If the triangle below is enlarged by a scale factor of 1.2, what will be the area of the new triangle?

Answer:

0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

North Catalina:

Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:

[tex]\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188[/tex]

Chapel Mountain:

Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:

[tex]\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735[/tex]

What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?

We want that: [tex]N - C > 5[/tex]

Distribution N - C:

The mean is:

[tex]\mu = \mu_N - \mu_C = 130 - 120 = 10[/tex]

The standard deviation is:

[tex]s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5 - 10}{7.3937}[/tex]

[tex]Z = -0.68[/tex]

[tex]Z = -0.68[/tex] has a pvalue of 0.2483

1 - 0.2483 = 0.7517

0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students

Answer:

6 and 1/2

Step-by-step explanation:

The distance from Greg's house to Melissa's is 8 mi.

Step-by-step explanation:

Multiply 4 by 2.

Answer:

I believe the answer is 300

Step-by-step explanation:

Answer:

The answer is 5

Step-by-step explanation:

get to the middle of the 5's and that's your answer =>=

Answer:

The answer is 5

Step-by-step explanation:

Answer:

The four most common are probably line graphs, bar graphs and histograms, pie charts, and Cartesian graphs.

Answer:

5 more people studied more in 0-30 minutes than people who studied 121-120 minutes.

Step-by-step explanation:

Hi there!

[tex]\large\boxed{3 \text{ boxes}}[/tex]

Calculate the number of boxes of cubes needed by calculating the volume of the pictured figure.

We can see that it has a width of 4 blocks, depth of 2 blocks, and a height of 8 blocks.

Calculate volume: V = l × w × h

V = 4 × 2 × 8  = 64 cubes in each box.

Since she needs 140 cubes, we can find how many boxes she would need for this amount:

140 ÷ 64 = 2.1875.

However, you cannot buy a part of a box, which is why you must round to a whole number. However, only buying 2 boxes would be too little.

Thus, she would need to buy 3 boxes.

Answer:

62.5%

Step-by-step explanation:

There are a total of 8 people on the data plot.

5 of them got 15 questions or more correct, meaning 5/8 people got 15 or more questions correct.

5/8 = 5 ÷ 8

5 ÷ 8 = 0.625

0.625 = 62.5%

Answer:

11/25

Step-by-step explanation:

we can divide both top/bottom by 100, to get 11/25

:)

Answer:

$2672.20

Step-by-step explanation:

2300(1+(0.03)/(365))^(5*365)

=$2672.20

Answer:

no

Step-by-step explanation:

-1 - (-12)

the two negative signs before the 12 cancel out so it ends up being

-1+12

-1+12=11

11 and -1 are not equal to each other

Answer:

No

Step-by-step explanation:

-3-(-12)=-3+12

-3+12=9

Answer:

Fixed Annuity

Step-by-step explanation:

Fixed annuity is the most common annuity

During the accumulation phase, the individual makes a lump-sum payment or multiple payments over time to the insurance company

The insurance company invests the money as it sees fit, along with the money of other participants, forming a pool of invested funds

Answer:

4

Step-by-step explanation:

Answer:

4 and thank u or the free points

Step-by-step explanation:

Step-by-step explanation:

The answer is A

PLEASE FOLLOW ME

Answer:

Step-by-step explanation:

g(x) = √(32x) = √(2⁵x) = 4√(2x)

(f∘g)(x) = f(g(x))

= f(4√(2x))

= √(2 ⋅ 4√(2x))

= √(8√(2x))

= √8∜2∜x

= ∜(2⁷x)

= ∜(128x)

which doesn’t match any of the choices. There’s an error in the question.

I believe that the functions were written incorrectly and the x should not be part of the radicands (see attachment). That makes the answer A.

Answer:

no answer

Step-by-step explanation:

This is because,before finding the width,length,and height of the block, there should be a stated volume,or some other parameters or properties of the prism must be stated, as such the answer cannot be determined

Answer:

thanks

Step-by-step explanation:

Answer:

m∠3 = 119°

Step-by-step explanation:

All the angles must equal 360° when added together. You have two known angles that are right next to each other. If you add m∠1 and m∠2, 119 + 61, it is equal to 180°. This means that m∠3 and m∠4 must be equal to 180° as well and since there are only two lines, it is safe to assume that opposing angles are the same so m∠1 = m∠3 and m∠2 = m∠4.

