Luke owns a trucking company. For every truck that goes out, Luke must pay the driver $17 per hour of driving and also has an expense of $1.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 40 miles per hour and Luke's total expenses for the driver, gas and truck maintenance were $522. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.

Step-by-step explanation:

[tex] - 3x - 3 = - 3(x + 1) \\ - 3x - 3 = - 3x - 3 \\ - 3x + 3x = - 3 + 3 \\ 0 = 0[/tex]

Step 1: Use 3 to open the bracket

Step 2 : Collect like terms and simplify

Answer = 0

Answer:

The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].

Step-by-step explanation:

The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:

[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]

[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]

[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]

[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]

The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].

Answer:

A

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

The average score of boys and girls is 68 and boys is 62

Think of it as an equation (62 + x)/2 = 68, where x is the average score of girls

First multiply each side by 2 making the equation 62 + x = 136

Now subtract each side by 62, which will make the average score for girls 74

(x = 74)

Answer:

9/3 = 3x/3

3 = x

The spring stretches 9 inches with 3 kilograms of weight attached to it

Step-by-step explanation:

Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:

y = 3x

9 = 3x.

Divide both sides of the equation by 3

Answer:The spring stretches 9 inches with 3 kilograms of weight attached to it.

Step-by-step explanation:

Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:

y = 3x

9 = 3x.

Divide both sides of the equation by 3:

The spring stretches 9 inches with 3 kilograms of weight attached to it.

Answer:

(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.

(b) The simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).

(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].

(d) The probability that only one of the three is a man is 0.375.

(e) The probability that all three are women is 0.125.

Step-by-step explanation:

We are given that three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.

(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.

(b) As we know that the gender of each person is noted by the county clerk, which means one is male and another female.

So, the simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).

Here, M is denoted for male and F for female.

(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].

Because there is 50-50 chance of selecting males or females.

(d) The probability that only one of the three is a man is given by;

The total cases in the sample space = 8

Number of cases of only one man out of three = 3

So, the required probability =  [tex]\frac{3}{8}[/tex] = 0.375.

(e) The probability that all three are women is given by;

The total cases in the sample space = 8

Number of cases of all three are women = 1

So, the required probability =  [tex]\frac{1}{8}[/tex] = 0.125.

Answer:

 $900

Step-by-step explanation:

To begin with let us estimate the total cash value of the prices

$1000 x 1= 1000

$500 x 1=  500

$50 x 2= 100

Total = $1600

Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets

2.5*1000= $2,500

Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600

Then the expected profit is = $2,500-$1600= $900

Answer:

x = 10°, y = 10° and z = 160°

Step-by-step explanation:

Given : m∠BAC = 85°

            CA ≅ CB and BD ≅ CD

In the given ΔABC,

Since, CA ≅ CB

Angles opposite to these equal sides will be equal in measure.

m∠BAC ≅ m∠ABC ≅ 85°

Since, sum of interior angles of a triangle = 180°

m∠BAC + m∠ABC + m∠BCA = 180°

85° + 85° + m∠BCA = 180°

m∠BCA = 180° - 170°

m∠BCA = 10°

x = 10°

In ΔBDC,

Since, BD ≅ DC [Given]

Opposite angles to these equal sides will be equal in measure.

Therefore, x° = z° = 10°

Since, x° + y° + z° = 180°

10° + y° + 10° = 180°

y = 180 - 20°

y = 160°

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.

Answer:

n = 9 is the answer.

Step-by-step explanation:

Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.

AK = 25 units and

AM = 3n -2

To find:

Value of n = ?

Solution:

First of all, let us learn about perpendicular bisectors and their intersection points.

Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.

And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.

We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.

i.e.

Circumcenter of a triangle is equidistant from all the three vertices of the triangle.

In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].

Please refer to the attached image for the given triangle and sides.

The distance of A from all the three vertices will be same.

i.e. AK = AM

[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]

Therefore, n = 9 is the answer.

Answer:

x = 1/e^-5 - 1

Step-by-step explanation:

–2 ln (x + 1) − 3 = 7

–2 ln (x + 1) = 10

ln (x + 1) = –5

x + 1 = e^-5

x = e^-5 - 1

x = 1/e^-5 - 1

the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:

1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.

2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.

3. Simplify: -2 ln(x + 1) = 10.

4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.

5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.

6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.

7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.

8. Simplify: x ≈ -0.9933.

Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

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Answer:

The full answer is 4.40625 but rounded it would be 4.41

Answer:

C

Step-by-step explanation:

Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.

