i need help with this asap please

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that applies to data that is approximately normally distributed. It states that:
Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard deviations of the mean

In the context of your question, where the mean IQ is 100 and the standard deviation is 15, we can use the empirical rule to answer certain questions.
Approximately 68% of individuals would have an IQ between 85 and 115, since this range falls within one standard deviation of the mean.

Approximately 95% of individuals would have an IQ between 70 and 130, since this range falls within two standard deviations of the mean. Approximately 99.7% of individuals would have an IQ between 55 and 145, since this range falls within three standard deviations of the mean.

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Approximately 99.7% of the IQ scores will fall between 55 and 145. The empirical rule, also known as the 68-95-99.7 rule, is a statistical principle that applies to data that follows a normal distribution. It states that:

1. Approximately 68% of the data falls within one standard deviation of the mean.
2. Approximately 95% of the data falls within two standard deviations of the mean.
3. Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the standardized test of intelligence has a mean IQ of 100 and a standard deviation of 15.

1. To determine the range of IQ scores within one standard deviation of the mean, we can use the empirical rule. Since 68% of the data falls within one standard deviation of the mean, we can calculate the range as follows:
  - Lower bound: Mean - Standard deviation = 100 - 15 = 85
  - Upper bound: Mean + Standard deviation = 100 + 15 = 115
  Therefore, approximately 68% of the IQ scores will fall between 85 and 115.

2. To determine the range of IQ scores within two standard deviations of the mean, we can use the empirical rule. Since 95% of the data falls within two standard deviations of the mean, we can calculate the range as follows:
 \(- Lower bound: Mean - (2 \times Standard deviation) = 100 - (2 \times 15) = 70\\- Upper bound: Mean + (2 \times Standard deviation) = 100 + (2 \times 15) = 130\)
  Therefore, approximately 95% of the IQ scores will fall between 70 and 130.

3. To determine the range of IQ scores within three standard deviations of the mean, we can use the empirical rule. Since 99.7% of the data falls within three standard deviations of the mean, we can calculate the range as follows:
 \(- Lower bound: Mean - (3 \times Standard deviation) = 100 - (3 \times 15) = 55\\ -Upper bound: Mean + (3 \times Standard deviation) = 100 + (3 \times 15) = 145\)
  Therefore, approximately 99.7% of the IQ scores will fall between 55 and 145.

These ranges give us an idea of where the majority of IQ scores are likely to fall based on the standard deviation from the mean.

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Answer:

49950

Step-by-step explanation:

111% of 45000 is 49950

Answer:

The amount Craig financed at the beginning(P) = 45000

Number of years he took to repay(T) = 5

Rate of interest(R) = 11%

Total interest he paid = PTR/100

= 45000(5) (11) / 100

= 450 × 55 = 24,750

Therefore Craig will have paid $24,750

Step-by-step explanation:

Answer:

1. 2

2. 17

3. 6

4. 36

5. 37

6. 12

Step-by-step explanation:

1. 7-5=2

2. 30x17=510

3. 12x6=72

4. 4x9=36

5. 49-12=37

6. 9 plus 3=12

Answer:

The letter t occurs more than 26 times on approximately 420 of these pages.

Step-by-step explanation:

1 standard deviation below mean = M - SD

                                                      = 44 - 18 = 26

This implies that that "26" is 1 s.d. below the mean, which is at the 16th percentile.

Thus,  there is a 0.16 chance that "t" will occur less than 26 times on any single page.

consequently, there is a 0.84 chance that it will occur more than 26 times on any single page.

Answer:

7 millimeters

Step-by-step explanation:

\( {7 }^{2} = 49\)

Answer:

3

Step-by-step explanation:

Let's find the first term in terms of p.

So an arithmetic sequence is a linear relation.

That means it will have the same slope no matter the pair of points used. We are given the slope, the common difference, is 2. We are going to use point (9, 3+3p) and (1, t(1)) along with m=2 to find t(1).

[t(1)-(3+3p)]/[1-9]=2

Simplify denominator

[t(1)-(3+3p)]/[-8]=2

Multiply both sides by -8

t(1)-(3+3p)=-16

Add (3+3p) on both sides

t(1)=-16+3+3p

Combine like terms

t(1)=-13+3p

This means we can find the next term by adding 2 this.

t(2)=-11+3p

Let's find the next term by adding 2 this.

t(3)=-9+3p

Finally we can find the 4th term by adding 2 to this

t(4)=-7+3p

We are given the sum of the first 4 terms is 2p-10. So we can write:

-13+3p+-11+3p+-9+3p+-7+3p=2p-10

Combine like terms on left

12p-40=2p-10

Subtract 2p on both sides

10p-40=-10

Add 40 on both sides

10p=30

Divide both sides by 10

p=3.

-----------------

Checking:

t(1)=-13+3p=-13+3(3)=-13+9=-4

t(2)=-11+3p=-11+3(3)=-11+9=-2

t(3)=-9+3p=-9+3(3)=-9+9=0

t(4)=-7+3p=-7+3(3)=-7+9=2

----sum of the first 4 is -4

And 2p-10 at p=3 gives 2(3)-10=6-10=-4

So this part checks out

In general, the pattern that those 4 terms I wrote out follow t(n)=(-13-2)+2n+3p. I know this because the 0th term would have been (-13-2)+3p and this part goes up by 2 each time. The plus 3p part doesn't change.

Anyways t(9)=(-13-2)+2(9)+3p=-15+18+3p=3+3p. And this part looks good too.

If Judy's refund is $535, to pay for furniture worth $800, she will have to come up with $265, which is the difference.

The difference is the result of the subtraction operation.

The subtraction operation is one of the four basic mathematical operations.

Subtraction operations involve the minuend, subtrahend, the subtraction operator (-), the difference, and the equal symbol (=).

The cost of furniture = $800

Expected credit refund = $535

The difference between the cost and refund = $265 ($800 - $535)

Thus, Judy will bring $265 to make up for the purchase of the furniture.

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5 ori 5 fac 25 și cu 25 egal 14 și cu 14 egal 100 și cu 100 egal 12

Step-by-step explanation:

sper ca team ajutat

Answer:

∠ 6 = 45°

Step-by-step explanation:

∠ 6 and 45° are vertically opposite angles and are congruent , so

∠ 6 = 45°

The probability that calls to exactly two randomly selected households will both go unanswered is 0.1849

From the question, we have the following parameters that can be used in our computation:

Probabiity of answering, p = 57%

This means that the probability that no one answers the call is

q = 1 - 57%

Evaluate

q = 43%

So, the probability that both calls will go unanswered is

P = q²

This gives

P = (43%)²

Evaluate

P = 0.1849

Hence, the probability is 0.1849

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Answer:

0.25 hours, or 15 minutes

Step-by-step explanation:

Ok, so the rate is 32 miles per hour, so it would take about 1/4 of a hour to go 8 miles (8/32= 0.25)

The number sentence that represents 6 times as many as 12 is 6x = 12

Let the unknown number be x

6 times the number will be expressed as 6x

6 times as many as 12 means we are to equate the result of the product of 6 and x to 12. This is expressed as 6x = 12

Hence the number sentence that represents 6 times as many as 12 is 6x = 12

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Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

The standard deviation for this data set is approximately 8.9.

The standard deviation for this data set is approximately 103.4 calories.

What is standard deviation?

Standard deviation is a measure of variability or spread in a set of data. It is the square root of the variance, which is the average of the squared differences from the mean.

a. To find the range of the data set, we need to subtract the smallest value from the largest value.

Range = Largest value - Smallest value

The smallest value is 15 and the largest value is 25.

Range = 25 - 15 = 10 grams

b. To find the standard deviation of the data set, we can use a calculator or software program that has a built-in formula for calculating standard deviation.

Using a calculator, we get:

Standard deviation ≈ 2.8 grams

Therefore, the standard deviation for this data set is approximately 2.8 grams.

For the second question:

a. To find the range of the calorie data set, we need to subtract the smallest value from the largest value.

Range = Largest value - Smallest value

The smallest value is 340 calories and the largest value is 600 calories.

Range = 600 - 340 = 260 calories

b. To find the standard deviation of the calorie data set, we can use a calculator or software program that has a built-in formula for calculating standard deviation.

Using a calculator, we get:

Standard deviation ≈ 103.4 calories

Therefore, the standard deviation for this data set is approximately 103.4 calories.

For the third question:

To calculate the standard deviation of the given data set, we first need to find the mean:

mean = (2 + 12 + 27 + 14 + 4) / 5 = 59 / 5 = 11.8

Next, we need to find the deviations of each data point from the mean:

(2 - 11.8) = -9.8

(12 - 11.8) = 0.2

(27 - 11.8) = 15.2

(14 - 11.8) = 2.2

(4 - 11.8) = -7.8

Then, we need to square each deviation:

(-9.8)² = 96.04

(0.2)² = 0.04

(15.2)² = 231.04

(2.2)² = 4.84

(-7.8)² = 60.84

Next, we need to find the average of the squared deviations, which is the variance:

variance = (96.04 + 0.04 + 231.04 + 4.84 + 60.84) / 5 = 78.96

Finally, we can find the standard deviation by taking the square root of the variance:

standard deviation = sqrt(78.96) ≈ 8.9

Therefore, the standard deviation for this data set is approximately 8.9.

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Answer:

=======================

Any rational number can be written in the form of p/q as per definition of a rational number.

In case with zero, it can be:

So, we'll have:

Answer:

domain = {6,16,41,49}

range = {4,-10,7}

The value of x is 17

The congruent arcs are (b) PQ and SR

The radius is 12 units

The value of PQ is 4

The length YZ is 19 units

In this question, we make use of the property of congruent sides

So, we have

3x - 24 = x + 10

When evaluated, we have

2x = 34

Divide by 2

x = 17

By the definition of congruent arcs, congruent arcs are arcs that have equal measures

In this figure, the congruent arcs are PQ and SR i.e. (b) PQ and SR

The radius of the circle is calculated as

r² = (25 + r)² - 35²

When expanded, we have

r² = 625 + 50r + r² - 1225

So, we have

50r = 600

Divide both sides by 50

r = 12

In this question, we make use of the property of congruent sides

So, we have

PQ = SR

Where

SR = 4

When evaluated, we have

PQ = 4

The length of YZ in the circle is calculated as

YZ² = (9 + 8)² + 8²

So, we have

YZ² = 17² + 8²

When expanded, we have

YZ² = 289 + 64

So, we have

YZ² = 353

Take the square root of both sides

YZ = 19

Hence, the length YZ is 19 units

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Answer:

3645

Step-by-step explanation:

65610/18=3645

Answer:

Hi, there

Question 1: B. 6x^3(x-6)

Question 2: A. (8x+3)^2

Question 3: A. (5x+9y)(5x-9y)

Question 4: D.(x-2)(x-3)

Step-by-step explanation:

Hope this helps :)

Answer:

1) I would remove the '-2' first by adding '2' to both sides. Technically, it does not matter the order you remove the '5' or '-2' though it would be more of a hassle if you were to remove the number associated w/ a variable as you would do extra steps when there is a possibility to do it in less steps. So, ideally, it does matter but depending on your perspective.

2) You would begin by turning '1' into a fraction that has the same denominator as the fraction it is to be added to. This would get you 7/7. Then, you add 7/7 to 4/7 in order to get your final answer of 11/7. You could also just put the two numerical values together as '1 4/7' but I am inferring they want it in an improper fraction format. The steps to get an improper fraction are ideal since it is the simplest way to get to the final answer.

If you have any more questions please comment them and I will be happy to answer them if I can ^^

When the diameter is 100 mm, the volume is increasing at a rate of 300π mm^3/s.

We use the derivative of the volume equation with respect to time. Given that the radius is increasing at a rate of 3 mm/s, we can differentiate the volume equation and substitute the values.

The equation for the volume (V) of a sphere with radius (r) in mm is given by: V = (4/3)πr^3 mm^3

To find the radius of a sphere when its diameter is 100 mm, we can divide the diameter by 2: Radius = Diameter / 2 = 100 mm / 2 = 50 mm

When the radius is 50 mm, we can substitute this value into the volume equation to find the volume: V = (4/3)π(50^3) mm^3 = (4/3)π(125000) mm^3

To determine how fast the volume is increasing when the diameter is 100 mm, we need to find the derivative of the volume equation with respect to time. Since the radius is increasing at a rate of 3 mm/s, we can express the derivative of the volume with respect to time as dV/dt.

dV/dt = (dV/dr) * (dr/dt)

We know that dr/dt = 3 mm/s and we can differentiate the volume equation to find dV/dr:

(dV/dr) = 4πr^2 mm^3/mm

Substituting the values:

dV/dt = (4πr^2) * (dr/dt) = (4π(50^2)) * (3) mm^3/s

Simplifying:

dV/dt = 300π mm^3/s

Therefore, when the diameter is 100 mm, the volume is increasing at a rate of 300π mm^3/s.