Answer:

K12 answer

Step-by-step explanation:

-16p was my answer after simplifying it

Answer:

120p - 16p = 104p

Step-by-step explanation:

-3p x -3p = 9p + 6p = 15p x 8p = 120p

8p x -2 = -16p

120p - 16p = 104p

Please wait for more responses if needed thank you.

Answer:

the island is 1787.63ft far.

Step-by-step explanation:

<P=40° alternate angle

in triangle

relationship between perpendicular and base is given by tan angle

tan 40=p/b

tan40=1500/b

b=1500/tan40=1787.63ft

Answer:

The moving average (MA) is a simple technical analysis tool that smooths out price data by creating a constantly updated average price. The average is taken over a specific period of time, like 10 days, 20 minutes, 30 weeks or any time period the trader chooses. There are advantages to using a moving average in your trading, as well as options on what type of moving average to use. Moving average strategies are also popular and can be tailored to any time frame, suiting both long-term investors and short-term traders.

Step-by-step explanation:

One disadvantage to solving systems using substitution is that isolating a variable often involves dealing with messy fractions. There is another method for solving systems of equations: the addition/subtraction method.

In the addition/subtraction method, the two equations in the system are added or subtracted to create a new equation with only one variable. In order for the new equation to have only one variable, the other variable must cancel out. In other words, we must first perform operations on each equation until one term has an equal and opposite coefficient as the corresponding term in the other equation.

sorry it is so long, i hope this helps!

Answer:

Frame A width = 6.67 inches

Frame B width = 6 inches

Step-by-step explanation:

WA = width of frame A

WB = width of frame B

(WA)(6.75) = 45

WA = 6.67

(WB)(7.5) = 45

WB = 6

Answer:

Step-by-step explanation:

y = 4x + 1

Slope of line = 4

Slope of perpendicular to line = -¼

Point-slope equation for line of slope -¼ that passes through (12, -7):

y+7= -¼(x-12)

Answer:

a. committed a type 1 error

Step-by-step explanation:

The correct option is - a. committed a type 1 error

Reason -

Type 1 error occurs  when a true null Hypothesis is rejected

Type 2 error occurs when a false null Hypothesis is accepted

Now,

Let us state that,

The null hypothesis and alternate hypothesis is

H0 : There is no difference between the mean lifetimes of the new and old designs

H1 : There is a difference between the mean lifetimes of the new and old designs

Now,

As there is no difference between the mean lifetimes of the new and old designs.

⇒ The null hypothesis is true.

But p value suggests that null hypothesis should be rejected

∴

We have committed a Type 1 error that is rejecting a true null hypothesis.

So,

The correct option is - a. committed a type 1 error

Answer:

Hello your question is incomplete attached below is the complete question

answer : first 7 terms ( option 3 )

Step-by-step explanation:

Determine the number of terms of the series that is needed to find a sum with an absolute value of its error to be less than 0.001

The number is : 7

attached below is the detailed solution

From the above explanation, the option B statement is not correct.

From the given options we need to identify which statement is not correct.

An obtuse angle is any angle greater than 90° and less than 180°.

From option A:

100° angle is an obtuse angle, because which is greater than 90° and less than 180°.

From option B:

175° angle is a reflex angle because it is greater than 180° and less than 360°.

From option C:

Less than 90° lies in I quadrant, more than 90° and less than 180° lies in II quadrant and more than 180° and less than 270° lies in III quadrant.

From option D:

An 85° angle is an acute angle because it is greater than 0° and less than 90°.

From the above explanation, the option B statement is not correct.

To learn more about an obtuse angle visit:

https://brainly.com/question/1581660.

#SPJ5

Answer:

x = 8

y = 14

Step-by-step explanation:

2x + 6 = 4x - 10 (Corresponding angles so they're equal)

2x - 4x = -10 - 6

-2x = -16

x = 8

2x + 6 + 13y - 24 = 180 (Supplementary angles so they add up to 180)

2(8) + 6 + 13y - 24 = 180

16 + 6 + 13y - 24 = 180

13y - 2 = 180

13y = 182

y = 14

Answer:

2x+6=4x-10[corresponding angle]

16=2x

x=8

again

2×8+6+13y-24=180°[linear pair]

13y=180+2

y=182/13

y=14