g(x)4x^2-16x+7 completing the square

Answer:

Step-by-step explanation:

line equation:  y=mx + C

substitute given values

-7 = -3*0 + C

C=y= -7      ANS

Answer:

  65°

Step-by-step explanation:

Short arc AC is the difference between 360° and long arc ABC:

  arc AC = 360° -230° = 130°

The inscribed angle ABC that intercepts this short arc will have half the measure of the arc:

  ∠ABC = 130°/2 = 65°

Answer:

a) Q1= 144.10

Median = 150

Q3=155.90

b) The 99 percentile would be:[tex]a=150 +2.33*8.75=170.39[/tex]

And represent a value who accumulate 99% of the values below

Step-by-step explanation:

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

[tex]X \sim N(150,8.75)[/tex]  

Where [tex]\mu=150[/tex] and [tex]\sigma=8.75[/tex]

Part a

Lets begin with the first quartile:

[tex]P(X>a)=0.75[/tex]   (a)

[tex]P(X<a)=0.25[/tex]   (b)

We can find the quantile in the normal standard distribution and we got z=-0.674.

And we can apply the z score formula and we got:

[tex]z=-0.674<\frac{a-150}{8.75}[/tex]

And if we solve for a we got

[tex]a=150 -0.674*8.75=144.10[/tex]

The median for this case is the mean [tex]Median =150[/tex]

For the third quartile we find the quantile who accumulate 0.75 of the area below and we got z=0.674 and we got:

[tex]a=150 +0.674*8.75=155.90[/tex]

Part b

We can find the quantile in the normal standard distribution who accumulate 0.99 of the area below and we got z=2.33.

And we can apply the z score formula and we got:

[tex]z=2.33<\frac{a-150}{8.75}[/tex]

And if we solve for a we got

[tex]a=150 +2.33*8.75=170.39[/tex]

And represent a value who accumulate 99% of the values below

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean GPA of night students and μ2 be the mean GPA of day students.

The random variable is μ1 - μ2 = difference in the mean GPA of night students and the mean GPA of day students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 2.35

μ2 = 2.58

s1 = 0.46

s2 = 0.47

n1 = 30

n2 = 25

t = (2.35 - 2.58)/√(0.46²/30 + 0.47²/25)

t = - 1.8246

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.46²/30 + 0.47²/25]²/[(1/30 - 1)(0.46²/30)² + (1/25 - 1)(0.47²/25)²] = 0.00025247091/0.00000496862

df = 51

We would determine the probability value from the t test calculator. It becomes

p value = 0.0746

Since alpha, 0.05 < than the p value, 0.0746, then we would fail to reject the null hypothesis.

Answer:

4 ( a+2)

Step-by-step explanation:

The average rate of change is

(f(a) - f(2))/(a-2)

f(a) = 4a^2 -8

f(2) = 4*2^2 -8 = 4*4 -8 = 16-8 = 8

(4a^2 - 8  - 8))/(a-2)

(4a^2 -16) / (a-2)

Factor the numerator

4( a^2 -4) / (a-2)

4( a-2)(a+2) / (a-2)

Cancel

4 ( a+2)

Answer:

8/3

Step-by-step explanation:

6(x-2)=4

x-2=4/6

x= 8/3

Answer:

x = 8/3

Step-by-step explanation:

Use Distributive Property

6(x-2) = 4

6x -12 = 4

add 12 on both sides

6x = 16

Divide by 6

x = 8/3

In decimal form: 2.667

Answer:

1/4 probability of getting a product that isn't divisible by 2.

Step-by-step explanation:

These are all the possible outcomes

1 x 1 = 1    2 x 1 = 2    3 x 1 = 3     4 x 1 = 4     5 x 1 = 5      6 x 1 = 6

1 x 2 = 2   2 x 2 = 4   3 x 2 = 6     4 x 2 = 8    5 x 2 = 10    6 x 2 = 12

1 x 3 = 3  2 x 3 = 6    3 x 3 = 9     4 x 3 = 12   5 x 3 = 15   6 x 3 = 18

1 x 4 = 4   2 x 4 = 8   3 x 4 = 12     4 x 4 = 16   5 x 4 = 20  6 x 4 = 24

1 x 5 = 5   2 x 5 = 10  3 x 5 = 15   4 x 5 = 20  5 x 5 = 25  6 x 5 = 30

1 x 6 =  6   2 x 6 = 12  3 x 6 = 18   4 x 6 = 24   5 x 6 = 30  6 x 6 = 36

All of the outcomes that aren't divisible by 2 are in bold

There are 9 out of 36 possible outcomes that aren't divisible by 2

9/36 = 1/4

The first differences are 8, 14, 20.

