An art teacher buys 4 packs of oil paints. Each pack contains 18 tubes of paint. Which equations represent the total
number of tubes of paint the teacher bought? Check all that apply.
4x 18 = 72
18 + 18 + 18 + 18 = 72
22-4 = 18
18 + 4 = 22
72 - 18 = 4
I’m

You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

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Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.

The first question shows how the value of x is bigger than the value of -3 while the second question shows how the value of x is smaller than the value of -3.

Hope this helps!

9514 1404 393

Answer:

  18°

Step-by-step explanation:

Angle ACD is the complement of the 18° angle shown, 72°. Arc AB is double that measure, so is 144°. Arc BE is the supplement to that, so is 36°. This is the arc subtended by inscribed angle BAE. That inscribed angle is half the measure of arc BE, so is 36°/2 = 18°.

  angle BAE = 18°

Given:

The coordinates are X (0,0), Y (6,3), and Z (1.5, 0.75).

To find:

The ratio where point Z partitioned segment XY.

Solution:

Section formula: If a point divides a line segment is m:n, then

\(Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\)

Let point Z partitioned segment XY in k:1.

Using section formula, we get

\(Z=\left(\dfrac{k(6)+1(0)}{k+1},\dfrac{k(3)+1(0)}{k+1}\right)\)

\((1.5,0.75)=\left(\dfrac{6k}{k+1},\dfrac{3k}{k+1}\right)\)

On comparing both sides, we get

\(\dfrac{6k}{k+1}=1.5\)

\(6k=1.5k+1.5\)

\(6k-1.5k=1.5\)

\(4.5k=1.5\)

Divide both sides by 4.5.

\(k=\dfrac{1.5}{4.5}\)

\(k=\dfrac{1}{3}\)

So, the required ratio is

\(k:1=\dfrac{1}{3}:1\)

\(k:1=1:3\)

Therefore, point Z partitioned segment XY in 1:3.

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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This axiom says that there is no upper bound to the number of elements that a set can have, thus, sets with infinite elements do exist.

First, we need to give the definition of an axiom. This is a proposition that is assumed to be true, and don't need a demonstration.

Axioms are the logical base of mathematics, so these are usually used to define concepts or basic rules.

In set theory,  the axiom of infinity just claims (and because it is an axiom, it must be true) that there are sets that have a infinite number of elements.

A trivial case is the set of real numbers, which we know has infinite elements because there are infinite real numbers.

So there is not a maximum for the number of elements that a set can have.

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a/b The decay can be modeled by this equation, (1 - r), the r being the rate of decay. So it would be 1-0.115. (0.115 is your answer for a) You have to convert the percent into a decimal by moving the deicmal place two places to the left. 0.885 is your answer for b.

c. For function notation, that just means write an equation. So you want your decay times your inital.  V(t)=15000(0.885)^x. We get the V(t) from the directions that they want us to put it in; it's basically y.

d. Since it's two years, plug in 2 for x. This shows the decay after two years

V(t)=15000(0.885)^2

e. As with d, plug in 10 for x. V(t)=15000(0.885)^t

Answer:

The relationship is not proportional

Step-by-step explanation:

Create two ratios and compare (e.g. 2:36 and 6:216, 6 divided by 2 is 3 but 3 multiplied by 36 is 108 meaning that the relationship is not proportional).

Answer:

If in an Oregon state gubernatorial election, 2 of the 5 candidates are women, and a statistics student establishes that there is a 2/5 chance that the person elected for governor is a woman, this reasoning will be wrong.

This will be the case because not all candidates have the same amount of votes, that is, not all start with the same conditions: thus, there are more popular candidates than others, who will have greater probabilities of being elected as governors, regardless of their sexual identity.

The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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Answer: cubic inches.

Step-by-step explanation: When calculating volume, all of the units must be cubed. And all of the measurements are in inches.

