Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses.

Answers

Answer 1

Answer:

Step-by-step explanation:

1. 4/4+4-4=1

2. 4/4+4/4=2

3. 4+4/4-4=3

4. 4 × (4 − 4) + 4=4

5. (4 × 4 + 4) / 4=5

6. 44 / 4 − 4=6

7. 4+4-4/4=7

8. 4+4+4-4=8

9. 4+4+4/9=9

10. 44 / 4.4=10

Answer 2

Answer:

1 = (4 x 4)/(4 x 4) or  (4 + 4)/(4 + 4) or  (4 / 4) x (4 / 4) or  (4 / 4)/(4 / 4)  

2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)

3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4

4 = 4 - (4 - 4)/4

5 = (4 x 4 + 4)/4

6 = 4 + (4 + 4)/4

7 = 4 - (4/4) + 4

8 = 4 + (4 x 4)/4

9 = 4 + 4 + (4/4)

10 - I tried the best. You might need ! or sqrt operator to get 4.

Updated:

I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:

10 = (44 - 4)/4


Related Questions

What is the difference between congurent and similar ?

Answers

Answer:

When a shape is congruent they are equal in shape, size, and measure. Although if a shape is similar they will be the same shape, but not the same size, instead they will be proportionate.

Step-by-step explanation:

Answer:

CongruentCongruent figures are identical in size, shape and measure. SimilarTwo figures are similar if they have the same shape, but not necessarily the same size.

Step-by-step explanation:

For the following polynomial, find P(a), P(-x) and P(x + h).

P(x) = 7x-6

Answers

Answer:

Step-by-step explanation:

Hello, please consider the following.

P(a) = 7 * a - 6

P(-x)= 7 *(-x) - 6 = -7x - 6

P(x+h) = 7 * (x+h) - 6 = 7x + 7h - 6

Hope this helps.

Thank you.

The values of the polynomial for the given expressions are:

P(a) = 7a - 6

P(-x) = -7x - 6

P(x + h) = 7x + 7h - 6

To find P(a), P(-x), and P(x + h) for the given polynomial P(x) = 7x - 6, we need to substitute the respective values of x into the polynomial expression.

1. P(a):

P(a) = 7a - 6

2. P(-x):

P(-x) = 7(-x) - 6

P(-x) = -7x - 6

3. P(x + h):

P(x + h) = 7(x + h) - 6

P(x + h) = 7x + 7h - 6

To know more about polynomial:

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Heights of men on a baseball team have a​ bell-shaped distribution with a mean of and a standard deviation of . Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a.166 cm and 202 cm b. 172cm and 196cm

Answers

Let assume that the mean is 184 and the standard deviation is 6

Heights of men on a baseball team have a​ bell-shaped distribution with a mean 184 of and a standard deviation of 6 . Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a.166 cm and 202 cm b. 172 cm and 196cm

Answer:

P(156<X<202) =  99.7%

P(172<X<196) =  95.5%

Step-by-step explanation:

Given that :

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of and a standard deviation of . Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a.166 cm and 202 cm b. 172 cm and 196cm

For a.

Using the empirical​ rule, what is the approximate percentage of the men between the following​ values 166 cm and 202 cm.

the z score can be determined by using the formula:

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]z(166) = \dfrac{166-184}{6}[/tex]

[tex]z(166) = \dfrac{-18}{6}[/tex]

z(166) = -3

[tex]z(202) = \dfrac{202-184}{6}[/tex]

[tex]z(202) = \dfrac{18}{6}[/tex]

z(202) = 3

P(156<X<202) = P( μ - 3σ < X < μ + 3σ )

P(156<X<202) = P( - 3 < Z < 3)

P(156<X<202) = P( Z <  3) - P(Z < -3)

P(156<X<202) = 0.99865-  0.001349

P(156<X<202) =  0.997301

P(156<X<202) =  99.7%

For b.

b. 172 cm and 196cm

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]z(172) = \dfrac{172-184}{6}[/tex]

[tex]z(172) = \dfrac{-12}{6}[/tex]

z(172) = -2

[tex]z(196) = \dfrac{196-184}{6}[/tex]

[tex]z(196) = \dfrac{12}{6}[/tex]

z(196) = 2

P(172<X<196) = P( μ - 2σ < X < μ + 2σ )

P(172<X<196) = P( - 2 < Z < 2)

P(172<X<196) = P( Z <  2) - P(Z < -2)

P(172<X<196) = 0.9772 -  0.02275

P(172<X<196) =  0.95445

P(172<X<196) =  95.5%

how many meters are in 250 centimeters

Answers

Answer:

2.5 meters

Step-by-step explanation:

If the solutions for a quadratic equation are -2 and 5 what is the equation

Answers

Answer:

f(x) = x^2 - 3x -10

Step-by-step explanation:

If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).

