Factor completely 16x^3−36x

Answer:

the mean is equal to the median

Step-by-step explanation:

From the bar graph,

The mean is equal to the median.

Option B is the correct answer.

A bar graph is a type of chart used to represent data using rectangular bars, where the length or height of each bar corresponds to the value of the data.

The bars can be arranged horizontally or vertically and are usually separated by equal spaces.

The x-axis represents the categories or groups being compared, and the y-axis represents the scale or measurement of the data being shown.

We have,

For a graph that is perfectly symmetric, the mean and median are equal.

In the given bar graph, the bars are perfectly symmetric around the middle bar, which is bar 5.

This means that the median value of the data represented by the graph is 5.

To find the mean of the data, we can add up the heights of all the bars and divide by the total number of bars:

(2 + 4 + 6 + 8 + 10 + 8 + 6 + 4 + 2) ÷ 9 = 6

So the mean value of the data is also 6.

Therefore,

The mean is equal to the median.

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Answer:

1240 yd²

Step-by-step explanation:

Answer: 1440 square units

Step-by-step explanation:

40 x 36

A = L x w

Answer:

The mean is 0 and the deviation 1. And we can express this distribution with the following notation:

[tex] Z \sim N (\mu =0,\sigma =1)[/tex]

[tex]\sigma = 1[/tex] correct the deviation for this special distributionn is always 1

Step-by-step explanation:

The normal standard distribution is an special case of the normal distribution with some parameters on specific.

The mean is 0 and the deviation 1. And we can express this distribution with the following notation:

[tex] Z \sim N (\mu =0,\sigma =1)[/tex]

And when we analyze the options we can conclude this:

[tex]\mu[/tex] this value for this distribution is always equal to 0 and not 1

[tex]\sigma = 1[/tex] correct the deviation for this special distributionn is always 1

[tex]x[/tex] this value can be any value higher or lower than 1 so then is not the correct option

[tex]z[/tex] this variable can be different from 1 so then is not the correct option

Answer:

The mean is 0 and the deviation 1. And we can express this distribution with the following notation:

correct the deviation for this special distributionn is always 1

Step-by-step explanation:

The normal standard distribution is an special case of the normal distribution with some parameters on specific.

The mean is 0 and the deviation 1. And we can express this distribution with the following notation:

And when we analyze the options we can conclude this:

this value for this distribution is always equal to 0 and not 1

correct the deviation for this special distributionn is always 1

this value can be any value higher or lower than 1 so then is not the correct option

this variable can be different from 1 so then is not the correct option

Step-by-step explanation:

Answer:

51 and 42

Step-by-step explanation:

Use

x + y = 93

x - y = 9

Add those two equations together and you get 2x = 102

*y is not in the equation anymore because y + -y = 0*

Divide both sides by 2

x = 51

plug x into one of the equations; let's use x + y = 93

Then you get, 51 + y = 93

Subtract both sides by 51 and you get y = 42

Plug both in the other equation to make sure the numbers work.

51 + 42 = 93; true

51 - 42 = 9; true

Answer:

42 and 52

Step-by-step explanation:

Answer:

B) The median will increase.

Step-by-step explanation:

he original median was 35 and the new median is 36. The median will increase.

Answer:

The angle measure is 2700°

Step-by-step explanation:

Close wise rotation is positive.

Note that one rotation is equivalent to a revolution.

If one rotation = 360°

7.5 rotations will measure 360° ×7.5 which is equivalent to 2700°

Answer:

13.4 feet

Step-by-step explanation:

a²+b²=c²

12²+6²=c²

144+36=[tex]\sqrt{180}[/tex]

=13.4

The length of the cable is 13.416 feet.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have one end of the cable is attached to the top of a flagpole.

The other end is attached 6 feet away from the base of the pole.

The flagpole height = 12 feet

As we can see in the figure it is a right angle triangle in which the:

The length of the base of the right angle triangle b = 6 feet

The length of the perpendicular l = 12 feet

From the Pythagoras theorem:

[tex]\rm Hypotenuse^2 = Base^2+Perpendicular^2[/tex]

Let's suppose the length of the cable is x feet

[tex]\rm x^2 = 6^2+12^2[/tex]

[tex]x^2 = 36+144 \Rightarrow 180[/tex]

[tex]\rm x = \sqrt{180}[/tex]

x = 13.416 feet

Thus, the length of the cable is 13.416 feet.

