Each roll of tape is 30.5 feet long. A box contains 454 rolls of tape. How many yards are there in total

Answer:

(a)[tex]\dfrac{2}{13}[/tex]

(b)[tex]\dfrac{3}{13}[/tex]

(c)[tex]\dfrac{4}{13}[/tex]

Step-by-step explanation:

In a standard deck, there are 52 cards which are divided into 4 suits.

(a)

Number of Seven Cards =4

Number of King cards =4

Probability of randomly selecting a seven or king

=P(Seven)+P(King)

[tex]=\dfrac{4}{52} +\dfrac{4}{52} \\=\dfrac{8}{52}\\=\dfrac{2}{13}[/tex]

(b)

Number of Seven Cards =4

Number of King cards =4

Number of Jack(J) cards =4

Probability of randomly selecting a seven or king

=P(Seven)+P(King)+P(Jack)

[tex]=\dfrac{4}{52} +\dfrac{4}{52}+\dfrac{4}{52} \\=\dfrac{12}{52}\\=\dfrac{3}{13}[/tex]

(c)

Number of Queen Cards =4

Number of Spade cards =13

Number of Queen and Spade cards =1

Probability of randomly selecting a seven or king

[tex]=P$(Queen)+P(Spade)-P(Queen and Spade Card)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]

Answer:

The scale factor is 3.

Step-by-step explanation

Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.

Answer:

108 pages

Step-by-step explanation:

Angelina read 30% of the book that contains 360 pages.

30% of 360 pages

"of" also means multiply, so we must multiply 30% and 360.

30% * 360

Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.

30/100=0.30

or

30.0---> 3.0---> 0.30

Plug the decimal in for the percent.

0.30*360

Multiply the 2 numbers together

108

Angelina has read 108 pages so far.

easy claps!!

Answer: 30=2x+4 and there are 17 girls in the class.

Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.

It's BASIC prealgebra so you should probably practice bit more with linear equations!

Answer:

ofn

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since there are 44 average people out of 80. We can do this,

Total students : 600

Checked: 80

Average: 44

Number of averaged throughout the school: 600/80 * 44

                                                                        l: 7.5 * 44

Thus it is: 330 average students

Answer:

4 - 7 = -3

-3 / 3 = -1

Answer:

C

Step-by-step explanation:

Given

x + 10 = 3(x - 1)² ← expand (x - 1)² using FOIL

x + 10 = 3(x² - 2x + 1) ← distribute

x + 10 = 3x² - 6x + 3 ← subtract x + 10 from both sides

0 = 3x² - 7x - 7 → C

Answer:

Step-by-step explanation:

Answer:

answer for the question is 130 length

Answer:

-The total area of a Rectangular Prism:

[tex]A = 366[/tex] [tex]in^{2}[/tex]

Step-by-step explanation:

-To find the total area of a rectangular prism, you need this formula:

[tex]A = 2(l \cdot w + l \cdot h + w \cdot h)[/tex]

[tex]l =[/tex] Length

[tex]w =[/tex] Width

[tex]h =[/tex] Height

-Apply the length, width and height for the formula:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]l =[/tex] 11 in

[tex]w =[/tex] 8 in

[tex]h =[/tex] 5 in

-Then, solve for the area:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]A = 2(88 + 55 + 40)[/tex]

[tex]A = 2(143 + 40)[/tex]

[tex]A = 2 \times 183[/tex]

[tex]A = 366[/tex]

So, the total area would be [tex]366[/tex] [tex]in ^{2}[/tex].

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean salary of city 1 librarians

x2 = sample mean salary of city 2 librarians

s1 = sample standard deviation for city 1

s2 = sample standard deviation for city 2

n1 = number of soles for city 1

n1 = number of soles for city 2

For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28

z = 2.048

x1 - x2 = 28,900 - 30,300 = - 1400

Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)

= 1647

The upper boundary for the confidence interval is

- 1400 + 1647 = 247

The lower boundary for the confidence interval is

- 1400 - 1647 = - 3047

Answer:  EF = 15

Step-by-step explanation:

The given description is that of an isosceles triangle. The base angles are congruent, therefore the sides opposite of those angles are also congruent.