The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10

Shyla's research shows that 8 empty cans make 1/4 pound of aluminum. Shyla wants to know how many cans does it take to make 5 pounds of aluminum. How many cans are there per pound of aluminum?

Answers

Answer:

They will need 160 cans to make 5 lbs

32 cans for 1 lbs

Step-by-step explanation:

We can use ratios to solve

8 cans             x cans

--------------- = ---------------

1/4 lbs             5 lbs

Using cross products

8 * 5 = 1/4x

40 = 1/4 x

Multiply each side by 4

4 * 40 = 1/4 x * 4

160 =x

They will need 160 cans to make 5 lbs

8 cans             x cans

--------------- = ---------------

1/4 lbs             1 lbs

Using cross products

8 * 1 = 1/4x

Multiply each side by 4

8*4 = x

32 cans for 1 lbs

Answer:

32 cans per pound of aluminum

160 cans per 5 pounds of aluminum

Step-by-step explanation:

will make it short and simple.

8 empty cans can make 1/4 pound of aluminum.

therefore... 8 x 4 = 32 cans per pound of aluminum.

Number of cans to make 5 pounds of aluminum = 32 x 5

= 160 cans per 5 pounds of aluminum

Question: The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Which equation can be used to find the length of the remaining side?

Answers

Answer:

The hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

14^2=9^2+c^2.

c^2=196-81.

c^2=115.

c=√115.

c=10.72~11cm

3x18 = 3 (10+8) is an example of the _________ property of multiplication.

Answers

Answer:

3x18 = 3 (10+8) is an example of the commutative property of multiplication

Step-by-step explanation:

Answer: commutative property of multiplication

Step-by-step explanation:

A random sample of 1400 Internet users was selected from the records of a large Internet provider and asked whether they would use the Internet or the library to obtain information about health issues. Of these, 872 said they would use the Internet

1. The standard error ˆp SE of the proportion pˆ that would use the Internet rather than the library is:_______

a. 0.013.
b. 0.25.
c. 0.485.
d. 0.623.

2. If the Internet provider wanted an estimate of the proportion p that would use the Internet rather than the library, with a margin of error of at most 0.02 in a 99% confidence interval, how large a sample size would be required? (Assume that we don’t have any prior information about p).

a. 33
b. 3909
c. 2401
d. 4161

Answers

Answer:

1   [tex]\sigma_{\= x } = 0.0130[/tex]

2  [tex]n = 3908.5[/tex]

Step-by-step explanation:

From the question we are told that

     The  sample size is  [tex]n_p = 1400[/tex]

      The  number of those that said the would use internet is [tex]k = 872[/tex]

       The margin of error is  [tex]E = 0.02[/tex]

Generally the sample proportion is mathematically evaluated as

            [tex]\r p = \frac{k}{n_p}[/tex]

substituting values

            [tex]\r p = \frac{ 872}{1400}[/tex]

substituting values

           [tex]\r p = 0.623[/tex]

Generally the standard error of  [tex]\r p[/tex] is mathematically evaluated as

           [tex]\sigma_{\= x } = \sqrt{\frac{\r p (1- \r p)}{n} }[/tex]

substituting values

              [tex]\sigma_{\= x } = \sqrt{\frac{0.623 (1- 0.623)}{1400} }[/tex]

              [tex]\sigma_{\= x } = 0.0130[/tex]

For  a  95% confidence interval the confidence level is  95%

Given that the confidence interval is 95% the we can evaluated the level of confidence as

                    [tex]\alpha = 100 - 99[/tex]

                   [tex]\alpha = 1\%[/tex]

                   [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from normal distribution table (reference math dot  armstrong dot edu) , the value is  

         [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

Give that the population size is very large  the sample size is mathematically represented as

            [tex]n = [ \frac{Z_{\frac{\alpha }{2} ^2 * \r p ( 1 - \r p )}}{E^2} ][/tex]

substituting values  

             [tex]n = [ \frac{2.58 ^2 * 0.623 ( 1 -0.623 )}{0.02^2} ][/tex]

             [tex]n = 3908.5[/tex]

These figures are similar. The area of one is given. Find the area of the other. PLZ HELP

Answers

Answer: 6

Step-by-step explanation:

If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?​

Answers

Answer:

[tex]p = 2[/tex] if given vectors must be linearly independent.

Step-by-step explanation:

A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:

[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]

In other words, the following system of equations must be satisfied:

[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)

[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)

[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)

By Eq. 1:

[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]

Eq. 1 in Eqs. 2-3:

[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]

[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]

[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)

[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)

By Eq. 3b:

[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]

Eq. 3b in Eq. 2b:

[tex](p-2)\cdot \alpha_{2} = 0[/tex]

If [tex]p = 2[/tex] if given vectors must be linearly independent.

A study of 200 computer service firms revealed these incomes after taxes: Income After Taxes Number of Firms Under $1 million 102 $1 million up to $20 million 61 $20 million or more 37 What is the probability that a particular firm selected has $1 million or more in income after taxes

Answers

Answer:

The probability that a particular firm selected has $1 million or more in income after taxes is 49%.

Step-by-step explanation:

We are given a study of 200 computer service firms revealed these incomes after taxes below;

         Income After Taxes                  Number of Firms

           Under $1 million                              102

      $1 million up to $20 million                    61

           $20 million or more                          37      

                 Total                                           200    

Now, the probability that a particular firm selected has $1 million or more in income after taxes is given by;

Total number of firms = 102 + 61 + 37 = 200

Number of firms having $1 million or more in income after taxes = 61 + 37 = 98  {here under $1 million data is not include}

So, the required probability =  [tex]\frac{\text{Firms with \$1 million or more in income after taxes}}{\text{Total number of firms}}[/tex]

                                           =  [tex]\frac{98}{200}[/tex]

                                           =  0.49 or 49%

The probability that a particular firm selected has $1 million or more in income after taxes is 0.49 or 49%.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

A study of 200 computer service firms revealed these incomes after taxes:

Income After Taxes Number of Firms Under

$1 million 102

$1 million up to $20 million 61

$20 million or more 37.

Then the total event will be

Total event = 102 + 37 +61 = 200

The probability that a particular firm selected has $1 million or more in income after taxes will be

Favorable event = 37 + 61 = 98

Then the probability will be

[tex]\rm P = \dfrac{98}{200} \\\\P = 0.49 \ or \ 49 \%[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Identify whether the sampling method is simple random, systematic, stratified, cluster, or convenience. Explain.

In a nationwide study of registered voters conducted by The New York Times, 390 people are randomly selected out of those registered as Republicans, 430 people are randomly selected out of those registered as Democrats, and 180 people are randomly selected out of those registered as Independents.

Answers

Answer: stratified

Step-by-step explanation:

In stratified sampling, you divide the population into subgroups, or strata, with similar characteristics, like here we have divided the population into subgroups that depend on their political alignment. This is used when you can expect that the results have a noticeable variation between the different subgroups. Usually, you want to have the same number of population for eac subgroup, but sometimes it is hard for different reasons (not enough people in one subgroup, for example)

In cluster sampling we also use subgroups, but the subgroup itself is the unit of the sampling, while in this case, we are randomly selecting individuals of the given subgroups.

So this would be a "stratified sampling".

Write 8x8x88888 as power

Answers

Answer:

8[2]×88888

Step-by-step explanation:

[8×8]=8[2]×88888

NEED HELP ASAP!! Angles of Elevation and Despression! Need to find y! Round to the nearest tenth!!

Answers

Answer:

y = 178.3 ft

Step-by-step explanation:

Since the above figure is a right angled triangle we can use trigonometric ratios to find y

To find y we use tan

tan∅ = opposite/ adjacent

From the question

the opposite is y

the adjacent is 350 ft

Substitute the values into the above formula

That's

[tex] \tan(27) = \frac{y}{350} [/tex]

y = 350 tan 27

y = 178.3339

We have the final answer as

y = 178.3 ft to the nearest tenth

Hope this helps you

Find the surface area of the solid given the net.

Answers

Answer:

288

Step-by-step explanation:

Area of two triangles=2(½bh)

=bh

=8×6

=48

For the rectangles=lb + lb +lb

l(b+b+b)

=12(8+6+6)

=12×20

=240

Total area=240 +48=288

What is the x-coordinate of the point shown in the graph?
______

Answers

Answer:

Hey there!

The x coordinate would be -5.

Let me know if this helps :)

As we can see in the Graph,

x-coordinate = - 5

y-coordinate = - 7

Find the total amount in the compound interest account.
$10000 is compounded semiannually at a rate of 9% for 22 years.
(Round to the nearest cent.)

Answers

Answer:

$69,361.23

Step-by-step explanation:

[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]

[tex] A = 10000(1 + \dfrac{0.09}{2})^{2 \times 22} [/tex]

[tex]A = 10000(1.045)^{44}[/tex]

[tex] A = 69361.23 [/tex]

Answer: $69,361.23

Need help with this as soon as possible pls

Answers

Answer:

i think

x=6.77

y=11.33

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet.