Answer:

Constant of proportionality \( = \frac{1}{400} \)

Step-by-step explanation:

A. The constant of proportionality can be calculated as the ratio of y to x. In this case, y = amount of paint, while x = the area of the wall

The area of the wall determines the amount of paint needed to cover the wall.

Constant of proportionality, k = y/x.

Any given pair cam be used as y and x to find k.

Thus, using (100, ¼),

\( k = \frac{\frac{1}{4}}{100} = \frac{1}{4}*\frac{1}{100} \)

Constant of proportionality \( = \frac{1}{400} \)

This means that as area of the wall increases, amount of paint increases and the ratio between them would always be \( \frac{1}{400} \).

Answer:

approx 26%

Step-by-step explanation:

you try find the multiplier

200000 * 1. ???? ^3= 400000

rearrange equation

\(\sqrt[3]{\frac{400000}{200000} }\)       =   multiplier

1.25992105

subract one

0.25992105

multiply by 100 to get percentage

25.9%

rounded to whole number = 26%

a) Approximately 77.94% of possums have heads less than 95.4 mm.

b) Approximately 96.93% of possums have heads more than 85.8 mm.

c) Approximately 74.93% of possums have heads between 85.8 and 95.4 mm.

d) The maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.

a) We can use the normal distribution to answer this question. Let X be the head length of a brushtail possum. Then X has a normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm. We want to find P(X < 95.4 mm).

Using the standard normal distribution table or a calculator, we can find the z-score corresponding to a head length of 95.4 mm:

\(z = \frac{(95.4 - 92.6)}{3.6} = 0.78\)

Then, using the standard normal distribution table, we can find the probability that a standard normal variable is less than 0.78:

P(Z < 0.78) = 0.7794

Therefore, approximately 77.94% of possums have heads less than 95.4 mm.

b) Again, using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find P(X > 85.8 mm).

Finding the corresponding z-score:

\(z = \frac{(85.8 - 92.6)}{3.6} = -1.89\)

Using the standard normal distribution table, we find:

P(Z > -1.89) = P(Z < 1.89) = 0.9693

Therefore, approximately 96.93% of possums have heads more than 85.8 mm.

c) To find the percentage of possums with heads between 85.8 and 95.4 mm, we can subtract the probability of heads less than 85.8 mm from the probability of heads less than 95.4 mm:

P(85.8 < X < 95.4) = P(X < 95.4) - P(X < 85.8)

Using the same calculations as in parts (a) and (b), we get:

P(85.8 < X < 95.4) = 0.7794 - 0.0301 = 0.7493

Therefore, approximately 74.93% of possums have heads between 85.8 and 95.4 mm.

d) We want to find the maximum head length of the shortest 10% of possum heads. This is equivalent to finding the 10th percentile of the distribution. Using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find the head length x such that P(X < x) = 0.1.

Using the standard normal distribution table or a calculator, we can find the z-score corresponding to the 10th percentile:

P(Z < z) = 0.1

z = -1.28

Then, we can find the corresponding head length x:

x = μ + zσ = 92.6 + (-1.28)(3.6) = 87.68

Therefore, the maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.

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Answer:

A = 68 in^2

Step-by-step explanation:

A of Rectangle = 6 * 10 = 60 in^2

A of Triangle = (4 * 4)/2 = 8 in^2

Answer:

a₂ = G(m₁ + m₂)/(R - √[G(m₁ + m₂)/a₁])²

Step-by-step explanation:

Since the gravitation force of attraction of the center of mass on m₁ equals the centripetal force, then

G(m₁ + m₂)m₁/R₁ = m₁a₁ where (m₁ + m₂) = total mass of the system and R₁ = distance of m₁ from the center of mass

So, G(m₁ + m₂)m₁/R₁² = m₁a₁

G(m₁ + m₂)m₁/m₁a₁ = R₁²

R₁² = G(m₁ + m₂)/a₁

R₁ = √[G(m₁ + m₂)/a₁]

The distance of m₂ from the center of mass is thus R₂ = R - R₁ = R - √[G(m₁ + m₂)/a₁] where R is the distance between the two stars.

