Grandma Marlene and Grandpa Gary are putting holiday lights on the gutters of their house. Grandma Marlene leans a 16-foot ladder up against the house, which makes the base of the ladder 9 feet from the house. How far up the house is the ladder?

Answer:

97 students must be randomly selected for IQ tests.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The Standard Deviation is 15.

This means that [tex]\sigma = 15[/tex]

How many statistics students must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 3 IQ points of the population mean?

This is n for which M = 3. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]3 = 1.96\frac{15}{\sqrt{n}}[/tex]

[tex]3\sqrt{n} = 1.96*15[/tex]

Simplifying both sides by 3

[tex]\sqrt{n} = 1.96*5[/tex]

[tex](\sqrt{n})^2 = (1.96*5)^2[/tex]

[tex]n = 96.04[/tex]

Rounding up(as with a sample size of 96 the margin of error will be slightly above 3):

97 students must be randomly selected for IQ tests.

Answer:

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees.

Answer:

0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.

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.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean of 48.3 ppm and a standard deviation of 8 ppm.

This means that [tex]\mu = 48.3, \sigma = 8[/tex]

Sample of 40:

This means that [tex]n = 40, s = \frac{8}{\sqrt{40}}[/tex]

Find the probability that the disposal of such capacitors will be regulated.

Sample mean above 48.5, which is 1 subtracted by the p-value of Z when X = 48.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{48.5 - 48.3}{\frac{8}{\sqrt{40}}}[/tex]

[tex]Z = 0.16[/tex]

[tex]Z = 0.16[/tex] has a p-value of 0.5636.

1 - 0.5636 = 0.4364

0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.

Answer:

at 95% confidence interval,  the mean amount of sleep per night is ( 7.87, 8.05 ).

Option b) (7.87, 8.05) is the correct answer.

Step-by-step explanation:

Given the data in the question;

sample size n = 1140

sample mean x" = 7.96

standard deviation σ = 1.6

At 95% confidence interval,

significance level ∝ = 1 - 95% = 1 - 0.95 = 0.05

∝/2 = 0.05 / 2 = 0.025

Z-Critical [tex]Z_{\alpha /2[/tex] = [tex]Z_{0.025[/tex] = 1.96

Top get the Margin of error E;

E = [tex]Z_{\alpha /2[/tex] × ( σ /√n )

we substitute

E = 1.96 × ( 1.6 /√1140 )

E = 0.09

So, At 95% confidence interval of the population mean is;

⇒ x" ± E

⇒ x" - E or x" + E

we substitute

⇒ 7.96 - 0.09, 7.96 + 0.09

⇒ 7.87, 8.05

Therefore, at 95% confidence interval,  the mean amount of sleep per night is ( 7.87, 8.05 ).

Option b) (7.87, 8.05) is the correct answer.

Answer:

Step-by-step explanation:

Find the diagram attached

If W and X are the endpoints of a diameter on the circle, this means that arc WX is 180degres

Since the angle at the vertex is half the angle at the intercepted arcs.

<V = 1/2(arcWX)

4x+18 = 1/2*180

4x+18 = 90

4x = 90-18

4x = 72

x = 72/4

x = 18

Hence the value of x is 18

Answer:

160000m³

Step-by-step explanation:

Volume of a rectangular prism= A x h

V= l x b x h

V= 80x 50 x 40

V= 160000m³

Answer:

y = 0x + (-10) or y = 0x - 10

Step-by-step explanation:

y= 0x + b

-10= 0(3) + b

-10 = b

Which gives you the equation

y= 0x + (-10)

Answer:

i need more informatiion

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

.

Answer:

Ok!