The second differences are 6.

Half of 6 is 3, so the first term of the sequence is 3n^2.

If you subtract 3n^2 from the sequence you get 0,-1,-2,-3 which has the nth term of -n + 1.

Therefore your final answer will be 3n^2 - n + 1

Answer:

Step-by-step explanation:

George Fox university = 10,000,000 + 10,000,000

                                    = full bag + full bag

                                    ( click 2 full bag}

Rockhurst university = 10,000,000 +10,000,000 +10,000,000 + 5,000,000

                                  = full bag + full bag + full bag + half bag

       (click 3 full bag and 1 half bag}

Lebanon Valley college = 10,000,000 +10,000,000 +10,000,000 +10,000,000+5,000,000

( click 4 full bag and 1 half bag)

Grand view college = 10,000,000

 (click 1 full bag}

[tex]\displaystyle\bf\\AB=\sqrt{\Big(-6-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AB=\sqrt{\Big(-6+2\Big)^2+\Big(4+7\Big)^2}\\\\AB=\sqrt{\Big(-4\Big)^2+\Big(11\Big)^2}\\\\AB=\sqrt{16+121}\\\\\boxed{\bf AB=\sqrt{137}}[/tex]

.

[tex]\displaystyle\bf\\BC=\sqrt{\Big(-2-(-6)\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(-2+6\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(4\Big)^2+\Big(3\Big)^2}\\\\BC=\sqrt{16+9}\\\\BC=\sqrt{25}\\\\\boxed{\bf BC=5}[/tex]

.

[tex]\displaystyle\bf\\CD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(2+2\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(4\Big)^2+\Big(-3\Big)^2}\\\\CD=\sqrt{16+9}\\\\CD=\sqrt{25}\\\\\boxed{\bf CD=5}[/tex]

.

[tex]\displaystyle\bf\\AD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AD=\sqrt{\Big(2+2\Big)^2+\Big(4+7\Big)^2}\\\\AD=\sqrt{\Big(4\Big)^2+\Big(11\Big)^2}\\\\AD=\sqrt{16+121}\\\\\boxed{\bf AD=\sqrt{137}}[/tex]

.

[tex]\displaystyle\bf\\P=AB+BC+CD+AD=\sqrt{137}+5+5+\sqrt{137}\\\\\boxed{\bf P=10+2\sqrt{137}}[/tex]

Answer:

The equations are linearly independent so there is no parametric vector form

Step-by-step explanation:

I attached the solution.

Answer:

Part a

Null hypothesis: [tex] \mu = 69.3[/tex]

Alternative hypothesis: [tex]\mu \neq 69.3[/tex]

Part b

[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] \bar X = 69.8[/tex] the sample mean

[tex] n= 140[/tex] represent the sample size

[tex] s = 11.2[/tex] represent the standard deviation

Part a

And we want to test if the true mean is equal to 69.3 so then the system of hypothesis:

Null hypothesis: [tex] \mu = 69.3[/tex]

Alternative hypothesis: [tex]\mu \neq 69.3[/tex]

Part b: Find the statistic

The statistic is given by:

[tex] z= \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing the info we got:

[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]

Answer:

(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Step-by-step explanation:

The  cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:

[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]

(a)

Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:

[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]

The probability is:

[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]

                  [tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b)

The probability density function of X is:

[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]

Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:

[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]

                  [tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Answer:

The probability that exactly eight of them take more than 93.6 minutes is 5.6015 [tex]\times 10^{-6}[/tex] .

Step-by-step explanation:

We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.

A random sample of twelve service calls is taken.

So, firstly we will find the probability that service calls take more than 93.6 minutes.

Let X = times for service calls.

So, X ~ Normal([tex]\mu=75,\sigma^{2} =15^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                              Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean time = 75 minutes

           [tex]\sigma[/tex] = standard deviation = 15 minutes

Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)

       P(X > 93.6 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{93.6-75}{15}[/tex] ) = P(Z > 1.24) = 1 - P(Z [tex]\leq[/tex] 1.24)

                                                                = 1 - 0.8925 = 0.1075

The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.

Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;

[tex]P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........[/tex]

where, n = number of trials (samples) taken = 12 service calls

            r = number of success = exactly 8

            p = probability of success which in our question is probability that

                   it takes more than 93.6 minutes, i.e. p = 0.1075.