The base angles are ∠E and ∠G and the vertex angle is ∠F.

The sides opposite to the base angles are EF and FG.

Thus, EF ≡ FG.

Since FG = 15 and FG = EF, then 15 = EF.

Based on the definition of an isosceles triangle, the length of EF in the triangle is: 15 units.

An isosceles triangle has two sides that are congruent. The angles opposite these congruent sides are also congruent.

ΔEFG is an isosceles triangle. The congruent sides are, FG and EF.

Therefore, EF = FG = 15 units.

Learn more about isosceles triangle on:

https://brainly.com/question/11884412

Answer:

(2,-2)

Step-by-step explanation:

In the attached file

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" values correspond to safer​ cars). The listed values correspond to cars​ A, B,​ C, D,​ E, F, and​ G, respectively.

514 541 302 400 507 406 369

Find the

a.​ mean,

b.​ median,

c.​ midrange,

d. mode for the data.

Also complete parts e. and f.

e. Which car appears to be the safest?

f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

Answer:

a) Mean = 434.14

b) Median = 406

c) Midrange = 421.5

d) Mode = 0

e) Car C appears to be the safest

f) The small cars does not appear to have about the same risk of head injury in a crash.

Step-by-step explanation:

We are given the head injury measurements from small cars that were tested in crashes.

The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion.

The listed values are;

A = 514

B = 541

​C = 302

D = 400

​E = 507

F = 406

G = 369

a)​ Mean

The mean of the measurements is given by

Mean = Sum of measurements/ Number of measurements

Mean = (514 + 541 + 302 + 400 + 507 + 406 + 369)/7

Mean = 3039/7

Mean = 434.14

b)​ Median

Arrange the measurements in ascending order (low to high)

302, 369, 400, 406, 507, 514, 541

The median is given by

Median = (n + 1)/2

Median = (7 + 1)/2

Median = 8/2

Median = 4th

Therefore, the 4th measurement is the median that is 406

Median = 406

c)​ Mid-range

The midrange is given by

Midrange = (Max + Min)/2

The maximum measurement in the data set is 541

The minimum measurement in the data set is 302

Midrange = (541 + 302)/2

Midrange = 843/2

Midrange = 421.5

d)​ Mode for the data

The mode of the data set is the most repeated measurement.

302, 369, 400, 406, 507, 514, 541

In the given data set we don't have any repeated measurement therefore, there is no mode or we can say the mode of this data set is 0.

Mode = 0

e) Which car appears to be the safest?

Since we are given that the measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" values correspond to safer​ cars)

The lowest hic value corresponds to car C that is 302

Therefore, car C appears to be the safest among other cars.

f) Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

302, 369, 400, 406, 507, 514, 541

As you can notice, the hic values differ a lot from each other therefore, we can conclude that the small cars does not appear to have about the same risk of head injury in a crash.

Answer:

40 litres

Step-by-step explanation:

V = l x w x h

50 x 40 x 20 = 40000

40000 cm^3

1cm^3 = 1ml

40000 cm^3/ 1cm^3 = 40000ml

40000 x 10^-3 = 40 litres

Answer:

16.67% probability of getting 2 blues

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

What is the probability of getting 2 blues?

Desired outcomes:

Two blue marbles, from a set of 4.

[tex]D = C_{4,2} = \frac{4!}{2!(4-2)!} = 6[/tex]

Total outcomes:

Two marbles, from a set of 9.

[tex]T = C_{9,2} = \frac{9!}{2!(9-2)!} = 36[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{6}{36} = 0.1667[/tex]

16.67% probability of getting 2 blues

Answer:

(a) The probability that all five have used a computer while under the influence of alcohol is 0.0021.

(b) The probability that at least one has not used a computer while under the influence of alcohol is 0.9979.

(c) The probability that none of the five have used a computer while under the influence of alcohol is 0.1804.

(d) The probability that at least one has used a computer while under the influence of alcohol is 0.8196.

Step-by-step explanation:

We are given that among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol.

Suppose five 25- to 30-year-olds are selected at random.

