Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact 40. If the mean amperage is lower than 40, customers will complain because the fuses require replacement too often. If the mean amperage is higher than 40, the manufacturer might be liable for damage to an electrical system due to fuse malfunction. To verify the amperage of the fuses, a sample of fuses is to be selected and inspected. If a hypothesis test were to be performed on the resulting data, what null and alternative hypotheses would be of interest to the manufacturer? Describe type I and type II errors in the context.

Answer:

3

Step-by-step explanation:

14/2=7 6/2=3  7+3=10 which is also half of 20 (20 is how many fruits he has) He gave away 3 bananas

Answer:

[tex]P=0.4737[/tex]

Step-by-step explanation:

First, we need to know that nCx give as the number of ways in which we can select x elements from a group of n. It is calculated as:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

Then, to select 3 fish in which at least one a them is a black goldfish we can:

1. Select one black goldfish and 2 yellow goldfish: There are 9 different ways to do this. it is calculated as:

[tex]3C1*3C2 =\frac{3!}{1!(3-1)!}* \frac{3!}{2!(3-2)!}=9[/tex]

Because we select 1 black goldfish from the 3 in aquarium and select 2 yellow goldfish from the 3 in the aquarium.

2. Select 2 black goldfish and 1 yellow goldfish: There are 9 different ways. it is calculated as:

[tex]3C2*3C1 =\frac{3!}{2!(3-2)!}* \frac{3!}{1!(3-1)!}=9[/tex]

3.  Select 3 black goldfish and 0 yellow goldfish: There is 1 way. it is calculated as:

[tex]3C3*3C0 =\frac{3!}{3!(3-3)!}* \frac{3!}{0!(3-0)!}=1[/tex]

Now, we identify that just in part 2 (Select 2 black goldfish and 1 yellow goldfish), two yellow goldfish and a black goldfish remain in the tank after the customer has left.

So, the probability that two yellow goldfish and a black goldfish remain in the tank after the customer has left given that the customer purchased a black goldfish is equal to:

[tex]P=\frac{9}{9+9+1} =0.4737[/tex]

Because there are 19 ways in which the customer can select a black fish and from that 19 ways, there are 9 ways in which two yellow goldfish and a black goldfish remain in the tank.

Answer:

The minimum score required for the scholarship is 644.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 488, \sigma = 111[/tex]

What is the minimum score required for the scholarship?

Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.

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

[tex]1.405 = \frac{X - 488}{111}[/tex]

[tex]X - 488 = 1.405*111[/tex]

[tex]X = 644[/tex]

The minimum score required for the scholarship is 644.

Answer:

Event 4, Event 2, Event 1, Event 3 (least to most likely)

Step-by-step explanation:

Let's take a look at each event:

Event 1- Spinner B lands on a black slice.

2 black slices, 8 total slices

2/8=1/4=25% probability

Event 2- Spinner A lands on a black slice.

3 black slices, 15 total slices

3/15=1/5=20%

Event 3- Spinner B lands on a black or purple slice.

8 black or purple slices, 8 total slices

8/8=1=100%

Event 4- Spinner A lands on a green slice.

0 green slices, 15 total slices

0/15=0=0%

So, in order of least to most likely, we have Event 4 (0%), Event 2 (20%), Event 1 (25%), and event 3 (100%).

Answer:

a. For n=25, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are ​$63,800 and ​$1,580​, respectively.

b. For n=50, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are ​$63,800 and ​$1,117​, respectively.

Step-by-step explanation:

In this case, for each sample size, we have a sampling distribution (a distribution for the population of sample means), with the following parameters:

[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{n}[/tex]

For n=25 we have:

[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{25}=7,900/5=1,580[/tex]

The spread of the sampling distribution is always smaller than the population spread of the individuals. The spread is smaller as the sample size increase.

This has the implication that is expected to have more precision in the estimation of the population mean when we use bigger samples than smaller ones.