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Answer:

OZQ=125°

OZP=62°

PZQ=OZQ+OZP

PZQ=125+62

PZQ=187°

Answer:

9

Step-by-step explanation:

4-x = 5(16-x)

44-x = 80-5x

4x = 36

x = 9

9in,12in,13in

Step-by-step explanation:

9in,12in,13in

The side lengths that form a right triangle are:

Option D is the correct answer.9 in., 12 in., 13 in.

We have,

To determine if a set of side lengths forms a right triangle, we can use the Pythagorean theorem.

According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's examine the given sets of side lengths:

15 in., 12 in., 9 in.

Applying the Pythagorean theorem:

\((9^2) + (12^2) = 81 + 144 = 225\)

(15²) = 225

Since 225 is equal to 225, this set of side lengths does form a right triangle.

12 in., 9 in., 17 in.

Applying the Pythagorean theorem:

\((9^2) + (12^2) = 81 + 144 = 225\)

(17²) = 289

Since 225 is not equal to 289, this set of side lengths does not form a right triangle.

21 in., 12 in., 9 in.

Applying the Pythagorean theorem:

(9²) + (12²) = 81 + 144 = 225

(21²) = 441

Since 225 is not equal to 441, this set of side lengths does not form a right triangle.

9 in., 12 in., 13 in.

Applying the Pythagorean theorem:

(9²) + (12²) = 81 + 144 = 225

(13²) = 169

Since 225 is equal to 169, this set of side lengths does form a right triangle.

Therefore,

Only the set of side lengths 9 in., 12 in., 13 in. forms a right triangle, as it satisfies the Pythagorean theorem.

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Answer:

5

Step-by-step explanation:

15 has 2 factors 5 and 3

80 gets split into 16 and 5

then split into 8 and 2

then 2 and 4

then 2 and 2

the GCF therefore is 5

Answer:

442

Step-by-step explanation:

Answer:

Vertex is (3, 256)

Step-by-step explanation:

The vertex means that at 3 seconds, the highest point the ball will reach is 256 units in the air.

The critical value of a one-tailed t-test with degrees of freedom of 8 and using an alpha level of 0.01 is approximately 2.896.

To find the critical value of a one-tailed t-test with degrees of freedom (df) = 8 and an alpha level of 0.01, follow these steps:

1. Identify the degrees of freedom (df): In this case, df = 8.
2. Determine the alpha level: Here, the alpha level is 0.01.
3. Check a t-distribution table for the critical value corresponding to the given degrees of freedom and alpha level.

Using a t-distribution table, the critical value for a one-tailed t-test with df = 8 and an alpha level of 0.01 is approximately 2.896.

Your answer: The critical value of a one-tailed t-test with degrees of freedom of 8 and using an alpha level of 0.01 is approximately 2.896.

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Based on the 2009 Current Population Survey, 40% of the U.S. population aged 25 years and over has completed a bachelor's degree or more. In a random sample of 50 people aged 25 or over, the mean number of people who have completed a bachelor's degree can be found by multiplying the sample size (50) by the percentage (40%).

Mean = (Sample size) * (Percentage of people with a bachelor's degree)
Mean = 50 * 0.40
Mean = 20

So, in a random sample of 50 people aged 25 years or over, the mean number of people that have completed a bachelor's degree is 20.

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Answer:

Step-by-step explanation:

An isosceles triangle is a one that has two of its sides equal. Hence option (c) is correct because here two sides have length of 11.9.

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To solve the system of linear equations using Cramer's Rule, we need to find the values of x, y, and z by using determinants.

The given system of equations is:

4x – 3y + 4z = 10 (Equation 1)

5x – 2z = -2 (Equation 2)

3x + 2y – 5z = -9 (Equation 3)

To apply Cramer's Rule, we first calculate the determinant of the coefficient matrix, denoted as D:

D = | 4 -3 4 |

| 5 0 -2 |

| 3 2 -5 |

Next, we calculate the determinants of the matrices obtained by replacing the first column of the coefficient matrix with the constants from the right-hand side of the equations. These determinants are denoted as Dx, Dy, and Dz:

Dx = | 10 -3 4 |

| -2 0 -2 |

| -9 2 -5 |

Dy = | 4 10 4 |

| 5 -2 -2 |

| 3 -9 -5 |

Dz = | 4 -3 10 |

| 5 0 -2 |

| 3 2 -9 |

Finally, we can find the values of x, y, and z using the formulas:

x = Dx / D

y = Dy / D

z = Dz / D

By evaluating these determinants and performing the calculations, we can find the solutions to the system of linear equations.

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