3x(x + 2) and 6x(2x-3)

To determine the area that can be covered with 15 gallons of paint, knowing that 3 gallos can be used to paint 675ft², first determine the area that can be covered per gallon.

To do so, divide 675 by 3

Each gallon of paint covers an area of 225ft²

Next multiply the area per gallon by 15 to determine how much will 15 gallons of paint cover

With 15 gallons of paint you'll be able to cover an area of 3375ft²

Answer:

11

Step-by-step explanation:

for each full cup of sugar, you need 3 one-third measuring cups.

we have 3 full cups so 3×3=9

and another 2 for the 2/3, 9+2=11

so a total of 11 scoops

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

Step-by-step explanation:

1/4 < 3/8

Answer:

The third one, 1/4 < 3/8

Step-by-step explanation:

The sign < means 3/8 is bigger than 1/4

Answer:

rational algebraic expression

Answer:

C

Step-by-step explanation:

Answer:

The most basic common unit is Liters (L), but people also commonly use milliliters (mL) and cubic centimeter (cm^3).

Answer: D

Step-by-step explanation:

2x-36=0                                                

+36     +36

___________

2x=36

x=18

Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.

Answer:

Conversion a mixed number 2 5/

6

to a improper fraction: 2 5/6 = 2 5/

6

= 2 · 6 + 5/

6

= 12 + 5/

6

= 17/

6

To find new numerator:

a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/

6

= 12/

6

b) Add the answer from previous step 12 to the numerator 5. New numerator is 12 + 5 = 17

c) Write a previous answer (new numerator 17) over the denominator 6.

Two and five sixths is seventeen sixths

Unary minus: -17/

6

= -17/

6

Conversion a mixed number 5 1/

4

to a improper fraction: 5 1/4 = 5 1/

4

= 5 · 4 + 1/

4

= 20 + 1/

4

= 21/

4

To find new numerator:

a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/

4

= 20/

4

b) Add the answer from previous step 20 to the numerator 1. New numerator is 20 + 1 = 21

c) Write a previous answer (new numerator 21) over the denominator 4.

Five and one quarter is twenty-one quarters

Divide: -7/

8

: 21/

4

= -7/

8

· 4/

21

= -7 · 4/

8 · 21

= -28/

168

= 28 · (-1)/

28 · 6

= -1/

6

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 21/

4

is 4/

21

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - minus seven eighths divided by twenty-one quarters = minus one sixth.

Add: the result of step No. 2 + the result of step No. 4 = -17/

6

+ (-1/

6

) = -17 + (-1)/

6

= -18/

6

= 6 · -3/

6 · 1

= -3

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 6) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 6 = 36.

In words - minus seventeen sixths plus minus one sixth = minus three.

(a) The probability of winning at least one prize in a randomly chosen week is 0.3935.

(c) The probability that it takes exactly 5 weeks to win for the first time is 0.041.

A lottery ticket is bought every week in 50 lotteries. The chance of winning a prize in each of the lotteries is 0.01.

The Poisson's distribution is given below :

P(X=x) = (e^-λ)(λ^x)/x!

λ = np

λ = 50*0.01 = 0.5

The probability of getting at least one prize is :

P(x≥1) = 1 - P(x<1)

P(x≥1) = 1 - P(x=0)

P(x≥1) = 1 - [(e^-0.5)(0.5^0)/0!]

P(x≥1) = 1 - 0.6065

P(x≥1) = 0.3935

The probability of winning exactly in the fifth week is :

The probability of losing in the first four weeks and winning in the fifth week is :

P = [(e^-0.5)^4]*P(x=1)

P = [(e^-0.5)^4]*(e^-0.5)(0.5)

P = [(e^-0.5)^5]*(0.5)

P = (e^-2.5)*(0.5)

P = 0.041

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Answer:

D They will attract each other

Answer:

x=5/3

Step-by-step explanation:

there is only 1

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

\(y - 9 = -2(x + 1)\)

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

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The function f(x) = 2x² - 7x + 10 is an odd function.

f(-x) = 2(-x)² - 7(-x) + 10

      = 2x² + 7x + 10

-f(x) = -[2x²- 7x + 10]

      = -2x² + 7x - 10

To determine whether the function f(x) = 2x² - 7x + 10 is even, odd, or neither, we compare f(-x) and -f(x).

1. f(-x) = 2x² + 7x + 10

2. -f(x) = -2x² + 7x - 10

To determine if f(-x) = -f(x) (even function), we substitute -x for x in f(x) and check if the equation holds.

1. f(-x) = 2x² + 7x + 10

         = f(x) (not equal to -f(x))

Since f(-x) is not equal to -f(x), the function is not even.

Next, to determine if f(-x) = -f(x) (odd function), we substitute -x for x in f(x) and check if the equation holds.

2. -f(x) = -2x² + 7x - 10

        = -(2x² - 7x + 10)

        = -(f(x))

Since -f(x) is equal to -(f(x)), the function is odd.

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Answer:

yes your correct

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

He needs to write 300*9 pages which is 2700

We know that he writes 45 pages a minute

his speed can be shown through the following equations

45x=pages typed

where x=minutes

so we set up our problem

45x=2700

we divide by 45 and get x=60

Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

Refer to the attached images.

32 x 1 x 1

16 x 1 x 2

8 x 2 x 2

4 x 2 x 4

8 x 4 x 1

These are the ones that come to my mind

Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

CAnswer:

Step-by-step explanation:

it is i got an 100

The small medium from in center to all the three sides of triangle is equal.

The length of the SQ is 5 units.

The in-center of a triangle is the point of intersection of all the three interior angle bisectors of a triangle.

The small medium from in center to all the three sides of triangle is equal. Thus,

\(SQ=SP=SR\)

Given information-

The length of MR is 12 units.

The length of MS is 13 units.

In the \(\Delta MRS, \angle MRS\) is the right angle triangle. Thus by the Pythagoras theorem,

\(MS^2=MR^2+RS^2\)

Rewrite the equation as,

\(RS^2=MS^2-MR^2\)

Put the  values,

\(RS^2=13^2-12^2\\RS^2=169+144\\RS^2=25\\RS=\sqrt{25}\\RS=5\\\)

Thus the length of RS is 5 units. As the length of RS is equal tot he length of the SQ. Thus,

\(SQ=RS=5\)

Hence the length of the SQ is 5 units.

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Divide rulers by rooms:

672/21 = 32

Each room gets 32 rulers

Answer:

32 rulers per classroom

Step-by-step explanation:

672rulers ÷ 21 classroom

=32 rulers per classroom

Answer:

send the image of the exercise

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

1 out of 9

Step-by-step explanation:

I did this on khan academy a minute ago

Probability that both marbles are teal is 0.0571

Probability is a field of mathematics concerned with numerical representations of the likelihood of an event occurring or a statement being true.

Number of yellow marbles = 27

Number of teal marbles  = 9

Probability that both marbles are teal

\(=\frac{9}{36}\times \frac{8}{35} \\=0.0571\)

Hence the probability that both marbles are teal is 0.0571.

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In Bridget's bathroom, the scale indicated the muffin weighed 8 pounds. The more accurate scale at the veterinarian's office indicated that the muffins weighed 8.2 pounds. The bathroom scales' measurement error is 2.4% percent.

To find the percent error, we need to compare the difference between the two measurements (the actual weight and the weight measured by the bathroom scale) with the actual weight, and express it as a percentage.

The actual weight of muffin is 8.2 pounds. The weight measured by the bathroom scale is 8 pounds.

The difference between the two measurements is:

8.2 - 8 = 0.2 pounds

To calculate the percent error, we divide the difference by the actual weight, and multiply by 100:

percent error = (difference / actual weight) x 100

percent error = (0.2 / 8.2) x 100

percent error = 0.0244 x 100

percent error = 2.44

To the nearest tenth of a percent, we round and obtain:

percent error ≈ 2.4%

Therefore,  the percent error for the bathroom scale's measurement is approximately 2.4%.

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Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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