Simplify the following expression:

-5a⁷ b⁻³ • 4a⁻⁶ b⁶

[tex]\displaystyle\\x^4+10x^2+25=\\\\=x^4+5x^2+5x^2+25=\\\\=(x^4+5x^2)+(5x^2+25)=\\\\=x^2(x^2+5)+5(x^2+5)=\\\\=(x^2+5)(x^2+5)=\\\\=\left(x^2+\left(\sqrt{5}\right)^2\right)\left(x^2+\left(\sqrt{5}\right)^2\right)=\\\\=\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)=\\\\=\Big(x+i\sqrt{5}\Big)\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)=\\\\=\boxed{\Big(x+i\sqrt{5}\Big)^2\Big(x-i\sqrt{5}\Big)^2}[/tex]

All you have to do is combine the number of yards that they lost on the first play. The total yards lost is 9 yards.

The probability that at least one of the three randomly selected internet users is more careful about personal information when using a public wi-fi hotspot is 97.3%.

To find the probability that at least one of the three randomly selected internet users is more careful about personal information when using a public wi-fi hotspot, we can calculate the probability of the complement event, which is the event that none of the users are more careful. Since the probability that an internet user is more careful is 70%, the probability that a user is not more careful is 1 - 70% = 30%. The probability of the complement event for all three users is (0.3)^3 = 0.027. Therefore, the probability that at least one user is more careful is 1 - 0.027 = 0.973, or 97.3%.

Additional information that the survey subjects volunteered to respond does not affect the calculation of the probability. The probability is based solely on the given percentage from the poll, which represents the proportion of internet users who are more careful about personal information when using a public wi-fi hotspot.

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The probability that at least one internet user is more careful about personal information when using a public wi-fi hotspot is 0.973.

To find the probability that at least one person is more careful about personal information when using a public​ wi-fi hotspot, we can use the complement rule. The complement of at least one person being more careful is that no one is more careful. So, the probability that no one is more careful is 0.3 multiplied by 0.3 multiplied by 0.3 (since there are three internet users). Then we subtract this probability from 1 to find the probability that at least one person is more careful. So, the probability that at least one person is more careful is 1 - (0.3 x 0.3 x 0.3) = 0.973.

The additional information that the survey subjects volunteered to respond does not affect the result of the probability calculation. The probabilities are based on the initial survey results, and any additional information would be separate from those probabilities.

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12x + 6y = 24

add -6 to both side

12x + 6y + -6y = 24 + -6y

Combine like terms:

6y + -6y = 0

12x + 0 = 24 + -6y

12x = 24 + -6y

Divide each side by '12'

x = 2 + -0.5y (your answer)

Answer: 35.4 yards

Step-by-step explanation:

Area of a square = s²

1255 = s²

35.4 = s

100p-5p^2 = 0

Factor out 5p out of 100p and -5p^2:

5p(20) + 5p(-p) = 0

Factor:

5p(20-p)=0

Divide each term by 5:

p = 0

Set 20-p to 0 and solve for p:

p = 20

The answer is 0, 20

Answer:

In order to increase humidity by 49.17 grams per kilogram, the increase in temperature will be 18 degree Celsius approx.

Step-by-step explanation:

Initial humidity = 5.75 g/kg

Final humidity= 49.17 g/kg

Percentage increase in humidity= (49.17-5.75)/5.75 *100= 755.13

Increase in temperature= 755.13/43 = 17.56

Increase in temperature = 18 degree Celsius approx.

Answer:

The temperature must increase by more than 6 degree Celsius for the humidity to reach at least 49.17 grams per kilogram

Step-by-step explanation:

Given : Humidity on Monday morning = 5.75 grams per kilogram

To Find: He wants to know how much the temperature must increase for the humidity to reach at least 49.17 grams per kilogram.

Solution :

Let T be the increase in temperature, in degrees celsius, from monday morning.

According to question

The humidity measured in grams of water per kilogram of air, increases by 43% for every 1 degree Celsius increase in temperature.