Required:
Do the results support the manufacturer's claim?

Answers

Complete question is;

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:

Do the results support the manufacturer's claim?

Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed

Answer:

We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Step-by-step explanation:

For the first sample, we have;

Mean; x'1 = 1160 ft

standard deviation; σ1 = 32 feet

Sample size; n1 = 19

For the second sample, we have;

Mean; x'2 = 1130 ft

Standard deviation; σ2 = 30 ft

Sample size; n2 = 11

The hypotheses are;

Null Hypothesis; H0; μ1 = μ2

Alternative hypothesis; Ha; μ1 > μ2

The test statistic formula for this is;

z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]

Plugging in the relevant values, we have;

z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]

z = 2.58

From the z-table attached, we have a p-value = 0.99506

This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Transform the given parametric equations into rectangular form. Then identify the conic. x= 5cos(t) y= 2sin(t)

Answers

Answer:

Solution : Option D

Step-by-step explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = 5cos(t) ⇒ x / 5 = cos(t)

y = 2sin(t) ⇒ y / 2 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / 5 )² = cos²(t)

+ ( y / 2 )² = sin²(t)

_____________

x² / 25 + y² / 4 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

Repeated-measures and matched-subjects experiments Aa Aa Repeated-measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. Which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions? Check all that apply.
A. The researcher computes difference scores to compute a t statistic
B. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment
C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
D. Participants in both types of experiments are all measured the same number of times
A matched-subjects experiment produced a t statistic with a df of 9. How many subjects participated in this study?
A. 20
B. 10
C. 18
D. 9
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 11. How many subjects participated in this study?
A. 12
B. 22
C. 24
D. 11

Answers

Answer:

1. C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistics.

2. B. 10

3. A. 12

Step-by-step explanation:

The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution.

A box is dragged across 20 meters with a force of 60 Newtons, which are kg*m/s^2

Answers

Answer:

Mass= 6kg

Acceleration= 10 ms^-2

Work done = 1200Nm

Step-by-step explanation:

kg*m/s^2 represent the force.

The kg represent the mass

The m/s^2 represent the acceleration

The acceleration here will be due to gravity force= 10 ms^-2

Then the mass= 60/10

Mass= 6 kg

The force = 60 Newton

Distance covered in the direction of the the force= 20 Meters

The work done in the direction of the force= force* distance

The work done in the direction of the force=60*20

The work done in the direction of the force=1200 Nm

Answer: 20 • 60

Step-by-step explanation:

Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?​

Answers

Answer: There are 75 books.

Price of each book = $4.

Step-by-step explanation:

Let x = Number of books in the box.

Then as per given,

Cost of x books = $300

Cost of one book = [tex]\$(\dfrac{300}x)[/tex]

Books left after giving 15 of them = x-15

Selling price of (x-15) books=  $330

Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]

Profit on each book= $1.50

Profit = selling price - cost price

[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]

[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]

Number of books cannot be negative.

So, there are 75 books.

Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]

So price of each book = $4.

Each of three identical jewelry boxes has two drawers. Each drawer of the first box contains a gold coin. Each drawer of the second box contains a silver coin. In the third box, one drawer has a gold coin and the other drawer a silver coin. If a box and drawer are selected at random, and the selected drawer has a silver coin, what is the probability that the other drawer has a gold coin

Answers

Answer:

75%

Step-by-step explanation:

75% of possibility to have gold coin

Suppose you were exploring the hypothesis that there is a relationship between parents’ and children’s party identification. Would we be correct in inferring that such a relationship also exists in the population? Explain your answer. What is the probability that any relationship we found is due to pure chance?

Answers

Answer:

No

It could be purely due to chance.

Step-by-step explanation:

A population is defined as the whole group which has the same characteristics. For example a population of the college belongs to the same college . But a sample may be an element of a population.

So it is not necessary for a population to have the same characteristics as the sample.

But it is essential for the sample to have at least one same characteristics as the population.

So we would not be correct in inferring that such a relationship also exists in the population.

It is a hypothesis which can be true or false due to certain conditions or limitations as the case maybe.

For example in a population of smokers some may be in the habit of taking cocaine. But a sample of cocaine users does not mean the whole population uses it.

It could be purely due to chance if we find out that there is a relationship between parents’ and children’s party identification in the population.

Suppose that a random sample of 16 measures from a normally distributed population gives a sample mean of x=13.5 and a sample standard deviation of s=6. the null hypothesis is equal to 15 and the alternative hypothesis is not equal to 15. using hypothesis testing for t values do you reject the null hypothesis at alpha=.10 level of significance?

