Gravel is graded by how fine the stones are. For a particular grade of gravel, there are 26 stones with a diameter of 0.75 inches or greater per one cubic yard of gravel, on average. (a) We would like to determine the probability of finding at most two stones with a diameter of 0.75 inches or greater in one cubic foot of the same gravel. Which of the following is the correct probability statement? P(x < 2) PX S2) P(x > 2) P(X22) (b) We would like to determine the probability of finding at most two stones with a diameter of 0.75 inches or greater in one cubic foot of the same gravel. (1 cubic yard = 27 cubic feet. Round your answer to three decimal places.) 0.960 HE -0.963 27

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Answer:

General equation of a line perpendicular to y = − 2x + 3 is y = 1/2x + k where is the k is the y intercept.

Answer:

$243.92 for 8 is cheaper

Step-by-step explanation:

To find the unit price for the 6 shirts you would do 188.94 divided by 6.

To find the unit price for the 8 shirts you would do 243.92 divided by 8

for 6 shirts it's: $31.49/shirt

for 8 shirts it's: $30.49/shirt

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

Answer:

2850

Step-by-step explanation:

19% of 15000 is 2850

\(\textbf{19\% prefer sedans}\)

\(\textbf{The company should plan on manufacturing}\\\\ \textbf{19\% of the cars as sedans}}\)

\(19\% \times 15000 = 2850\)

\(\textbf{2,850 sedans}\)

Answer:

7.5

Step-by-step explanation:

thirty divided by 4 is 7.5 or 7 1/2

Answer:

That might be possible though.

Step-by-step explanation:

If you divide 30 by 7.5, you'll get 4. With any other number, you'll get 3,10,6,5,1, and 30. If you use a decimal, it might be possible it'll give you the answer you wanted.

Answer:

\(\angle 7=151\textdegree\)

Step-by-step explanation:

Note that ∠7 is the vertical angle to 151°.

Recall that vertical angles are congruent and thus have equivalent measures.

Hence, ∠7 is also 151°.

In conclusion, the measure of ∠7 is 151°.

Answer:

151°

Step-by-step explanation:

Angle 7 and the Angle that measures 151° are congruent and vertical angles.

This means they will be equal to the same angle measure.

Angle 7 = 151°

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Answer:

50 I think

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

All multiples of 5 end in 0 or 5. 2,102 does not end in 0 or 5, so it is not a multiple of 5.

                  420

            ---------------------

      5   |   2102

               20

              ----------

                 10

                 10

                --------

                   02

                     0

                  -----

                      2

2,102 divided by 5 equals 420 remainder 2. Since there is a remainder, it is not divisible.

Answer:

r = t + q - s

Step-by-step explanation:

t = r - q + s

goal is to isolate the variable

add q to both sides (this cancels the q out on the right side)

t + q = r - q + q + s

t + q = r + s

subtract s from both sides

t + q - s = r + s - s

t + q - s = r

In other words:

r = t + q - s

Answer:

To calculate the percent increase in the amount of interest paid between a household with a 740 credit score and one with a 730 credit score , we need to find the total amount paid for each score and then calculate the percent increase.

From the given table , we can see that the simple interest rate for a credit score of 740-799 is 15%, and the total number of payments is 33 . So, the total amount paid for a principal balance of $18,000 with a credit score of 740 is:

Principal + Total Interest = Total Amount Paid

$18,000 + ($18,000 * 15% * 33/12) = $20,700

Similarly, for a credit score of 730, we need to use the simple interest rate for a credit score of 670-739 , which is 18%, and the total number of payments is 38. So, the total amount paid for a principal balance of $18,000 with a credit score of 730 is:

Principal + Total Interest = Total Amount Paid

$18,000 + ($18,000 * 18% * 38/12) = $21,240

Now, to calculate the percent increase in the amount of interest paid , we can use the following formula:

Percent increase = |(New value - Old value) / Old value| * 100%

Plugging in the values, we get:

Percent increase = |($21,240 - $20,700) / $20,700| * 100%

Percent increase = 2.6%

Rounding to the nearest tenth, we get the final answer as:

Percent increase = 2.6% ≈ 2.5%   (rounded to the nearest tenth)

Therefore, the answer is O 2.5%.

Step-by-step explanation:

The probability that at least 8 out of the 10 chips work properly is 0.2614, or 26.14%.