If n=50, we have:

[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{50}=7,900/7.07=1,117[/tex]

For samples of size 25 and 50, the mean of x bar is $63,800. The standard deviation of x bar is $1580 for a sample size of 25 and $1117 for a sample size of 50.

a. For samples of size 25, the mean of x bar is equal to the population mean, which is $63,800. The standard deviation of x bar is equal to the population standard deviation divided by the square root of the sample size. So, the standard deviation of x bar is $7900/sqrt(25) = $1580.

b. For samples of size 50, the mean of x bar is still $63,800. The standard deviation of x bar is $7900/sqrt(50) = $1117. Note that as the sample size increases, the standard deviation of x bar decreases.

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Answer:

The 99% of confidence limits for the proportion that plan to vote for the incumbent.

(0.6473 ,0.7527)

Step-by-step explanation:

Explanation:-

Given data the election of a local construction union involves 2,000 union members. Among them, 500 members are randomly selected.

Given large sample size 'N' = 2000

Given sample size 'n' = 500

Given data Of the 500 surveyed, 350 said they would vote for the incumbent.

The sample Proportion

                        [tex]p = \frac{x}{n} = \frac{350}{500} =0.7[/tex]

                       q = 1-p = 1 - 0.7 = 0.3

Confidence intervals:-

The 99% of confidence intervals are determined by

[tex](p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p+Z_{\alpha }\sqrt{\frac{pq}{n} } )[/tex]

The z- score of 0.99 level of significance =2.576

[tex](0.7-2.576\sqrt{\frac{0.7X0.3}{500} } , 0.7+2.576\sqrt{\frac{0.7X0.3}{500} } )[/tex]

on using calculator, we get

(0.7 - 0.0527 ,0.7+0.0527)

(0.6473 ,0.7527)

Conclusion:-

The 99% of confidence limits for the proportion that plan to vote for the incumbent.

(0.6473 ,0.7527)

Answer:

x= 3,1

Step-by-step explanation:

-b ±  √b²-4(ac)/2a

4 ±  √(-4)² - 4 · (1·3)/2·1

x = 2 ± 1

x = 3,1

Answer:

Each friend would receive Half (1/2) of an apple.

Each friend receives 1/2 apple.

The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Total number of friends = 6

Total number of apples = 3

The apple gets each friend is determined in the following steps given below.

[tex]\rm Each \ friend =\dfrac{Total \ Apple}{Total \ frineds}\\\\Each \ friend = \dfrac{3}{6}\\\\Each \ friend =\dfrac{1}{2}[/tex]

Hence, each friend receives 1/2 apple.

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Answer:

3n + 2

Step-by-step explanation:

-n + 4n -4 + 6

3n + 2

Answer:

M = Log (10S/S)

Step-by-step explanation:

We are told that the magnitude, M, of an earthquake is defined to be;

M = Log l/S

Where I is intensity and S is standard earthquake.

Now, we want to find the magnitude of an earthquake that is 10 times more intense than a standard earthquake

Since 10 times more intense than standard earthquake, it means that;

I = 10S

So plugging in 10S for I in the original equation for magnitude gives;

M = Log (10S/S)

Answer:It’s C on edge

Step-by-step explanation:

Answer: 320°

Step-by-step explanation:

This is a circle geometry.

The arc length of the circle is given to be 8πcm and the radius is 4.5cm.

Now the length of an arc of a circle is

Arc length = πr0°/180° or 2πr0°/360°

To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go

πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.