A. The sample proportion is 0.52.

B. The standard error of the sample proportion is approximately 0.041.

C. The standard error of the sample proportion estimate is approximately 0.041.

A. To calculate the sample proportion, we divide the number of people who support the special transportation tax (78) by the total number of people surveyed (150):

Sample proportion = 78 / 150 = 0.52

B. To calculate the standard error of the sample proportion (SE), we use the formula:

[tex]SE = \sqrt{(p * (1 - p)) / n}[/tex]

where p is the sample proportion and n is the sample size. Substituting the values into the formula:

[tex]SE = \sqrt{(0.52 * (1 - 0.52)) / 150}\\\\SE = \sqrt{0.2496 / 150}\\\\SE = \sqrt{0.001664}\\\\SE = 0.0407[/tex]

Therefore, the standard error of the sample proportion is approximately 0.041 (rounded to three decimal places).

C. The standard error of the sample proportion estimate (SEest) is the same as the standard error of the sample proportion (SE) calculated in part B. Hence, the standard error of the sample proportion estimate is also approximately 0.041 (rounded to three decimal places).

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Answer:

the percentage of  bearings   that will  not be acceptable = 7.3%

Step-by-step explanation:

Given that:

Mean = 0.499

standard deviation = 0.002

if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.

Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )

= ( 0.496 , 0.504)

If x represents the diameter of the bearing , then the probability for the  z value for the random variable x with a mean and standard deviation can be computed as follows:

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)[/tex]

From the standard normal tables

[tex]P(0.496\leq X \leq 0.504) = 0.9938-0.0668[/tex]

[tex]P(0.496\leq X \leq 0.504) = 0.927[/tex]

By applying the concept of probability of a  complement , the percentage of bearings will now not be acceptable

P(not be acceptable)  = 1 - P(acceptable)

P(not be acceptable)  = 1 - 0.927

P(not be acceptable)  = 0.073

Thus, the percentage of  bearings   that will  not be acceptable = 7.3%

Answer:

$17,480 per year.

Step-by-step explanation:

Amount earned per hour = $8.74

If a person works for 40 hours every week for 50 weeks in a year, number of hours worked in a year = [tex] 40hrs*50weeks = 2000 hrs [/tex]

Estimated amount earned per year by the person = [tex] 2000hrs * 8.74 dollars [/tex]

= $17,480 per year.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where

l is the length

w is the width

From the question

The length of a rectangle six times its width which is written as

l = 6w

Area = 150cm²

Substitute these values into the formula for finding the area

That's

150 = 6w²

Divide both sides by 6

w² = 25

Find the square root of both sides

width = 5cm

Substitute this value into l = 6w

That's

l = 6(5)

length = 30cm

So the perimeter of the rectangle is

2(30) + 2(5)

= 60 + 10

Hope this helps you

Answer:

Step-by-step explanation:

The summary of the given statistics data include:

sample size n = 400

sample mean [tex]\overline x[/tex] = 6.86

standard deviation = 4.37

Level of significance ∝ = 0.01

Population Mean [tex]\mu[/tex] = 6.00

Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

To start with the hypothesis;

The null and the alternative hypothesis can be computed as :

[tex]H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00[/tex]

The test statistics for this two tailed test can be computed as:

[tex]z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}[/tex]

[tex]z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}[/tex]

[tex]z= \dfrac{0.86}{\dfrac{4.37}{20}}[/tex]

z = 3.936

degree of freedom = n - 1

degree of freedom = 400 - 1

degree of freedom = 399

At the level of significance ∝ = 0.01

P -value = 2 × (z < 3.936)  since it is a two tailed test

P -value = 2 × ( 1  - P(z ≤ 3.936)

P -value = 2 × ( 1  -0.9999)

P -value = 2 × ( 0.0001)

P -value =  0.0002

Since the P-value is less than level of significance , we reject [tex]H_o[/tex] at level of significance 0.01

Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is  5.00 km.

Answer:

approx  193200

Step-by-step explanation:

As known for normal distribution is correct the rule 95.4% of the results are situation within mean+-2*s  ( where s is a standard deviation)

So the border is 100+-2*15=70 and that is approx=67.

95.4% of 84000000 citizens are= 8 400 000*0.954=8013600 persons

So the residual number of the citizens =8400000-8013600=386400 citizens

Because of the simmetry of normal distribution to find the number of the citizens that have IQ below 67 we have to divide 386400 by 2.

N=386000/2=193200

Answer:

Step-by-step explanation:

The gross profit rate of the company is expressed as [tex]P = \dfrac{S - C}{S}[/tex] where C is the cost of goods sold and S is the net sales. If the net sales S = $1,200,000, and gross profit ratio is 0.20, the cost of goods sold will be expressed as shown;

Making C the subject of the formula from the expression given.

[tex]P = \dfrac{S - C}{S}\\\\cross \ multiply\\\\SP = S-C\\\-C = SP-S\\\\C = S -SP\\[/tex]

Substituting P = 0.20 and S = $1,200,000 into the resulting equation, we will have;

[tex]C = $1,2000,000 - 0.2($1,2000,000)\\C = $1,2000,000- 240,000\\ C = 960,000[/tex]

Hence the cost of goods sold is $960,000

Answer:

3(9t^5-7p^4)(9t^5+7p^4)

Step-by-step explanation:

243 t^10 - 147 p^8

3 ( 81 t^10-49 p^8 )

Then we need to factor what is in the parentheses

3 ( ( 9t^5) ^2 - ( 7p^4) ^2)

This is the difference of squares  ( a^2 -b^2) = ( a-b) (a+b)

3(9t^5-7p^4)(9t^5+7p^4)

Answer: see below

Step-by-step explanation:

The standard form of an exponential equation is: y = a(b)ˣ    where

Growth:

Exponential growth is where the final value (y) is greater than the initial value (a).

An example would be the spreading of a rumor:  

You tell 1 person (a = 1) who then tells 2 people each minute (b = 2).  How many people will they have spread the rumor to after 5 minutes (x = 5)?

y = 1(2)⁵

  = 32

Decay:

Exponential decay is where the final value (y) is less than the initial value (a).

An example would be the decrease of bacteria in a person:

A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2).  How many bacteria will the person have after 2 hours (x = 2)?

[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]

Answer:

A 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .

Step-by-step explanation:

We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                             P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of defective items = [tex]\frac{24}{200}[/tex] = 0.12

            n = sample of items = 200

            p = population proportion  of defective items

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                      of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

  = [ [tex]0.12-1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] , [tex]0.12+1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] ]

 = [0.075, 0.165]

Therefore, a 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .

Answer:

-4

Step-by-step explanation:

Hey there!

Well the slopes of 2 parallel lines have the same slope,

meaning if the green line has a slope of -4 then the slope of the red line has a slope of -4.

Hope this helps :)

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5

x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5

x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5

x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

The only table that represents a linear function is; Table 1

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

Slope = 5/1 = 5

Slope = 10/2 = 5

Slope = 15/3 = 5

Slope = 20/4 = 5

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

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Answer:

A. It will definitely be a t-test

Step-by-step explanation:

T-test is a type of inferential statistic test which used to determine whether there is a significant difference between mean of two group sets or variables.The t-test technique is widely used in hypothesis testing in statistics.  When the model building for game play is determine through regression analysis, it will require t-test to be conducted to reach a conclusion.

To convert miles per hour to meters per second divide by 2.237

128 miles per hour / 2.237 = 57.22 meters per second.

Using the first equation:

57.22 = sqrt(2 x 9.81 x h)

Remove the sqrt by raising both sides to the second power:

57.22^2 = (2 x 9.81 x h)

Simplify Both sides:

3274.1284 = 19.62h

Divide both sides by 19.62:

H = 3274.1284/ 19.62

H = 166.88 meters

Answer:

3x^2 + 3xy/2 - 7xy^2/2

Step-by-step explanation:

So we know the perimeter is 20x^2 + xy - 7y^2,

To find any perimeter you need 2l + 2w = P so,

One of the sides is 7x^2 - xy

First plug in the values,

2(7x^2-xy) + 2w = 20x^2 + xy - 7y^2

Multiply,

14x^2-2xy + 2w = 20x^2 + xy - 7y^2

Subtract,

14x^2 - 2xy - 14x^2 + 2xy + 2w = 20x^2 + xy - 7y^2 - 14x^2 + 2xy

2w = 6x^2 + 3xy - 7y^2

w = 3x^2 + 3xy/2 - 7xy^2/2

Answer:

yes

Step-by-step explanation:

every negative any positive number is an integer

Answer:

Step-by-step explanation:

No.  Integers do not have fractions in them.

-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer

Answer:

It is still 2 to 7

Step-by-step explanation:

It is still 2 to 7 because if you triple the recipe, it will become 6 to 21 which still simplifies to 2 to 7.

Answer:

67.5p.

Step-by-step explanation:

315p in total.

- Baseball has 55p.

- Soccer teams points = 55x2 = 110p.

-  Football team points = 110 x 0.5 = 55 x 1.5 = 82.5p.

So then you just do 315p - 82.5p - 55p - 110p = 67.5p