Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.

y-1=-5(x-5)​

Answer:

2 2/5 hours

Step-by-step explanation:

In 6 hours Brian can lay 1 slab of concrete

dividing both side by 6

in 6/6 hours Brian can lay 1/6 slab of concrete

Thus, in 1 hour  Brian can lay 1/6 slab of concrete

In 4 hours Greg can lay 1 slab of concrete

dividing both side by 4

in 4/4 hours Greg can lay 1/4 slab of concrete

Thus, in 1 hour  Greg can lay 1/4 slab of concrete

Thus, total part of slab laid by both in 1 hour when they work together

1/6 + 1/4 = 4+6/(6*4) = 10/24 = 5/12

5/12 of slab of concrete is laid by both of them in 1 hour

time taken to lay 5/12 of slab = 1 hour

dividing both side by 5/12

time taken to  5/12/ 5/12 of slab = 1/5/12 hour = 12/5 hours

time taken to 1/1 of slab = 12/5 hours = 2 2/5 hours

Thus,

it takes 2 2/5 hours to lay the full slab of concrete when Brian and Greg work together,

Answer:

-2x³ + x² - 3x - 15

Step-by-step explanation:

Simply combine like terms together:

-5x² - 3x - 7 - 2x³ + 6x² - 8

-2x³ + (-5x² + 6x²) - 3x + (-7 - 8)

-2x³ + x² - 3x + (-7 - 8)

-2x³ + x² - 3x - 15

Answer: -2x^3+x^2-3x-15

Step-by-step explanation:

As there is only addition and subtraction here, and the two groups of parenthesis are added, you can ignore the parenthesis.

Thus, simply combine like terms to get.

-2x^3+x^2-3x-15

Hope it helps <3

Answer:

C

Step-by-step explanation:

The reason we can use this method is because we are given a composite figure with a house shape with one triangle on top. We can use the guidance of the dotted lines to make out that a rectangle can be used to find the figure. We can see that apart from the figure, there are two congruent triangles. To find the area we would do -

First find the missing height of the smaller triangles. We would use the pythagorean theorem to find that the missing height is√5

We could do 8(4) = 32 to find the area of the rectangle.

Then, we could do 2√5/2 to find one missing triangle. We could then add the triangles to find the measures of the combined triangles as 2√5. Then, we could do 32 - 2√5 to find the area as 27.5.

Hope this helps :)

Answer:

it is A,B,D

Step-by-step explanation:

i got it right on edge

Answer:

C. 4.02%

Step-by-step explanation:

Anna spends $4.65 each weekday (20 weekdays/month) on coffee and buys a bag of coffee for $8.99 that lasts 6 months. Her monthly income is $2,350. What percent of her monthly income does she spend on coffee? 1) 0.58% 2)4.34% 3) 4.02% 4) 4.65%

She spends $4.65/weekday, and there are 20 weekdays/month

In 1 month, she spends:

$4.65/weekday * 20 weekdays/month = $93/month

In 6 months, she spends 6 * $93 = $558

She buys a bag of coffee for $8.99 that lasts 6 months.

The total cost of all coffee in 6 months is:

$558 + $8.99 = $566.99

Her income in 1 month is $2,350

Her income in 6 months is 6 * $2,350 = $14,100

The percent is:

566.99/14,100 * 100% = 4.02%

Answer: 3) 4.02%

Answer:

268m²

Step-by-step explanation:

given,

l= 10m

b= 8m

h= 3m

A = ?

we know,

A = 2 (lb + bh + lh)

= 2 (10m×8m + 8m×3m + 10m×3m)

= 2 ( 80m² + 24m² + 30m² )

= 2 ( 134m² )

= 268m²

Answer:

b. 1.15

Step-by-step explanation:

The z statistics is given by:

[tex]Z = \frac{X - p}{s}[/tex]

In which X is the found proportion, p is the expected proportion, and s, which is the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.

This means that [tex]X = \frac{13}{53} = 0.2453[/tex]

She find that the proportion of satisfied teachers nationally is 18.4%.

This means that [tex]p = 0.184[/tex]

Standard error:

p = 0.184, n = 53.

So

[tex]s = \sqrt{\frac{0.184*0.816}{53}} = 0.0532[/tex]

Z-statistic:

[tex]Z = \frac{X - p}{s}[/tex]

[tex]Z = \frac{0.2453 - 0.184}{0.0532}[/tex]

[tex]Z = 1.15[/tex]

The correct answer is:

b. 1.15

We assume that question b is asking for the distribution of [tex] \\ \overline{x}[/tex], that is, the distribution for the average amount of pollutants.