πr0° = 8π × 180

0°. = 8π × 180

-----------

π × r

= 8 × 180. 8 × 180

-------- or ---------

9/2. 4.5

= 8 × 180 × 2

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

9

= 8 × 20 × 2

= 320°

or 8 × 180/4.5

= 1440/4.5

= 320°

The equation of the hyperbola with vertices at[tex](0,±\sqrt{54}) and foci at (0,±\sqrt{89}) is \(\frac{y^2}{54} - \frac{x^2}{35} = 1\).[/tex]

To write the equation of a hyperbola, you need to know the values of a (which determines the distance from the center to the vertices) and c (which determines the distance from the center to the foci). The general equation for a hyperbola centered at the origin (h, k) with a vertical transverse axis is:

[tex]\(\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1\)[/tex]

Since the hyperbola is centered at the origin (0,0), this simplifies the equation:

[tex]\(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)[/tex]

For this hyperbola, the vertices are at [tex](0,\(\pm\sqrt{54}\)), so a is \(\sqrt{54}\)[/tex]. The foci are at [tex](0,\(\pm\sqrt{89}\))[/tex], so c is [tex]\(\sqrt{89}\)[/tex]. To find b, we use the relationship [tex]c^2 = a^2 + b^2 (since e > 1)[/tex].

Calculating b, we have:

[tex]\(c^2 = a^2 + b^2\)[/tex]

[tex]\(89 = 54 + b^2\)[/tex]

[tex]\(b^2 = 35\)[/tex]

Thus, the equation of the hyperbola is:

[tex]\(\frac{y^2}{54} - \frac{x^2}{35} = 1\)[/tex]

The equation of the hyperbola is : [tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

To write the equation of the hyperbola given its vertices and foci, we need to determine the major axis, minor axis, and eccentricity.

The vertices of the hyperbola are at [tex]\( (0, \pm \sqrt{54}) \)[/tex] and the foci are at [tex]\( (0, \pm \sqrt{89}) \).[/tex]

The distance from the center to a vertex is [tex]\( \sqrt{54} \)[/tex], which is the length of the semi-major axis, [tex]\( a \)[/tex]. The distance from the center to a focus is [tex]\( \sqrt{89} \),[/tex] which is the length of [tex]\( c \)[/tex], the distance from the center to a focus.

The relationship between [tex]\( a \), \( b \)[/tex] (the length of the semi-minor axis), and [tex]\( c \)[/tex] for a hyperbola is given by the equation [tex]\( c^2 = a^2 + b^2 \).[/tex]

Substituting the given values, we get:

[tex]\[ 89 = 54 + b^2 \][/tex]

[tex]\[ b^2 = 89 - 54 \][/tex]

[tex]\[ b^2 = 35 \][/tex]

So, [tex]\( b = \sqrt{35} \)[/tex].

The standard form equation of a hyperbola centered at the origin with vertices on the y-axis is:

[tex]\[ \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \][/tex]

Substituting [tex]\( a = \sqrt{54} \) and \( b = \sqrt{35} \),[/tex] we get:

[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

Therefore, the equation of the hyperbola is:

[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

This equation represents a hyperbola centered at the origin with vertices at [tex]\( (0, \pm \sqrt{54}) \) and foci at \( (0, \pm \sqrt{89}) \).[/tex]

Answer:

1.4

Step-by-step explanation:

4.6 + (- 3.2)

A plus sign and a minus sign results in a minus sign

Re-write the expression without the parenthesis

4.6 - 3.2

Subtract

1.4

Hope this helps :)

Answer:

the answer is attached to the picture

Answer:

A

Step-by-step explanation:

48 softballs

Divided among b bags

Divide 48 by b

48 ÷ b

Division expressions can also be written as fractions

Rewrite

48/b

The correct answer is A, 48/b

Hope this helps :)

Final answer:

Kate should use the expression 48/b to determine how many softballs go into each bag, which means dividing 48 softballs by the number of bags she has.

Explanation:

The expression that represents how many softballs Kate should put into each bag is 48/b. This expression shows that Kate will divide her total number of 48 softballs by the variable b, which represents the number of softball bags she has. The correct choice is therefore a. 48/b, which suggests that each bag will receive an equal share of the total softballs.

Answer:

8.1 moles

Step-by-step explanation:

Given parameters: Mass of water to be decomposed = 29.2g Unknown: Number of moles of oxygen. Solution: To solve this problem, we first write the balanced reaction equation :                 2H₂O    →     2H₂    +    O₂ Now convert the given mass of the water to number of moles;   Number of moles of water =      Molar mass of water = 2(1) + 16 = 18g/mol   Number of moles of water =   = 16.2moles     From the balanced reaction equation:     2 moles of water produced 1 mole of oxygen gas;     16.2 mole of water will produce     = 8.1moles of oxygen gas

Hope this helps you :3

Answer:

The next score he needs to have an overall average of 79 is 89.

Step-by-step explanation:

Gary earned an average score of 77 on his 5 quizzes . The number of score he needs to have an average of 79 can be calculated below.

average score = 77

number of quizzes = 5

sum of Garry score = a

a/5 = 77

cross multiply

a = 77 × 5

a = 385

let

the next score he needs be  b to score an average of 79

average = 79

number of quizzes = 6

385 + b/6 = 79

cross multiply

385 + b = 474

b = 474 - 385

b = 89

The next score he needs to have an overall average of 79 is 89.

Given Information:

Probability of super event = P(S) = 0.0023

Number of suppliers = n = 3

Probability of unique event = P(U) = 0.014

Required Information:

Probability that all three suppliers will be disrupted = ?

Answer:

P(3) = 0.0023

Step-by-step explanation:

We want to find out the approximate probability that all three suppliers will be disrupted at the same time at some point during the next five years.

The required probability is given by

P(n) = P(S) + (1 - P(S))*P(U)ⁿ

Where P(S) is the probability of super event that will disrupt all suppliers, P(U) is the probability of unique event that would disrupt one of the suppliers and n is the number of suppliers.

P(3) = 0.0023 + (1 - 0.0023)*(0.014)³

P(3) = 0.0023 + (0.9977)*(0.014)³

P(3) = 0.0023

The correct option is C = 0.0023

Therefore, there is 0.23% probability that all three suppliers will be disrupted at the same time at some point during the next five years.

Answer:

The null hypothesis is rejected.

There is  enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.

P-value=0.0036 (two tailed test).

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women that vote is differs from the proportion of men that vote.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

Being π1: proportion of men that vote, and π2: proportion of women that vote.

The significance level is 0.05.

The sample 1 (men), of size n1=(2744+1599)=4343 has a proportion of p1=0.6318.

[tex]p_1=X_1/n_1=2744/4343=0.6318[/tex]

The sample 2 (women), of size n2=(3733+1924)=5657 has a proportion of p2=0.6599.

[tex]p_2=X_2/n_2=3733/5657=0.6599[/tex]

The difference between proportions is (p1-p2)=-0.0281.

[tex]p_d=p_1-p_2=0.6318-0.6599=-0.0281[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{2744+3733}{4343+5657}=\dfrac{6477}{10000}=0.6477[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.6477*0.3523}{4343}+\dfrac{0.6477*0.3523}{5657}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00004}=\sqrt{0.00009}=0.0096[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0281-0}{0.0096}=\dfrac{-0.0281}{0.0096}=-2.913[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=2\cdot P(t<-2.913)=0.0036[/tex]

As the P-value (0.0036) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.

Answer:

The series is absolutely convergent.

Step-by-step explanation:

By ratio test, we find the limit as n approaches infinity of

|[a_(n+1)]/a_n|

a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)

a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)

[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]

= |-3n³/2(n+1)³|

= 3n³/2(n+1)³

= (3/2)[1/(1 + 1/n)³]

Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity

= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity

= 3/2 × 1

= 3/2

The series is therefore, absolutely convergent, and the limit is 3/2

Answer:

1.53

Step-by-step explanation:

Find the attachment for explanation

The z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53 and this can be determined by using the given data.

Given :

Assuming that the distribution is normal so the probability for being within the maximum limit is given by:

[tex]\rm P=1-\dfrac{6.3}{100}[/tex]

P = 0.937

Now, the z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53.

