At a certain university, the average cost of books was $330 per
student last semester and the population standard deviation was $75. This
semester a sample of 50 students revealed an average cost of books of $365 per
student. The Dean of Students believes that the costs are greater this semester.
What is the test value for this hypothesis?

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

The formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase is given as follows: V (t) = Ct - rt, where C is the initial cost of the machine in thousands of dollars, r is the depreciation rate per year, and t is the time in years since the machine was purchased. V(t) = 710 - 13.7925t Answer: V(t) = 710 - 13.7925t

The value of an industrial milling machine after two years of purchase is $710,000 and after five years, the value is $180,000. Let us find the depreciation rate of the machine.

Linear Depreciation Method: Linear depreciation method is one of the methods used to calculate depreciation in accounting. It is also called straight-line depreciation. Under this method, the depreciation expense of an asset is the same for each year of its useful life.

The formula to calculate the depreciation expense using the straight-line depreciation method is:Depreciation Expense = (Cost of Asset - Salvage Value)/Useful Life Let,

The cost of the industrial milling machine = C = 710The value of the industrial milling machine after five years = S = 180The useful life of the machine in years = LWe have to find a formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase.

To find the useful life of the machine, use the following formula:Cost of Asset = Depreciation Expense x Useful Life + Salvage Value710 = (710 - 180)/L * L + 180

Simplifying the above equation, we get:710 = 530/L + 180Multiplying both sides of the equation by L and then subtracting 180 from both sides, we get:530L = 530L = 530 - 180L = 350/53.

Therefore, useful life, L = 350/53 yearsThe depreciation rate of the industrial milling machine is the difference between its cost and salvage value divided by its useful life.

Using the given information, the cost of the machine and the value of the machine after five years, we get: Depreciation Rate = (Cost of Machine - Salvage Value) / Useful LifeDepreciation Rate = (710 - 180) / (350/53)Depreciation Rate = 13.7925

Hence, the formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase is given as follows:V (t) = Ct - rt, where C is the initial cost of the machine in thousands of dollars, r is the depreciation rate per year, and t is the time in years since the machine was purchased. V(t) = 710 - 13.7925t Answer: V(t) = 710 - 13.7925t

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Answer:

no

Step-by-step explanation:

4+6 does not equal 12 so there for it is incorrect

Answer:

x = 49

Step-by-step explanation:

Given

\(\frac{x-16}{x+6}\) = \(\frac{3}{5}\) ( cross- multiply )

5(x - 16) = 3(x + 6) ← distribute parenthesis on both sides

5x - 80 = 3x + 18 ( subtract 3x from both sides )

2x - 80 = 18 ( add 80 to both sides )

2x = 98 ( divide both sides by 2 )

x = 49

Answer:

x = - 49

Step-by-step explanation:

Solve for X by cross multiplying.

It will take 36 seconds until animals are 156 yards apart.

Relative speed is speed of object with respect to each other. In relative speed:

There relative speed with respect to each other will be (A + B)

There relative speed with respect to each other will be (A - B) (given speed A is quantitatively greater than speed B).

________________________________________________________

Given

Direction of the animals with respect to each other is opposite.

Therefore, their relative speed will be (8 + 5) = 13 feet per second

This can be understood intuitively as well

if deer and beer are covering 8 feet and 5 feet in one second in opposite direction then the distance will increase between them.

distance increased between them in one second will be sum of 8 feet and 5 feet which is equal to 13 feet.

Thus, distance covered per second is nothing but speed. Here, this speed is relative to each other. Thus, 13 feet per second is the relative of each animal.

_______________________________________________

Now in problem of speed, distance and time.

\(\sf Time = \dfrac{Distance}{Speed}\)

Distance = 156 yards

one yard is equal to 3 feet

So, 156 yards is equal to 3 x 156 feet

156 yards in feet is 468 feet

Distance in feet  = 468 feet

Therefore,

\(\sf Time = \dfrac{468}{13} = 36 \ seconds\)

_________________________________________

Thus, It will take 36 seconds until animals are 156 yards apart.