So. Rate of increment is 43%

So, it becomes : [tex]100+43=143\% =1.43[/tex]

43% increases for every 1 degree celsius.

So, for T the increase is 1.43*T

So, [tex]1.43T\geq \frac{49.17}{5.75}[/tex]

[tex]1.43T\geq 8.55[/tex]

[tex]T\geq \frac{8.55}{1.43}[/tex]

[tex]T\geq 5.97[/tex]

Thus the temperature must increase by more than 6 degree Celsius for the humidity to reach at least 49.17 grams per kilogram

Look at the picture.

It are the examples of a normal distribution.

Answer: B.

Answer:

$639.98 is budgeted for the rent.

Step-by-step explanation:

Joshua's monthly salary is $2,909 and the budget for the rent is 22% of her salary.

For finding the amount of rent, we just need to find 22% of $2909. For that, first we need to convert 22% into decimal by dividing it by 100 and then multiply this result with $2909.

So, [tex]22\%= \frac{22}{100}=0.22[/tex]

Now,  [tex](\$2909*0.22)= \$639.98[/tex]

Thus, $639.98 is budgeted for the rent.

Answer:

Percentage decrease ( from $4.09 to $3.59) is 0.1% ( Rounded to nearest tenth)

Percentage increase (from $3.59 to 4.09) is 0.1% ( Rounded to nearest tenth)

Percentages are not same for the both price changes. As we can see from the calculations percentage change from $3.59 to $4.09 is higher.

Step-by-step explanation:

$4.09 has been changed to $3.59.

Percent change = [(Value after  - Value before) / Value before]*100

                          =[tex]\frac{3.59-4.09}{4.09}*100[/tex]%

                          =[tex]\frac{-0.5}{4.09}*100[/tex]%

                          =[tex]-0.122249[/tex]%

                           =[tex]-0.1[/tex]% ( Rounded to nearest tenth)

Percentage decrease is 0.1% ( Rounded to nearest tenth)

Now lets calculate the percentage change from $3.59 to $4.09.

Percent change = [(Value after  - Value before) / Value before]*100

                          =[tex]\frac{4.09-3.59}{3.59}*100[/tex]%

                          =[tex]\frac{0.5}{3.59}*100[/tex]%

                          =[tex]0.13927[/tex]%

                           =[tex]0.1[/tex]% ( Rounded to nearest tenth)

Percentage increase is 0.1% ( Rounded to nearest tenth)

Percentages are not same for the both price changes. As we can see from the calculations percentage change from $3.59 to $4.09 is higher.

This mathematical problem involves calculating percentages of increase and decrease, using the same technique to calculate both. The percentage decrease when the price was marked down from $4.09 to $3.59 is approximately 12.2%, while the percentage increase from $3.59 back to $4.09 is approximately 13.9%, making the percentages of change different for the two price shifts. The greatest change occurs with the increase back to the original price.

The subject of this question is mathematics, specifically the calculation of percentage increases and decreases. To find the percentage decrease when the price was marked down from $4.09 to $3.59, we use the formula:

[(Old Price - New Price) / Old Price] x 100

[(4.09 - 3.59) / 4.09] x 100 ~ 12.2%

So the percentage decrease is around 12.2%. Now, to calculate the percentage increase from $3.59 back to $4.09, we use the same approach:

[(4.09 - 3.59) / 3.59] x 100 ~ 13.9%

This gives us a percentage increase of approximately 13.9%. Therefore, the percentage of change is not the same for both price changes. The greater change is seen with the increase back to the original price, which results in a larger percentage of 13.9% compared to the decrease of 12.2%.

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The value of x is -4.

Here,

The expression is;

6 (-3 - x ) - 2x = 14

We have to find the value of x.

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Now,

The mathematical expression is,

6 (-3 - x ) - 2x = 14

Solve this, we get;

6 (-3 - x ) - 2x = 14

- 18 - 6x - 2x = 14

Add 18 both sides,

- 8x = 14 + 18

- 8x = 32

Divide both sides by -8,

x = -4

Hence, The value of x is -4.

