factorise fully 24x+16

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: 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:

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:

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:

51.38% probability that they requested regular gas

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question, we have that:

Event A: Not filling the tank

Event B: Regular gas

40% of the customers request regular gas

This means that [tex]P(B) = 0.4[/tex]

Of those customers requesting regular gas, 70% only fill up part of their tank.

This means that [tex]P(A|B) = 0.7[/tex]

Probability of not filling the tank:

70% of 40%(regular gas)

100 - 60 = 40% of 35%(unleaded gas).

100 - 50 = 50% of 25%(premium gas).

So

[tex]P(A) = 0.7*0.4 + 0.4*0.35 + 0.5*0.25 = 0.545[/tex]

What is the probability that they requested regular gas?

[tex]P(B|A) = \frac{0.4*0.7}{0.545}[/tex] = 0.5138

51.38% probability that they requested regular gas

Answer: A ≈ 3.25 in squared

Step-by-step explanation:

So we can work backward using the perimeter of a circle formula to find the radius.

Perimeter of a whole circle: C = 2* 3.14 * r

Since we are only given a quarter of the perimeter we need to multiply the 3.57 by 4 to find C.

C = 14.28

Now we can solve for r using algebra.

[tex]14.28 = 2 *3.14*r[/tex]

Multiply 2 and 3.14

[tex]14.28 = 6.28*r[/tex]

Isolate r through division.

[tex]2.2739 =r\\[/tex]

Now that we have the radius of the circle we can plug that into the area of a circle.

Formula: [tex]A = 3.14* r^2[/tex]

Plug in and solve.

[tex]A = 3.14 * 2.2738^2[/tex]

A = 16.2355 in squared

This however is the area of the whole circle it is just looking for a quarter.

So we can divide the area of the whole circle by 4 to find the final answer.

16.2355 / 4 = 3.2471

Now round to the nearest hundreds which is the second number after the decimal.

A ≈ 3.25

Answer:

15.87% probability that 48 or more from this sample were insured by the FHA

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]p = 0.28, n = 150[/tex]

So

[tex]\mu = E(X) = np = 150*0.28 = 42[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.28*0.72} = 5.5[/tex]

What is the probability that 48 or more from this sample were insured by the FHA?

Using continuity correction, this is [tex]P(X \geq 48 - 0.5) = P(X \geq 47.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 47.5. So

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

[tex]Z = \frac{47.5 - 42}{5.5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413.

1 - 0.8413 = 0.1587

15.87% probability that 48 or more from this sample were insured by the FHA

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:

Step-by-step explanation:

Proportion of retired people under the age of 65 would return to work on a full-time basis if a suitable job were available = 60/100 = 0.6 = P

Null hypothesis: P ≤ 0.6

Alternative: P > 0.6

First, to calculate the hypothesis test, lets workout the standard deviation

SD =  √[ P x ( 1 - P ) / n ]

where P = 0.6, 1 - P = 0.4, n = 500

SD = √[ (0.6 x 0.4) / 500]

SD = √ (0.24 / 500)

SD = √0.00048

SD = 0.022

To calculate for the test statistic, we have:

z = (p - P) / σ where p = 315/500 = 0.63, P = 0.6, σ = 0.022

z = (0.63 - 0.6) / 0.022

z = 0.03/0.022

z = 1.36

At the 2% level of significance, the p value is less than 98% confidence level, thus we reject the null hypothesis  and conclude that more than 60% would return to work.

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:

a=12

Step-by-step explanation:

if a=6b

and b=2

a=2×6

a=12

Answer:

The correct answer will be:

[tex]-\dfrac{62}{23}[/tex]

Step-by-step explanation:

It is given that :

Initial temperature, [tex]T_1 = 0^\circ F[/tex]

Final temperature,

[tex]T_2 = -15\dfrac{1}{2}^\circ F\\\Rightarrow T_2 = -\dfrac{15\times 2+1}{2} ^\circ F\\\Rightarrow T_2 = -\dfrac{31}{2} ^\circ F[/tex]

Time taken :

[tex]5\dfrac{3}{4}\ hrs = \dfrac{5 \times 4+3}{4}\ hrs = \dfrac{23}{4}\ hrs[/tex]

Change in temperature per hour:

