Identify the two factors that were multiplied together to form the array of tiles. Then identify the product of the two factors. Use the variable x in your expressions.

By the binomial theorem,

(1 + x)⁴ = 1 + 4x + 6x² + 4x³ + x⁴

(1 + 2x)³ = 1 + 6x + 12x² + 8x³

In the expansion of (1 + x)⁴ (1 + 2x)³, we get an x⁴ when multiplying

• x⁴ and 1 to get x⁴;

• 4x³ and 6x to get 24x⁴;

• 6x² and 12x² to get 72x⁴; and

• 4x and 8x³ to get 32x⁴.

Add these up:

x⁴ + 24x⁴ + 72x⁴ + 32x⁴ = 129x⁴

Answer:

y = $346.90

Step-by-step explanation:

Given:

y = 1.67x + 12.90

Where,

y = total monthly cost,

x = month. If we let x represent the number of cubic feet of water (in hundreds)

If the Johnson family used 200 ft3 more water this month than last month, then they can expect

x = 200 ft³

y = 1.67x + 12.90

y = 1.67(200) + 12.90

= 334 + 12.90

= 346.90

y = $346.90

Answer: D

Step-by-step explanation: i did the math

Answer:

36.7

Step-by-step explanation:

Since 33 is 90% of a number, you can divide 33 by 9 to get 3 2/3. This 3 2/3 is 10% of the number, so multiply 3 2/3 by 10 to get 36 2/3. 36 2/3 rounded to the nearest tenth is 36.7, so there's your answer. Hope it helps!

Answer:

$5.50

Step-by-step explanation:

1.) The first step is finding what 45% of $10 is. We can do this by turning 45% into a decimal number (45%=0.45). We then multiply 0.45 by the $10.

2.) 0.45×$10=$4.50 ; We just found that 45% of $10 is $4.50

3.) Because the shirt is 45% less than the original price (45% off), we need to subtract the 45% (which is equal to $4.50) from the original price, $10

4.) $10-$4.50=$5.50, the new price

Answer:

one bag is heavier and the other is lighter.

Step-by-step explanation:

5/8 = more than half a pound

1/4 = less than half a pound

Answer:

3/8

Step-by-step explanation:

You have to make 1/4's denominator match the denominator of 5/8.

By multiplying it by 2.

1/4 =2/8

You then subtract 2/8 into 5/8 to get 3/8

Answer: slope is -1/2 y intercept is (0,2)

Step-by-step explanation: How I Got This Was Using The Slope Formula Y = mx + b to find slope then graphed by using those two points

Answer: 56 miles/hour

Step-by-step explanation: 498-106=392

9-2=7

392/7= 56 , units- miles/hour

The average rate of change of the distance over the interval 2 < t < 9 is 56 units- miles/hour.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

The distance, d, that a car has traveled, as a function of time, t, is given in the table below.

Difference  = 498 - 106

= 392

= 9 - 2

= 7

From the formula:

Rate of change = change in distance/change in time

= 392/7

= 56 units- miles/hour

Thus, the average rate of change of the distance over the interval 2 < t < 9 is 56 units- miles/hour.

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Answer: m= -1/5

Step-by-step explanation:

Find the Slope (4, 2) and (9, 1)

Slope is equal to the change in y over the change in x, or rise over run.

              change in y

     m =    _________

              change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).        y₂ − y₁

     m =   _____

              x₂ − x₁

Substitute in the values of x and y into the equation to find the slope.

              1 − (2)

     m =   _____

              9 − (4)

Simplify the numerator.

                −1

     m =   _____

              9 − (4)

Simplify the denominator.

                −1

     m =   _____

                 5

Move the negative in front of the fraction.

                −1

     m =   _____

               − 5

Answer:

The slope of the line is [tex]\displaystyle -\frac{1}{5}[/tex].

Step-by-step explanation:

We are given two coordinate points:

We are asked to find the slope of the line.

We can use the rise-over-run formula to solve for the slope of the line.

[tex]\displaystyle \text{slope} = \frac{\text{rise}}{\text{run}}\\\\\text{slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]

However, we firstly need to name our coordinate points.