Answers

Answer:

Step-by-step explanation:

The summary of the statistics given include:

population mean [tex]\mu[/tex] = 15

sample mean [tex]\oerline x[/tex] = 13.5

sample size n = 16

standard deviation s = 6

The level of significance ∝ = 0.10

The  null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu = 15} \\ \\ \mathtt{H_1 : \mu \neq 15}[/tex]

Since this test is two tailed, the t- test can be calculated by using the formula:

[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]t = \dfrac{13.5 - 15}{\dfrac{6}{\sqrt{16}}}[/tex]

[tex]t = \dfrac{- 1.5}{\dfrac{6}{4}}[/tex]

[tex]t = \dfrac{- 1.5\times 4}{6}}[/tex]

[tex]t = \dfrac{- 6.0}{6}}[/tex]

t = - 1

degree of freedom = n - 1

degree of freedom = 16 - 1

degree of freedom = 15

From the standard normal t probability distribution table, the p value when t = -1 at  0.10 level of significance, the p - value = 0.3332

Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.10

Conclusion: Therefore, we can conclude that  there is insufficient evidence at the 0.10 level of significance to conclude that the population  mean μ is different than 15.

The manager of a garden shop mixes grass seed that is 60% rye grass with 140 pound of grass seed that is 80% rye grass to make a mixture that is 74% rye grass. How much of the 60% mixture is used?

Answers

Answer:

60 pounds

Step-by-step explanation:

Let x = number of pounds of grass seeds A

The number of pounds of grass seed B = 140 pounds

Total pounds of the resulting mixture = (140 + x) pounds

Rye grass A = 60% = 0.6

Rye grass B = 80% = 0.8

Total percent of mixture formed = 74% = 0.74

Hence, we have the equation:

0.6x + 0.8 × 140 = 0.74 ( 140 + x)

0.6x + 112 = 103.6 + 0.74x

Collect like terms

112 - 103.6 = 0.74x - 0.6x

8.4 = 0.14x

x = 60 pounds

Therefore, the quantity of the 60% mixture used is 60 pounds.

The manager of a garden shop mixes grass seed that is 60% rye grass with 140 pound of grass seed that is 80% rye grass to make a mixture that is 74% rye grass. How much of the 60% mixture is used?

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (csc(x) − cot(x))

Answers

Answer:

0

Step-by-step explanation:

[tex]\lim_{x \to 0} (csc(x)-cot(x))\\= \lim_{x \to 0}(\frac{1}{sin x}-\frac{cos(x)}{sin (x)} )\\=\lim_{x \to 0}(\frac{1-cos x}{sin x} )\\=\lim_{x \to 0}(\frac {2 sin ^2 \frac{x}{2}}{2sin \frac{x}{2} cos\frac{x}{2} } )\\=\lim_{x \to 0}(tan \frac{x}{2} )\\=\lim_{x \to 0}\frac{tan \frac{x}{2} }{\frac{x}{2} } \times \frac{x}{2} \\=1 \times 0\\=0[/tex]

The Bay Area Online Institute (BAOI) has set a guideline of 60 hours for the time it should take to complete an independent study course. To see if the guideline needs to be changed and if the actual time taken to complete the course exceeds60 hours, 16 students are randomly chosen and the average time to complete the course was 68hours with a standard deviation of 20 hours. What inference can BAOI make about the time it takes to complete this course?

Answers

Answer:

 At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Step-by-step explanation:

From the question we are told that

   The  population mean is [tex]\mu = 60 \ hr[/tex]

    The sample size is  [tex]n = 16[/tex]

    The  sample mean is  [tex]\= x = 68 \ hr[/tex]

     The  standard deviation is  [tex]\sigma = 20 \ hr[/tex]

The  null hypothesis is  [tex]H_o : \mu = 60[/tex]

The  alternative [tex]H_a : \mu > 60[/tex]

Here we would assume the level of significance of this test to be  

         [tex]\alpha = 5\% = 0.05[/tex]

Next we will obtain the critical value of the level of significance from the normal distribution table, the value is    [tex]Z_{0.05} = 1.645[/tex]

  Generally the test statistics  is mathematically represented as

           [tex]t = \frac{ \= x - \mu}{ \frac{ \sigma }{\sqrt{n} } }[/tex]

substituting values

           [tex]t = \frac{ 68 - 60 }{ \frac{ 20 }{\sqrt{16} } }[/tex]

          [tex]t = 1.6[/tex]

Looking at the value of t and  [tex]Z_{\alpha }[/tex] we see that [tex]t< Z_{\alpha }[/tex] hence we fail to reject the null hypothesis

   This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course

So

   At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

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