Given:

number of chips selected = 10

probability of a chip working= 0.95

The probability of getting exactly k successes in n trials with a success probability p is given by the formula:

\(P(X = k) =\) \({\text} ^nC_k p^k (1 - p)^{(n - k)\)

Now, the probability

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

\(P(X = k) =\) \({\text} ^{10}C_k (0.95)^k (1 - 0.95)^{(10 - k)\)

So, P(X = 8) = \(^{10}C_8 (0.95)^8(1-0.95)^{10-8}\)

                  =  \((45) (0.95)^8 (0.05)^2\)

                 = 0.2753

and, P(X = 9) = \(^{10}C_9 (0.95)^9(1-0.95)^{10-9}\)

                  = \((10) * (0.95)^9 * (0.05)^1\)

                  = 0.3874

P(X = 10) = \(^{10}C_{10} (0.95)^{10}(1-0.95)^{10-10}\)

                  = \((1) * (0.95)^{10} * (0.05)^0\)

                  = 0.5987

Finally, sum up these probabilities to get the desired result:

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

             = 0.2753 + 0.3874 + 0.5987

             = 0.2614

Therefore, the probability is 0.2614.

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Answer:

he drove 192 miles

Step-by-step explanation:

why bc I did 0.85 x 192= 183.15

so that makes 192 the miles Chris drove

Answer:

\(x1=\frac{49+\sqrt{2429}}{14} \\x2=\frac{49-\sqrt{2429}}{14} \\\)

Step-by-step explanation:

\(x^2-7x-\frac{1}{7} =0\\7x^2-49x-1=0\\D=b^2-4ac=(-49)^2-4*7*(-1)=2429\\x1=\frac{49+\sqrt{2429} }{14} \\x2=\frac{49-\sqrt{2429} }{14} \\\)

Answer:

S-8=9

or, s= 9+8

or, S= 17

Because 8 is in - so to become it's positive sign we should bring it to right hand side

Answer:

1/10 of the days in September had rainfall more than 2 cm

Step-by-step explanation:

Use the information given:

Answer:

C + 1 < 3 is not equivalent.

Step-by-step explanation:

B - 1 < 2 ⇒ B < 3

C + 1 < 3 ⇒ C < 2

D - 2 < 1 ⇒ D < 3

Therefore, all inequalities are equivalent except C + 1 < 3.

people who are unemployed but actively searching employment.

The Bureau of Labor Statistics (BLS) is a US government agency that provides data on labor market activity, working conditions and price movements in the economy.

Part of the U.S. Department of Labor, it is responsible for the collection, analysis, and public dissemination of economic data. BLS produces a wide range of statistical information, including data on employment, unemployment, wages, productivity, consumer price inflation, and occupational injuries and illnesses.

They also conduct research and publish reports on various labor market and business issues. The BLS is an invaluable resource for policy makers, businesses, workers and others who need reliable and up-to-date information on the state of the economy and labor market.

The workforce is defined as the total number of people who are employed or unemployed but are actively looking for work. Pensioners, students and housewives are not included. To be considered an active job seeker, you must have taken certain steps to find a job within the last four weeks. The size of the labor force is an important indicator of the health of the economy as a whole, as it reflects the number of people contributing to economic activity or looking for work.

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To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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The factory must produce 6,400 parts  so that there is 1 ton of scrap aluminum for recycling.

It is given that For every part produced by a factory there are 5 ounces of scrap aluminum that can be recycled there are 16 ounces in 1 pound and 2,000 in 1 ton we need to find how many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling

What is a Ratio?

A quantitative relation between two amounts showing the number of times one value contains in another

1 part produced  ⇒ 5 ounces scrap aluminium recycled.

So, the ratio of parts produced : Scrap of aluminium = 1   : 5  .... (a)

Let us assume for m parts produced ,  1 ton of scrap is recycled.

Also, 1 ton = 2, 000 pounds

and 1 pound = 16 ounces

⇒ 1 ton = 2000 x (16 ounces)  = 32,000 ounces

So, for m parts made in the  factory, 32,000 ounces scrap is recycled.

So, the ratio of parts produced : Scrap of aluminium =  m   : 32,000  .... (b)

From both the given ratio, we get

1   : 5  = m   : 32,000

m=32000/5

m=6400

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9514 1404 393

Answer:

  (b)  976 m³

Step-by-step explanation:

The total surface area is the sum of the areas of the faces and bases.

