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The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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Answer:

24 and 45

Step-by-step explanation:

Okay, now that I can answer this question with the right answers:

The easy way to do this is to first solve the left hand side of the equation.

1/2 of 12 is the same as 12/2 = 6.

So 6 = 1/4 * x

To solve for that unknown x, just multiply both sides by 4 to cancel out the fraction:

6*4 = 4* 1/4*x

24 = x

For the other equation, do the same thing:

1/3 * 90 = 90/3 = 30

30 = 2/3*x

30*3 = 3* 2/3 *x

90 = 2x

90/2 = 2x/2

45 = x

Answer:

d (-5,0)

Step-by-step explanation:

If a point is located on the x-axis, then the y-coordinate is 0.  

d is the only point that sits on the x-axis. I know this because it's y-coordinate is 0.

(0,8) is actually a point sitting on the y-axis.

Answer:

\(x = ± \frac{5 \sqrt{3} }{3} \)

Step-by-step explanation:

\((x + 3)(x - 3) = 16 - 2 {x}^{2} \)

Use the quick multiplication formula:

\( {x}^{2} - 9 = 16 - 2 {x}^{2} \)

\( {x}^{2} + 2 {x}^{2} = 16 + 9\)

\(3 {x}^{2} = 25\)

Divide both parts by 3 to make x the subject:

\( {x}^{2} = ±8 \frac{1}{3} \)

\(x = ± \frac{5 \sqrt{3} }{3} \)

Answer:

a y = 2

b.y = 14

c. y =56

Step-by-step explanation:

a .6 (1)- 4=2

y=2

b. 6 (3)- 4

=18-4

y=14

c. 6 (10) - 4

= 60 - 4 =56

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Option A

A large naturally occurring community of flora and fauna occupying a major habitat, e.g. forest or tundra. A biome is a large area characterized by its vegetation, soil, climate, and wildlife.

Answer:

(- 3, 1.5)

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

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

The number of multiple-choice and short-answer questions on a test with 65 questions will be 40 and 25 respectively.

To determine the number of multiple-choice and short-answer questions on a test with 65 questions, we can set up a proportion based on the given ratio:

Multiple-choice questions : Short-answer questions = 8 : 5

Let x be the number of multiple-choice questions.

Let y be the number of short-answer questions.

Using the proportion, we can set up the following equation:

8/5 = x/y

8y = 5x

x = (8y)/5

Since the total number of questions on the test is 65, we have the equation:

x + y = 65

Substituting the expression for x from the previous equation:

(8y)/5 + y = 65

(8y + 5y)/5 = 65

13y/5 = 65

13y = 65 * 5

13y = 325

Dividing both sides by 13:

y = 325/13

y = 25

Substituting this value of y back into the equation x = (8y)/5:

x = (8 x 25)/5

x = 40

Therefore, there are 40 multiple-choice questions and 25 short-answer questions on the test with a total of 65 questions.

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Answer:

78 degrees

Step-by-step explanation:

Angles PLR and NLR are supplementary, so 102+x=180.

x=78

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week \(\sf = 19 \times 40 = \$760\)

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, \(\sf \dfrac{8x}{100}=760\)

Or, \(\sf 8x= 76000\)

Or, \(\sf x= \dfrac{76000}{8}=9500\)

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

Answer:-2, 0, 2, 3, 4

Step-by-step explanation:

-2 is smaller than 0, 0 is smaller than 2, 2 is smaller than 3, and 3 is smaller than 4.

Answer:

4, 3, 2, 0, -2

Answer: 0.3964

Step-by-step explanation:

Given: A particular fruit's weights are normally distributed, with a mean\((\mu)\) of 230 grams and a standard deviation\((\sigma)\) of 37 grams.

Sample size : n= 87

Let \(\overline{X}\) be the sample mean.

The probability that their mean weight will be between 231 grams and 240 grams will be :

\(P(231<\overline{X}<240)=P(\dfrac{231-230}{\dfrac{37}{\sqrt{81}}}<\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}},\dfrac{231-230}{\dfrac{37}{\sqrt{81}}})\)

\(=P(0.2432<Z<2.4324)\ \ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z<2.4324)-P(Z<0.2432)\\\\=0.9925- 0.5961=0.3964\)

Hence, the required probability = 0.3964

Answer:

2 slices

Step-by-step explanation:

As given, Stephen buys a melon and divides it into 6 servings. And he eats 1/3 melon over the weekend. Hence, Stephen eats 2 slices over the weekend.

Answer: -13/17

Step-by-step explanation: To find the slope of the line that passes through the points (-9, 7) and (8, -6), you can use the slope formula:

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

where (x1, y1) = (-9, 7) and (x2, y2) = (8, -6)

Substituting the values in the formula, we get:

slope = (-6 - 7) / (8 - (-9))

slope = -13 / 17

Therefore, the slope of the line that passes through the points (-9, 7) and (8, -6) is -13/17.

Answer:

\(\frac{-14}{17}\)

Step-by-step explanation:

Slope is the change in y's (-9,7) (8,-6) over the changes in x's (-9,7)(8,-6).  You find the changes by subtraction

\(\frac{-6-7}{8-(-9)}\) = \(\frac{-14}{8+9}\) = \(\frac{-14}{17}\)

Helping in the name of Jesus.

Answer:

-235+84i

Step-by-step explanation:

I hope this is what you were looking for.

Answer:

\(20\pi\) m

OR

62.8318531 m

Step-by-step explanation:

This is actually pretty simple

The distance the tip travels is the arc length and the length of the pendulum is the radius of a circle

The formula for arc length is Angle in Radians x Radius

So pi/12 * 4 = pi/3 m

We know this is how much it travels every second so it is going at pi/3 m/s

One minute is 60 seconds

pi/3 * 60 = 20pi m

The fraction of silver or brown canoes is 7/10.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Total canoes team = 10

5 teams have silver canoes team.