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The equation 1/2(b + 14) = b + 14/2 simplifies to 14 = 14, suggesting that any value for b is a solution, and the equation is an identity.

The given equation is 1/2(b + 14) = b + 14/2. To solve for the variable b, we can perform algebraic operations. First, we recognize that the equation on the left side is already simplified, but we need to clarify whether the denominator 2 applies to the whole right-hand side or just to the 14 in the equation b + 14/2. Assuming it applies only to the 14, we can multiply both sides of the equation by 2 to eliminate the denominators:

After simplifying, we see that b on both sides cancels out, leaving us with an equality 14 = 14, which is always true. This means that the equation has infinitely many solutions, since any value of b will satisfy the equation. If the denominator 2 applied to the entire right-hand side (b + 14), then the equation is already balanced as written, again indicating that any value of b would be a solution.

This balance shows that the original equation represents an identity rather than a conditional equation with a specific solution.

Answer:

$157.38 per day is used.

Step-by-step explanation:

Van distance 198

9km per L

198÷9=22L

Truck distance 620

6.2km per L

620÷6.2=100L

truck 100L

+van 22L

=122Lx1.29

=157.38

Daily fuel consumption is calculated for trucks and vans by dividing their respective average distances travelled per day by their averages distances travelled per litre. These amounts are multiplied by the respective numbers of each vehicle and then by the cost of fuel (£1.29 per litre) to give a total daily fuel bill of £1,517.04.

The first step in calculating the daily bill for the delivery company is to determine how many litres of fuel both the vans and trucks consume per day. To do this, divide the average distance travelled per day by the average distance travelled per litre for each type of vehicle.

For the vans, this would be 198 / 9 = 22 litres per day. For the trucks, 620 / 6.2 = 100 litres per day.

The company has 8 vans and 10 trucks, so the total daily fuel consumption would be: (8 * 22) + (10 * 100) = 176 + 1000 = 1176 litres.

The cost of fuel is £1.29 per litre, so the daily bill would be 1176 * £1.29 = £1,517.04.

Therefore, the delivery company's total fuel bill for one working day is £1,517.04.

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Answer:

3/2 units^2

Step-by-step explanation:

The area of the entire circle is 16π.  What is the area of a sector of this circle if the central angle (not angel) is 8/5 radians?

Formula:   (fraction of circle represented by the sector)(area of the circle

Area of the sector described above is

  8/5 radians                                         8*16π square units

----------------------- * 16π square units = ------------------------------ = 3/2 units^2

    2π radians                                                      10π

Answer:

D

Step-by-step explanation:

You can drive anywhere less than or equal to 30 mph, and it'd be legal

The correct use of conversion factors will result in the cancellation of the unwanted units and retention of the desired unit.

Conversion factors are essential in unit conversions, allowing us to switch from one unit of measurement to another within the same system, such as U.S. customary units or the SI unit system. To use conversion factors effectively, one must ensure that the unit of measure they wish to convert from or to is correctly positioned in the conversion factor equation. For instance, when converting meters to centimeters, a factor of 1 cm/10-2 m or 100 cm/1 m is used because 'centi' means 10-2 in the SI unit system.

It is important to keep track of units being canceled during the conversion. If you have units in the numerator and denominator that are the same, they will cancel out, leaving only the desired unit. In the process of conversion, if the unit you want to convert is in the denominator of the original quantity, the conversion factor should have that unit in the numerator.

Choosing the right conversion factor and accurately performing the calculations are crucial. A proper conversion factor will cancel out unwanted units. Using an incorrect conversion factor without an opposing unit to cancel out will leave an unwanted unit in your answer, indicating an error in the process.

Dimensional analysis, which often involves conversion factors, simplifies the process of converting units and ensures that measurements within calculations are consistent. This technique is fundamental for scientific calculations and everyday applications, such as determining the appropriate unit to measure large volumes or distances.

Answer: 64 + 32 + 16 + 8 + 4 + 2 + 1 + .5 + .25 = 127.75

Step-by-step explanation: the sequence divides the next number by 2 ; 64/2 = 32, 32/2 = 16, etc

Answer:

127.75

Step-by-step explanation:

Answer:

(-2, 1)

Step-by-step explanation:

The coordinates of the vertex A of square ABCD is (1, 6).

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Given that,

A square ABCD undergoes a translation of (-4, -1) and a rotation of 90° to form the square A''B''C''D''.

Let (x, y) be the coordinates of A.

