A cylinder truck all paint cans to be inches across the top diameter in about 10 inches high. How many cubic inches of pink it all to the nearest hundredth?

Answer:

15

Step-by-step explanation:

5x + 9 and 84 are alternate interior angles.

Since,

lines l and m are parallel, alternate interior angles are equal.

So,

5x + 9 = 84

Step 1 : Subtract 9 on both sides.

5x = 84 - 9

5x = 75

Step 2 : Divide 5 on both sides.

x = 75/5

x = 15

Hence,

The value of x is 15.

Answer:

Yes.  r = 3 + 3sin θ is symmetrical along the y axis

Step-by-step explanation:

Original polar equation is

r = 3 + 3sinθ

If this plot is to be symmetrical about the y axis then replacing Θ with (π-θ) in the original equation should not change the equation and thereby should not change the plot

r = 3 + 3sinθ

Replace θ with π-θ:

==>  3 + 3sin(π-θ)

But sin(π-θ) = sinθ

So the equation is unchanged at 3 + 3sin(π-θ) from the original equation r = 3 + 3sinθ

Hence the equation is symmetrical along the y-axis

This can be also be clearly seen if you plot both the equations, you will see the plot does not change

Answer:

Step-by-step explanation:

We're going to use length DC and ML, along with DA and MJ

[tex]\frac{DC}{ML} = \frac{5}{6}[/tex] which is 0.833333333

now for

[tex]\frac{DA}{MJ} =\frac{7}{8.4}[/tex] which is 0.833333333 (again)

as you can see since the shapes ABCD and JKLM are similar, they have a relationship which in this case is 0.833333333

and we can use this 0.833333333 to help us find the length of KL

knowing that any length for ABCD divided by JKLM is 0.833333333

we can do

[tex]\frac{CB}{LK}=0.833333333[/tex]

since we don't know what KL is, we can switch the spots and enlongate it, to become:

[tex]\frac{CB}{0.833333333} =LK[/tex]

put in the value for CB

[tex]\frac{3}{0.833333333} =LK[/tex]

and we get 3.6

The length of x of KL is...

Answer:

C

Explanation:

Given:

Volume of a cylinder (V) = 4pi cubic units

To find:

Base area(A) and height(h)

Recall that the volume of a cylinder(A) is usually given as;

So let's go ahead and try each of the options and see which gives us 4pi on the left-hand side as we have on the right-hand side for Volume.

For option A;

We have that A = 1 and h = 2, so we'll have;

For option B;

We have A = 2pi and h = 1, so we'll have;

For option C;

We have A = 2pi and h = 2, so we'll have;

We can see from the above that option C is the right option.

The value of the bill was $58. The tip was $8.7. Percentage is expressed in terms of 100. To determine the percentage of the bill that was the tip, we would find the ratio of the tip to the bill and multiply by 100. It becomes

8.7/58 * 100

= 15%

The tip was 15% of the bill

Since he has the same number of nickels as dimes.

x = nickels

x = dimes

500 - 2x = quarters

the total value of the coins is $72.50

5x + 10x + 25(500-2x) = 7250

Solve for x

15x + 25(500) + 25(-2x) = 7250

15x + 12,500 - 50x = 7250

Combine like terms

15x - 50x = 7250 - 12500

-35x = -5250

Divide both sides of the equation by -35

-35x/-35 = -5250/-35

x = 150

150 quarters

The value of the car after 5 years is $13,500 and the value of the car after 9 years is $10,500.

According to the question,

We have the following information:

The value of the car is given by V(x) where x is the number of years.

V(x) = -1500x + 21,000

(a) Now, to find the value of car after 5 years, we will put 5 in place of x in the given expression:

V(5) = -1500*5+21000

V(5) = -7500+21000

V(5) = $13,500

(b) Now, to find the value of car after 9 years, we will put 9 in place of x in the given expression:

V(9) = -1500*9+21000

V(9) = -10500+21000

V(9) = $10,500

(c) When V(12) = 3000 then it means that the value of the car after 12 years is $3000.

Hence, the value of car after 5 years and 9 years is $13,500 and $10,500 respectively.

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the figure below to better undesrtand the problem

Applying proportion

h/17.35=1.55/(17.35-12.70)

solve for h

h=17.35*1.55/4.65

Answer:

5

Step-by-step explanation:

put it in order

6056605570546055

and the one that appears the most is the mode

We will solve as follows:

Solution:

Given:

Two parallel lines have identical slopes.

Hence, the slope of line 1 is gotten by comparing the equation given to the equation of a line in the slope-intercept form.

Thus,

Since both lines are parallel, then the slopes are equal.

To get the equation of line 2 through the point (2,11), the formula below is used;

Therefore, the equation of the line that is parallel to y = 3x - 2 passing through the point (2,11) is;

SOLUTION

Write out the given point

The equation of the line passing through the point above will be obtain by following the steps

Step1: Obtain the slope of the line

Substituting the values we have

Step 2: Obtain the y- intercept

The y-intercept is the point where the graph touch the y, axis

Steps 3; use the slope intercept rule

Hence

The equation in slope intercept form is

y = - 3/4 x + 6

1) Using the data from the table, we plot the following segmented bard chart for the relationship between age and behaviour toward humans.

2) From the graph we see that for each behaviour towards humans, we have approximately the same percentage of juveniles (around 10%) and adults (around 90%), that's because the blue and green portions are proportionally the same for each bar. Based on what we see from the graph, we conclude that there is no association between age and behaviour towards humans.

Given:

Required:

To determine the possibilities for the nature of the roots of the given equation.

Explanation:

(A)

Given

The expression is given as

Explanation

To find x, add the expression.

