hey found that 27 occurred in the Spring, 39 in the Summer, 31 in the Fall, and 53 in the Winter. Can it be concluded at the 0.05 level of significance that car accidents are not equally distributed throughout the year

9514 1404 393

Answer:

  f(x) = -4(x +3)(x -8)²

Step-by-step explanation:

Each zero (z) gives rise to a factor (x -z). The given zeros mean the factored form is ...

  f(x) = a(x -8)²(x +3)

The value of this at x=0 is ...

  f(0) = a(-8)²(3) = 192a

We want the value to be -768, so ...

  -768 = 192a

  -4 = a . . . . . . . . divide by the coefficient of 'a'

Then the factored form is ...

  f(x) = -4(x +3)(x -8)²

Answer:

Step-by-step explanation:

25+125+(-5x)=180 degree(sum of interior angles of a triangle is 180 degree)

150-5x=180

-5x=180-150

x=30/-5

x=-6

Answer:

the standard error of data set is 2.628

Step-by-step explanation:

Given the data in the question;

set;

x = 9, 13, 21, 30, 31, 31, 34, 25, 28, 20

To get the standard of Error for this data set, we use the formual

S.E = s / √n

First we determine the mean average;

Mean x' = ∑x / n =  ( 9 + 13 + 21 + 30 + 31 + 31 + 34 + 25 + 28 + 20 ) / 10

x' = 242 / 10

Mean x' = 24.2

Next we find the standard deviation s:

x             (x-x')²

9           231.04

13          125.44

21          10.24

30         33.64

31         46.24

31         46.24

34        96.04

25        0.64

28        14.44

20        17.64

Total ∑(x-x')² = 621.6

so Variance = ∑(x-x')² / (n-1) = 621.6 / ( 10 - 1 )  = 621.6 / 9

Variance = 69.0667

Standard deviation S = √Variance

Standard deviation S = √69.0667

Standard deviation S = 8.3106

So we substitute into our formula to get the standard of error;

S.E = 8.3106 / √10

S.E = 2.628

Therefore, the standard error of data set is 2.628

Answer:

2.63

Step-by-step explanation:

Answer: A weak positive correlation

Step-by-step explanation: Took the testtt

Answer:

Weak negative correlation

Step-by-step explanation:

From the data given, we can fit the model using technology,

The correlation Coefficient obtained is - 0.129 ; this value being negative means that there exist a negative relationship between the two variables. Also, the correlation Coefficient value is closer to 0 ; this also depicts a weak relation ship between the variables, hence, resulting in the conclusion that the variables have a weak negative correlation.

Answer:

a. [ 2 , ∞ )

Step-by-step explanation:

Answer:

3.066543

Step-by-step explanation:

This number is between 3.077243 and 3.0721

Answer:

The sample size should be:

c. 204

Step-by-step explanation:

This is based on the assumption that in this campus, there are no more than 2040 students.  The sample size should be around 10% of the population, which is considered a good representative of the real population for the specific study.  If, however, the population is so large that 10% of the population will be more than 1,000, then the sample size should be limited to 1,000.

Answer:

We want to expand the expression:

[tex](x - \frac{1}{x^2} )^4[/tex]

We can just do it by brute force, this is:

First, rewrite our expression as the product of two square factors:

[tex](x - \frac{1}{x^2} )^4 = (x - \frac{1}{x^2} )^2*(x - \frac{1}{x^2} )^2[/tex]

Now we can expand each one these two factors:

[tex](x - \frac{1}{x^2} )^2 = (x - \frac{1}{x^2} )*(x - \frac{1}{x^2} ) = x^2 + \frac{1}{x^4} -2*x*\frac{1}{x^2}[/tex]

That can be simplified to

[tex]x^2 - \frac{2}{x} + \frac{1}{x^4}[/tex]

Now we can replace that in our original expression to get:

[tex](x^2 - \frac{2}{x} + \frac{1}{x^4})*(x^2 - \frac{2}{x} + \frac{1}{x^4})[/tex]

Now we can expand that last product, to get:

[tex](x^2)^2 + 2*(x^2)*(-\frac{2}{x} ) + 2*(x^2)*(\frac{1}{x^4}) + 2*(\frac{-2}{x})*(\frac{1}{x^4}) + (\frac{-2}{x} )^2 + (\frac{1}{x^4})^2[/tex]

We can simplify that to:

[tex]x^4 - 4x + 2x^2 - \frac{4}{x^5} + \frac{4}{x^2} + \frac{1}{x^8}[/tex]

That is the expanded expression.

Answer:

think it's the last one

Step-by-step explanation:

sorry if i'm wrong

Answer:

I got ya :D

the answer is

[tex] \binom{ - 18 \: \: \: 10 }{5 \: \: \: - 3} [/tex]

explanation in the attachment

Answer:

23833.41cm²

Step-by-step explanation:

A=πr2=π·87.12≈23833.40992cm²

That rounds up to 23833.41cm²

Step-by-step explanation:

its formula is pi r square so calculate iin own

Answer:

0.. everything just cancels out

Answer:

True

Step-by-step explanation:

Because this sign < eats the 3

Answer:

98

Step-by-step explanation:

The absolute value of a number different from 0 is always positive

- * - = +

15 + 83 = 98

Answer:

A 5.5% = 5400 B 5% = 1800

Step-by-step explanation:

