The variance of the scores on a skill evaluation test is 203,401
with a mean of 1469
points.

If 358 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 41
points? Round your answer to four decimal places.

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

Step-by-step explanation:

Let's just say this circle has value x.

x increases by 5%, or 0.05 of x.

x + 0.05x = 1.05x

1.05x now increases by 5% again:

1.05x + 0.05(1.05x) = 1.1025x

The total increase is equal to (1.1025-1)*100 = 10.25%

Hope this helps!

Answer:

4.24

Step-by-step explanation:

round the hundredths place according to the thousandths place

if the thousandths place (in this case 9) is 5 or greater, round the hundredths place up

if the thousandths place is less than 5, keep the hundredths place the same number

Answer:

4.24

Step-by-step explanation:

since there's a 9 in the thousandths it will change the 3 to a 4

To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

The meter reading, in ccf, indicated by each of the gas meters would be  8.83 ccf.

Required to find the meter reading in ccf

Let x be \(m^{2}\) - meter readings.

The readings in ccf is:

Reading = x/ 2.832

Now, Assume the value of x is 25; The readings will be:

Reading = 25/ 2.832 ccf

Reading = 8.83 ccf

The complete question is

Manuel works for the water company as a meter reader. The meter below is the Jansen's water meter. What is the reading, in ccf, on the meter shown?

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The factory will put 441 cans of soda in 7 cases.

If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.

Given:

Number of flavors = 9

Cans per flavor = 7

Number of cases = 7

To calculate the total number of cans, we can multiply these values:

Total cans = Number of flavors × Cans per flavor × Number of cases

Total cans = 9 × 7 × 7

Total cans = 441

To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).

Hence, the factory will put 441 cans of soda in 7 cases.

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Answer: hello your question is incomplete below is the missing part

Determine the proportion of radishes grown without fertilizers with weight less than 50grams

answer : p( x < 50 ) = 0.84

Step-by-step explanation:

Radish grown in without fertilizers ( normally distributed )

mean = 40 g

standard deviation = 10 g

Radish grown with fertilizers ( normally distributed )

Mean = 140 g

standard deviation = 40 g

Determine the proportion of radishes grown without fertilizers with weight less than 50 grams

lets assume x = radish without fertilizers

                    y = radish with fertilizers

hence

p( x < 50 )  = P (  (x-μ / б)  < \(\frac{50-40}{10}\)  )

                  = p ( z < 1 ) = 0.5 + p ( 0 < z < 1 )

                                   p( x < 50 ) = 0.5 + 0.3413 = 0.8413

attached below is the distribution related to this solution

Answer:

Cant see the pic

Step-by-step explanation:

Answer:

Bc is intersected by segment AD

Answer:

Bc is intersected by segment AD

Step-by-step explanation:

The statement F(5) = 0.27 means that the probability that a tree is less than or equal to 5 meters tall is 0.27. In other words, the correct answer is: The probability that a tree is at most 5 meters tall is 27%.

The cumulative distribution function (CDF) gives the probability that a random variable is less than or equal to a certain value. In this case, F(5) gives the probability that a tree's height is less than or equal to 5 meters.

Therefore, the statement F(5) = 0.27 tells us that the probability that a tree's height is at most 5 meters is 0.27 or 27%. This means that 27% of the trees in the forest are 5 meters tall or shorter.

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It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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Answer:

Gerald should expect the spinner to land on 3, 126 times.

Step-by-step explanation:

Because we don't know what's actually going to happen, we can determine the theoretical probability by multiplying 1/5 by 630 to get 126.

Answer:

126

Step-by-step explanation:

Given that all of the spaces are equally sized, each space has an equal chance of being landed on by the spinner. As there are 5 spaces, the probability of landing on any one space is 1/5. This means that one fifth of the number of spins are expected to land on 3.

630 × 1/5 = 126

The median of the randomly selected list of prices of trucks will be 26 thousands dollars.

To find the median , first we need to arrange the list in either ascending form or descending form. Let us arrange the list in ascending form  :

List before sorting : 20,46,19,14,42,26,33

List after sorting it in ascending form : 14,19,20,26,33,42,46

Here, the number of observations is 7 which is odd. So, The formula to find the median term from a given number of "Odd" observations in a set is :

⇒ {(n+1) / 2}th term (where n is the number of observations in a set)

⇒({7+1}/2)

⇒8/2

⇒4th term

Therefore, the 4th term in our list of prices of trucks is the median which is 26 thousand dollars

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There are 4 quarts in a gallon, and a gallon weighs 8.34 pounds, so a quart weighs 2.085 pounds.