Answer

Hence the value of x is 8.

[tex]4x + 3x = 56\\7x = 56\\x = 56/7\\x = 8[/tex]

The answer is X=8

Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.​

we know that

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=11,000

t=8 years

n=12

r=4.5%=0.045

substitute in the formula above

therefore

the answer is

Answer:

Son's age (y) = 14 years

Step-by-step explanation:

According to the question,

Father's age = 42 years

Son's age = y years

Difference between father's & son's age is 28 years. i.e.

Father's age - son's age = 28

42 - y = 28

42 - 28 = y

y = 42 - 28

y = 14

ANSWER

5 pairs

EXPLANATION

We have that:

- one pair of pants cost $24.95

- one t-shirt costs $22.50

- one pair of socks cost $5.95

You want to buy one pair of pants, one t-shirt and several pairs of socks and you don't want to spend more than $80.

This means that everything you spend must be less than or equal to $80.

Let the number of pairs of socks you can buy be x.

This therefore means that:

Because we know that the number of pairs of socks must be a whole number, we have to approximiate to whole number, which will be:

x = 5

Therefore, you can buy at most 5 pairs of socks.

From the information available;

The population is 52% and the sample size is 7. The probability that exactly 4 of them use smartphones (if 7 adults are randomly selected) would be calculated by using the formula given;

We shall insert the values as follows;

Rounded to four decimal places, this becomes;

ANSWER:

The probability of selecting exactly 4 smartphone users is 0.2830

The diameter of the cylinder is 24 mm.

Therefore, the radius is given by:

The height of the cylinder is given as 5 mm.

The formula for the volume V of a cylinder with radius r and height h is given by:

Substitute r = 12mm and h = 5 mm into the formula for volume:

Therefore, the volume of the cylinder is approximately 2261.9 mm².

.

ANSWER:

A. 15%

STEP-BY-STEP EXPLANATION:

We can determine the percentage using the following formula:

Therefore, the correct answer is A. 15%

Given the functions:

By definition, (f+g)(x) is equivalent to:

Finally, using the expressions for f and g:

Answer:

2.3

Explanation:

The formula for calulating mean deviation is expressed as:

where;

m is the mean of the data set

Xi are individual values

n is the total sample space

Get the mean;

n = 7

mean = (10+12+11+15+9+8+5)/7

mean = 70/7

mean = 10

Get the mean deviation:

Mean deviation = (10-10)+(12-10)+(11-10)+(15-10)+(9-10)+(8-10)+(5-10)/7

Since the values is in modulus |xi - m| will give a positive value, hence;

Mean deviation = (0+2+1+5+1+2+5)/7

Mean deviation = 16/7

Mean deviation = 2.28

Mean deviation = 2.3 (to the nearest tenth)

Take into account that there are 7 chices for the first course, and there are 10 choices for the entree.

The total number of choices is given bye:

total_choices = Choices_for_first_course x choices_fro_entree

Then, by replacing the values of the previous parameters you get:

total_choices = 7 x 10 = 70

There are 70 ways a person can order a two-course meal

We need to find the equation of the new function g(x) obtained by vertically stretching the function:

Vertically stretching a function by a factor of k corresponds to multiplying the whole expression of function by k:

In this problem, we have k = 18. Thus, we obtain:

Answer: C. g(x) = 18x²

Step-by-step explanation:

9)

it is not linear, because while x is increasing with every data point by 1, y is decreasing and increasing again, and the differences from one point to the other vary.

for a linear relationship also y has to change in a constant way, and the difference from one point to the next would be the same for all points.

10)

so, since it is not linear, it is quadratic then (since that was our only given alternative).

y = ax² + bx + c

we know c from point (0, -6). c = -6.

for a and b we need to use 2 data points with their x and y coordinates.

let's start with the first (-2, 14)

14 = a×(-2)² + b×-2 - 6 = 4a - 2b - 6

we can simplify that

7 = 2a - b - 3

and then

10 = 2a - b

the next point is (-1, -1)

-1 = a×(-1)² + b×-1 - 6 = a - b - 6

5 = a - b

so, we have the 2 equations

10 = 2a - b

5 = a - b

from the second we get

a = 5 + b

and that we can use in the first equation

10 = 2×(5 + b) - b = 10 + 2b - b

0 = b

therefore

5 = a - b = a - 0 = a

a = 5

and the equation is

y = 5x² - 6

11)

f(-7) = 5×(-7)² - 6 = 5×49 - 6 = 245 - 6 = 239

We have to solve the equation.

We have 2 unknowns and one equation, so we can only express one in function of the other.

We already have x in function of y, so we will now express y in function of x:

Answer:

y = -x/8 + 9/8

(-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5 as it's definition states "a relationship between two expressions or values that are not equal to each other".

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b. a ≤ b means that a is less than or equal to b. a ≥ b means that a is greater than or equal to b.

When using interval notation, we first write the set's leftmost number, then a comma, and finally its rightmost number. Depending on whether those two numbers are a part of the set, we then enclose the pair in parentheses or square brackets (sometimes we use one parenthesis and one bracket!).

Here,

3x+4≤5

3x≤1

x≤1/3

(-∞,1/3]

As it's definition states "a relationship between two expressions or values that are not equal to each other" (-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5.

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Answer:

Explanation:

What we want to answer in this question is simply, the area of the room that will be painted blue if he decides he would paint exactly have the room blue

So, we need to simply get the area of the room and divide this by half

Mathematically, the area of a rectangle is the product of its two sides

Thus, we have it that the area of the room is:

Now, to get the area painted blue, we divide this by 2 as follows or multiply by 1/2

We have this as: