A right rectangular prism is packed with cubes of side length 1 inch. If the prism is packed with 16 cubes along the length, 8 cubes along the width and 6 cubes
8
along the height, what is the volume of the prism?​

Answer:

5

Step-by-step explanation:

(14 × 5 × 4) ÷ (28 × 2)

Solve brackets.

280 ÷ 56

Divide.

= 5

Answer:

a. The plane's speed in mph is 560

b. At this rate, the plane can travel 5,600 miles in 10 hours.

Step-by-step explanation:

In order to find the planes speed in mph, some simple arithmetic must be done and you should divide 3,360 by 6.   Now that you have determined that 3,360/6 equals 560, you know that in order to figure out how many miles the plane can travel in 10 hours, all you must do is multiply 560 by 10 which equals 5,600.

Answer:

Step-by-step explanation:

Answer:

B) One sheet of paper is 0.0042 inches thick

Step-by-step explanation:

All the other values are not give from just a sheet of paper, and/or they are either a cumulative value, or values that will be used to calculate another value

Only option B defines a value for a unit of paper, and the value is definite.

Option A indicates  the number in a group (gross)

Option C shows two values that can be used to calculate one value; the area.

Option D indicates an accumulated value of weight.

Answer:I think it's TRUE not sure

Step-by-step explanation:

Answer:

here,

a=b+12

b=a-12----> equation (i)

b= c+4

putting the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

hope this helps...

Good luck on your assignment...

The value of a + c is 16.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

a=b+12

So, b=a-12 ---- equation (i)

and, b= c+4

Substitute the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

Hence, the value of a+ c is 16.

Learn more about Algebra here:

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Answer:

x=2

Step-by-step explanation:

5(2x - 3) = 5

Divide by 5

5/5(2x - 3) = 5/5

2x-3 = 1

Add 3 to each side

2x-3 +3 = 1+3

2x = 4

Divide by 2

2x/2 = 4/2

x =2

Answer:

x = 2

Step-by-step explain:

5(2x-3) = 5

Divide both sides by 5

2x-3 = 1

Add 3 to both sides

2x = 4

Divide both sides by 2

x = 2

Answer:

50%

Step-by-step explanation:

Even numbers on a 6-sided die are 2, 4, and 6.

3 numbers out of 6 are even.

3/6 = 1/2

0.5 = 50%

Answer:

[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]

Step-by-step explanation:

hello,

first of all let's assume that r is different from 0 as this is not allowed to divide by 0

[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]

multiply by 13r it comes

[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]

now multiply by 15

[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]

hope this helps

Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....

Step-by-step explanation:

[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]

[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex]    =-104/15

simplify

[tex]r=-\frac{104}{15}[/tex]

MARK BRAINLIEST PLEASE

Answer:

Step-by-step explanation:

For private Institutions,

n = 20

Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95

Standard deviation = √(1527829234.95/20

s1 = 8740.22

For public Institutions,

n = 20

Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15

Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95

Standard deviation = √(283738188.55/20

s2 = 3766.55

This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.

The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.

We would set up the hypothesis. The correct option is

-B. H0: μ1 = μ2 ; H1: μ1 > μ2

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)

t = 9559.9/2128.12528473889

t = 4.49

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114

df = 26

We would determine the probability value from the t test calculator. It becomes

p value = 0.000065

Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.

Answer:

D(4,-3)

Step-by-step explanation:

Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)

Let the coordinate of the fourth vertex be D(x,y).

We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.

The diagonals are BD and AC

Midpoint of BD = Midpoint of AC

[tex]\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3[/tex]

The coordinates of the fourth vertex is D(4,-3)

Answer:

(4,-3)

Step-by-step explanation:

Answer: NO, class limits and class marks are not meaningful to qualitative data.

Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.

Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.

