principal: $1000, annual interest rate: 4.8%, time: 2 yr

Answer:

4 sisters

Step-by-step explanation:

-This is a logic question.

-Given that she has 3 sisters, it only means that the 4 are siblings of the same family.

-As such, eaxh sister can correctly claim to have 3 sisters.

Hence, there is a total of 4 sisters.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]  

And rounded up we have that n=385

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

We can use as an estimator for p [tex]\hat p =0.5[/tex]. And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]  

And rounded up we have that n=385

Step-by-step explanation:

= 5- 2 + 12 /4

= 5 -2 + 3

= 8- 2

= 6

Answer:

6

Explanation:

What you do is you take 12 divided by 4 and you get 3. The equation is now 5-2+3, you subtract 2 from 5 and get 3. Now you have 3 plus 3 which gets you 6.

Answer:

Each notebook costs $2

Step-by-step explanation:

We have to find the amount she spent on each notebook.

22-10=12

We know she spent $12 on six notebooks

We need to divide to find the answer

12/6=2

Each notebook costs $12

Answer:

$2

Step-by-step explanation:

First subtract 10 from 22 to get the price she spent on notebooks which is $12.

Then divide 12 by 6 to get the price she spent on each which is, $2

Answer:

1 cm cubed

Step-by-step explanation:

The volume of a rectangular prism is found by the equation: [tex]V=lwh[/tex] , where [tex]l[/tex] is the length, w is the width, and h is the height.

Here, our dimensions are 2 by 1/4 by 2. So: [tex]l=2,w=1/4,h=2[/tex].

Substituting these into the equation, we have:

[tex]V=2*(1/4)*2=1[/tex]

Thus, the volume is 1 cm cubed.

Hope this helps!

Answer:

1

Step-by-step explanation:

2*2=4

4*1/4=1

multiplying 1/4 is the same as dividing by 4

Answer:

P = 12x +8

Step-by-step explanation:

The perimeter of a square is given by

P = 4s  where s is the side length

P = 4(3x+2)

Distribute

P = 12x +8

Answer:

[tex]12x+8[/tex]

Step-by-step explanation:

[tex]3x+2[/tex] for one side of a square, for a perimeter for the square we need 4 times the side length, so we need:

[tex]4(3x+2)=12x+8[/tex]

Answer:

The probability that the mean is less than 110

P(x⁻<110) =0.5

Step-by-step explanation:

Explanation:-

Given the standard deviation of the Population' σ' = 1250

Given sample size 'n' = 350

The standard error of the mean determined by

                                                                             [tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]

                                             Standard error = [tex]\frac{1250}{\sqrt{350} } = 66.8153[/tex]

  by using normal distribution    [tex]z = \frac{x -mean}{S.E}[/tex]

                                         [tex]z = \frac{x^{-} -110}{66.8}[/tex]

                                   cross multiplication  66.8z = x⁻-110

                                                                         x⁻  =  66.81Z+110

P(x⁻<110)=P(66.81Z+110<110)

             = P(66.81Z < 110-110)

            = P(66.81Z<0)

           = P(Z<0)

           = 0.5- A(z₁)

          = 0.5 - A(0)  (here z₁=0)

         = 0.5 -0.00

        =0.5

Conclusion:-                            

The probability that the mean is less than 110

P(x⁻<110) =0.5

Answer:

Positive. From those two points the line would slant upwards. Going left to right it would be going up, therefore it's a positive slope

Step-by-step explanation:

The slope of the given lines with two points is positive.

Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

Thus, we get:

Slope = rise/ run

y-y₁ = m(x-x₁)

We are given that;

The points =(-3 -2) and (7,2)

Now,

For this line, let’s use (-3, -2) and (7, 2) as the two points. Plugging these values into the formula, we get:

m = (2 - (-2)) / (7 - (-3)) = 4 / 10 = 0.4

Therefore, the slope of this line is 0.4.

A positive slope means that the line goes up from left to right3. A negative slope means that the line goes down from left to right3.

Since 0.4 is a positive number,

Therefore, the slope of this line will be positive.