Let Y = Number of service calls which takes more than 93.6 minutes

So, Y ~ Binom(n = 12, p = 0.1075)

Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)

               P(Y = 8)  =  [tex]\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}[/tex]

                             =  [tex]495 \times 0.1075^{8} \times 0.8925^{4}[/tex]

                             =  5.6015 [tex]\times 10^{-6}[/tex] .

Answer:

The company will expect to replace 13.03% of batteries.

The company should guarantee the batteries for 35 months.

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 45, \sigma = 8[/tex]

If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. So

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

[tex]Z = \frac{36 - 45}{8}[/tex]

[tex]Z = -1.125[/tex]

[tex]Z = -1.125[/tex] has a pvalue of 0.1303.

The company will expect to replace 13.03% of batteries.

If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries

They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

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

[tex]-1.28 = \frac{X - 45}{8}[/tex]

[tex]X - 45 = -1.28*8[/tex]

[tex]X = 34.76[/tex]

Rounding to the nearest month

The company should guarantee the batteries for 35 months.

Answer:

A 16 inches diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let r be the radius and [tex]\theta[/tex] be the angle of a circle.

According with the graph, the area of the sector is given by

[tex]A=\frac{1}{2}r^2\theta[/tex]

The arc length of a circle with radius r  and angle  [tex]\theta[/tex] is r [tex]\theta[/tex]

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.

Thus the perimeter has length

[tex]2r+r\theta=32 \:in[/tex]

We need to express the area as a function of one variable, to do this we use the above equation and we solve for [tex]\theta[/tex]

[tex]2r+r\theta=32\\\\r\theta=32-2r\\\\\theta=\frac{32-2r}{r}[/tex]

Next, we substitute this equation into the area equation

[tex]A=\frac{1}{2}r^2(\frac{32-2r}{r})\\\\A=\frac{1}{2}r(32-2r)\\\\A=16r-r^2[/tex]

The domain of the area is

[tex]0<r<12[/tex]

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

[tex]\frac{d}{dr} A=\frac{d}{dr}(16r-r^2)\\\\A'(r)=\frac{d}{dr}(16r)-\frac{d}{dr}(r^2)\\\\A'(r)=16-2r16-2r=0\\\\-2r=-16\\\\\frac{-2r}{-2}=\frac{-16}{-2}\\\\r=8[/tex]

To check if r=8 is a maximum we use the Second Derivative test

if [tex]f'(c)=0[/tex] and [tex]f''(c)<0[/tex] , then f(x) has a local maximum at x = c.

The second derivative is

[tex]\frac{d}{dr} A'(r)=\frac{d}{dr} (16-2r)\\\\A''(r)=-2[/tex]

Because [tex]A''(r)=-2 <0[/tex]  the largest slice is when r = 8 in.

The diameter of the pizza is given by

[tex]D=2r=2\cdot 8=16 \:in[/tex]

A 16 inches diameter will reward you with the largest slice of pizza.

Answer:

4 pizza recipes

Step-by-step explanation:

It shows 4 Xs after the [tex]\frac{3}{4}[/tex] mark. So there are 4 recipes that use MORE than [tex]\frac{3}{4}[/tex] cups of cheese.

Answer:

4 cups of cheese

Step-by-step explanation:

More than 3/4 are (3+1) = 4 cups of cheese

Mark Wishing the Brainliest because he deserves it :)

Answer:

-8.5

Step-by-step explanation:

-4x+8=42

-4x=42-8

-4x=34

x=34/-4

x=-8.5

Answer:

Step-by-step explanation:

Inventory turn over is the same as the inventory turn over ratio. Inventory turn over is defined simply as the ratio of the cost of goods that was sold (net sales) to the average inventory at the selling price.

Inventory turn over = Cost of goods/average inventory

Cost of goods sold = $50000

Average inventory = beginning of inventory + ending inventory/2

Average inventory = $16000+$20000/2

Average inventory = $36000/2

Average inventory = $18000

Inventory turn over = $50000/$18000

Inventory turn over= 2.78

Answer:

A =50.24 in ^2

Step-by-step explanation:

The diameter is 8 inches

The radius is 1/2 diameter

r = d/2 = 8/2 = 4

The area of the circle is given by

A = pi r^2

A = 3.14 (4)^2

A =50.24 in ^2

Answer:

C. 50.24 in²

Step-by-step explanation:

d= 8 in

r= 8/2= 4 in

Area= πr²= 3.14×4²= 50.24 in²

Answer:

35

Step-by-step explanation:

3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9

a+b=?

------

all numbers get cancelled apart from the first denominator and the last numerator:

1/2*a= 9

then

a+b= 18+17= 35

Answer:

y=-3x-2

Step-by-step explanation:

There is enough information to make a point-slope form equation that which we can convert into slope-intercept form.

Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex]

We are given the slope of -3 and the point of (1,-5).

[tex]y-y_1=m(x-x_1)\rightarrow y+5=-3(x-1)[/tex]

Convert into Slope-Intercept Form:

[tex]y+5=-3(x-1)\\y+5-5=-3(x-1)-5\\\boxed{y=-3x-2}[/tex]

[tex]answer \\ \\ \frac{ \sqrt{5} }{2 \sqrt{a} } \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

[tex]2^{6}[/tex]

Step-by-step explanation:

[tex]2^3 \div 2^{-3}[/tex]

[tex]2^{3-(-3)}[/tex]

[tex]2^{3+3}[/tex]

[tex]2^{6}[/tex]

Answer:

The question is not complete, as the table containing the data is missing, but I found a matching table that can be used to answer the question.

The Question is:

Which is the highest rated, of the four European cities under consideration, using the table.

The correct answer is: City A is the highest rated European city.

Step-by-step explanation:

The highest rated European city can be found by multiplying the factor and the importance of the factors, and summing up their final values. the cty with the highest number is the one with the highest rated city. Having this in mind, let us calculate the ratings for each of the cities as follows:

City A:

(70 × 20) + (80 × 20) + (100 × 20) + (80 × 10) + (90 × 10) + (65 × 10) + (70 × 10) = 1400 + 1600 + 2000 + 800 + 900 + 650 + 700 = 8050

City B:

(70 × 20) + (60 × 20) + (50 × 20) + (90 × 10) + (60 × 10) + (75 × 10) + (60 × 10) = 1400 + 1200 + 1000 + 900 + 600 + 750 + 600 = 6450

City C:

(60 × 20) + (90 × 20) + (75 × 20) + (65 × 10) + (50 × 10) + (85 × 10) + (65 × 10) = 1200 + 1800 + 1500 + 650 + 500 + 850 + 650 = 7150

City D:

(90 × 20) + (75 × 20) + (90 × 20) + (65 × 10) + (70 × 10) + (70 × 10) + (80 × 10)   = 1800 + 1500 + 1800 + 650 + 700 + 700 + 800 =7950

Therefore, from the ratings computed above, City A with a rating of 8050, is the highest rated, while City B with a rating of 6450, is the lowest rated.

Answer:

[tex]a^{\frac{9}{2}}[/tex]

Step-by-step explanation:

[tex]\left(a^{\frac{3}{2}}\right)^3[/tex]

[tex]=a^{\frac{3}{2}\cdot \:3}[/tex]

[tex]=a^{\frac{3}{2}\cdot \frac{3}{1}}[/tex]

[tex]=a^{\frac{9}{2}}[/tex]

Answer:

The difference between the games won and lost = 21 - 6 =15

Step-by-step explanation:

According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.

A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.

The team played a total of 34 games.

Total games played = 34

Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,

34 - 6 = 28 games was won or draw

Let

the number of games won = x

the number of game drew = y

3x + y = 70.............(i)

x  + y = 28................(ii)

x = 28 - y

insert the value of x in equation(i)

3(28 - y) + y = 70

84 - 3y + y = 70

84 - 70 = 3y -y

14 = 2y

divide both sides by 2

y = 14/2

y = 7

insert the value of y in equation(ii)

x + y = 28

x = 28 - 7

x = 21

The team won 21 games , drew 7 games and lost 6 games.

The difference between the games won and lost = 21 - 6 =15

Answer:

8.20 am

Step-by-step explanation:

First, we have that Bus A will be back after 20 minutes, then after 40, then 60, 80, 100, 120, 140, 160 minutes, etc.

Then, we have that Bus B will be back after 35 minutes, then 70, then 105, then 140, 175....

From the list above we see that the first time they are both back at the station is after 140 minutes. (it's the MCM).

If we express this in terms of minutes, since one hour has 60 minutes, 2 hours have 120 minutes and thus, 140 minutes is 2 hours and 20 minutes.

Therefore, they will be both back at the station 2 hours and 20 minutes after they first departed at 6 am, so they will be back at the depot at 8.20 am