2 teams have brown canoes team.

Now,

The fraction of silver and brown canoes.

= (5 + 2) / 10

= 7/10

Thus,

7/10

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Answer:

1,536

Step-by-step explanation:

3,200×52%=1,664

3,200-1,664=1,536

Answer:

1,536

Step-by-step explanation:

Total students = 3,200

Percentage of boys = 52%

Percentage of girls = (100 - 52) % = 48%

No of girls enrolled in the school

= 48% of 3200

= 0.48 * 3200

= 1,536

Answer:

A+S=22

A=S/2+4

Multiply second equation by 2 and rearrange.

2A-S=8

Add equations 1 and 3.

3A=30

A=10

Substitute for A in either of the first 2 equations to get

S=12

Step-by-step explanation:

Answer:

B) in the modern art section of an art museum

Step-by-step explanation:

Hope it helps! =D

Answer:

Null Hypothesis: The proportion of clients satisfied at the uptown office is 76%.

Alternative Hypothesis: There is no difference in the satisfaction between the uptown and the downtown clients.

Null Hypothesis: The proportion of clients satisfied at the downtown office is greater than the proportion of clients satisfied at the uptown office.

Alternative Hypothesis: Downtown clients are less satisfied with the dental office staff than uptown clients.

Null Hypothesis: The proportion of clients satisfied at the downtown office is 84%.

Alternative Hypothesis: Uptown clients are more satisfied with the dental office staff than downtown clients.

Null Hypothesis: The proportion of clients satisfied at the downtown office is equal to the proportion of clients satisfied at the uptown office.  

Alternative Hypothesis: There is a difference in the satisfaction between the uptown and the downtown clients.

Step-by-step explanation:

pls mark as brainliest

Answer and Step-by-step explanation:

The domain of the exponential function is whole real line numbers. The range of an exponential function is only positive real numbers.

The domain of a function is a set of input (x) values in which the function is defined, and the range of a function is a set of output (y) values that a function takes.

Let an exponential function:  f(x) = 2x, the domain of this function is whole real line numbers, and the range is only positive numbers on the real line. When y > 0, f(x) never take negative values and never approaches to zero.

Suppose we change the function by replacing x to –x. the domain and range do not change.

If we have a negative exponential function: f(x) = - 2x, then the domain is the same (whole real line numbers), but the range is negative numbers because of y < 0.

In general, the basic exponential function y = ax, defined as  ∞ to 0 when 0 < a < 1 and x varies from -∞ to ∞ and rises from o to ∞ as a > 1.

Answer:Function k is a reflection of the parent function f over the x-axis. As x approaches negative infinity,

approaches but never reaches the constant 0. As x approaches positive infinity,

approaches negative infinity.

Therefore, the domain of function k is still all real numbers, or

. The range of function k is all real numbers less than but not equal to 0, or

.

Step-by-step explanation:

Answer:

\( \displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3} \)

Step-by-step explanation:

we would like to figure out the derivative of the following:

\( \displaystyle \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} } \)

to do so, let,

\( \displaystyle y = \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} } \)

By simplifying we acquire:

\( \displaystyle y = 3 - \frac{2}{x} - \frac{1}{ {x}^{2} } \)

use law of exponent which yields:

\( \displaystyle y = 3 - 2 {x}^{ - 1} - { {x}^{ - 2} } \)

take derivative in both sides:

\( \displaystyle \frac{dy}{dx} = \frac{d}{dx} (3 - 2 {x}^{ - 1} - { {x}^{ - 2} } )\)

use sum derivation rule which yields:

\( \rm\displaystyle \frac{dy}{dx} = \frac{d}{dx} 3 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2} \)

By constant derivation we acquire:

\( \rm\displaystyle \frac{dy}{dx} = 0 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2} \)

use exponent rule of derivation which yields:

\( \rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ - 1 -1} ) - ( - 2 {x}^{ - 2 - 1} )\)

simplify exponent:

\( \rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ -2} ) - ( - 2 {x}^{ - 3} )\)

two negatives make positive so,

\( \displaystyle \frac{dy}{dx} = 2 {x}^{ -2} + 2 {x}^{ - 3} \)

by law of exponent we acquire:

\( \displaystyle \frac{dy}{dx} = \frac{2 }{x^2}+ \frac{2}{x^3} \)

simplify addition:

\( \displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3} \)

and we are done!

Answer:

uhhhhhhh you have to figure out what x is then choose wether it is the other variable a dependent variable, and explanatory variable, or a response variable

Step-by-step explanation:

easy as that

The profit function for this problem is given as follows:

P(x) = -0.5x³ + 100x² - 500x + 300.

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The functions for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = -0.5x³ + 600x² - 200x + 300 - 500x² - 300x

P(x) = -0.5x³ + 100x² - 500x + 300.

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Answer:

The number of people who became aware at the time T = 20 days = 2.5 million

Step-by-step explanation:

p(t) = 5 million

To = 0

T1 = 20 days

P(T1 ) = 50% * 5 = 2.5 million

hence to confirm the value of t where t = 20

P(T1) = \(6 - 4 (\frac{4}{5} )^{\frac{1}{50}t }\)

        = \(6 - 4 (\frac{4}{5} )^{0.4}\)

        = 6 - 4(0.9146)

p(20 ) ≈ 2.5 million

The circumference of the pool is 26.38 meters

The radius, r is given as:

r = 4.2

The circumference, C is calculated using:

\(C =2\pi r\)

This gives

C =2 * 3.14 * 4.2

Evaluate

C = 26.38

Hence, the circumference of the pool is 26.38 meters

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The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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