A + B = 7200

A * 0.055 + B * 0.05 = $387

A = 7200 - B

(7200 - B)*0.055 + B*0.05 = 387

396 - 0.055B + 0.05B = 387

396 - 0.005B = 387

0.005B = 9

B = 1800

A = 7200 - B = 7200 - 1800

A = 5400

Answer:

46

Step-by-step explanation:

the number is 46

Answer:

x = -1

y = 6

Step-by-step explanation:

We can multiply the second equation by two, so we can have opposite y terms:

2 (3x - 2y = -15)

6x - 4y = -30

Now, we can add the equations, and the y terms can cancel out:

  7x + 4y = 17

+ 6x - 4y = -30

13x = -13

x = -1

Now, we can plug in x:

3(-1) - 2y = -15

-3 - 2y = -15

-2y = -12

y = 6

Answer:

y = 5/16

Step-by-step explanation:

[tex]y\ \alpha\ \frac{1}{x^2}\\\\y = k \times \frac{1}{x^2}\\\\y = \frac{4}{5}, x = 5.\\\\\frac{4}{5} = k \times \frac{1}{5^2}\\\\\frac{4}{5} \times 5^2 = k\\\\20 = k\\\\Now \ find\ y, \ when \ x = 8\\\\y = k \times \frac{1}{x^2} = 20 \times \frac{1}{8^2} = 20 \times \frac{1}{64} = \frac{5}{16}[/tex]

Step-by-step explanation:

10/30

hope this helps.............

Answer:

x = 3.2

Step-by-step explanation:

Since they are similar the ratio of the side lengths must be the same

Using the bottom side and the unknown side from the left figure and the right figure

5            4

----- = --------

4            x

Using cross products

5x = 4*4

5x = 16

Divide by 5

x = 16/5

x =3.2

Answer:

:)

Step-by-step explanation:

[tex](\frac{f}{g}) (x) = \frac{f(x)}{g(x)} = \frac{6x^2 + 12x}{2x^2 + 8x + 8}[/tex]

                    [tex]= \frac{6x(x + 2)}{2(x^2 + 4x + 4)}\\\\=\frac{3x(x+2)}{(x+2)(x+2)}\\\\=\frac{3x}{(x+2)}[/tex]

Answer:

The answer is:

0.18

0.92

0.15

1.80

Answer:

0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.

88.54% of shoppers are expected to spend between $30 and 80 per week.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of $50 and a standard deviation of $15.

This means that [tex]\mu = 50, \sigma = 15[/tex]

Find the probability that any shopper selected at random spends more than $80 per week?

This is 1 subtracted by the p-value of Z when X = 80. So

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

[tex]Z = \frac{80 - 50}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.

Find the percentage of shoppers who are expected to spend between $30 and 80 per week?

The proportion is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 30.

X = 80

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

[tex]Z = \frac{80 - 50}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 30

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

[tex]Z = \frac{30 - 50}{15}[/tex]

[tex]Z = -1.33[/tex]

[tex]Z = -1.33[/tex] has a p-value of 0.0918

0.9772 - 0.0918 = 0.8854

0.8854*100% = 88.54%

88.54% of shoppers are expected to spend between $30 and 80 per week.

Answer:

Mean will be affected.

Step-by-step explanation:

The mean value of the data set will be affected as it depends on the magnitude of data points and not its position. The median however will not change since it depends on the relative position of data points.

Answer:

[tex]C=25^{\circ},\\a\approx 10.72,\\b\approx 11.83[/tex]

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be [tex]180-90-65=25^{\circ}[/tex].

In any triangle, the Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex].

Therefore, we have:

[tex]\frac{\sin 90^{\circ}}{b}=\frac{\sin 25^{\circ}}{5},\\\\b=\frac{5\sin90^{\circ}}{\sin 25^{\circ}}=11.8310079158\approx \boxed{11.83}[/tex]

[tex]\frac{a}{\sin 65^{\circ}}=\frac{5}{\sin25^{\circ}},\\a=\frac{5\sin 65^{\circ}}{\sin25^{\circ}}=10.7225346025\approx \boxed{10.72}[/tex]

Answer:

15 pounds of plaster

Step-by-step explanation:

First, convert ounces to pounds.

In 1 pound, there are 16 ounces. Create a proportion to convert 12 ounces to pounds.

[tex]\frac{1}{16}[/tex] = [tex]\frac{x}{12}[/tex]

Cross multiply and solve for x:

16x = 12

x = 0.75

So, each student will need 0.75 pounds of plaster. Multiply this by 20 to find the total amount the teacher will need:

20(0.75)

= 15

So, the teacher will need 15 pounds of plaster

Answer:

15 pounds

Step-by-step explanation:

Answer:

30 years

Step-by-step explanation:

Given data

P=$17,000

A= $41,000

R=2.95%

the expressio for the time is

t= ln(A/P)/r

t= ln(41,000 /17000)/0.0295

t= ln(2.41176)/0.0295

t= 0.8803/0.0295

t= 29.8

about 30 years

Answer:

Solution given:

Volume of cone=⅓πr²h

Volume of cylinder=πr²h

1.

volume =πr²h=π*(10/2)²*6=471.23mm³

2.

Volume =πr²h=π*8*12.5=314.16in³

3.

volume =⅓πr²h=⅓*π*4²*3=50.26cm³

4.

Volume =⅓πr²h=⅓*π*(8/2)²*12=201.06in³

that alot of work no cap

Answer:

B)Goal Function