Answer:

x = 3.6

Step-by-step explanation:

In similar polygons, corresponding sides are in same ratio

[tex]\frac{AB}{EF}=\frac{AD}{EH}\\\\\frac{3}{2}=\frac{x}{2.4}\\\\\frac{3}{2}*2.4=x\\[/tex]

3 * 1.2 = x

x = 3.6

Answer:

Q1 is: 2.2 percent per minute

Q2 is: 35 minutes

Step-by-step explanation:

For the first question, take 89 percent, and subtract 23 from it, then divide by 30 minutes for the rate per minute.

For the second question take 23 percent, find out how much is left until 100 percent (77 percent) and use the rate from the last question (2.2 percent per minute), to find out how much time charging 77 percent takes. (You get 35 by using: 77 divided by 2.2)

Answer:124

Step-by-step explanation:

2x + 8 + x - 2 = 180

Add like terms

3x + 6 = 180

Subtract the 6 from both sides

3x + 6 - 6 = 180 - 6

3x = 174

Divide by 3

x = 58

Now we have to find the measure of angle ACD

2(58) + 8 = 124

Answer:

Option B

Step-by-step explanation:

Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -

[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]

Convert this to slope - intercept form -

[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]

Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -

( 0, 10 ),

( 15, 9 ),

( 17, 0 )

When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -

Option B

Answer:

A

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, 0) , thus

y = a(x - 1)² + 0

To find a substitute the coordinates of the y- intercept (0, 1) into the equation

1 = a(- 1)² = a , thus

a = 1

y = (x - 1)² → A

Considering it's y-intercept and vertex, the equation of the parabola is given by:

[tex]y = (x - 1)^2[/tex]

The equation of a quadratic function, of vertex (h,k), is given by:

[tex]y = a(x - h)^2 + k[/tex]

In which a is the leading coefficient.

In this problem, the vertex is (1,0), hence h = 1, k = 0 and:

[tex]y = a(x - 1)^2[/tex]

The y-intercept is of 1, hence, when x = 0, y = 1, so:

[tex]y = a(x - 1)^2[/tex]

[tex]1 = a(0 - 1)^2[/tex]

[tex]a = 1[/tex]

Hence, the equation is:

[tex]y = (x - 1)^2[/tex]

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

Answer:

a = 5

b = 1.3

c = 6.3

Step-by-step explanation:

To find the values of a, b and C respectively, let's find a first by recalling that the diagonals of a rhombus are perpendicular to each other.

Therefore, the angle given as (14a + 20) = 90°

Solve for a

14a + 20 = 90

14a = 90 - 20

14a = 70

a = 70/14

a = 5

==>To find b, also recall that all sides of a rhombus are equal.

Therefore 3b + 4 = 13b - 9

Solve for b

4 + 9 = 13b - 3b

13 = 10b

13/10 = b

b = 1.3

==>Find value of c

c = a + b

c = 5 + 1.3

c = 6.3

Answer:

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Step-by-step explanation:

Data given

20 13 21 18 19 22 19 15 12 12 18 21

We can calculate the sample mean and deviation with the following formulas:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And we got:

[tex]\bar X = 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=3.61 represent the sample standard deviation

n=12 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=12-1=11[/tex]

Since the Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be given by [tex]t_{\alpha/2}=[/tex]

Now we have everything in order to replace into formula (1):

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Answer:

Four brothers and three sisters.

Step-by-step explanation:

Answer:

1. The 99% confidence interval is from 941.527 to 958.473

2. The 99% confidence interval is from 933.054 to 966.946

3. The 99% confidence interval is from 916.108 to 983.892

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 and Margin of error is given by

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

Where n is the sample size,

s is the sample standard deviation,

[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level

The t-score corresponding to 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 13 - 1 = 12

From the t-table at α = 0.005 and DoF = 12

t-score = 3.055

1. 99% Confidence Interval when s = 10

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]

The 99% confidence interval is from 941.527 to 958.473

2. 99% Confidence Interval when s = 20

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]

The 99% confidence interval is from 933.054 to 966.946

3. 99% Confidence Interval when s = 40

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]

The 99% confidence interval is from 916.108 to 983.892

As the sample standard deviation increases, the range of confidence interval also increases.

Answer: The value of the test statistic is z= 1.63 .

