Use the rectangle at the right to answer the following questions. a. Find the area of the entire rectangle. Show your work. b. Calculate the perimeter of the figure. Show your work.

We have the next formula to find the volume of a triangular prism-

where

B= area of the base

h= height

in our case

B=18 square inches

H= 5 inches

the volume of the triangular prism is 90 cubic inches

Answer:

  -3, 0, 5

Step-by-step explanation:

You want the zeros of P(x) = x³ − 2x² − 15x using the factored form.

We notice right away that x is a factor of every term. Factoring that out gives us a quadratic to factor:

  P(x) = x(x² -2x -15)

To factor this, we need two factors of -15 that have a sum of -2. The factors -5 and +3 have those properties. That means our factored form is ...

  P(x) = x(x +3)(x -5) . . . . factored form

This product will be zero when any of its factors is zero. Considering them one at a time, we find the zeros of P(x) to be ...

  x = 0

  x +3 = 0   ⇒   x = -3

  x -5 = 0   ⇒   x = 5

The zeros of P(x) are -3, 0, 5.

Given :

The total questions = 300

Time of starting = 5:00

At 6:30 the number of answered questions = 55

The time spent to answer 55 questions = 6:30 - 5:00 = 1:30 hours

Which is equal to : 1 hour and 30 minutes = 90 minutes

So, the rate of answering the questions =90/55 = 18/11 minute per question

So, for solving the 300 questions, the time will be :

So, 490 10/11 minutes = 8 hours and

Answer:

[tex]v = 40000( {.91}^{x} )[/tex]

Consider the 5 main types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.

In the case of systematic sampling, every kth element of the data set is taken.

In our case, consider all the shoppers and imagine that they can be ordered in a line; then, Betsy selected the 10th shopper in the line, the 20th one, and so on.

The division of two fractions is the same as multiplying the first by the inverted second fraction:

Then, in this case:

We multiply two fractions by multiplying the numerators and the denominators:

We know that

Then, we can use this in our fraction:

We know that if we have a division of same base expressions (same letters), the exponent is just a substraction:

Then,

Since negative exponents correspond to a division, then we can express the answer in two different ways:

From the given graph

The asymptotes are the dotted lines in the graph, then

The vertical asymptote is x = 3

The horizontal asymptote is y = 1

The domain is all values of x that make the function defined

Since x can not equal 3, then

The domain is

The range is all values of y corresponding to the values of the domain (x)

Since y can not equal 1, then

The range is

The x-intercept is the value of x at the graph intersecting the x-axis

Since the graph intersects the x-axis at the point (6, 0), then

The x-intercept is 6

The answer is the first choice 6

The y-intercept is the value of y at the graph intersection the y-axis

Since the graph intersects the y-axis at point (0, 2_, then

The y-intercept is 2

The answer is the second answer 2

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Knowing that [tex]{-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1[/tex],

so x can be positive or negative 4/5,

and we know that x coordinate of any point in quadrant IV is positive,

so x = 4/5.

Linear function f(x) = 2/7x - 2

It has no domain or range restrictions, so both of them include all real numbers.

The graph is attached

ABC and​ A'B'C' are congruent triangle. The length of the side AC is 5.31cm.

congruent triangle - Congruent triangles are those whose two sides and included angle match those of another triangle's matching sides and angle.

rules -

(given)

AB = 17 cm

BC = 34 cm

Using the trigonometric functions

cos x = B/H

cos(81°) = B/34

B = Cos(81°) x 34

B = 5.31.

ABC and​ A'B'C' are congruent triangle. The length of the side AC is 5.31cm.

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step 1

the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder

Find out the volume of the cylinder

we have

r=2.8/2=1.4 cm

h=10.7 cm

substitute given values

Find out the volume of the frustum

the formula to calculate the volume is

we have

R=5.6/2=2.8 cm

r=2.8/2=1.4 cm

h=1.9 cm

substitute given values

Adds the volumes

V=20.972pi+8.689pi

V=29.661pi cm3

Multiply by the density

29.661pi*0.0173=1.6 lb

therefore

ANSWER

There are 913,952 different 5-letter combinations that can be formed.

EXPLANATION

Recall that there are 26 letters in the English Alphabet.

From the question, we are to find the arrangement of 5 letters with the first letter being either W or K, and repetition of letters is allowed.

The possibilities for the 1st letter is 2 since the 1st letter can be either W or K;

More so, the possibilities for the 2nd letter is 26;

The possibilities for the 3rd letter is 26;

The possibilities for the 4th letter is 26, and

The possibilities for the 5th letter is 26;

The possibilities of arranging 5 letters = 2 x 26 x 26 x 26 x 26 = 913,952.