Learn more about slope here:

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Complete question:

He amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.3 minutes and standard deviation 1.4 minutes. Suppose that a random sample of n equals 47 customers is observed. Find the probability that the average time waiting in line for these customers is

a) less than 8 minutes

b) between 8 and 9 minutes

c) less than 7.5 minutes

Answer:

a) 0.0708

b) 0.9291

c) 0.0000

Step-by-step explanation:

Given:

n = 47

u = 8.3 mins

s.d = 1.4 mins

a) Less than 8 minutes:

[tex]P(X<8) = P \frac{X'-u}{s.d/ \sqrt{n}} < \frac{8-8.3}{1.4/ \sqrt{47}}][/tex]

P(X' < 8) = P(Z< - 1.47)

Using the normal distribution table:

NORMSDIST(-1.47)

= 0.0708

b) between 8 and 9 minutes:

P(8< X' <9) =[tex] [\frac{8-8.3}{1.4/ \sqrt{47}}< \frac{X'-u}{s.d/ \sqrt{n}} < \frac{9-8.3}{1.4/ \sqrt{47}}][/tex]

= P(-1.47 <Z< 6.366)

= P( Z< 6.366) - P(Z< -1.47)

Using normal distribution table,

[tex] NORMSDIST(6.366)-NORMSDIST(-1.47) [/tex]

0.9999 - 0.0708

= 0.9291

c) Less than 7.5 minutes:

P(X'<7.5) = [tex] P [Z< \frac{7.5-8.3}{1.4/ \sqrt{47}}] [/tex]

P(X' < 7.5) = P(Z< -3.92)

NORMSDIST (-3.92)

= 0.0000

Answer:

Arlin has to give lauren 1.37

Step-by-step explanation:

9.37 + 6.63 / 2 = 16 / 2 = 8

9.37 - 8 = 1.37

Answer:

$1.37

Step-by-step explanation:

I would start by adding up the total money between them. $9.37 + $6.63 = $16.00. They want the same amount of money, so divide the total by two.

$16.00/2 = $8.00.

Now take the difference between how much Arlin had ($9.37) and how much she has now ($8.00).

$9.37 - $8.00 = $1.37

Final answer:

To find the volume of a cone with a radius of 3 inches and a height of 10 inches, use the formula V = [tex]\frac{1}{3}[/tex] * π * r² * h. Substitute the values and calculate to find a volume of B) 94.26 cubic inches.

Explanation:

The volume of the cone can be calculated using the formula V = [tex]\frac{1}{3}[/tex] * π * r² * h.

Substitute the values for the radius (3 inches) and height (10 inches) into the formula to find the volume:

V = [tex]\frac{1}{3}[/tex] * 3.142 * 3² * 10

V = [tex]\frac{1}{3}[/tex] * 3.142 * 9 * 10

V = 94.26 cubic inches

Therefore, the cone's volume is 94.26 cubic inches.

Answer:

17576

Step-by-step explanation:

Each of the three rotors contained the letters A through Z.

For the first rotor: There are 26 Possible Initial Settings

(A,B,...Z)

For the second rotor: There are 26 possible initial combination with the first rotor likewise.

For the third rotor:There are also 26 possible combinations with the first and second rotors.

Therefore:

Number of Possible Initial Setting of the three rotor=26*26*26=17576

Answer:

A= 69

Step-by-step explanation:

A= h*b/2= (6*23)/2=69

Answer:

A = 69 [tex]ft^{2}[/tex]

Step-by-step explanation:

The formula utilised to determine the area of a triangle is:

A = [tex]\frac{1}{2}[/tex] * b * h

The base and height are given, and thus, can easily be substituted for in the formula to find the area.

A = [tex]\frac{1}{2}[/tex] * 23 * 6

A = 69 [tex]ft^{2}[/tex]

Answer:

C

Step-by-step explanation:

The samples are independent because there is not a natural pairing between the two samples.

Since Independent samples are samples that are selected randomly so that its observations do not depend on the values other observations also data set in which each data point in one sample is not paired to a data point in the second sample

Answer:

We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.

Step-by-step explanation:

The null Hypothesis: Geographical distribution of hotline callers could be the same as the U.S. population distribution

Alternative hypothesis: Geographical distribution of hotline callers could not be the same as the U.S. population distribution

The populations considered are the Midwest, South, Northeast, and west.

