round 8.51348434552 to 3 decimal places.

Answer:

C

Step-by-step explanation:

The surface area (SA) of a sphere is calculated as

SA = 4πr² ( r is the radius )

Here diameter = 4 , then r = 0.5 × 4 = 2 , then

SA = 4π × 2² = 4π × 4 = 16π ft² → C

Answer:

16π  m²

Step-by-step explanation:

Screenshot down below that i got it correct on founders education

Yes, this is a discrete sample space because there are a finite number of possible outcomes. The possible outcomes are: TTTT, HTTTT, HHTTTT, HHHTTTT, THHTTTT, TTHHTTTT, TTTHHTTTT, TTTHTTTT. These are the only elements of the sample space that require 7 or less tosses.

To find these elements, we can start by listing the outcomes that require exactly 4 tosses: TTTT. Then we can add a head to the beginning of each of these outcomes to get the outcomes that require exactly 5 tosses: HTTTT. We can continue this process to get the outcomes that require exactly 6 tosses: HHTTTT, THHTTTT, and the outcomes that require exactly 7 tosses: HHHTTTT, TTHHTTTT, TTTHHTTTT, TTTHTTTT.

Therefore, the sample space is discrete because there are a finite number of possible outcomes, and we can list all of the elements of the sample space that require 7 or less tosses.

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Answer: The area of square A is 28 square units because the area is decreasing by 36 and the angles on each side is decreasing by 9

Step-by-step explanation:

100 divide by 4 sides = 25

64 divide by 4 sides = 16

28 divide by 4 sides = 7

Answer:

Part A: so that no single branch has to much power

Part B: "Each branch of government must check the actions of the other two branches to prevent one branch from having too much power."

Answer:

Part A is the first choice and part B is the second choice

The question states that a study suggests that 60% of college students spend 10 or more hours per week communicating with others online.

However, you believe that this information is incorrect and decide to collect your own sample for a hypothesis test. You randomly sample 160 students from your dorm and find that 70% of them spent 10 or more hours a week communicating with others online.

A hypothesis test is used to determine whether the results from a sample are statistically significant and can be generalized to the larger population. In this case, your friend has come up with the following set of hypotheses:

1. Null hypothesis (H0): The proportion of college students who spend 10 or more hours per week communicating with others online is 60%.

2. Alternative hypothesis (Ha): The proportion of college students who spend 10 or more hours per week communicating with others online is not 60%.

Based on the information given, there are a couple of errors in the set of hypotheses proposed by your friend.

Firstly, the null hypothesis should reflect the information from the initial study, which states that 60% of college students spend 10 or more hours per week communicating online. So, the correct null hypothesis should be:

1. Null hypothesis (H0): The proportion of college students who spend 10 or more hours per week communicating with others online is 60%.

Secondly, the alternative hypothesis should reflect your belief that the initial study is incorrect, and your sample suggests a different proportion. In this case, your alternative hypothesis should be:

2. Alternative hypothesis (Ha): The proportion of college students who spend 10 or more hours per week communicating with others online is not 60%.

To summarize, the correct set of hypotheses for your hypothesis test would be:

H0: The proportion of college students who spend 10 or more hours per week communicating with others online is 60%.

Ha: The proportion of college students who spend 10 or more hours per week communicating with others online is not 60%.

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Answer:

29, height is > 30

Step-by-step explanation:

all the angles in a triangle add up to 180, they give 1 angle 61 degrees and it's a right triangle so 61 + 90 = 151

180 - 151 = 29

the third angle is 29 degrees

The height of the building is found using trigonometry

tangent o/a

tan(61 degrees) = o/30

height = 54.1

height is > 30

The magnification n can be found by using the formula n = -s'/s, where s' is the image distance and s is the object distance. The value of s' obtained from this new equation can be found by rearranging the formula to s' = -ns.

To find the magnification n, we can use the formula n = -s'/s, where s' is the image distance and s is the object distance. In this case, the object is placed 45.0 centimeters from the mirror, so s = 45.0 cm. The magnification can be found by calculating the ratio of the image distance to the object distance. By rearranging the formula, we get n = -s'/s.

To find the value of s' obtained from this new equation, we can rearrange the formula n = -s'/s to solve for s'. This gives us s' = -ns. By substituting the value of n calculated earlier, we can find the value of s'. The negative sign indicates that the image is inverted.