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Answer:

To me it means that challenges are meant to show your strengths and weaknesses, and that things will challenge your weakness but it ends up making them into strengths.

Step-by-step explanation:

There are 11 zeros in the given fraction's terminating decimal representation.

To determine the number of zeros to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of  \($\frac{1}{2^5\cdot5^8}$\) , we need to simplify the fraction.

\($\frac{1}{2^5\cdot5^8}$\)  can be rewritten as \($\frac{1}{32\cdot390625}$\) .

To find the decimal representation of this fraction, we divide 1 by the product of the denominators: \($32\cdot390625$\) .

Performing the division, we get:

\($0.000000000000512$\)

In this decimal representation, there are 11 zeros located to the right of the decimal point and before the first non-zero digit, which is 5. Therefore, there are 11 zeros in the given fraction's terminating decimal representation.

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The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5

side A'B' = 8 × 1/2

side A'B' = 4

Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

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Answer:

the answer is B, 4. :)

Minimum value is 103, lower quartile (Q1): median of first 15 values s 137, median (Q2): median of all 30 values is 153.5, upper quartile (Q3): median of last 15 values is 174 and maximum value is 216

To construct a boxplot from the given data, follow these steps:

1. Arrange the data in ascending order.
2. Find the minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value.

Arranged data:
103, 105, 114, 121, 128, 133, 134, 137, 140, 142, 143, 144, 150, 153, 160, 161, 163, 166, 169, 171, 173, 174, 175, 177, 179, 181, 189, 206, 212, 216

Minimum value: 103
Lower quartile (Q1): Median of first 15 values = 137
Median (Q2): Median of all 30 values = 153.5
Upper quartile (Q3): Median of last 15 values = 174
Maximum value: 216

Based on the calculated values, the important characteristics of the boxplot are as follows:

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Answer:

Step-by-step explanation:

9000-500h=0+500h

h= 9 hours

9 hours will the silos have the same amount of wheat.

This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

Let's first list the data that we currently have. The number of ice creams is 5. It costs $125 for 5 ice creams.

Step 1 :Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.

Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.

A 9,000-gallon silo of wheat is being drained at a rate of 500 gallons per hour.

So, every hour after draining = 9000 - 500x

A 7,000-gallon silo of wheat is being filled at a rate of 500 gallons per hour.

So, after every hour after filling = 0 + 500x

Now, number of hours will the silos have the same amount of wheat

9000 - 500x = 0+ 500x

9000 = 1000x

x= 9000/1000

x= 9 hours.

Hence, 9 hours will the silos have the same amount of wheat.

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• Equation 1:, y = 2x - 4

• Equation 2: ,y = -1/2 x + 1

Choosing point ( 2, 0 ) -where the equations intersect-:

• Equation 1:

• Equation 2:

Answer: ( 2, 0 )

It is not a proportional relation, it is a regular linear equation.

And the slope of that line is -3.

One easy way to identify if a graph is proportional, is to check if the line passes through the origin (the point (0, 0) on the coordinate axis).

In this case we can see that the line does not pass through that point, so this is not a proportional relation.

Now we can try to find the slope of that line. Remember that if a line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope of that line is:

a = (y₂ - y₁)/(x₂ - x₁)

On the graph we can identify the points (1, 1) and (0, 4), so the slope is:

a = (4 - 1)/(0 - 1) = -3

The slope of the line is -3.

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The sample mean age is 19.4444 and the sample standard deviation of the age is 1.1547. The sample mean age of the 9 college students in the intermediate-level art course can be computed by summing up all the ages and dividing by the sample size.

The ages given in the dataset are: {19, 19, 21, 22, 19, 20, 18, 18, 19}. Adding up these ages gives a total of 175. Dividing this sum by 9 gives a sample mean age of 19.4444 (rounded to four decimal places).

To compute the sample standard deviation of the age, we need to calculate the deviation of each age from the sample mean, square the deviations, sum them up, divide by the sample size minus 1 (which is 8), and take the square root of the result. The deviations from the mean for the given dataset are: {-0.4444, -0.4444, 1.5556, 2.5556, -0.4444, 0.5556, -1.4444, -1.4444, -0.4444}. Squaring these deviations, summing them up, dividing by 8, and taking the square root of the result gives a sample standard deviation of 1.1547 (rounded to four decimal places).