The number of categories, k = 4

Number of recent calls = 200

Let the number of estimated parameters that must be estimated, m = 0

The degree of freedom is given by the formula:

df = k - 1-m

df = 4 -1 - 0 = 3

Let the significance level be, α = 5% = 0.05

For  α = 0.05, and df = 3,

from the chi square distribution table, the critical value = 7.815

Observed and expected frequencies of calls for each of the region:

Northeast

Observed frequency = 39

It contains 18.1% of the US Population

The probability = 0.181

Expected frequency of call = 0.181 * 200 = 36.2

Midwest

Observed frequency = 55

It contains 21.9% of the US Population

The probability = 0.219

Expected frequency of call = 0.219 * 200 =43.8

South

Observed frequency = 60

It contains 36.7% of the US Population

The probability = 0.367

Expected frequency of call = 0.367 * 200 = 73.4

West

Observed frequency = 46

It contains 23.3% of the US Population

The probability = 0.233

Expected frequency of call = 0.233 * 200 = 46

[tex]x^{2} = \sum \frac{(O_{i} - E_{i}) ^{2} }{E_{i} } , i = 1, 2,.........k[/tex]

Where [tex]O_{i} =[/tex] observed frequency

[tex]E_{i} =[/tex] Expected frequency

Calculate the test statistic value, x²

[tex]x^{2} = \frac{(39 - 36.2)^{2} }{36.2} + \frac{(55 - 43.8)^{2} }{43.8} + \frac{(60 - 73.4)^{2} }{73.4} + \frac{(46 - 46.6)^{2} }{46.6}[/tex]

[tex]x^{2} = 5.535[/tex]

Since the test statistic value, x²= 5.535 is less than the critical value = 7.815, the null hypothesis will not be rejected, i.e. it will be accepted. We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.  

Answer:

Step-by-step explanation:

(1,4) (6,-1)

1-6= -5

6--1= 7 its 7 because 6 minus negative 1 would be 7

-5/7  would be your slope

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

y=mx+b

y= -5/7x+b

-1= -5/7(6)+b

-1= 6[tex]\frac{-5}{7}[/tex]+b

you take those two numbers and subtract

5 [tex]\frac{-5}{7}[/tex] is y intercept

y=[tex]\frac{-5}{7}[/tex]x+5[tex]\frac{-5}{7}[/tex]

Answer:

-3 (x-3) (x+1)

Step-by-step explanation:

− 3 x ^2 + 6 x + 9

Factor out -3

-3( x^2 -2x-3)

The terms inside the parentheses can be factored

What 2 numbers multiplies to -3 and adds to -2

-3*1 = -3

-3+1 =-2

-3 (x-3) (x+1)

Answer:

0.23 or 3/13.

Step-by-step explanation:

There are 52 cards in a deck. There are four different suits, dividing the decks into 4 sets of 13. There are three face cards for each suit so 3/13. 3 divided by 13 is 0.23. Use fractions if you can because they are easier and more accurate.

To find the probability that at least one of the 4 cards drawn is a face card, calculate the probability of all cards not being face cards and subtract that from 1, resulting in approximately 64.9%.

The problem can be approached by finding the probability that none of the 4 cards drawn is a face card and then subtracting that from 1 to find the probability that at least one is a face card. There are 12 face cards in a standard deck of 52 cards, leaving 40 non-face cards. When the audience members draw and replace the cards, each draw is independent of the previous draw.

First, calculate the probability of drawing a non-face card (P(NF)):

P(NF) = number of non-face cards / total number of cards = 40/52

Since the card is replaced each time, the probability remains the same for each of the four draws. Thus, the probability that all 4 cards are non-face cards is:

P(all four are NF) = [tex]P(NF)^4 = (40/52)^4[/tex]

Then subtract this probability from 1 to get the probability of at least one face card:

P(at least one face card) = 1 - P(all four are NF)

Calculation:

P(at least one face card) = [tex]1 - (40/52)^4 = 1 - (0.7692)^4[/tex]

P(at least one face card) ≈ 1 - 0.3515 ≈ 0.6485

Therefore, the probability that at least one of the 4 cards drawn is a face card is approximately 64.9% (rounded to one decimal place).