Step-by-step explanation:

Religion: the belief and worship in what is usually a god

Bones: pieces of hard whitish tissiue in a skeloton

Agriculture: the practice of farming

Artifacts: historical objects

Answer:

xy

Step-by-step explanation:

xy³ and x³y

GCF is xy

Answer:

I think it's xy

Step-by-step explanation:

just find the prime factors of each term

Answer:

Q1 z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the that means have no difference

Q2  CI 95 %  =  (  0,056 ;  0,164 )

Step-by-step explanation:

Sample information for people under 18

n₁  =  500

x₁ =  180

p₁  =  180/ 500    p₁  =  0,36    then  q₁  =  1 -  p₁     q₁ =  0,64

Sample information for people over 18

n₂  =  600

x₂  =  150

p₂  =  150 / 600   p₂ =  0,25   then   q₂  =  1 - p₂   q₂ =  1 - 0,25   q₂ = 0,75

Hypothesis Test

Null hypothesis                        H₀              p₁  =  p₂

Alternative Hypothesis           Hₐ              p₁  ≠  p₂

The alternative hypothesis indicates that the test is a two-tail test.

We will use the approximation to normal distribution of the binomial distribution according to the sizes of both samples.

Testin at CI =  95 %    significance level is  α = 5 %   α  =  0,05  and

α/ 2  =  0,025   z (c) for that α  is from z-table:

z(c) = 1,96

To calculate   z(s)

z(s)  =  ( p₁  -   p₂ ) / EED

EED = √(p₁*q₁)n₁  +  (p₂*q₂)/n₂

EED = √( 0,36*0.64)/500  +  (0,25*0,75)/600

EED = √0,00046  +  0,0003125

EED = 0,028

( p₁  -  p₂  )  =  0,36  -  0,25  = 0,11

Then

z(s)  =  0,11 / 0,028

z(s) = 3,93

Comparing  z(s) and  z (c)    z(s) > z(c)

z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the idea of equals means

Q2  CI  95 %   =  (  p₁  -  p₂  ) ±  z(c) * EED

CI 95%  =  ( 0,11   ±  1,96 * 0,028 )

CI 95%  = (  0,11  ±  0,054 )

CI 95 %  =  (  0,056 ;  0,164 )

Area is length x width

Area = 2/5 x 3/4

When multiplying fraction, multiply the numerators by each other and the denominators by each other:

Area = 2/5 x 3/4 = (2 x3)/(5 x 4) = 6/20

6/20 reduces to 3/10

Area = 3/10 square yards

9514 1404 393

Answer:

  A.  0.949

Step-by-step explanation:

Use your favorite calculator or spreadsheet to compute the correlation coefficient.

  r ≈ 0.949

_____

Additional comment

The values of y generally increase as the values of x increase--with only one exception. This tells you the correlation coefficient is positive and fairly high. Of the two positive choices 0.901 and 0.949, the higher one is the better guess.

Answer:

336+76+48+38= 498

Step-by-step explanation:

add all those sides up because it is just the perimeter

Answer:

336+76+48+38= 498

Step-by-step explanation:

4/15 !! hope it helps loll

Answer:

8/9 (simplified)

Step-by-step explanation:

Total marbles = 18

Total of marbles not white = 16

Numerator = 16 / Denominator = 18

= 16/18

= 8/9 (simplified)

Total number of marble=18

probability of getting white marble = 2/18 =1/9

Now,

probability of not getting white marble = 1 - 1/9 = 8 / 9

210 - 30 = 180

180 ÷ 15 = 12

12 weeks

It would take her 12 weeks to pay for the DVD player.

none of the above

Step-by-step explanation:

SSS - only two legs are defined so this doesn't apply

SAS - the two legs of one triangle are not proportional to the legs of the other triangle.

AA - only one angle is defined to be congruent to the other (the rule requires two)

Answer:

3.33

Step-by-step explanation:

I just took the test! :D

The estimated margin of error, using standard deviation is 3.33.

The margin of error shows an estimated percentage, or that surrounds a guess related to the real value of the population. For example, a confidence interval that has a margin of error tells you that your findings will be within the real population value of the time.

Typically, the higher the standard deviation, the more dispersed the data is. Understanding standard deviation is an essential part of calculating the margin of error for your data. If you do not have the value for your sample data proportion.

Standard deviation describes variability within a single sample, while standard error describes variability across multiple samples of a population. Standard deviation is a descriptive statistic that can be calculated from sample data, while standard error is an inferential statistic that can only be estimated.

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Answer:

B. 50

Step-by-step explanation:

180-80=100

100 divided by two equal angles is 50.

Answer:

90-30=60

Its 60 because its a right angle triangle

Answer:

Step-by-step explanation:

let the number be x %

according to the question the equation is

x% of 15=45

x/100*15=45

15x=45*100

x=4500/15

x=300

therefore x=300%

Answer:

The test statistic is t = 3.36.

Step-by-step explanation:

You're testing the claim that the mean difference is greater than 0.7.

At the null hypothesis, we test if the mean difference is of 0.7 or less, that is:

[tex]H_0: \mu \leq 0.7[/tex]

At the alternate hypothesis, we test if the mean difference is greater than 0.7, that is:

[tex]H_1: \mu > 0.7[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that [tex]\mu = 0.7[/tex]

A survey of 35 people was conducted to compare their self-reported height to their actual height.

This means that [tex]n = 35[/tex]

From the sample, the mean difference was 0.95, with a standard deviation of 0.44.

This means that [tex]X = 0.95, s = 0.44[/tex]

Calculate the test statistic

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}[/tex]

[tex]t = 3.36[/tex]

The test statistic is t = 3.36.

Answer:

1.)

H0 : p = 1/6

H1 : p > 1/6

2.)

Pvalue = 0.3029

3.)

No

Step-by-step explanation:

Probability of rolling 5 in a 6-sided die by chance :

Number of 5's = 1

Number of 6 = 6

p = 1/6

The Null hypothesis :

H0 : p = 1/6

Since Pedro thinks he'd roll more than just by chance ;

Alternative hypothesis :

H1 : p > 1/6

Given that :

n = 38 ` x = 5

Phat = x / n = 5 / 38

Teat statistic : (phat - p) / √p(1-p)/n

1-p = 1 - 1/6 = 5/6

phat - p = 5/38 - 1/6 = −0.035087

√p(1-p) /n = (1/6 * 5/6) / 30 = √0.0046296 = 0.0680

Test statistic = −0.035087 / √0.0046296 =

Test statistic = −0.515673

Using the Pvalue calculator :

Pvalue at 0.05 , 1 - tail = 0.3029

Pvalue = 0.3029

Hence, at α = 0.05

Pvalue > α ;

There is no evidence to support Pedro's claim

The required round of the time 97.5 is 98 seconds.

Given that,

Albert jumped 100 times in 97.5 seconds. To round off the time taken to the nearest second.​

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
in 97.5 seconds 0.5 in the tenth place is close to 1,

So the round off the number will be 98 seconds,

Thus, the required round of the time 97.5 is 98 seconds.

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Answer:

 64degrees

Step-by-step explanation:

Give the following

Height of tree H = 36feet

length of the shadow L = 40feeet

Requires

Angle of eleation

Using the SOH CAH TOA identity

Sin theta = opposite/hypotenuse

Sin theta = H/L

Sin theta = 36/40

SIn theta = 0.9

theta  = arcsin0.9

theta = 64.16

Hence the required angle is  64degrees

Answer:

$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.

Step-by-step explanation:

95% confidence interval: $72 to $198.

This means that we are 95% sure that the true mean spending is between $72 and $198.

From this confidence interval the assistant concluded that people spend an average of $200 a month on entertainment. Is this a reasonable conclusion and why?

$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.

Answer:

f(-2) =3

Step-by-step explanation:

f(x) = 9+3x

Let x=-2

f(-2) = 9+3(-2)

      = 9-6

      = 3

f ( -2 ) = 9 + 3( - 2 )

f ( -2 ) = 9 - 6

f ( -2 ) = 3