*.50

43.50

Add this to the wholesale price

87+43.50 =130.50

This is what they charge the customer

This is 150% percent of the wholesale price

100% + 50% = 150%

To find the percent increase

Take the new price and subtract the wholesale price

Then divide by the wholesale price

(130.50-87)/87 =50 % increase

Answer:

  -6 only

Step-by-step explanation:

f(0) is the value of y when x=0. This is the graph of a 4th-degree polynomial, so is a function. There is only one y-value for x=0. That is where the graph crosses the y-axis, at y = -6.

  f(0) = -6 . . . . only

Answer:

The answer is option 2.

Step-by-step explanation:

Given that the formula for length of arc is :

[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]

Answer:

B

Step-by-step explanation:

It could also be

[tex] \frac{\pi \times r \times m}{180} [/tex]

Answer:

9 quarters, 12 nickels, and 15 dimes.

Step-by-step explanation:

Let's start by naming the number of quarters x.

That means that the number of nickels is x+3.

(There are three fewer quarters than nickels)

The number of dimes would be x+6.

(There are six more dimes than quarters)

We know the total number of coins is 36.

We can set up an equation.

quarters+nickels+dimes=36

x+x+3+x+6=36

Combine like terms.

3x+9=36

Subtract 9 from both sides.

3x=27

Divide both sides by 3.

x=9

There are 9 quarters.

Use given info to find the number of other coins.

9+3=12

There are 12 nickels.

9+6=15

There are 15 dimes.

Answer:

90

Step-by-step explanation:

14×7=98

188-98=90 so she had 90 left

Answer:

90

Step-by-step explanation:

14×7=98

188-98=90 so she had 90 left

Answer:

a) 0.206 = 20.6% probability that 2 or fewer will withdraw.

b) 0.2182 = 21.82% probability that exactly 4 will withdraw.

c) 0.5886 = 58.86% probability that more than 3 will withdraw.

d) The expected number of withdrawals is 4.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they withdraw without completing the introductory statistics course, or they do not. Each student is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

20% of its students withdraw without completing the introductory statistics course.

This means that [tex]p = 0.2[/tex]

Assume that 20 students registered for the course.

This means that [tex]n = 20[/tex]

(a) Compute the probability that 2 or fewer will withdraw.

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115[/tex]

[tex]P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576[/tex]

[tex]P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0115 + 0.0576 + 0.1369 = 0.206[/tex]

0.206 = 20.6% probability that 2 or fewer will withdraw.

(b) Compute the probability that exactly 4 will withdraw.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{20,4}.(0.2)^{4}.(0.8)^{16} = 0.2182[/tex]

0.2182 = 21.82% probability that exactly 4 will withdraw.

(c) Compute the probability that more than 3 will withdraw.

Either less than 3 withdraw, or more than 3 withdraw. The sum of the probabilities of these events is 1. So

[tex]P(X \leq 3) + P(X > 3) = 1[/tex]

We want P(X > 3). So

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115[/tex]

[tex]P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576[/tex]

[tex]P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369[/tex]

[tex]P(X = 3) = C_{20,3}.(0.2)^{3}.(0.8)^{17} = 0.2054[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0115 + 0.0576 + 0.1369 + 0.2054 = 0.4114[/tex]

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.4114 = 0.5886[/tex]

0.5886 = 58.86% probability that more than 3 will withdraw.

(d) Compute the expected number of withdrawals.

The expected value of the binomial distribution is:

E(X) = np

In this question:

E(X) = 20*0.2 = 4

The expected number of withdrawals is 4.

Answer:

Step-by-step explanation:

Since the roof has 4 identical faces and each face is a triangle, we would determine the area of each face of the triangle by applying the formula,

Area of triangle = 1/2 × base × height

Area of each triangular face = 1/2 × 7.6 × 4.8 = 18.24m²

Area of the 4 faces = 4 × 18.24 = 72.96 m²

Since 1 pack of tiles covers 13.8 m², the number of packs needed to cover 72.96 m² is

72.96/13.8 = 5.29 packs

Since samir can only buy whole packs of these tiles, the number of packs of tiles that he needs to buy would be 6.