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

Let [tex]\mu[/tex] = true average writing lifetime under controlled conditions

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 10 hr   {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 hr    {means that the true average writing lifetime under controlled conditions is less than 10 hr}

The test statistics that is used here is one-sample t test statistics;

                           T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean

             s = sample standard deviation

             n = sample size of pens = 18

          n - 1 = degree of freedom = 18 -1 = 17

Now, the decision rule based on the critical value of t is given by;

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as  -1.74 < 0.57, so we fail to reject our null hypothesis.

Answer:

The correct option is 16.041 ounces.

Step-by-step explanation:

A single mean test can be used to determine whether the average amount of shampoo per bottle is 16 ounces.

The hypothesis can be defined as:

H₀: The average amount of shampoo per bottle is 16 ounces, i.e. μ = 16.

Hₐ: The average amount of shampoo per bottle is different from 16 ounces, i.e. μ ≠ 16.

The information provided is:

[tex]n=64\\\sigma=0.20\\\alpha =0.10[/tex]

We can compute a 90% confidence interval to determine whether the population mean is 16 ounces or not.

Since the population standard deviation is known we will compute the z-interval.

The critical value of z for 90% confidence interval is:

[tex]z_{0.05}=1.645[/tex]

*Use a z-table.

Compute the 90% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\[/tex]

Since the sample size is quite large, according to the law of large numbers the on increasing the sample size, the mean of the sample approaches the whole population mean.

So, the 90% confidence interval estimate for sample mean is:

[tex]CI=\mu\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\=16\pm 1.645\times \frac{0.20}{\sqrt{64}}\\=16\pm0.041125\\=(15.958875, 16.041125)\\\approx (15.959, 16.041)[/tex]

Thus, the correct option is 16.041 ounces.

Answer:

60

Step-by-step explanation:

15cubes assuming 3rows of 5 cubes in one layer so volume of first layer is 3x5x1 =15

4 layers means 4 times or 4 inch in height, either way 4x15 = 60

Answer:

75

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3x4=12

Answer:

12

Step-by-step explanation:

Multiply the number of bags times the apples per bag

4*3 = 12

He needs 12 apples

Answer:

x=4

Step-by-step explanation:

4x-6 + 2x = 18

Combine like terms

6x -6 = 18

Add 6 to each side

6x-6+6 =18+6

6x = 24

Divide each side by 6

6x/6 = 24/6

x =4

Answer:

235.75

Step-by-step explanation:

Answer:

Math answers to fraction 943 divided by 4 can be calculated as follows.

943/4 math problems division = 235.75. Therefore 235.75 to 2 decimal places= 235.75

943/4 divided by 2 » (943/4) ÷ 2 » 235.75 ÷ 2 = 117.875 .

Step-by-step explanation:

Answer:

$2.62

Step-by-step explanation:

[tex]2.4\% \: of \: \$109 \: \\ \\ = \frac{2.4}{100} \times 109 \\ \\ = 0.024 \times 109 \\ \\ = \$2.616 \\ \\ \approx \: \$2.62[/tex]

Answer:

the answer to the question is 3/5

Answer:

y = -x+3

Step-by-step explanation:

We have two points so we can find the slope

m =(y2-y1)/(x2-x1)

    (1-2)/(2-1)

    -1/1

 The slope is -1

We can use the slope intercept form of the equation

y = mx+b where m is the slope and b is the y intercept

y = -x+b

Substitute a point into the equation to find b

2 = -1 +b

Add 1 to each side

2+1 =-1+1 +b

3 =b

y = -x+3

Hey there!

"A number" is referred to an unknown number so we can say it is labled as

[tex]x[/tex]

"Increased" means you're going up/ adding

ten = 10

150 stays the same

"Ten times a number" =

[tex] \bf{10x}[/tex]

"Increased by 150" =

[tex] \bf{ + 150}[/tex]

Thus your answer should look like this:

[tex] \bf{10x + 150}[/tex]

Good luck on your assignment and enjoy your day!

~

[tex] \frak{loveyourselffirst }[/tex]

To solve this problem, we can use the algebraic expression 10x + 150, where 'x' represents the number.

To solve the problem, we can translate the given phrase into an algebraic expression. Let's assume the number is represented by the variable 'x'. 'Ten times a number increased by 150' can be written as 10x + 150. This expression represents ten times the number 'x' plus 150.

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