The gallon is a volumetric unit that is used in both imperial and American customary measurements. In use right now are three different variations:

the imperial gallon (imp gal), defined as 4.54609 litres, which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries; the US gallon (US gal), defined as 3.785411784 L,[1] (231 cubic inches), which is used in the US and some Latin American and Caribbean countries; and the US dry gallon ("usdrygal"), defined as 18 US bushel (exactly 4.40488377086 L).

gallon equals 4 quarts

2.1*4 =8.4

gallon of water weigh is 8.4

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Answer:

The answer is Offer 3 because it has the lowest total loan cost of the offers with a monthly payment in his budget

Answer: c, offer 3

Step-by-step explanation: just did the quiz

Answer: -39

Step-by-step explanation:

The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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dy/dx = 4 + √(y - 4x + 6)

Make a substitution of v(x) = y(x) - 4x + 6, so that dv/dx = dy/dx - 4. Then the DE becomes

dv/dx + 4 = 4 + √v

dv/dx = √v

which is separable as

dv/√v = dx

Integrating both sides gives

2√v = x + C

Get the solution back in terms of y :

2√(y - 4x + 6) = x + C

You can go on to solve for y explicitly if you want.

√(y - 4x + 6) = x/2 + C

y - 4x + 6 = (x/2 + C )²

y = 4x - 6 + (x/2 + C )²

Answer:

  A: f(x)=2x^2 +12x +10

  B: f(0) = 10

Step-by-step explanation:

Part A:

f(0) is a constant in the equation if the form is such that for x=0, all terms are zero except one of them. Standard form is one such form. This is the equation in standard form:

  f(x) = 2x^2 +12x +10

__

Part B:

  f(0) = 0 + 0 + 10

  f(0) = 10

Answer:

4.5

Step-by-step explanation:

Let's set up an equation:

1.1n=4.95

n is the number

We can use a calculator to figure this out:

n=4.5

Answer:

x = 33 degrees.

Step-by-step explanation:

You can see that there is triangle ABC. There are 180 degrees in a triangle. One angle of the triangle is 42 degrees, and the other is 105 degrees. 105 + 42 = 147. The angle at point C would then be 180 - 147 = 33 degrees.

Because lines BC and DE are parallel, you can say that the 33 degree angle and the x-degree angle are the same, since they are alternate angles. Hence, the x is 33 degrees.

Answer:

300+ 80+6

Step-by-step explanation:

i think i not sure

3, x, x+6 are the first 3 terms of G.P

common ratio is x/3=x+6/x

so we cross multiply x×x=3×x+6

ײ= 3x+18 so we have x²-3x-18

(x-6)(x+3)=0

the possible value of x are 6 and -3

b) tenth term of the seauence

first of all the possible sequence are 3, 6, 12 and 3, -3, 3

but we need only the positive GP

so the common ratio of.the GP r is 6/3=2

the 10th term of a GP sequence is ar^10-1=ar^9

where a = first time

3×2^9=3×512=1536

the 10th term is 1536

It would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.

To find the number of years necessary for an investment to double at a simple interest rate of 11%, we can use the following formula:

n = 72 / r

where n is the number of years required for the investment to double, and r is the interest rate.

Plugging in the values, we get:

n = 72 / 11

n ≈ 6.5 years (rounded to the nearest tenth)

Therefore, it would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.

Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested, and it is not compounded over time.

The formula for calculating simple interest is:

I = P * r * t

where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.

For example, if you borrow $1,000 for two years at a simple interest rate of 5%, the interest you would pay is calculated as follows:

I = 1,000 * 0.05 * 2

I = $100

So, you would have to pay back the $1,000 principal plus $100 in interest, for a total of $1,100.

Simple interest is commonly used in short-term loans or investments, and it is usually easier to calculate and understand than compound interest, which takes into account the effect of earning interest on previously earned interest.

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The set of 3 lengths that make a right triangle is {8, 15, 17}

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.

So if the 3 sides are A, B, and C, such that:

A < B < C

We will have:

A² + B² = C²

Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:

8² + 15² = 17²

289 = 289

That equationis true, thus, these 3 lengths make a right triangle.

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