Using the given values, we can now calculate the magnification and the value of s'. Plugging in s = 45.0 cm, we find that s' = -ns = -(2/3)(45.0 cm) = -30.0 cm. This means that the image is located 30.0 centimeters from the mirror and is inverted compared to the object.

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The exponential function models the data for the amount earned by Miguel when he invests his money is f(x) = $400 x (1.08)^y

Exponential functions are in the form: a\(b^{x}\)

Where:

FV = $400 x (1.08)^y

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Miguel invested $400 in a bank account that pays interest. The account’s value over time, in x years, is given in the table.

Which exponential function models the data? Round the numerical values to the nearest hundredth.

f(x) = 1.41(30.69)x

f(x) = 37.74(396.48)x

f(x) = 390.60(1.41)x

f(x) = 401.19(1.08)x

ANSWER>D

Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48

The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:

Single Sampling Plan (n=80, c=3):

ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79

Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):

ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48

The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.

For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.

For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.

These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.

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If the credit card did not have a promotional offer, Lori would have had to pay approximately $110.58 more in interest.

a. To determine how long it will take Lori to pay off the balance, we need to calculate the number of months it will take for the total balance to reach zero.

Let's assume it takes n months for Lori to pay off the balance. Each month, Lori pays $75 towards the balance. Since there is no interest during the promotional period, the balance decreases by $75 each month.

The initial balance is $562, so the remaining balance after n months can be represented as:

Remaining balance = Initial balance - (Monthly payment * Number of months)

0 = 562 - (75 * n)

Solving this equation for n:

75n = 562

n = 562 / 75

n ≈ 7.49

Therefore, it will take Lori approximately 7.49 months (or rounded up to 8 months) to pay off the balance.

b. To calculate the total interest paid, we need to subtract the initial balance from the total amount paid over the repayment period. The total amount paid is the monthly payment multiplied by the number of months.

Total interest paid = Total amount paid - Initial balance

Total amount paid = Monthly payment * Number of months

Total interest paid = (Monthly payment * Number of months) - Initial balance

Total interest paid = (75 * 8) - 562

Total interest paid = 600 - 562

Total interest paid = $38

Therefore, Lori will pay a total of $38 in interest.

c. If the credit card did not have a promotional offer, the interest would have been charged at a rate of 19.7% compounded daily after the promotional period.

To calculate the additional interest, we can use the formula for compound interest:

Additional interest = Initial balance * (1 + interest rate)^Number of months - Initial balance

Additional interest = 562 * (1 + 0.197/365)^(30 * 4) - 562

Calculating this value:

Additional interest ≈ $110.58

Therefore, if the credit card did not have a promotional offer, Lori would have had to pay approximately $110.58 more in interest.

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Answer:

  B. 5 seconds

Step-by-step explanation:

A graphing calculator shows the answer easily.

__

h(t) = 0 = -16t^2 +400

t = √(400/16) = 5

It will take 5 seconds for the sandbag to hit the ground.

Answer:

Step-by-step explanation:

They are not wrong exactly. Their answers are just incomplete. They did not take the factoring process to it's end.

Victoria could pull out another three.

Rebecca could pull out another five.

The answer is 15(y + 2)

Answer:

because:  3(5y + 10)=15y+30 (Distributive property between addition and multiplication )

the same we have  5(3y + 6)=15y+30

Step-by-step explanation:

The amount of water left in the tank 10 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present is 147.26L.

A 300-liter tank initially full of water develops a leak at the bottom. Given that 30% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 10 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present. As 30% of the water leaks out in the first 5 minutes, we can find the remaining water as 100% - 30% = 70% of 300L = 210L water is left in the tank.

Now, the rate of water drained off is proportional to the amount of water present. Let V be the volume of water left in the tank after t minutes. Then we can write the following differential equation:dV/dt = -kVwhere k is a constant of proportionality

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Check the picture below.

The formula to determine the total cost of the monthly rental is R300 + (Number of minutes beyond 500 * R0.50)

The formula to calculate the total cost (in rands) for CALL PACKAGE 2 can be expressed as:

Total cost (in rands) = Monthly rental + (Number of minutes beyond the free minutes * Cost per minute)

In this case, the monthly rental for PACKAGE 2 is R300, and the first 500 minutes are free. Calls beyond the free minutes cost R0.50 per minute.

Therefore, the formula becomes:

Total cost (in rands) = R300 + (Number of minutes beyond 500 * R0.50)

This formula calculates the total cost by adding the monthly rental fee to the cost of the minutes used beyond the free minutes, which is calculated by multiplying the number of minutes beyond 500 by the cost per minute, R0.50.

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Answer:

b

Step-by-step explanation:

The  equation of the line is y =  x + 6.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

= 1/-m  =1/ 4  

then,

y =  x/4 + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

hence, y =  x/4 + 6 ← equation of perpendicular line.

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The speed of the rock just before it strikes the ground is given by v = √(2 * 9.8 m/s² * h), where h is the height from which the rock falls.

To calculate the kinetic energy gained by the rock while falling, we need to determine the change in potential energy. The potential energy lost by the rock is converted into kinetic energy.

The potential energy lost by the rock is given by the formula: ΔPE = m * g * h, where m is the mass of the rock (2.2 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height from which the rock falls.

Since the rock starts from rest, its initial kinetic energy is zero. Therefore, the change in kinetic energy is equal to the change in potential energy.

Using the conservation of energy principle, the change in potential energy is equal to the gained kinetic energy: ΔKE = ΔPE.

Now, we can calculate the gained kinetic energy: ΔKE = 2.2 kg * 9.8 m/s² * h.

To find the speed of the rock just before it strikes the ground, we can equate the gained kinetic energy to the final kinetic energy using the formula: KE = (1/2) * m * v², where KE is the kinetic energy, m is the mass of the rock, and v is the velocity or speed of the rock.

Setting ΔKE equal to KE and solving for v, we have: 2.2 kg * 9.8 m/s² * h = (1/2) * 2.2 kg * v².

Simplifying the equation, we get: v² = 2 * 9.8 m/s² * h.

Taking the square root of both sides, we find: v = √(2 * 9.8 m/s² * h).

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The complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

To describe the complement of the given event, we need to first understand what complement means in probability theory. The complement of an event is the set of outcomes that are not included in the event.

So, the given event is that 71% of a person's credit card purchases are seventy dollars or more. This means that 100% - 71% = 29% of the person's credit card purchases are less than seventy dollars. This is the complement of the given event.

Hence, the complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

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Answer:

5050

Step-by-step explanation:

To solve via calculator, go to the MATH menu, then the 0th option should say "summation" and insert it from there.

To solve algebraically, break the summation into 2 parts. Excuse the strange formatting, I can't find a way to do it normally.

4(\(\frac{50}{1}\)∑n) -

= 4( \(\frac{50(50+1)}{2}\)) - 50(1)

= 5100 - 50

= 5050

The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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SORRY PLEASE DELETE THIS ANSWER IT ISN'T GOOD AND IS INCOMPLETE I ACCIDENTALLY WROTE IT

Answer:

615,000

Step-by-step explanation:

When you "round to the nearest _____" regardless of what goes in the blank the steps are nearly always the same:

Identify which place value you are rounding to. The smaller the place value, the more accurate the final result will be.

Look to the next smallest place value, the digit to the right of the place value you're rounding to. For example, if you want to round to the nearest ten you'd look at the ones place.

If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round to as-is. Any digits after that number (including the next smallest place value you just looked at) become zeros, or drop-off if they're located after the decimal point. This is called rounding down.

If the next smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding to by one (+1). Just like before, any remaining digits before the decimal point become zeros, and any that are after the decimal point are dropped. This is called rounding up.

Answer:

615,000

Step-by-step explanation:

614,952

Locate the thousands place:

614,952

Check next door:

614,952

If the number is greater than or equal to 5, then we round up. If it is less than or equal to 4, we round down.

9 is greater than 5. We would round up.

614,952 ≈ 615,000

Hope this helps.

answer:

75 times

explanation:

just add 25 per 10 seconds

Answer:

The correct answer is 75 jumps in 30 seconds.

Step-by-step explanation:

All you do is multiply 25x3=75. Because 3x10=30.

The perimeter p, in feet, of the fountain, will increase 0.25 feet for each additional square foot of the path's area.

The area function for this problem is given as follows:

A = 4p + 64.

In which p is the perimeter.

The perimeter function can be written as follows:

4p = A - 64

p = 0.25A - 16.

The slope of the linear function of m = 0.25 means that the perimeter p, in feet, of the fountain, will increase 0.25 feet for each additional square foot of the path's area.

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