Therefore, the correct option is D) 1.53.

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Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 536

p = 37/100 = 0.37

q = 1 - 0.37 = 0.63

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.005 = 0.995

The z score corresponding to the area on the z table is 2.53. Thus, confidence level of 99% is 2.58

Therefore, the 99% confidence interval is

0.37 ± 2.58 × √(0.37)(0.63)/536

= 0.37 ± 0.054

The lower limit of the confidence interval is

0.37 - 0.054 = 0.316

The upper limit of the confidence interval is

0.37 + 0.054 = 0.424

Therefore, with 99% confidence interval, the proportion of all teenagers that want more discussions with their parents about school is between 0.316 and 0.424

Plugging in the values and calculating, we find that the 98% confidence interval is approximately (0.5847, 0.6553).

To construct a 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders, we can use the formula:

CI = p ± z * √(p * (1-p) / n)

Where:

Using a standard normal distribution table or a calculator, we can find that the z-score for a 98% confidence level is approximately 2.33.

Plugging in the values into the formula:

CI = 0.62 ± 2.33 * √(0.62 * (1-0.62) / 3100)

Calculating the values:

CI = 0.62 ± 2.33 * √(0.62 * 0.38 / 3100)

CI = 0.62 ± 2.33 * √(0.235 / 3100)

CI = 0.62 ± 2.33 * 0.01516

CI = 0.62 ± 0.03535

CI ≈ (0.5847, 0.6553)

Therefore, the 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is approximately (0.5847, 0.6553).

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Answer:

Here, we have:

P(5 days snow in this 8 days) = 8C5 x (0.85)^5 x (1 - 0.85)^3 = 0.084

P(6 days snow in this 8 days) = 8C6 x (0.85)^6 x (1 - 0.85)^2 = 0.238

P(7 days snow in this 8 days) = 8C7 x (0.85)^7  x (1 - 0.85)^1  = 0.385

P(8 days snow in this 8 days) = 8C8 x (0.85)^8 x (1 - 0.85)^0 = 0.272

Add up those above, then the probability that it will snow AT LEAST five of those days in February:

P = 0.084+ 0.238 + 0. 385 + 0.272 = 0.979

Hope this helps!

:)

Answer:

260

Step-by-step explanation:

A = bh

Answer:[tex](g,h)=(-2,2)[/tex]

Step-by-step explanation:

Given

Midpoint is [tex](-2,3)[/tex]

Endpoints are [tex]G(g,4)[/tex] and [tex]H(-2,h)[/tex]

Mid point of any two point is given by

[tex]x=\frac{x_1+x_2}{2}[/tex]

and [tex]y=\frac{y_1+y_2}{2}[/tex]

So,[tex]-2=\frac{g+(-2)}{2}[/tex]

[tex]-4=g-2[/tex]

[tex]g=-2[/tex]

Also

[tex]3=\frac{4+h}{2}[/tex]

[tex]6=4+h[/tex]

[tex]h=2[/tex]

Therefore [tex](g,h)=(-2,2)[/tex]

Answer:

1/4 of his income.

Step-by-step explanation:

If Wilbur spends 2/3 of his income, 1/3 or 4/12 of it is left for other purposes (It is easier if everything has a common denominator of 12). And if he shares 1/12 of that remaining amount, there is 3/12 left. And when we simplify 3/12, we get 1/4.

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Answer:

f(x)=-3+14x

Step-by-step explanation:

its the opposite

The inverse of the following function f(x)=3-14x will be [tex]f^-(x)[/tex] = [3 -f(x)]/14.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

A function is basically a relationship between which one variable will be dependent and another will be independent.

For example, let's say y = sinx then here x will be independent but y will be dependent.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +9 like that.

Given that the function

f(x)=3-14x

⇒ f(x) + 14x =3

⇒ 14x = 3 -f(x)

⇒ x =  [3 -f(x)]/14 hence, it will be the correct answer.

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25

Step-by-step explanation:

25