If 1 pack costs £716.1, then the total cost of the tiles needed for the 4 faces of this roof is

6 × 716.1 = £4296.6

Answer:

YT AND RQ

Step-by-step explanation:

The first step is to multiply both sides by h^2. Afterwards, divide both sides by 660 to fully isolate w.

c = 660w/(h^2)

ch^2 = 660w

660w = ch^2

w = (ch^2)/660 is the answer

Answer:

a) The probability that exactly 17 of them enroll in college is 0.116.

b) The probability that more than 14 enroll in college is 0.995.

c) The probability that fewer than 11 enroll in college is 0.001.

d) It would be be unusual if more than 24 of them enroll in college since the probability is 0.009.

Step-by-step explanation:

We can model this with a binomial distribution, with n=29 and p=0.65.

The probability that k students from the sample who graduated from high school in 2012 enrolled in college is:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{29}{k} 0.65^{k} 0.35^{29-k}\\\\\\[/tex]

a) The probability that exactly 17 of them enroll in college is:

[tex]P(x=17) = \dbinom{29}{17} p^{17}(1-p)^{12}=51895935*0.0007*0=0.116\\\\\\[/tex]

b) The probability that more than 14 of them enroll in college is:

[tex]P(X>14)=\sum_{15}^{29} P(X=k_i)=1-\sum_{0}^{14} P(X=k_i)\\\\\\P(x=0)=0\\\\P(x=1)=0\\\\P(x=2)=0\\\\P(x=3)=0\\\\P(x=4)=0\\\\P(x=5)=0\\\\P(x=6)=0\\\\P(x=7)=0\\\\P(x=8)=0\\\\P(x=9)=0\\\\P(x=10)=0.001\\\\P(x=11)=0.002\\\\P(x=12)=0.005\\\\P(x=13)=0.013\\\\P(x=14)=0.027\\\\\\P(X>14)=1-0.005=0.995[/tex]

c) Using the probabilities calculated in the point b, we  have:

[tex]P(X<11)=\sum_0^{10}P(X=k_i)\approx0.001[/tex]

d) The probabilities that more than 24 enroll in college is:

[tex]P(X>24)=\sum_{25}^{29}P(X=k_i)\\\\\\ P(x=25) = \dbinom{29}{25} p^{25}(1-p)^{4}=23751*0*0.015=0.007\\\\\\P(x=26) = \dbinom{29}{26} p^{26}(1-p)^{3}=3654*0*0.043=0.002\\\\\\P(x=27) = \dbinom{29}{27} p^{27}(1-p)^{2}=406*0*0.123=0\\\\\\P(x=28) = \dbinom{29}{28} p^{28}(1-p)^{1}=29*0*0.35=0\\\\\\P(x=29) = \dbinom{29}{29} p^{29}(1-p)^{0}=1*0*1=0\\\\\\\\P(X>24)=0.007+0.002+0+0+0=0.009[/tex]

Answer:

415people

Step-by-step explanation:

20%of250=100people

15%of the 100people=15people

So 100 went out remaining(500-100)400

Then 15 returned=400+15

415

Answer:

458 people in the building now.

Step-by-step explanation:

20%x500/2 = 20% x 250=50

15% x 50 = 7.5

7.5 + (500 - 50) =457.5 =458people.

Tell me if it's correct plz.

Hope this helps..

Answer:

Irene had $3744 at first.

Step-by-step explanation:

Let Angie and Irene had the money initially = $a

At a shopping mall Angie spent money = $2595

Money left with Angie = $(a - 2595)

Similarly, Irene spent the money = $297

Money left with Irene = $(a - 297)

Money left with Irene was thrice as much as Angie,

(a - 297) = 3(a - 2595)

a - 297 = 3a - 7785

3a - a = 7785 - 297

2a = 7488

a = [tex]\frac{7488}{2}[/tex]

a = $3744

Therefore, Irene had $3744 at first.

