A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest hundredth. Enter your answer in the box.

Answer:

10.5 gallons are equal to 48000 cm3

Step-by-step explanation:

Answer:

25/6

Step-by-step explanation:

a²=6 -> a=✓6 (a must be positive so reject negative solutions)

ab=5 -> b = 5/✓6

thus area of C is b² = 25/6

Answer:

income tax=13% of total salary

Step-by-step explanation:

Here,

let salary be 'x'

Now,

13%of x = $10 000

13/100 × x = $10 000

13x = 1000000

x=10 00000/13

Therefore x =76,923.0769

His salary that year was 76,923.0769

Step-by-step explanation:

A) as you can see there is no current flowing in a bar magnet so (incorrect)

B) Lines of magnetic field is going in A-->B direction so it have starting and ending points.(incorrect)

C) Yes whenever a magnetic object is placed near the another magnetic object they either attract or repell so they have a force in a form of push and pull [correct]

D)No because magnetic field lines goes from North--> South so A is the South pole [ incorrect]

E) Yes it will point always towards North pole of the magnet [correct]

F) yes it depends upon the density of field lines[correct]

G)No the near the magnet is it becomes more stronger as compared to magnet kept far.(incorrect)

So option C E F are correct

Hope this helps

Have a great day

[tex]\textbf{a)}\\\\~~~~~~8x+y = 15\\\\\implies y = 15-8x\\\\\textbf{b)}\\\\~~~~~~9x+y = 13\\\\\implies y = 13 -9x\\\\\textbf{c)}\\\\~~~~~-4x+y = -6 \\\\\implies y = 4x -6 \\\\\textbf{d)}\\\\~~~~~-5x +y = -1\\\\\implies y = 5x -1[/tex]

Step-by-step explanation:

1. 8x+y=15

y=15-8x

2. 9x+y=13

y=13-9x

3. -4x+y=-6

y=4x-6

4. -5x+y=-1

y=5x-1

Answer:

A. 4.

Step-by-step explanation:

The scale factor is 4.

If you multiply 8, 5, and 2 by 4, you get 32, 20, and 8.

Answer:

5% is the percetange for 3 out of 60

Answer:

5%

Step-by-step explanation:

you know 10% of 60 is 6. 3 is half of 6, and 5% is half of 10

I hope this helps and have a wonderful day :)

Answer:

C) Yes, because 1 and 5 are congruent

Step-by-step explanation:

Same-side congruent angles prove this to be true

Answer:

The answer is C

Step-by-step explanation:

Answer:

9/25

Step-by-step explanation:

3x3 is 9 and 5x5 is 25 so that would equal to 9/25

Answer:

9/25

Step-by-step explanation:

first you do 3x3=9

                   5x5

                   9

                 5x5=25

9/25 is your answer :)

Answer:

66$

Step-by-step explanation:

1/3 of 99 is 33

so 99 - 33 = 66

Check the picture below.

Answer:

(6, 0)

Step-by-step explanation:

Coordinates are written in the form (x, y), where x is the x-axis value that the point is in, in this case 6, and where y is the y-axis value, in this case 0.

Hi!

Answer:

(6, 0)

Step-by-step explanation:

Coordinate point "G" on this graph is on the very bottom. On the X axis, point G is on the 6. On the Y axis, its on the 0, so since the domain, (X) comes first before the range, (Y), you get (6, 0)

I hope this helped! Have a wonderful day! :)

[tex]~~~~~~150\times x\% = 35\\\\\implies 150 \times \dfrac{x}{100} = 35\\\\\implies \dfrac{3x}{2}=35\\\\\implies 3x = 35\cdot 2\\\\\implies 3x = 70\\\\\implies x = \dfrac{70}{3}\\\\\implies x =23.\overline{3}\\\\\text{So, 35 is}~ 23.\overline{3}\%~ \text{of} ~150.[/tex]

Answer:

Step-by-step explanation:

Discussion

You haven't given us any choices. Always do that it you have them. Look for the graph that looks like the one below. It has the following characteristics

The standard deviation of the population dataset is 9.35

The dataset is given as:

18, 14, 35, 34, 11, 26

Start by calculating the mean using:

Mean = Sum/Count

This gives:

[tex]\bar x = (18+ 14+ 35+ 34+ 11+ 26)/6[/tex]

Evaluate

[tex]\bar x = 23[/tex]

The standard deviation is then calculated using:

[tex]\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n}}[/tex]

This gives

[tex]\sigma = \sqrt{\frac{(18 - 23)^2 + (14- 23)^2 + (35- 23)^2 + (34- 23)^2 + (11- 23)^2 + (26- 23)^2}{6}}[/tex]

Evaluate

[tex]\sigma = \sqrt{\frac{524}{6}}[/tex]

This gives

[tex]\sigma = 9.35[/tex]

Hence, the standard deviation of the population is 9.35

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Answer:

[tex]m = \boxed 7[/tex]

Combine like terms

[tex]21=33\cdot \mathrm{m}-21-27\cdot \mathrm{m}[/tex]

Group like terms

[tex]21=\left(33\cdot \mathrm{m}-27\cdot \mathrm{m}\right)-21[/tex]

Simplify the arithmetic

[tex]21=6\cdot \mathrm{m}-21[/tex]

Swap sides

[tex]6\mathrm{m}-21=21[/tex]

The required value of the x in the expression of angle is 19.

An expression of angle is given as 7x + 2 = 135°, the value of the x is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
7x + 2 = 135
Simplifying,
7x = 135 - 2
7x = 133
x = 133 / 7
x = 19

Thus, the required value of the x in the expression of angle is 19.