After the translation of (-4, -1), it becomes,

A'(x - 4, y - 1)

When it rotates to 90°, it becomes,

A''(-(y - 1), x - 4) = A''(1 - y, x - 4) = (-5, -3)

1 - y = -5 ⇒ y = 1 + 5 = 6

x - 4 = -3 ⇒ x = 1

Coordinates are (1, 6)

Hence the coordinates of A is (1, 6).

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The complete question is as follows :

Square A"B"C"D" is the final image after the rule T -4, -1 • R 0, 90° (x, y) was applied to square ABCD. What are the coordinates of vertex A of square ABCD?

n a coordinate plane, a square A double-prime B double-prime C double-prime D double-prime has points (negative 5, negative 3), (negative 3, negative 1), (negative 1, negative 3), (negative 3, negative 5).

You can evaluate every percentage in two simple steps:

First of all, divide your number by 100. This will give you the 1% of your quantity:

[tex]\dfrac{76200}{100}=762[/tex]

Then, multiply the 1% by 27 to get the 27%:

[tex]762\cdot 27=20574[/tex]

27% of 76,200 is 20,574.

"To calculate 27% of 76,200, one can multiply the total amount by the percentage value, expressed as a decimal or fraction. Here is the step-by-step calculation:

First, convert the percentage to a decimal by dividing by 100:

"To calculate 27% of 76,200, one can multiply the total amount by the percentage value, expressed as a decimal or fraction. Here is the step-by-step calculation:

First, convert the percentage to a decimal by dividing by 100:

[tex]\[ 27\% = \frac{27}{100} = 0.27 \][/tex]

Next, multiply this decimal by the total amount:

[tex]\[ 0.27 \times 76,200 = 20,574 \][/tex]

Therefore, 27% of 76,200 is 20,574.

The answer is: 20,574."

Answer:

10 Male

16 Female

Step-by-step explanation:

Answer:

A) The volume of figure 1 is 45 cm³ greater than the volume of figure 2

Step-by-step explanation:

Let's start by calculating the volumes of both figures

Figure 1

Rectangular prism

V = Bh

V = (15*6)(5)

V = (90)(5)

V = 450 cm³

Triangular prism

V = Bh

V = 1/2(3*15)(6)

V = 1/2(45)(6)

V = 1/2(270)

V = 135 cm³

Add them together, you get 585 cm³

Figure 2

Rectangular prism

V = Bh

V = (6*15)(5)

V = (90)(5)

V = 450 cm³

Rectangular pyramid

V = 1/3 Bh

V = 1/3 (15*6)(3)

V = 1/3 (90)(3)

V = 1/3 (270)

V = 90 cm³

Add them together, you get 540 cm³

Subtract 540 from 585 and get 45

Answer:

A) The volume of figure 1 is 45 cm³ greater than the volume of figure 2

Step-by-step explanation:

Answer:

6361.6 grams

Step-by-step explanation:

A chef at a restaurant uses 14 pounds of butter each day

Given;

16 ounces per pound

And

28.4 grams per ounces

Converting 14 pounds to gram;

14 pounds × 16 ounces/pound = 224 ounces

Then;

224 ounces × 28.4 grams/ounce = 6361.6 grams

Answer:

x= [tex]-5+2i, -5-2i[/tex] aka No Real Solution

Answer:

102

Step-by-step explanation:

Since we know that the numbers are two consecutive even numbers, we can write an equation like this where n represents the 2 numbers.

n + (n+2) = 206

Simplify the left side:

n + (n+2) = 206 -----> 2n+2 = 206

Subtract 2 from both sides:

2n = 206-2 -----> 2n = 204

Now divide 204 by 2:

n = 204/2 -----> n = 102

The smallest of two consecutive even numbers, whose sum is 206, is 102.

The question is asking for the smallest of two consecutive even numbers whose sum is 206. Let’s denote the smaller even number by n. The next consecutive even number would be n+2 (since even numbers are two units apart).

The problem states that the sum of these two numbers is 206 which can be written in the equation form as n + (n+2) = 206. It simplifies to 2n + 2 = 206. Subtracting 2 from both sides, we get 2n = 204. And finally, dividing by 2, we find that n = 102. So, the smallest number is 102.

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Answer:

x=7                  x=-1

Step-by-step explanation:

x^2 - 6x - 7 = 0

Factor

What two numbers multiply to -7 and add to -6

-7*1 =-7

-7+1 = -6

(x-7) (x+1) = 0

Using the zero product property

x-7 =0          x+1 =0

x=7                  x=-1

Answer: x is -1 & 7

Step-by-step explanation:

X2-6x-7=0

Quadratic equation

Variables of -7 that will give-6 are

-7 & +1

X2-7x+x-7=0

X(x-7) +1(x-7)=0

(X+1)(x-7)=0

X+1=0

X= -1 or

X-7=0

X= 7

Therefore,

X is either -1 & 7

Answer:

10 units

Step-by-step explanation:

Divide the volume by the product of the length and height to calculate the rectangular prism's width.

1200 / 24 x 5 = 10 units

Answer:

The answer is 600

Step-by-step explanation:

V = A(h/3)

Answer:

3 =x

Step-by-step explanation:

f(x) = -10x + 45

f(x) = 15

15 = -10x +45

Subtract 45 from each side

15-45 = -10x+45-45

-30 = -10x

Divide each side by -10

-30/-10 = -10x/-10

3 =x

Answer:

A

Step-by-step explanation:

If each balloon holds 2 oz of water, you can multiply 19 by 2 to find out how many ounces you'll need. 19*2 is equal to 38, but rounding up is 40.

The total amount of water needed by Pat for the balloon fight is 40 ounces.

The correct option is (A).

The mathematical branch known as arithmetic deals with the study and application of numbers and their relationships.

As per the given data:

The number of balloons needed for a fight is equal to 19.

The amount of water each water balloon holds is also given.

We have to find out the total amount of water needed by Pat for the balloon fight.

The amount of water each water balloon holds = 2 ounces

Total amount of water needed by Pat for the balloon fight:

= number of balloons needed for a fight × amount of water each water balloon holds

= 19 × 2

= 38 ounces (after rounding off to the tenths place, it's equal to 40)

= 40 ounces

Hence, the total amount of water needed by Pat for the balloon fight is 40 ounces.

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Answer:

4

Step-by-step explanation:

Write y6 as a product of two powers with the same base in four different ways, using negative or zero exponents in each product.

Answer:

The 90% confidence interval for the proportion of married couples with three personality preferences in common compared  with the proportion of couples with two preferences in common is (-0.081, 0.025).

Step-by-step explanation:

The (1 - α)% confidence interval for difference in proportion formula is,

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

The given information is:

n₁ = 375,

n₂ = 571,

X₁ = 132,

X₂ = 217.

Compute the sample proportion as follows:

[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{132}{375}=0.352\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{217}{571}=0.38\\[/tex]

For the 90% confidence level, the z-value is,

z₀.₀₅ = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in proportion as follows:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

     [tex]=(0.352-0.38)\pm 1.645\sqrt{\frac{0.352(1-0.352)}{375}+\frac{0.38(1-0.38)}{571}}\\=-0.028\pm 0.05256\\=(-0.08056, 0.02456)\\\approx (-0.081, 0.025)[/tex]

The 90% confidence interval for the proportion of married couples with three personality preferences in common compared  with the proportion of couples with two preferences in common is (-0.081, 0.025).

This confidence interval implies that the true difference between the proportions lies in this interval with probability 0.90.

The 90% confidence interval for the difference in proportions of married couples with two and three personality preferences in common is (0.027, 0.089). This indicates that with 90% confidence, the proportion of couples with two preferences in common is significantly higher.

Firstly, we need to find the proportions for both samples. The proportion for three personality preferences in common is 132/375 = 0.352 and for two personality preferences in common is 217/571 = 0.380.

Next, to compute the standard error, we use the formula √[ P(1 - P) / n ]. For three personality preferences we get √[ 0.352(1 - 0.352) / 375] = 0.026. And for two personality preferences we obtain √[ 0.380(1 - 0.380) / 571] = 0.021.

From these, the difference in the two sample proportions can be calculated, which is 0.380 - 0.352 = 0.028. The standard error of the difference can then be calculated as √( 0.026 ^ 2 + 0.021 ^ 2) = 0.033. At the 90% confidence level, the z-score is 1.645.

To calculate the confidence interval, note that 0.028 ± 1.645 * 0.033 is the equation we are trying to solve. This produces a range from 0.027 to 0.089.

So, the 90% confidence interval for difference in proportions is (0.027, 0.089), meaning that with 90% confidence, the proportion of couples with two preferences in common is significantly higher than those couples with three personality preferences in common.

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Answer:

None of the above

Step-by-step explanation:

None of the above polynomials are in standard form.