Step-by-step explanation:

Test statistic for proportion :

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

, where p =population proportion.

[tex]\hat{p}[/tex] = sample proportion

n= sample size.

Let p be the proportion of chips do not fail in the first 1000 hours of their use.

As per given, we have

[tex]p=0.41\\ n= 1600\\\hat{p}=0.43[/tex]

Then, required test statistic would be

[tex]z=\dfrac{0.43-0.41}{\sqrt{\dfrac{0.41(1-0.41)}{1600}}}\\\\=\dfrac{0.02}{\sqrt{0.0001511875}}\\\\\approx\dfrac{0.02}{0.0123}\approx1.63[/tex]

Hence, the value of the test statistic is z= 1.63 .

Answer:

The time period is 13 years.

Step-by-step explanation:

Interest rate (r )= 5% or 5%/12 = 0.42% per months

The investment amount (Present value) = $10500

Final expected amount (future value) = $20000

Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.

Use the below formula to find the time period.

Future value = present value (1 + r )^n

20000 = 10500(1+0.0042)^n

1.9047619 = (1+0.0042)^n

1.9047619 = 1.0042^n

n = 153.74 months.

Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)

Answer:

Step-by-step explanation:

A) The constant of proportionality in terms of minutes per bracelet is

15/3 = 5 minutes per bracelet

B) The constant of proportionality represents man hour rate

C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

t = kb

D) the constant of proportionality in terms of number of bracelets per minute is

3/15 = 1/5

E) The constant of proportionality represents production rate

F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

b = kt

G) The constants of proportionality are reciprocals

H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.

Answer:the sample answers, change them up so you dont get in trouble

A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:

constant of proportionality=15 MINUTES/3 BRACELETS=5  minutes per bracelet.

B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.

C Here’s one way to set up the equation:

time = constant of proportionality × number of bracelets

Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.

thats all ik srry

Step-by-step explanation:

Answer:

y=x-1

Step-by-step explanation:

since the slope is just one up and one over and it's positive it would just be x

and since the intercept is just -1 it would be y=x-1

Answer:

  62.3538

Step-by-step explanation:

There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.

Answer:

The height of the hill is 116.9 meters.

Step-by-step explanation:

The diagram depicting this problem is drawn and attached below.

From Triangle ABC

[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]

From Triangle XBC

[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]

Therefore:

[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]

Therefore, the height of the hill

[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]

The height of the hill is 116.9 meters.

Answer:

The probability that he requires 18 shots is 0.04785

Step-by-step explanation:

To answer this, we shall be using the negative binomial distribution

From the question;

P = 0.25 , r = 6

q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial

P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)

P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785

Answer:

Systematic sampling is used.

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

Every 14th CD.

So systematic sampling is used.

Answer:

a) 294

b) 180

c) 75

d) 174

e) 105

Step-by-step explanation:

I assume that for each problem, the first digit can't be 0.

a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.

6×7×7 = 294

b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.

6×6×5 = 180

c) Again, each digit can only be used once, but this time, the last digit must be odd.

If only the last digit is odd, there are 3×3×3 = 27 possible numbers.

If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.

If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.

If all three digits are odd, there are 3×2×1 = 6 possible numbers.

The total is 27 + 24 + 18 + 6 = 75.

d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.

If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.

If the first digit is greater than 3, there are 3×7×7 = 147 numbers.

The total is 6 + 21 + 147 = 174.

e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.

If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.

The total is 15 + 90 = 105.

Hey there! :)

Answer:

56 m².

Step-by-step explanation:

To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:

Solve for the rectangle: (A = l × w)

A = 8 × 5

A = 40 m²

Solve for the triangle: (A = 1/2 (bh))

A = 1/2(4 · 8)

A = 1/2(32)

A = 16 m².

Add up the two areas:

40 + 16 = 56 m².

Answer:

Area of triangle+ the area of rectangle

Step-by-step explanation:

Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²

Area of rectangle is length × breadth= 5×8: 40 m²

Area of the shape is 40m²+16m²= 56m²