[tex]\dfrac{\text{Difference of temperature}}{\text{Total Time Taken}}\\\Rightarrow \dfrac{T_2-T_1}{\text{Total Time Taken}}[/tex]

Putting the values of temperatures and time:

[tex]\dfrac{\dfrac{-31}{2}-0}{\dfrac{23}{4}}\\\Rightarrow \dfrac{\dfrac{-31}{2}}{\dfrac{23}{4}}\\\Rightarrow \dfrac{-31 \times 4}{2 \times 23}} \text{---- Error done by Wen at this step}\\\Rightarrow \dfrac{-31 \times 2}{23}}\\\Rightarrow \dfrac{-62}{23}}[/tex]

The error done by Wen was during calculating the values of fraction.

So, the correct answer is :[tex]\frac{-62}{23}}[/tex] instead of [tex]\frac{-713}{8}[/tex]

Answer:

C. Wen did not take the reciprocal of the divisor

Step-by-step explanation:

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

Answer:

none of the above

Step-by-step explanation:

Take the absolute value of the second point and subtract the first point

| 1/3 -( -4/3)|

Since this answer does not match any of the above choices

Answer:

None of the above.

Step-by-step explanation:

The distance between -4/3 and 1/3 is

|1/3-(-4/3)| =|1/3 + 4/3|

This is not in the option so;

None of the above.

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:

she will purchase 8 pounds of potatoes.

But if she had on $3.0

She will purchase only two pounds

Step-by-step explanation:

first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30.

1.5+1.14+1.05+0.30=$ 3.99

6-3.99= 2.01

If the rest cost 0.5

Then there are 4 pounds of 0.5 in 2.01.

So total she will purchase 8 pounds of potatoes.

But if she had on $3.0

She will purchase only two pounds, as it will only purchase1.5+1.14+= 2.64 worth of potatoes.

With $6 Janice can get a total of 10.7 pounds, but with $3  she will be able to afford the first two pounds only

Given Data

Amount at hand = $6

First Pound cost = $1.50

Second Pound cost = $1.14

Third Pound cost = $1.05

Total = 1.5+1.14+1.05 =  3.69

Balance  = 6-3.69 = $2.31

Hence the number of pound we can get with $2.31 for subsequent purchase will be

= 2.31/0.3

= 7.7 pounds

This means that the total number of pounds will be

= 3+7.7

=10.7pounds

subsequent Pound cost = $0.3

Learn more about algebra here:

https://brainly.com/question/6143254

Answer:

Step-by-step explanation:

This is a ratio problem. there are 20 Blonde Teachers, and 12 brown haired teachers. The fraction is 12/20. We can simplify this fraction to 3/5. for every 3 brown haired Teacher, there is 5 other blonde hair teachers.

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:

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.

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:

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.

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: choice B

Step-by-step explanation:

Events A and B are independent if the equation P(B)=P(B|A) or P(A∩B) = P(A) · P(B) holds true.

in this example

p(A)=1/6    {5}

p(B)=1/2   {1,3,5}

P(B|A)=1

so

P(B)≠P(B|A)

=>A and B are dependent

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:

y = -4x + (any number)

Step-by-step explanation:

you want to use the negative reciprocal of the slope for line f

so m = -4, since you didn't say any points it has to go through then the

equation of the line is y = -4x + (any number)

Answer:

-4× - 4 That is the answer

Answer:

$204

Step-by-step explanation:

First, you have to find the price without VAT. To calculate it you have to divide the price including VAT by one plus the rate:

Price including VAT= $240

VAT= 14%

240/(1+0.14)= 240/1.14= 210.52

Now, you have to calculate the 15% of 210.52 and subtract that amount from the price:

210.52*0.15=31.57

210.52-31.57=178.95

Then, you have to calculate the 14% VAT by multiplying the price for 1 plus the rate:

178.95*(1+0.14)= 178.95*1.14= 204

According to this, the reduced price of the shoes including VAT is $204.

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:

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:

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:

The number of dimes is 3n - 8

Step-by-step explanation:

Here, we are interested in writing an expression for the number of dimes.

We proceed as follows;

Now, there are n nickels with the number of dimes been 8 less than 3 times the number of nickels

That would be;

3(n) -8 = 3n -8