Answer:

$3746

Step-by-step explanation:

A=2595. I=2595

(x-293)=(x-2595)

X-293=3x-7785

-293+7785=2x

7492/2=x

 So. x=3746

Answer:

x = 4

Step-by-step explanation:

Given 2 intersecting chords, then

The product of the parts of one chord is equal to the product of the parts of the other chord, that is

4x = 2 × 8 = 16 ( divide both sides by 4 )

x = 4

Answer:

4.65% probability that a randomly selected customer takes more than 10 minutes

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 7.45, \sigma = 1.52[/tex]

Probability that a customer takes more than 10 minutes:

This is 1 subtracted by the pvalue of Z when X = 10. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 7.45}{1.52}[/tex]

[tex]Z = 1.68[/tex]

[tex]Z = 1.68[/tex] has a pvalue of 0.9535

1 - 0.9535 = 0.0465

4.65% probability that a randomly selected customer takes more than 10 minutes

Answer:

C. y=36(1.2)t

Step-by-step explanation:

The number of members in the Club in t years after 2001 is given by an equation in the following format:

[tex]y = y(0)(1+r)^{t}[/tex]

In which y(0) is the number of members in 2001 and r is the growth rate, as a decimal.

The number of members in the Triathlon Club was 36 in 2001 and has increased by 20% each year.

This means that [tex]y(0) = 36, r = 0.2[/tex]

So

[tex]y = y(0)(1+r)^{t}[/tex]

[tex]y = 36(1+0.2)^{t}[/tex]

[tex]y = 36(1.2)^{t}[/tex]

The correct answer is C.

Start by subtracting 10 from both sides.

This gives us 4x - 32 = -20.

Now add 32 to both sides to get 4x = 12.

Now divide both sides by 3 to get x = 3.

Answer: The missing value from the data set is 4.

Step-by-step explanation: Let's put it from least to greatest to figure it out...

2, 2, (4, 4,) 5, 8,

It would have to be 4, because 8 divided by 2 will equal 4. And because there's an even amount of numbers we have to add two numbers then divide it by 2.

4 + 4 = 8

8 ÷ 2 = 4

The mean is 4, and the missing value from the data set is 4.

I hope this helps!

Answer:

6.25

Step-by-step explanation:

f(x)=x^2

f(2.5) = (2.5)^2

        =6.25

Answer: 6.25

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(2.5).

We find f(2.5) by plugging 2.5 in for x

everywhere that x appears in the function.

So we have f(2.5) = (2.5)².

(2.5)² is 6.25.

So our answer is 6.25.

Answer:

1/8

Step-by-step explanation:

there are 8 pieces therefore the numerator would be 1 and the denominator 8.

Answer:

2/3

Step-by-step explanation:

5/12+1/4

Make the fractions have the same denominator.

5/12 + 1×3/4×3

5/12 + 3/12

Add the fractions.

(5+3)/12

8/12

Simplify.

2/3

Answer:

[tex] = \frac{2}{3} \\ [/tex]

Step-by-step explanation:

[tex] \frac{5}{12} + \frac{1}{4} \\ \frac{5 + 1 \times 3}{12} \\ \frac{5 + 3}{12} \\ = \frac{8}{12} \\ = \frac{2}{3} [/tex]

Answer:

5

Step-by-step explanation:

Answer:

the answer is-

Step-by-step explanation:

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

HOPE IT HELPS!!!

Answer:

option D is correct, 4 ounces.

Step-by-step explanation:

In this case we have a random sample of 121 cologne bottles that showed an average content of 4 ounces.

The point estimate of the mean content of the bottles is average value.

What 4 ounces means is the correct answer since this is the mean, therefore the option D is correct

Given:

Four different positive intergers as a product of 110

To find:

The sumnof the four numbers whose product is 110

Solution:

1) To find the number we have to find the prime factorization of the given number 110

2) Prime factorization of 110 is

110 = 1×2 × 5 = 11

3) So the four numbers whose product is 110 are 1,2,5 and 11

4) The sum of number's are

1+2+5+11=19

Answer:

Option 1.

Step-by-step explanation:

y = x + 2

Put x as 1, 2 and 3 to find y.

y = (1) + 2

y = 3

y = (2) + 2

y = 4

y = (3) + 2

y = 5

When x = 1, y = 3.

When x = 2, y = 4.

When x = 3, y =5.

The values that represent the function is the first table.