Answer:

a. The distribution of X is a normal distribution [tex] \\ X \sim N(8.6, 1.3)[/tex].

b. The distribution for the average amount of pollutants is [tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].

c. [tex] \\ P(z>-0.08) = 0.5319[/tex].

d. [tex] \\ P(z>-0.47) = 0.6808[/tex].

e. We do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution.

f. [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.

Step-by-step explanation:

First, we have all this information from the question:

a. What is the distribution of X?

The distribution of X is the normal (or Gaussian) distribution. X (uppercase) is the random variable, and follows a normal distribution with [tex] \\ \mu = 8.6[/tex] ppm and [tex] \\ \sigma =1.3[/tex] ppm or [tex] \\ X \sim N(8.6, 1.3)[/tex].

b. What is the distribution of [tex] \\ \overline{x}[/tex]?

The distribution for [tex] \\ \overline{x}[/tex] is [tex] \\ N(\mu, \frac{\sigma}{\sqrt{n}})[/tex], i.e., the distribution for the sampling distribution of the means follows a normal distribution:

[tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].

c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?

Notice that the question is asking for the random variable X (and not [tex] \\ \overline{x}[/tex]). Then, we can use a standardized value or z-score so that we can consult the standard normal table.

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

x = 8.5 ppm and the question is about [tex] \\ P(x>8.5)[/tex]=?  

Using [1]

[tex] \\ z = \frac{8.5 - 8.6}{1.3}[/tex]

[tex] \\ z = \frac{-0.1}{1.3}[/tex]

[tex] \\ z = -0.07692 \approx -0.08[/tex] (standard normal table has entries for two decimals places for z).

For [tex] \\ z = -0.08[/tex], is [tex] \\ P(z<-0.08) = 0.46812 \approx 0.4681[/tex].

But, we are asked for [tex] \\ P(z>-0.08) \approx P(x>8.5)[/tex].

[tex] \\ P(z<-0.08) + P(z>-0.08) = 1[/tex]

[tex] \\ P(z>-0.08) = 1 - P(z<-0.08)[/tex]

[tex] \\ P(z>-0.08) = 0.5319[/tex]

Thus, "the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants" is [tex] \\ P(z>-0.08) = 0.5319[/tex].

d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.

Or [tex] \\ P(\overline{x} > 8.5)[/tex]ppm?

This random variable follows a standardized random variable normally distributed, i.e. [tex] \\ Z \sim N(0, 1)[/tex]:

[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]

[tex] \\ z = \frac{\overline{8.5} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ z = \frac{-0.1}{0.21088}[/tex]

[tex] \\ z = \frac{-0.1}{0.21088} \approx -0.47420 \approx -0.47[/tex]

[tex] \\ P(z<-0.47) = 0.31918 \approx 0.3192[/tex]

Again, we are asked for [tex] \\ P(z>-0.47)[/tex], then

[tex] \\ P(z>-0.47) = 1 - P(z<-0.47)[/tex]

[tex] \\ P(z>-0.47) = 1 - 0.3192[/tex]

[tex] \\ P(z>-0.47) = 0.6808[/tex]

Then, the probability that the average amount of pollutants is more than 8.5 ppm for the 38 cities is [tex] \\ P(z>-0.47) = 0.6808[/tex].

e. For part d), is the assumption that the distribution is normal necessary?

For this question, we do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution. Additionally, the sample size is large enough to show a bell-shaped distribution.  

f. Find the IQR for the average of 38 cities.

We must find the first quartile (25th percentile), and the third quartile (75th percentile). For [tex]\\ P(z<0.25)[/tex], [tex] \\ z \approx -0.68[/tex], then, using [2]:

[tex] \\ -0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ (-0.68 *0.21088) + 8.6 = \overline{X}[/tex]

[tex] \\ \overline{x} =8.4566[/tex]

[tex] \\ Q1 = 8.4566[/tex] ppm.

For Q3

[tex] \\ 0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]

[tex] \\ (0.68 *0.21088) + 8.6 = \overline{X}[/tex]

[tex] \\ \overline{x} =8.7434[/tex]

[tex] \\ Q3 = 8.7434[/tex] ppm.

[tex] \\ IQR = Q3-Q1 = 8.7434 - 8.4566 = 0.2868[/tex] ppm

Therefore, the IQR for the average of 38 cities is [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.

Answer:

a) 18 in x 18 in x 18 in

b) [tex]S = 1944\ in2[/tex]

Step-by-step explanation:

a) Let's call 's' the side of the square base and 'h' the height of the solid.