The two bases are triangles, each with area ...

  A = 1/2bh

So, the two of them together will have an area of ...

  A = 2(1/2)bh = bh

where b is the base of the triangle, and h is its height. These values are shown as 14 m and 24 m, respectively.

  Total base areas = (14 m)(24 m) = 336 m²

__

The total area of the rectangular faces is the sum of products of length and width. The width of each face is the same as the height of the prism, and the sum of face lengths is the perimeter of the triangular base.

The prism height is 10 m, and the perimeter of the base triangle is  (14 m +25 m +25 m) = 64 m. Then the lateral area of the prism is ...

  Total lateral area = (10 m)(64 m) = 640 m²

So, the total surface area of the prism is ...

  base area + lateral area = 336 m² + 640 m² = 976 m²

Answer:

26:30

Step-by-step explanation:

Compare to y=mx+b

Parallel lines have equal slopes

Now

equation in point slope form

Answer:

64

Step-by-step explanation:

We are given the limit of f(x) as x approaches 0 is 4.

We are asked to find the limit for 1/4 times (f(x))^4 as x approaches 0.

Let's use limit laws by bringing the limit inside the power.

So we have 1/4 * 4^4.

This equals 4^3=64.

The solution is : 64 is limit.

In mathematics, a limit is the value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

here, we have,

Given lim f(x) = 4.

We are given the limit of f(x) as x approaches 0 is 4.

We are asked to find the limit for 1/4 times (f(x))^4 as x approaches 0.

Let's use limit laws by bringing the limit inside the power.

So we have 1/4 * 4^4.

This equals 4^3=64.

Hence, The solution is : 64 is limit.

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Answer:

114 cents

Step-by-step explanation:

1. 66÷22=3 cents per inch

2. 3×38=114

3. 114 cents ($1.14) for 38 inches

Adrian must multiply his money by 1.03 to find his total balance in a year in one step.

Given that Adrian invests money in an account paying a simple interest of 3% per year, to determine, if no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step, the following calculation must be performed:

Therefore, Adrian must multiply his money by 1.03 to find his total balance in a year in one step.

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Answer:

Minimum = -1

Maximum = 3

Step-by-step explanation:

∛-10+9 = ∛-1 = -1

∛18+9 = ∛27 = 3

If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:

Total number of hours of work / Number of hours of work done by 4 men in a day

= 224 / (4 x 8)

= 7

So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.

II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:

Total number of men x Total number of days x Number of hours worked by each man per day

= 4 x 7 x 8

= 224 hours

Therefore, the total cost of employing all 4 men is:

Total number of hours x Rate per hour

= 224 x $57.50

= $12,880

III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:

Total number of hours of work / Total number of days to complete the project

= 224 / 4

= 56 hours

Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:

Number of hours of work per day - Number of hours worked by each man per day

= 56 - 8

= 48 hours

Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.

IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:

l x $57.50

= $57.50l

Let the overtime rate of payment be $r per hour. Then:

r = $57.50l

The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:

Number of regular hours x Regular hourly rate

= 4 x 8 x 7 x $57.50

= $16,240

The cost of overtime hours is:

Number of overtime hours x Overtime hourly rate

= 4 x 6 x 7 x $57.50l

= $12,180l

So, the total cost of the project is:

Total cost = Cost of regular hours + Cost of overtime hours

= $16,240 + $12,180l

Answer:

Step-by-step explanation:

(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:

Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days

So it will take 4 men, each working 8 hours per day, 7 days to complete the project.

(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:

Total cost = 4 men x $57.50/hour x 56 hours = $12,320

(iii) If the project is to be completed in 4 days, each man will need to work for a total of:

224 total hours / (4 men x 4 days) = 14 hours per day

Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.

(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:

Overtime rate = $57.50 x 1.5 = $86.25/hour

To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:

Regular hours cost = 224 regular hours x $57.50/hour = $12,880

The cost of the overtime hours is:

Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour

= 96 x $86.25

Therefore, the total cost of the project is:

Total cost = Regular hours cost + Overtime cost

= $12,880 + $8,280

= $21,160

where the overtime rate is 1.5 times the regular hourly rate.