Hence, a total of 913,952 different 5-letter combinations can be formed.

When the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.

As given in the question,

Spherical ball is coated with uniform thickness.

Ice melts at the rate of 8ml/min

= (8/60)cm³/sec

Consider r as the  radius of given spherical ball

Diameter = 24cm

⇒Radius 'r' =12cm

Volume 'V' = (4/3)πr³

⇒ dV /dt = (4/3)π(3r²r')

⇒-(8/60) = (4/3)π(3 ×12²×r')

⇒r' =-(8/60)×(1/576π)

⇒r' = - 1/ 4320π

Rate at which change in surface area

A =4πr²

⇒A' = 4πrr'

⇒A' = 4π (12) ( - 1/ 4320π)

      = -1/90 cm²/sec.

Decrease in surface area = 1/90 cm²/sec.

Therefore, when the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.

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To find the result function,

First stretch it, multiplying it by the factor we want to stretch.

So f(x) = x²

Stretching the function by a factor of 2:

g(x) = 2* f(x)

g(x) = 2* x²

On the other hand, to translate a function 4 units upward, we need to sum it to the function, so the result function is:

g(x) = 2x² + 4

The answer is option B.

Let the number of hours be x,

Initial fee is $50,

Amount charged per hour is $8

The charge for a number of x hours is'

The total amount Esmeralda has is $150,

Therefore,

Solving for x to find the greates number of hours,

Hence, the greates number of hours is 12.5 hours.

Option B is the right answe

Home Liquidators marks up its merchandise 35% on cost, the company's equivalent markup on the selling price is 25.9%.

An equivalent value represents equality.

Equivalent values show that two paired mathematical expressions are equal.

The markup on the selling price can be derived by equating the markup on cost with the markup on the selling price as follows:

Markup on cost = 35%

Cost = 100%

Selling price = 135%

Markup on selling price = 25.9% (0.35/1.35 x 100)

Thus, we can describe Home Liquidators' markup on the selling price as equivalent to 25.9% or simply 26%.

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GIVEN:

We are given a set of 4 statements as indicated in the attached image.

Required;

Determine whether each statement is TRUE or FALSE.

Solution;

(1) Look at the digit to the right of the digit to which you are rounding to tell whether to round up or leave it the same.

This statement is TRUE

(2) If the digit to the right of the digit to which you are rounding is four or less, you keep the digit the same.

This statement is TRUE.

(3) If the digit to the right of the digit to which you are rounding is five or more, you keep the digit the same.

This statement is FALSE.

(4) Look at the digit to the left of the digit to which you are rounding to tell whether to round down or leave it the same.

This statement is FALSE.

Here, we want to write ratios in part to part and in part to whole ratio

For the part to part

Writing carrot to peas, we have;

For the parts to whole ratio, we have;

The histogram is skewed to the left, the mean is less than the median.

Answer:

3,600 seats

Step-by-step explanation:

If you have 40 seats in a row, and there are 90 rows, you simply take the amount of seats, and multiply that by the amount of rows.

-Hope this helps

Answer:

Step-by-step explanation:

3600

If you were to multiply 40 seats by 90 rows, you would result with 3600 seats!

Answer:

50°

Step-by-step explanation:

[tex]\angle 1[/tex] and [tex]\angle 2[/tex] form a linear pair, and are thus supplementary (meaning they add to 180°).

we have that

34% represents 901 owners that take their dogs on vacation with them

so

the percentage of dog owners in the survey that do NOT take their dog on vacation is equal to

100%-34%=66%

Applying proportion

901/34=x/66

solve for x

x=(901/34)*66

Answer:

The length of FE is √286 units.

Explanation:

Let the length of FE = x

Since FG is parallel to CD, then triangles EFG and ECD are similar triangles.

The ratio of the corresponding sides are:

Substitute the given values from the diagram above:

We then solve the equation for x.

The length of FE is √286 units (in simplest radical form).

To arrange this from the greatest to the least

we will first look out for the positive numbers

Among the positive numbers, 56 comes first

then 25 and finally 8

Then we move to the negative numbers

-2 comes first

then -7 and then -34

Hence

56, 25, 8, -2, -7, -34

The price of gas = $2.85 per gallon

It was $1.36 cheaper than a year before.

So, the price before = 2.85 + 1.36 = $4.21

So, the percent of decrease = 1.36/4.21 = 0.323 = 32.3%

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