Also,  the gravitation force of attraction of the center of mass on m₂ equals the centripetal force, then

G(m₁ + m₂)m₂/R₂ = m₂a₂ where (m₁ + m₂) = total mass of the system and R₂ = distance of m₂ from the center of mass

So, G(m₁ + m₂)m₂/R₂² = m₂a₂

G(m₁ + m₂)m₂/m₂R₂² = a₂

a₂ = G(m₁ + m₂)/R₂²

Substituting R₂ into the equation, we have

a₂ = G(m₁ + m₂)/(R - √[G(m₁ + m₂)/a₁])²

Answer:

U simply multiply 483 by 3.5

                           =1690.5

Step-by-step explanation:  

Answer:

Step-by-step explanation:

1. Using the addition property of equality, we can add 3 to both sides of the equation. Then it can be rewritten as ...

  7x -3 +3 = -17 +3

  7x = -14

__

2. Using the division property of equality, we can divide both sides of the equation by 7. Then it can be rewritten as ...

  7x/7 = -14/7

  x = -2

_____

Additional comment

Note that we have used these steps to solve the equation, find the value of x that makes it true. We could use different steps to rewrite the equation to almost anything you want:

  7x -3 -95 = -17 -95   ⇒   7x -98 = -112 . . . . . subtract 95 from both sides

  12(7x -98) = 12(-112)   ⇒   84x -1176 = -1344 . . . . multiply both sides by 12

The resulting equation is not helpful for finding a solution, but it is an accurate rewrite of the original equation.

The value of the expression 28 - {15 (3+2)} is -47.

To evaluate the expression 28 - {15 (3+2)}, we need to follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the expression step by step:

First, we solve the expression inside the parentheses:

3 + 2 = 5

Now, we substitute the result back into the original expression:

28 - {15 * 5}

Next, we perform the multiplication:

15 * 5 = 75

Now, we substitute the result back into the expression:

28 - 75

Finally, we perform the subtraction:

28 - 75 = -47

Therefore, the value of the expression 28 - {15 (3+2)} is -47.

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The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.

The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.

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Answer:

11 can't be divided with negative number

so it's answer will be zero

hope it is helpful to you ☺️☺️☺️☺️☺️

Answer:

8 27/28 or 251/28

Step-by-step explanation:

Find common denominators then simply add.

Answer:

∠ AEB = 114°

Step-by-step explanation:

the chord- chord angle AEB is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is

∠ AEB = \(\frac{1}{2}\) (AB + CD) = \(\frac{1}{2}\) (140 + 88)° = \(\frac{1}{2}\) × 228° = 114°

Answer:

770,400

Step-by-step explanation:

770,400 seconds

Answer:

-3/2 or -2.5

Step-by-step explanation:

Use the y=mx+b formula

Subsitute given values...

y=-1/7x+b

use the point (-21,1/2) to substitute values for x and y

1/2=-1/7(-21)+b

solve

1/2=3+b

subtract both sides by 3

-3/2 = b

Therefore the answer is -3/2

Answer:

the answer is A or 0√5

hope it helps

BYE

Answer:

5/13

Step-by-step explanation:

OM is 5 and OL is 13 use Pythagoreans theorem

The values of a and b are a = -3 and b = 42. The solutions for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a perfect square:

(x + 3)² = 42

Step 5: Take the square root of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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Answer:

$67.75

Step-by-step explanation:

12% off means that 88% of $76.99 is the final price.

76.99×0.88= 67.7512

Answer:

$67.75

Step-by-step explanation:

To calculate 88% (which is 100% - 12%(the discount)) you need to multiply it by 67.75 and divide by 100

The coordinates of the final point after the reflections across the x-axis twice is (6, -4)

Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.

So reflecting (6,-4) across the x-axis gives us the point (6,4).

Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.

So reflecting (6,4) across the x-axis gives us the point (6,-4).

Therefore, the final point after both reflections is (6, -4).

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