Half of the sum of 32 and 2

Answer:

a) How many students took Marketing and Writing, but not History?

14 Students.

b) How many students took only History?

23 Students.

Step-by-step explanation:

We were given the following values in the question

Total number of students = 100

53 students took History = n(H)

41 students took Marketing = n(M)

48 students took Writing = n(W)

18 students took History and Marketing = n(H n M)

21 students took Marketing and Writing = n ( M n W)

7 students took all 3 courses = n ( H n M n W)

9 students took none of these courses

a) How many students took Marketing and Writing, but not History?

This is calculated as

= n(M n W) - n ( H n M n W)

= 21 - 7

= 14

Therefore, only 14 Students took Marketing and Writing but not History.

b) How many students took only History?

Step 1

Subtract the Total number of students from the number of students who did not take any course

100 - 9 = 91 students

Step 2

The number of students who took History and Writing (H n W) was not given, so we find it.

Therefore,

n(H) + n(M) + n(W) -n( H n M) - n( M n W) - n( H n W) + n( H n M n W) = 91

53 + 41 + 48 - 18 - 21 - n( H n W) + 7 = 91

n( H n W) = 149 - 39 -91

n( H n W) = 149 - 130

n( H n W) = 19

Step 3

To find the number of students taking History only, we calculate it as

Number of Students that took History only = n( H) - n(H n W) - n( H n M) + n( H n M n W)

= 53 - 19 - 18 + 7

= 53 + 7 -19 - 18

= 60 - 37

= 23

Therefore, the number of students that took only History is 23 Students.

The mean number of packages that will be filled before the process is stopped  is 100

Step-by-step explanation:

Step 1

Given that each package has probability 0.01 of falling outside the specification (Probability of Failure)

The probability of Success is (100-probability of failure)=(100-0.01)=0.99

It is important to note that the weight of the packages are independent

Using the data given in the  question we get  the following:

P(fail) =Probability of Failure

P(success)=Probability of Success

P(fail) = 0.01 and P(success) = 0.99

Step 2

The mean of the Geometric distribution is:

P = 0.01;

μx = 1/p = 1/0.01 = 100

Step 3

Thus, we can say that the mean number of packages that will be filled before the process is stopped is 100

Answer:

how do you thik,,, n vm

Step-by-step explanation:

Answer:

The statement is True.

Step-by-step explanation:

In this case we need to determine whether the rubber bands in a package of a particular brand of rubber band can hold a weight of 7 lbs or less.

A one-sample test can be used to perform the analysis.

The hypothesis can be defined as follows:

H₀: The mean weight the rubber bands can hold is 7 lbs, i.e. μ = 7.

Hₐ: The mean weight the rubber bands can hold is less than 7 lbs, i.e. μ < 7.

The information provided is:

 [tex]n=36\\\bar x=6.6\ \text{lbs}\\\sigma=2\ \text{lbs}[/tex]

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{6.6-7}{2/\sqrt{36}}=-1.20[/tex]  

The test statistic value is -1.20.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

 [tex]p-value=P(Z<-1.20)=0.1151[/tex]

*Use a z-table for the probability.

The p-value of the test is 0.1151.

The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.

Thus, it can be concluded that the mean weight the rubber bands can hold is 7 lbs.

Hence, the statement is True.

Answer:

test statistics = 11.57

Step-by-step explanation:

test statics = [tex]\frac{average spend from the sample - average spend from theory}{Standard deviation / \sqrt{no of samples} }[/tex]

= [tex]\frac{115-100}{41/\sqrt{1000} }[/tex]  = 11.57

The most appropriate hypothesis test for this task would be a one-sample t-test.

For this task, the most appropriate hypothesis test to use would be a one-sample t-test. A one-sample t-test is used to determine whether the mean of a sample is significantly different from a population mean.

In this case, the quality control specialist wants to test whether the mean thickness of the gum produced by the manufacturer is significantly different from the claimed value of 7.5 one-hundredths of an inch. The specialist takes a random sample of n = 100 pieces of gum and measures their thickness.

The one-sample t-test is appropriate because the population distribution is assumed to be right skewed and the standard deviation is known. The t-test allows for the use of a smaller sample size and accommodates the assumption of a non-normal distribution.

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Answer:

Step-by-step explanation:

Hi there,

The graph indicated is showing a horizontal asymptote. In fact, it is showing both a horizontal and a vertical asymptote.

To tell which type it is, notice where the graph "shoots off" and almost forms an imaginary straight line in one direction. Using this logic, the horizontal asymptote will be exactly horizontal, parallel to x-axis, and vertical asymptote will be exactly vertical, parallel to y-axis.

With this graph, we notice the horizontal asymptote is at y=0, where the x-axis is. The vertical asymptote is bit more difficult to determine graphically, but can definitely say it is past x=-10. We could determine it if we had the function, but that is not necessary for this question.

Study well, and persevere. If you liked this solution, leave a Thanks or give a rating!

thanks,

Final answer:

A horizontal asymptote is a horizontal line that a curve approaches but never touches as the x-values (or y-values) go to positive or negative infinity. In the case of the function y = 1/x, the graph has a horizontal asymptote at y = 0.

Explanation:

A horizontal asymptote is a horizontal line that a curve approaches but never touches as the x-values (or y-values) go to positive or negative infinity. To determine if a function has a horizontal asymptote, we need to analyze the behavior of the function as x approaches positive or negative infinity.

In the case of the function y = 1/x, as x approaches positive or negative infinity, the value of y approaches 0. Therefore, the graph of the function has a horizontal asymptote at y = 0.

Other functions may have different horizontal asymptotes, depending on their behavior as x approaches positive or negative infinity.

Answer:

[tex]t=\frac{219.2-205}{\frac{18}{\sqrt{20}}}=3.528[/tex]    

[tex]p_v =2*P(t_{19}>3.528)=0.0022[/tex]    

If we compare the p value and a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v <\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the lifetime is signficantly different from 205 hours.    

Step-by-step explanation:

Data given and notation    

[tex]\bar X=219.2[/tex] represent the sample mean

[tex]s=18[/tex] represent the sample standard deviation    

[tex]n=20[/tex] sample size    

[tex]\mu_o =205[/tex] represent the value that we want to test    

[tex]\alpha[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)    

[tex]p_v[/tex] represent the p value for the test (variable of interest)    

State the null and alternative hypotheses.    

We need to apply a two tailed  test.  

What are H0 and Ha for this study?    

Null hypothesis:  [tex]\mu = 205[/tex]  

Alternative hypothesis :[tex]\mu \neq 205[/tex]  

Compute the test statistic  

The statistic for this case is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic    

We can replace in formula (1) the info given like this:    

[tex]t=\frac{219.2-205}{\frac{18}{\sqrt{20}}}=3.528[/tex]    

Give the appropriate conclusion for the test  

The degreed of freedom are:

[tex] df = n-1= 19[/tex]

Since is a two sided test the p value would be:    

[tex]p_v =2*P(t_{19}>3.528)=0.0022[/tex]    

Conclusion    

If we compare the p value and a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v <\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the lifetime is signficantly different from 205 hours.    

Answer:

H0: mu equals 205 vs. H1: mu not equals 205.

Step-by-step explanation:

A null hypothesis (H0) is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing. It expresses equality.

An alternate hypothesis (H1) is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is true. It expresses inequality.

A two-tailed test is one in which the alternate hypothesis is expressed using any of the inequality signs below:

not equal to, less than or equal to, greater than or equal to.

Answer:

1 43/100

Step-by-step explanation:

10 boys divide 7 cereal bars equally or

10 / 7 = 1.428571428571429

Or 1.43 rounded Or 1 43/100

Answer:

1

Step-by-step explanation:

We are given that an expression

[tex]{(-14)^0)^{-2}[/tex]

We have to find the value of given expression.

We know that

[tex]a^0=1[/tex]

Using the property

[tex](-14)^0=1[/tex]

We know that

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

Using the property

[tex](1)^{-2}=\frac{1}{1^2}[/tex]

[tex](1)^{-2}=1[/tex]

[tex]((-14)^0)^{-2}=1[/tex]

Answer:

x^2-7x+6

Step-by-step explanation:

(x-6)(x-1)

x^2-1x-6x+6

x^2-7x+6

The quadratic function whose zeros are 6 and 1 is: f(x) = x² - 7x + 6.

To write a quadratic function f(x) with zeros at x=6 and x=1, we can start by representing it in factored form:

f(x) = a(x−6)(x−1)

Where a is a constant. Depending on the desired leading coefficient, you can choose any value for a. For simplicity, let's choose a=1.

Therefore, the quadratic function with zeros at 6 and 1 is:

f(x) = (x−6)(x−1)

f(x) = x² − 7x + 6

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The probability that the proportion of airborne viruses in the sample would be greater than 6% is approximately 0.5596.

To find the probability that the proportion of airborne viruses in a sample of 418 viruses would be greater than 6%, we can use the normal distribution. First, let's find the mean and standard deviation of the proportion of airborne viruses. The mean is 7% (0.07) and the standard deviation can be calculated using the formula: sqrt((p(1-p))/n), where p is the proportion and n is the sample size.

Using the given information, the standard deviation is sqrt((0.07(1-0.07))/418) ≈ 0.0064.

Next, we convert the 6% threshold to a z-score using the formula (x - mean) / standard deviation. So, the z-score is (0.06 - 0.07) / 0.0064 ≈ -0.156.

To find the probability that the proportion is greater than 6%, we look up the z-score (-0.156) in the standard normal distribution table and subtract the corresponding probability from 1. The probability is approximately 0.5596.

Answer: 6.07 I believe

Step-by-step explanation:

Answer:

-6.07

Step-by-step explanation:

What is the absolute magnitude of a star that has a period of 50 days?

Answer:

Rhada can make 48 ornaments if she uses all of the clay.

Step-by-step explanation:

The complete question is:

Rhada has a 6-pound bag of day . Her craft project requires 6 ounces of clay for each batch of 3 ornaments. If she uses all of the clay, how many ornaments can Rhada make?

Solution:

The amount of clay Rhada has, X = 6-pound.

Convert the weight of clay bag into ounces as follows:

1 pound = 16 ounces

6 pound = 16 × 6

              = 96 ounces.

So, Rhada has 96 ounces of clay.

It is provided that her craft project requires 6 ounces of clay for each batch of ornaments.

Compute the number of batches that can be made by 96 ounces of clay as follows:

Number of batches = Total weight of clay ÷ Amount required for each batch

                                [tex]=\frac{96}{6}\\=16[/tex]

Thus, Rhada can make 16 batches of ornaments.

Now, it is also provided that each batch has 3 ornaments.

Compute the number of ornaments in 16 batches as follows:

Number of ornaments = Number of batches × No. of ornament in 1 batch

                                     [tex]=16\times 3\\=48[/tex]

Thus, Rhada can make 48 ornaments if she uses all of the clay.

Answer:

[tex]z=\frac{0.52 -0.64}{\sqrt{\frac{0.64(1-0.64)}{100}}}=-2.5[/tex]  

The p value for this case is given by:

[tex]p_v =2*P(z<-2.5)=0.0124[/tex]  

Step-by-step explanation:

Data given and notatio  

n=100 represent the random sample selected

X=52 represent the shoppers stating that the supermarket brand was as good as the national brand

[tex]\hat p=\frac{52}{100}=0.52[/tex] estimated proportion of stating that the supermarket brand was as good as the national brand

[tex]p_o=0.64[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of shoppers stating that the supermarket brand was as good as the national brand is 0.64 or not, then the system of hypothesis are.:  

Null hypothesis:[tex]p=0.64[/tex]  

Alternative hypothesis:[tex]p \neq 0.64[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Calculate the statistic  

The statistic is given by:

[tex]z=\frac{0.52 -0.64}{\sqrt{\frac{0.64(1-0.64)}{100}}}=-2.5[/tex]  

Statistical decision  

The p value for this case is given by:

[tex]p_v =2*P(z<-2.5)=0.0124[/tex]  

Answer:

0.95%

Step-by-step explanation:

Simply divide 100 with 460 then multiply 4.37

100/460 = 0.2173913043

Multiply by 4.37 and you get 0.95

Answer:

54.1607142857

Step-by-step explanation:

just simplify it

The approximate value of -3,033 divided by -56 is -54 when rounded to two significant figures.

To approximate the value of -3,033 ÷ (-56), you can perform the division by changing both numbers into their absolute values and divide normally as the negative signs will cancel each other out. This results in the division of 3,033 by 56. Using a calculator, you would get 54.1607142857. However, since we need an approximate value with two significant figures, the result would be rounded to -54.

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

                           h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

                         h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

                         h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

                        v ( t ) = dh / dt

                        v ( t )= d ( −16t² + 54t + 40 ) / dt

                        v ( t )= -2*(16)*t + 54

                        v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

                        v ( 0 ) = vi = -32*( 0 ) + 54

                        v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

                     h ( t ) = 0

                     0 = −16t² + 54t + 40

                     0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

                    [tex]t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t = \frac{27 + 37}{16} \\\\t = 4[/tex]

Answer: The time taken for the baton to hit the ground is t = 4 mins

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent​ switches, each one set on or off. The receiver​ (wired to the​ door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches​ independently.The probability of at least one pair of neighbors using the same​ settings is 0.65633

Step-by-step explanation:

Step 1

In the question it is given that

Automatic garage door opener utilizes a transmitter control with four independent​ switches

So .the number of Combinations possible with the Transmitters =

2*2*2*2= 16

Step 2

Probability of at least one pair of neighbors using the same settings = 1- Probability of All Neighbors using different settings.

= 1- 16*15*14*13*12*11/(16^6)

Step 3

Probability of at least one pair of neighbors using the same settings=

= 1- 0.343666

Step 4

So the probability of at least one pair of neighbors using the same settings

is  0.65633

Answer:

Depending upon the golf score predictors we can conclude the answer from given Conditional statements

If Someone want Total golf score better then, following .condition

Yes, Because R squared is close to 1 .  ....(If Regression values are prefect to fit with model then only)

(But the data is not sufficient to say 100%, it depends on score given)

Step-by-step explanation:

Given :

Explanatory Question on r-squared in regression.

To Find :

Does regression equation help us to know total golf score much better.

Solution;

As  in Question there is no golf score given so we cant see "yes" or "no".

But we can be conditional here ,

1) If golf score to be accurate then , multiple regression predict points should fit the model prefect ,hence the R squared value "must be close to 1" .

2) If gold score is not accurate then multiple regression   suggest that model does  not explain any variables, no linear relationship.

then r squared value "must not be close to 1".

Depending upon the golf score predictors we can conclude the answer from given Conditional statements.

that  Yes, Because R squared is close to 1 .

Answer:

Medicare!

Step-by-step explanation:

Answer:

The answer is 153

Step-by-step explanation:

You multiply 17 by 3 by 3.

The volume of a rectangular prism-shaped freight container is calculated by multiplying its length, width, and height. For a container that is 17 meters long, 3 meters wide, and 3 meters high, the volume is 153 cubic meters.

The question is asking for the volume of the rectangular prism-shaped freight container.  In mathematics, the volume of a rectangular prism is found by multiplying its length, width, and height. For the freight container with dimensions of 17 meters long, 3 meters wide, and 3 meters high, we can find the volume by multiplying all these values together.

So, the volume V = length x width x height = 17m x 3m x 3m = 153 cubic meters. Therefore, each freight container on the train has a volume of 153 cubic meters.

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A teacher can use a hypothesis test for a population mean in situation A, where pretest scores are compared to posttest scores to determine if there is a significant improvement.

A hypothesis test for a population mean can be used in situation A. The teacher can use the pretest scores as the population mean and then compare it to the posttest scores to see if there is a statistically significant improvement. The hypothesis test will determine if the difference in scores is due to chance or if it is a result of the computer-based instruction.

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Answer: 11.24 miler per hour

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

The meaning of an event being independent is that one event doesn't effect the probability of they other event happening. So B is wrong because whether yo sleep or not can affect whether you dream or not and D is wrong because you earning and allowance is based off whether you do your chores or not.

Answer:

222.75 tons

Step-by-step explanation:

1 elephant = 8.25 tons

x 27               x 27

27 elephants = 222.75 tons

I hope this helps.

Final answer:

To find the weight of 27 elephants, multiply the weight of one elephant by 27. The total weight of 27 elephants, each weighing 8.25 tons, is 222.75 tons.

Explanation:

To calculate the total weight of 27 elephants each weighing 8.25 tons, we simply multiply the weight of one elephant by the number of elephants:

8.25 tons/elephant × 27 elephants = 222.75 tons

It's clear we need to multiply when converting from a single elephant's weight to the combined weight of multiple elephants. We use the fact that 1 ton = 2,000 pounds for conversion between units if needed, but here we keep the weight in tons as the question requested.

Step-by-step explanation:

1.)

[tex] - \frac{5}{3} \times \frac{1}{8} = - \frac{5}{24} \\ \\ [/tex]

2.)

[tex] - \frac{5}{2} \times \frac{1}{12} = - \frac{5}{24} \\ [/tex]

3.)

[tex] - \frac{1}{6} \times \frac{5}{4} = - \frac{5}{24} \\ [/tex]

Answer:105°

Step-by-step explanation:

The intersecting chords form a pair of vertical angles.

Given is a circle, with chords AB and CD intersecting at E and m∠DEB = 105°, we need to find, m∠AEC

By vertical angle theorem:

Vertically opposite angles are congruent.

⇒ m∠AEC = m∠DEB

⇒ m∠AEC = 105°

The measure of angle AEC is 105°.

Therefore, the intersecting chords form a pair of vertical angles.

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Answer: 1) 390625, 2) 1365, 3) 411105.

Step-by-step explanation:

Since we have given that

Number of types of cupcakes = 5

Number of chocolate type = 1

1/ How many different selections of 8 cupcakes are there?

Number of cupcakes we need to select = 8

Since we have 5 options for each 8 cupcakes.

So, the number of ways to select 8 cupcakes would be :

[tex]5^8=390625[/tex]

2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?

Number of different selection would be :

=[tex]4^5+4^4+4^3+4^2+4+1=1365[/tex]

3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?

Number of ways to select no chocolate + Number of ways to select 1 chocolate + Number of ways to select 2 chocolate

[tex]5^8+4^7+4^6=411105[/tex]

Hence, 1) 390625, 2) 1365, 3) 411105.