The above situation can be represented through the binomial distribution;

[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]

where, n = number of trials (samples) taken = Five 25- to 30-year-olds

            r = number of success

            p = probability of success which in our question is probability that

                  people used a computer while under the influence of alcohol,

                   i.e. p = 29%.

Let X = Number of people who used computer while under the influence of alcohol.

So, X ~ Binom(n = 5, p = 0.29)

(a) The probability that all five have used a computer while under the influence of alcohol is given by = P(X = 5)

               P(X = 5)  =  [tex]\binom{5}{5}\times 0.29^{5} \times (1-0.29)^{5-5}[/tex]

                              =  [tex]1 \times 0.29^{5} \times 0.71^{0}[/tex]

                              =  0.0021

(b) The probability that at least one has not used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)

Here, the probability of success (p) will change because now the success for us is that people have not used a computer while under the influence of alcohol = 1 - 0.29 = 0.71

SO, now X ~ Binom(n = 5, p = 0.71)

               P(X [tex]\geq[/tex] 1)  =  1 - P(X = 0)   

                              =  [tex]1-\binom{5}{0}\times 0.71^{0} \times (1-0.71)^{5-0}[/tex]

                              =  [tex]1 -(1 \times 1 \times 0.29^{5})[/tex]

                              =  1 - 0.0021 = 0.9979.

(c) The probability that none of the five have used a computer while under the influence of alcohol is given by = P(X = 0)

               P(X = 0)  =  [tex]\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]

                              =  [tex]1 \times 1 \times 0.71^{5}[/tex]

                              =  0.1804

(d) The probability that at least one has used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)

               P(X [tex]\geq[/tex] 1)  =  1 - P(X = 0)   

                              =  [tex]1-\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]

                              =  [tex]1 -(1 \times 1 \times 0.71^{5})[/tex]

                              =  1 - 0.1804 = 0.8196

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean. Based on this data, with a 95% confidence interval the researchers can determine that the actual average amount of time the entire population can hold their breath under water is?

Given Information:

sample mean time = 72.7

sample standard deviation = 0.92

Sampling size = n = 150

Confidence level = 95%

Required Information:

95% confidence interval = ?  

Answer:

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean time and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sampling size, s is the sample standard deviation, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 150 - 1 = 149

From the t-table at α = 0.025 and DoF = 149

t-score = 1.975

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 1.975\cdot \frac{0.92}{\sqrt{150} } \\\\MoE = 1.96\cdot 0.07512\\\\MoE = 0.14836\\\\[/tex]

So the required 95% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Therefore, we are 95% confident that actual average amount of time the entire population can hold their breath under water is within the range of (72.552, 72.848)

Answer:

P (subject had a positive test result or a negative test result) = 1

Step-by-step explanation:

Given

The table above

Required

P (subject had a positive test result or a negative test result)

This is calculated as follows;

P (subject had a positive test result or a negative test result) =

P (subject had a positive test result) + P (subject had a negative test result)

Calculating P (subject had a positive test result)

This can be calculated by number of subjects with positive results divided by 1000

Only data from the column of subjects with positive results will be considered.

Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs

Number of subjects = 76 + 95

Number of Subjects = 171

P (Subject had a positive test Result) = 171/1000

Calculating P (subject had a negative test result)

This can be calculated by number of subjects with negative results divided by 1000

Only data from the column of subjects with negative results will be considered.

Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs

Number of subjects = 6 + 823

Number of Subjects = 829

P (Subject had a negative test Result) = 829/1000

Hence, P (subject had a positive test result or a negative test result) =

P (subject had a positive test result) + P (subject had a negative test result) = 171/1000 + 829/1000

P (subject had a positive test result or a negative test result) = (171 + 829)/1000

P (subject had a positive test result or a negative test result) = 1000/1000

P (subject had a positive test result or a negative test result) = 1

Answer:

Dear Laura Ramirez

Answer to your query is provided below

1) option A is correct

2) option B is correct

Step-by-step explanation:

Explanation for the first question attached in image

Also note - The converse of the hinge theorem states that if two triangles have two congruent sides, then the triangle with the longer third side will have a larger angle opposite that third side.

Answer:

1) option A is correct2) option B is correct

Step-by-step explanation:

Answer: No.