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Answer:

7.1 inches

Step-by-step explanation:

perimeter you go round from apointof your choice so

add 2+2=4

then apply 1/4πd for the round part

d=4 and it's quarter a circle then add them together

Answer:

7.1 inches

Step-by-step explanation:

To find the perimeter of the circle you would need to follow the formula: 2piR. Since r=2, 2*2=4. So 4 multiplied by pi (3.14 or 22/7). Since this is a quarter of a circle you would divide the answer 12.56 by four which equals 3.14. Now just add the extra two 2s left on the flat sides of the figure which ends up with your answer of 7.14 OR 7.1.

Hope this helps!! <3

Electrical energy consumption is measured at kilowatt-hour (KWh). Thus the cost of energy consumed for the month is $28.512

What does kilowatt-hour mean?

The rate of consumption of energy is measured in kilowatt-hour.

In the given question

11 cent is paid per kilowatt-hour.

60 watts of light for 1 hour = 0.06 KWh

3 light bulbs of 60 Watts each for 1 hour = 3 x  0.06

                                          = 0.18 KWh

But,

30 days = 30 x 24 hours

                       = 1440 hours

The total energy consumed for the month = 1440 x 0.18

                                     =  259.20 KWH

The total cost for the month = 0.11 x 259.20

                                              = $28.512

Thus, the total cost for the month is $28.512

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Answer:

x = 17.9

Step-by-step explanation:

\(3x-24=29.7\\ Distribution Property\\\\3x=53.7\\\\Adding 24 to both sides\\\\x=17.9\\Divide by 3 to both sides\\\\Hope this helps:)\\\)

\(\text {Hello! Let's Solve this Equation!}\)

\(\text {The First Step is to Multiply 3 in the Parentheses:}\)

\(\text {3*x=3x}\\\text {3*8=24}\)

\(\text {Your new Problem is: 3x-24=29.7}\)

\(\text {The Next Step is to Add 24:}\)

\(\text {3x-24+24=29.7+24}\\\text {=53.7}\)

\(\text {Your new Problem is: 3x=53.7}\)

\(\text {The Final Step is to Divide 3:}\)

\(\text {3x/3=53.7/3}\)

\(\text {Your Answer would be:}\)

\(\fbox {x=17.9}\)

\(\text {Best of Luck!}\)

Answer:

3 11 19 27 35 43 51 59 67 75 83 91 99 107

Step-by-step explanation:

keep on adding 8 to each number to get your next number

the tenth term is 107

hope this helps!!:)

100% of the F2 generation plants are expected to be tall and produce round fruit.

The given information suggests that F1 and F1 represent heterozygous tall and round plants, respectively. When these two genotypes are crossed, we can predict the possible genotype and phenotype combinations of the offspring by using a Punnett square.

The Punnett square for this cross would be:

F1     F1

F2 F1F1 F1F1

F1F1 F1F1

From this square, we can see that all of the F2 generation plants will be homozygous for both tallness and roundness. This is because the F1 generation is heterozygous for both traits, so when they are crossed, the recessive alleles are masked by the dominant alleles.

Therefore, the genotype of all F2 plants will be F1F1, and they will all be tall and round.

In summary, 100% of the F2 generation plants are expected to be tall and produce round fruit.

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Answer:

3.6.

Step-by-step explanation:

15% = 15/100 = 0.15

so the answer is 0.15 * 24

= 3.6

Answer:

3.60

Step-by-step explanation:

Note:

Of = Multiply

15% can also be written as .15 as decimal

Solve:

.15 × 24 = 3.60

 Or we can solve like this:

\(\frac{24}{x}=\frac{100\%}{15\%}\)

\(\frac{x}{24}=\frac{15}{100}\)

\(\Rightarrow x=3.6\)

Therefore, 15% of  £24 is 3.60

~Lenvy~

Some triangle pairs are congruent triangles but some others are not, because:

A pair of triangles is congruent if they have one of these criterias:

Let's explore each triangle pairs we have:

Pair 1

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles .

Pair 1 meet ASA rules --> Congruent triangles

Pair 2

Pair 2 has 1 corresponding angle and 2 pairs of corresponding sides

Pair 2 meets SAS rules --> congruent triangles

Pair 3

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles.

Pair 3 meet ASA rules --> Congruent triangles

Pair 4

Pair 4 has 3 corresponding sides and meets SSS rules --> congruent triangles

Pair 5

Pair 5 only has 2 corresponding sides --> not congruent triangles

Pair 6

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides not between the angles.

Pair 6 meet AAS rules --> Congruent triangles

Pair 7

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 7 also has another 2 corresponding angles. In total, pair 7 has 3 corresponding angles.

Pair 7 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.

Pair 8

We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 8 also has another 2 corresponding angles. In total, pair 8 has 3 corresponding angles.

Pair 8 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.

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Answer:

Step-by-step explanation:

I am pretty sure the answer is b

Answer:

radius= 2miles

circumference =2Πr

= 2Π2miles

= let Π=x

(2x)(2miles)

Answer is = 4x miles

Answer:

a. 1.26

b. 0.1038

Step-by-step explanation:

The p-value is 1.0000 (rounded to four decimal places). This means that we fail to reject the null hypothesis, which in this case would be that the population mean is equal to the sample mean of 26.2.

To find the test statistic, we need to use the formula:

test statistic = (sample mean - population mean) / (standard deviation / square root of sample size)

Since the population standard deviation is given as 6, we can plug in the values:

test statistic = (26.2 - population mean) / (6 / √40)

To find the population mean, we can use the fact that the sample mean is an unbiased estimator of the population mean, so:

population mean = sample mean = 26.2

Plugging in the values, we get:

test statistic = (26.2 - 26.2) / (6 / √40) = 0

The test statistic is 0.

To find the p-value, we need to use a t-distribution table or calculator. Since we have a sample size of 40, we can use the t-distribution with 39 degrees of freedom.

Using a calculator or table, we can find that the area to the right of 0 (since the test statistic is 0) is 0.5. Since this is a two-tailed test, we need to double this value to get the p-value:

p-value = 2 * 0.5 = 1.0000
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5555555555555555555555555555555

Answer:

Only Joe is correct

Step-by-step explanation:

We can infer this by looking at the ratio provided. The ration states that for every 2 men there are 7 women. It doesn't specify the total. So using this ration we get the answer that for every 1 man there are 3 1/2 women which is equal to Joe's answers.

Answer:

\(C\)

Step-by-step explanation:

Jo is right. There are 3.5 times as many women as men.

\(2 \times 3.5 = 7\)

Paul is right. 2 in 7 people are men.

\(2 : 7\)

Answer:

I have answered. it is perfect answer

Answer:

9 and 135

Step-by-step explanation:

The GCF is 9, and 135 is divisble by 9. The GCF of a standalone number is itself, and the aforementioned divisibility of 135 by 9 rules 9 as one of the numbers. Since 9 is a multiple of 135, and 9 can multiply to be 135, this makes the second number 135.

Answer: 5x(x + 4)

hope i helped

Answer:

5x . (x+4)

Step-by-step explanation:

Make sure not to use too many points next time if anything only use ten unless your asking someone to write an essay or you need your answer quick

Answer:

New radius(r) = 3.65 (Approx)

Step-by-step explanation:

Given:

Radius of sphere(R) = 8

Find:

New radius(r)

Computation:

Volume of sphere = (4/3)πR³

Volume of sphere = (4/3)π(6)³

Volume of sphere = 288π

Volume of ring = (4/3)π(R²-r²)³/²

Half volume of sphere = Volume of ring

288π / 2 = (4/3)π(R²-r²)³/²

144 = (4/3)(6²-r²)³/²

108 = (6²-r²)³/²

New radius(r) = 3.65 (Approx)

Answer:

That would be infinity. Both sides of the equation are 4x. Therefore anything you plug in for x would work