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Answer:

[tex]-\frac{8}{4}[/tex]

Step-by-step explanation:

To find slope from 2 points: [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{-2-6}{2-(-2)} =-\frac{8}{4}[/tex]

Answer:

a) 11/100

b) 60 times

Step-by-step explanation:

a)

We want to find the probability that a 3 will be rolled.

Probability = # of favorable outcomes / total # of outcomes.

Here the number of favorable outcomes will be the number of times a 3 was rolled and the total number of outcomes will simply be the # of times that the dice was rolled which can be calculated by finding the sum of the frequencies of each number.

So # of favorable outcomes = 11 ( as the dice was rolled on a 3 11 times.)

And the total number of outcomes would be 100 ( the sum of the frequencies , 12 + 35 + 11 + 23 + 7 + 12 = 100 )

So the probability of rolling a 3 would be 11/100

b)

For this part we want to find the expected times that a 6 would be rolled if we rolled the die 500 more times.

To calculate this we simply find the probability of rolling a 6 and then multiply that by 500.

So again probability = # of favorable outcomes / total # of outcomes.

Here # of favorable outcomes is frequency of rolling a 6 which would be 12 and the total number of outcomes is 100 as we found out during the last part.

So the probability of rolling a 6 is 12/100 or 3/25

We then multiply this by 500 to find the expected number of times a 6 would be rolled if the dice was rolled 500 more times

So our answer = 3/25 × 500 = 60 times

Answer:

y = 15

Step-by-step explanation:

JKLM ~ PQRS means that quadrilateral JKLM is similar to quadrilateral PQRS.

In similar shapes the corresponding sides have same ratio and the corresponding angles are congruent.

This means angle J is congruent to angle P, K is congruent to Q, L is congruent to R and M is congruent to S. Order of the vertices matters.

Solving for y.

Angle J is congruent to angle P.

5y - 4 = 71 Add 4 on both sides.

5y = 71 + 4

5y = 75  Divide both sides with 5.

y = 15

(Btw your solution for x is wrong.)

The probability of rolling the die once to get a four is 1/6

So we do 1/6*1/6*1/6 which is 1/216 since it's combined probabilities

Hope this helped

Step-by-step explanation:

[tex] = ( - 3c + 6) + ( - c + 8)[/tex]

[tex] = - 3c + 6 - c + 8[/tex]

[tex] = - 3c - c + 6 + 8[/tex]

= -4c + 14

hence -4c + 14 is the answer ...

hope it helped !!

Quadratic equation has a leading degrees of 2. The correct equation in vertex form is (x - 3)^2 + 5

Quadratic equation has a leading degrees of 2.

Given the quadratic function expressed as:

f(x) = x^2 - 6x + 14

Complete the square

x^2 - 6x + (-3)^2 - (-3)^2 + 14

(x- 3)^2 - 9 + 14
(x - 3)^2 + 5

Hence the correct equation in vertex form is (x - 3)^2 + 5

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Answer: Solve for Y

y = -16x - 38

And then y intercept is

(0, -38)

Step-by-step explanation:

Answer:

There are 525 chairs in the hall.

Step-by-step explanation:

35 x 15 = 525

An example to learn this:

35 is the amount of all the chairs in ONE row, when you times 35 by 15, it is DUPLICATING those chairs by 15, equaling to an equal 35 chairs in EACH row! hope this helped.

For the spinner with 3 sectors, the total number of outcomes for 3 spins is 27.

A combination is a mathematical technique that determines the number of possible arrangements.

Let's we have to define

A, B, and C, as the regions in the spinner.

So, we spin it 3 times, and for each of these times there are 3 outcomes, so the outcomes will be of the form:

The outcome of spin 1, the outcome of spin 2, outcome of spin 3.

The total number of  different outcomes will be:

3^3 = 27

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Answer:  480 and 253.2

Step-by-step explanation:

For the first one we want to do (12 x 5 / 2) x 16 which equals 480.

For the next question, the answer is 253.2 because 2πrh is the formula of lateral area. If we just plug in the numbers it's (2 x 3.14 x 4.8 x 8.4) = 253.2cm

Answer:

9

Step-by-step explanation:

8 3/4 to the nearest whole number is 9

Answer:

26.17%

Step-by-step explanation:

P(Grey) = 1/4

P(Grey at least 2 times in 4) = 1 - P(no Grey in 4) - P(1 Grey in 4)

P(no Grey in 4) = 4C0 * 3/4 * 3/4 * 3/4 * 3/4 = 81/256

P(1 Grey in 4) = 4C1 * 1/4 * 3/4 * 3/4 * 3/4 = 27/64

P(Grey at least 2 times in 4) = 1 -  81/256 -  27/64 = (256-81-108)/256=67/256=26.17%

Answer:

[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]

Special Limit Rule [L’Hopital’s Rule]:
[tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]

Differentiation

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify given limit.

[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}[/tex]

Step 2: Find Limit

Let's start out by directly evaluating the limit:

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

∴ we have evaluated the given limit.

___

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Without using l'Hopitâl's rule, we can instead rationalize the numerator.

[tex]\dfrac{\sqrt{x+1} - 2}{x-3} = \dfrac{\left(\sqrt{x+1}-2\right)\left(\sqrt{x+1}+2\right)}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac{(x+1)-4}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac1{\sqrt{x+1}+2}[/tex]

We've removed the discontinuity at [tex]x=3[/tex], so the limand is continuous and

[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1}-2}{x-3} = \lim_{x\to3} \frac1{\sqrt{x+1}+2} = \frac1{\sqrt{3+1}+2} = \boxed{\frac14}[/tex]