Step-by-step explanation:

I guess that here we have the statement:

If the sum of two numbers is odd----> can their quotient be an odd number?

first, for n an integer number, we have that:

an odd number can be written as 2n + 1

an even number can be written as 2n.

The sum of two numbers is only odd if one of them is odd and the other even.

Then we have a number that is 2n and other that is 2k + 1, for n and k integer numbers.

Now, let's see if the quotient can also be an odd number.

One way to think this is:

There is an odd number such that when we multiply it by another odd number, the result is an even number?

no, and i can prove it as:

let 2k + 1 be an odd number, and 2j + 1 other.

the product is:

(2k + 1)*(2j + 1) = 2*(2*k*j + k + j) + 1

and as k and j are integers, also does 2*k*j + k + j, so:

2*(2*k*j + k + j) + 1 is an odd number.

This says that the product of two odd numbers is always odd, then we never can have that the quotient between an even number and an odd number is odd.

Answer: A (30)

Step-by-step explanation:

By defaults, data will be enabled in tens. And it increases by replicating the initial value.

There is no way the maximum number of dataflow definitions available in this situation will be 45, 25 or 35

The only possible replicant that can be available is 30

Answer:

Step-by-step explanation:

The point estimate is the sample proportion.

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 137

n = number of samples = 200

p = 137/200 = 0.685

From the information given,

Population proportion = 62% = 62/100 = 0.62

The correct options are

A) Yes, the sample size is greater than 30.

B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.

Answer:

Test statistic t = 5.25

P-value = 0.000002 (one-tailed test)

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=7\\\\H_a:\mu> 7[/tex]

The significance level is 0.05.

The sample has a size n=49.

The sample mean is M=8.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√s^2=√4=2.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{49}}=0.29[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{8.5-7}{0.29}=\dfrac{1.5}{0.29}=5.25[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=49-1=48[/tex]

This test is a right-tailed test, with 48 degrees of freedom and t=5.25, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>5.25)=0.000002[/tex]

As the P-value (0.000002) 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 average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.

Answer:

2

Step-by-step explanation:

Set the height of the bar to 2 since there are 2 numbers between 21-40.

Answer:

2 people.

Step-by-step explanation:

34 minutes and 40 minutes were recorded.

Therefore, 2 people.

Answer:

C

Step-by-step explanation:

C=2pier or pied

Answer:

a. C = 2πr

c. C= πd

both are correct

Answer:

1) [tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]

2) [tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]

3) [tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]

And the variance would be given by:

[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]

4) [tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]

And the variance would be given by:

[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]

Step-by-step explanation:

For this case we have the following distributions given:

Probability  M   J

0.3           14%  22%

0.4           10%    4%

0.3           19%    12%

Part 1

The expected value is given by this formula:

[tex] E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]

And replacing we got:

[tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]

Part 2

[tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]

Part 3

We can calculate the second moment first with the following formula:

[tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]

And the variance would be given by:

[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]

Part 4

We can calculate the second moment first with the following formula:

[tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]

And the variance would be given by:

[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]

Answer:

The correct option is (A).

Step-by-step explanation:

If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.

[tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]

Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:

[tex]\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right][/tex]

Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.

Thus, the correct option is (A).

The correct question is:

A circle has a radius of 45 units and is centered at (-2.4, -4.8).

What is the equation of this circle?

Answer:

Equation of the circle is;

(x + 2.4)² + (y + 4.8)² = 2304

Step-by-step explanation:

The standard equation of a circle is;

(x - a)² + (y - b)²  =  r²

where;

(a,b) is the center of the circle and r is the radius of the circle

Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45

Thus, plugging those values into the standard form of equation of a circle, we have;

(x - (-2.4))²  +  (y - (-4.8))²  = 48²

This gives;

(x + 2.4)² + (y + 4.8)² = 2304

-4y ≤ -12

Divide both sides by -4:

y ≤ 3

Because both sides were divided by a negative value you need to reverse the inequality sign:

y ≥ 3

Answer:

y = 3

Step-by-step explanation:

it says -4y ≤ -12 sooooooo    4 x 3 = 12!!!! so y = 3