In math, we can label our coordinates using the following label system:

[tex](x_1, y_1), (x_2, y_2)[/tex]

Therefore, we can also label our coordinates as such:

Now, we can supply these values into the formula and solve for our slope, or a better known variable, m.

[tex]\displaystyle m = \frac{1 - 2}{9 - 4}\\\\m = \frac{-1}{5}\\\\m = -\frac{1}{5}[/tex]

Therefore, our slope is [tex]\displaystyle -\frac{1}{5}[/tex].

Answer:

19 are blue

37

Step-by-step explanation:

35 - 16 = 19

35 + 3 = 38 & 75 - 38 = 37

Answer:

The value of y = 5⁰...........

Answer:

y=5

Step-by-step explanation:

Answer:

I do questions like these a little different than most people so...

384/12= 32 (32 is 1% of his sales)

32*100= 3200

His total sales were $3200.

Answer:

12

Step-by-step explanation:

You count all of the blue squares

Answer:

39

Step-by-step explanation:

Answer: c

Step-by-step explanation: good luck everyone

Ashley's z-score for the given table is -1.2.

''A z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units. The z-score is positive if the value lies above the mean, and negative if it lies below the mean.''

From the given table, we can calculate the mean, median, mode and standard deviation.

Therefore, mean = (75 + 60 + 75 + 100 + 75 + 75 + 75 + 95 + 60 + 65) ÷ 10

= 75.5

Median = middle term when scores are arranged in ascending order

= middle term of {60, 60, 65, 75, 75, 75, 75, 75, 95, 100}

= 75

Mode = number that occurs highest in {60, 60, 65, 75, 75, 75, 75, 75, 95, 100} = 75.

Standard deviation = [tex][\sqrt{(x_1-x)^{2}+(x_2-x)^{2}+........+(x_n-x)^{2}]/n[/tex]

=  [tex][\sqrt{(75-75.5)^{2}+(60-75.5)^{2}+........+(65-75.5)^{2}]/10[/tex]

= [tex]\sqrt{157.25}[/tex]

=12.54

Therefore, Ashley's Z-score = (Ashley's score - Mean)/ Standard Deviation

= (60 - 75.5)/12.54 = -1.2

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Answer:

x = 90

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, then

x = ∠ A + ∠ B = 30 + 60 = 90

Answer:

D. A graph shows both axes unnumbered. Points are scattered all over the graph.

Step-by-step explanation:

The r-value is also known as the correlation coefficient. This number shows how correlated points on a graph are. It ranges from -1 to 1, with numbers being closest to 0 being the least correlated. So a graph in which the points are scattered all over would have an r-value closest to 0 because the points are not correlated. If a graph shows either an upwards or downwards trend that means there is some correlation, therefore having an r-value of around -1 or 1.

Answer:

d

Step-by-step explanation:

edge

Answer:

53

Step-by-step explanation:

90 - 37 = 53

Answer:

A. y= -x + 3

Hope this helps!

Answer:

A)4 packs of footballs

B)$83.88

Step-by-step explanation:

If every boy needs a football then he is unable to buy just 3 cause then he would only have 12 footballs

3*4=12

So he would need 4 packs of footballs

B) because he needs 4 packs he multiplies 4 by 20.97 a pack.

4*20.97=83.88

Answer:

2/5 ; 2/5 ; 1/5

Step-by-step explanation:

Given that :

Numbe red gumballs = 2

Number of green gumballs = 2

Number of Blue gumballs = 1

The probability of making a random choice :

Probability = required outcome / Total possible outcomes

Probability of choosing (red) :

P(red) = number of red balls / total number of balls

P(red) = 2 / 5

P(green) = number of green balls / total number of balls

P(green) = 2 / 5

P(blue) = Number of blue balls / total number of balls

P(blue) = 1 / 5

Answer:

D

Step-by-step explanation:

She only cut the 15% extra and no the other 75%

Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric. The correct option is B.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that The directions on a sewing pattern say to cut an extra 15% of fabric to account for errors. Chloe needs 0.75 yards of fabric to make a skirt, and she cuts 0.1125 yards.

Calculate the percentage of the fabric from the given data,

Percentage = 0.1125 / 0.75

Percentage = 0.15 x 100

Percentage = 15%

Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric.

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