The surface area is given by the equation:

[tex]S = 2s^2 + 4sh[/tex]

The volume of the solid is given by the equation:

[tex]V = s^2h = 5832[/tex]

From the volume equation, we have that:

[tex]h = 5832/s^2[/tex]

Then, using this value of h in the surface area equation, we have:

[tex]S = 2s^2 + 4s(5832/s^2)[/tex]

[tex]S = 2s^2 + 23328/s[/tex]

To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:

[tex]dS/ds = 4s - 23328/s^2 = 0[/tex]

[tex]4s = 23328/s^2[/tex]

[tex]4s^3 = 23328[/tex]

[tex]s^3 = 23328/4 = 5832[/tex]

[tex]s = 18\ inches[/tex]

The height of the solid is:

[tex]h = 5832/(18)^2 = 18\ inches[/tex]

b) The minimum surface area is:

[tex]S = 2(18)^2 + 4(18)(18)[/tex]

[tex]S = 1944\ in2[/tex]

Answer:

f(g(0)) = -1

g(f(0)) = -8

using substitution

Answer:

12345678901234567890

Answer:

[tex]95ft^2[/tex]

Step-by-step explanation:

First, note the surfaces we have. We have four triangles and one square base.  Thus, we can find the surface area of each of them and them add them all up.

First, recall the area of a triangle is [tex]\frac{1}{2} bh[/tex]. We have four of them so:

[tex]4(\frac{1}{2} bh)=2bh[/tex]

The base is 5 while the height is 7. Thus, the total surface area of the four triangles are:

[tex]2(7)(5)=70 ft^2[/tex]

We have one more square base. The area of a square is [tex]b^2[/tex]. The base is 5 so the area is [tex]25ft^2[/tex].

The total surface area is 70+25=95.

Answer:

9

Step-by-step explanation:

p^2 -4p +4

Let p = -1

(-1)^1 -4(-1) +4

1 +4+4

9

Answer:

The 12th percentile of the working lifetime is 7.65 years.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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 = 10, \sigma = \sqrt{4} = 2[/tex]

12th percentile:

X when Z has a pvalue of 0.12. So X when Z = -1.175.

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

[tex]-1.175 = \frac{X - 10}{2}[/tex]

[tex]X - 10 = -1.175*2[/tex]

[tex]X = 7.65[/tex]

The 12th percentile of the working lifetime is 7.65 years.

Answer:

a) [tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]  

b) [tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]

[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]  

[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]  

And replacing we got:

[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.375)[/tex]  

The probability mass function for the Binomial distribution is given as:  

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

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

Part a

[tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]  

Part b

[tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]

[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]  

[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]  

And replacing we got:

[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]

Answer:(x-5)(x+9)

Step-by-step explanation:

You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.

Answer:  (x - 5)(x + 9)

If you have to solve, x=5 or x= -9

Step-by-step explanation: You need two numbers that multiply to be 45.

(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.

9 - 5 =4, so use those.  -45 has a negative sign, so one of the factors must be + and the other -  Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.

So (x -5)(x + 9) are your factors. You can FOIL to be sure

x × x += x² . x × 9 = 9x .  -5 ×  x = -5x . -5 × 9 = -45 .

Combine the x terms: 9x -5x = +4x  

Answer:

a) Null and alternative hypothesis

[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]

b) Test statistic t=-1.565

P-value = 0.0612

NOTE: the sample size is n=65.

c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

d) Null and alternative hypothesis

[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]

Test statistic t=-1.565

Critical value tc=-1.669

t>tc --> Do not reject H0

Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]

The significance level is 0.05.

The sample has a size n=65.

The sample mean is M=30.15.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=65-1=64[/tex]

This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.565)=0.0612[/tex]

As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Critical value approach

At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.

As the test statistic is greater than the critical value, it falls in the acceptance region.

The null hypothesis failed to be rejected.

Answer:

40

Step-by-step explanation:

Angles in a circle add up to 360 degrees.

135 + 145 + x + x = 360

280 + 2x = 360

2x = 80

x = 40

Answer:

40

Step-by-step explanation:

The sum of the measures of the central angles of a circle is 360 deg.

145 + 135 + x + x = 360

280 + 2x = 360

2x = 80

x = 40

Answer:

34.65 / 3.3 = 10.5

Step-by-step explanation:

Answer:

10.5 meters

Step-by-step explanation:

1 meter = 3.3 feet.

1 feet = 1/3.3 meters

then, 34.65/3.3 = 10.5 meters

Answer: [tex]\frac{6}{25}[/tex]

In this case, we're asked to pick one of 12 blue popsicles out of a bag of 50 – from this, we can just write that the probability of picking a blue popsicle is 12/50. Simplifying this, we can divide both the numerator and denominator by 2 to get our final answer of  [tex]\frac{6}{25}[/tex]

Hope this helped you!

Step-by-step explanation:

Answer:

Hello!

_____________________

The total amount of income tax to withhold is: 35.70 + 34.67 = 70.37$

Step-by-step explanation: Subtract this amount from the salary: 830 - 77.90 = 752.1 $. This is the amount subject to withholding.

The amount subject to withholding is between 521 and 1613$, which means that the income tax to withhold is: 35.70$ + 15% of excess over $521

Therefore, calculate the excess: 752.1 - 521 = 231.1$

Now, calculate the percentage: 231.1 × 15 ÷ 100 = 34.67$

Hope this helped you!

Step-by-step explanation:

input x , output y

if x= x1 then y=y1 and y1 is the only value then it is a function

if we get multiple values of y then it is not a function

Answer:

(a) P(0≤x≤2) = 0.41

(b) P(x≥3) = 0.59

(c) P(x≤5) = 0.63

(d) P(x≥6) = 0.37

Step-by-step explanation:

(a) The probability to have at most two errors is the probability to have 0, 1 or 2 errors or the probability of making zero to two errors. So, the probability to have at most two error is:

P(0≤x≤2) = 0.41

(b) The probability to have at least three errors is the probability to have 3 or more errors. So, it can be calculated as:

P(x≥3) = 1 - P(x≤2)

P(x≥3) = 1 - 0.41

P(x≥3) = 0.59

(c) The probability to have at most five error is the probability to have 0, 1, 2, 3, 4 or 5 errors. This can be calculated as the sum of the probability to have zero to two errors and the probability to have three to five errors as:

P(x≤5) = P(0≤x≤2) + P(3≤x≤5)

P(x≤5) = 0.41 + 0.22

P(x≤5) = 0.63

(d) The probability to have more than five errors is the probability to have 6 or more errors. So, it can be calculated as:

P(x≥6) = 1 - P(x≤5)

P(x≥6) = 1 - 0.63

P(x≥6) = 0.37

Answer:

p = 2

Step-by-step explanation:

p + 4/p - 4

multiplying through by p,

p×p + 4/p ×p - 4×p

p² + 4 - 4p = 0

p² - 4p + 4 = 0

factorizing,

p(p - 2) -2(p - 2) =0

(p -2)(p -2) =0

p-2 =0

p=2

Answer:

7 to 15, 7:15, 7/15

Step-by-step explanation:

Ratios can be written as:

a to b

a:b

a/b

We want to find the ratio of exercise days to days in the month. She exercises 14 days out of 30 days in the month. Therefore,

a= 14

b= 30

14 to 30

14:30

14/30

The ratios can be simplified. Both numbers can be evenly divided by 2.

(14/2) to (30/2)

7 to 15

(14/2) : (30/2)

7:15

(14/2) / (30/2)

7/15

Answer:

divide both numbers by 14.. the ans is 1: 2

Answer:

The solution:

X = 16 and Y = -6

Step-by-step explanation:

The equations to be solved are:

x+y = 10 ------- equation 1

x+2y = 4 ----------- equation 2

we can multiply equation 1 by -1 to make the value of x and y negative.

This will give us

-x- y = - 10 ------- equation 3

x+2y = 4 ----------- equation 2

We will now add equations 3 and 2 together so that x will cancel itself out.

this will give us

y = -10 +4 = -6

hence, we have the value of y as -6.

To get the value of x, we can put this value of y into any of the equations above.  (I will use equation 1)

x - 6 = 10

from this, we have that x = 4

Therefore, we have our answer as

X = 16 and Y = -6

Answer:

1 or 9.

Step-by-step explanation:

A coefficient is "a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy)".

So, in this case, the coefficient of 9x would be 9.

The coefficient of x^2 would be 1.

Hope this helps!

In the given quadratic expression 9x - 20 + x, 1, 9, and -20 are the coefficients.

In a quadratic expression of the standard form ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.

In the question, we are asked to identify the coefficients from the given quadratic expression 9x - 20 + x².

First, we try to express the given quadratic expression, 9x - 20 + x², in the standard form of a quadratic expression, ax² + bx + c.

Therefore, 9x - 20 + x² = x² + 9x - 20.

Comparing the expression x² + 9x - 20 with the standard form of a quadratic expression ax² + bx + c, we get a = 1, b = 9, c = -20.

We know that in a quadratic expression ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.

Thus, we can say that in the given quadratic expression 9x - 20 + x², 1, 9, and -20 are the coefficients.

Learn more about quadratic expressions at

https://brainly.com/question/1214333

#SPJ2

Answer:

P-value = 0.002

Step-by-step explanation:

The claim is that for a smartphone​ carrier's data speeds at​ airports, the mean is μ = 10.00 Mbps. This is the null hypothesis that is tested.

Then, the alternative hypothesis will represent the claim that the mean data speed is less than 10.00 Mbps.

We can write this as:

[tex]H_0: \mu=10\\\\H_a:\mu< 10[/tex]

We have a sample size n=32. As the test statistic is z, and not t, we don't need to calculate the degrees of freedom.

The test statistic is z=-2.816. This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-2.816)=0.002[/tex]