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[tex]\frac{3}{4}[/tex]

the original price = 1 = [tex]\frac{1}{4}[/tex] + [tex]\frac{3}{4}[/tex]

the customer obtains a [tex]\frac{1}{4}[/tex] discount

and has to pay [tex]\frac{3}{4}[/tex] of the original price

so it is 87.5 so what you do do is 25 x 3.50 and it will give you 87.5

Joe has a bonus of $25 and he needs to earn a total of $165. He needs to make $140 on his hourly wage of $3.50. By dividing $140 by $3.50, we find that Joe needs to work 40 hours to reach his goal.

The subject of this question is Mathematics, particularly dealing with real-life word problems. To solve this, we first have to account for the bonus that Joe has already received. If Joe has a bonus of $25 this week, then he needs to earn $165 - $25 = $140 from his hourly wage in order to reach his goal. Joe earns $3.50 per hour. To figure out how many hours he needs to work to earn $140, you divide the total amount of money he needs to earn by the amount he earns in one hour. Hence, $140 ÷ $3.50 = 40 hours. So, Joe needs to work 40 hours to make at least $165 if he gets a bonus of $25 this week.

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Let number of plastic containers collected by fourth grade= x

Then number of plastic containers collected by fifth grade students=x-216

OR

If number of plastic container collected by fifth grade is y

then number of plastic container collected by fourth grade=y+216

So, we can write it as follows

⇒ number of plastic containers collected by fourth grade= number of plastic containers collected by fifth grade +216

Remark

I take it the semicircles cover the full width of the paper.

So the radius is 12/2 = 6 cm

Since there are two of them, the area = a full circle.

Step One

Find the area of the rectangle before the cuts were made.

Area = L * W

L = 27

W = 12

Area = 27 * 12 = 324 cm^2

Step Two

Find the area of the circle cut outs.

r = 6

Area = pi * r^2

Area = 3.14 * 6^2

Area = 3.14 * 36

Area = 113.04 cm^2

Step Three

Find the total area left

Total Area Left = rectangle - circle

Total Area Left = 324 - 113.04

Total Area left = 210.96 cm^2   Answer

Answer:

Side of Squared shaped plot = x foot

Then the farmer fences off a 25 foot wide section to create an area to store equipment.

As width=25 foot

and Length =x foot

Area = 25 x square foot

So 25 x represents area which is used for storing equipment.

So out of all the options Option D is correct which is The area of the land fenced off to store equipment .

Answer

The statement best describes the term 25x is  option ( D)

i.e  The area of the land fenced off to store equipment.

Reason

As given in the question

A farmer has a square-shaped plot of unused land

After the farmer fences off

he fences off a 25-foot wide section to create an area to store equipment.

x represent the original length of the plot.

this shows that the plot used to store equipment is not square.

Formula

Area of the rectangle = length × breadth

length = x

breadth = 25

put in the above equation

Area = 25x feet²

therefore 25x feet² shows the area of the land fenced off to store the equipment.

Hence proved

Answer: 1045 cm of red ribbon and 1045 cm of yellow ribbon

Step-by-step explanation:

Let R represent the amount red ribbon and Y represent the amouont of yellow ribbon.

Use substitution method to solve:

5(R - 836) = R

5R - 4180 = R   distributed 5 on the left side

4R - 4180 = 0   subtracted R from both sides

4R = 4180         added 4180 to both sides

R = 1045         divided both sides by 4

Answer:

Step-by-step explanation:

Answer:

760,000

Step-by-step explanation:

5.3  is  one rational number between 5.2 and 5.5.

It is a rational because it can be written as a fraction  a/b where a and b are integers ( not = 0):-

5.3 = 53/100.

Regular pay: $12/hour

Time and a half: $12/hour * 1.5 = $18/hour

40 hours * $12/hour + 2 hours * $18/hour = $480 + $36 = $516

Answer: $516

Step One

Find the area of the rectangle

Area = L * W

Area = 89 cm * 70 cm

Area = 6230 cm^2

Step Two

What is the formula for the two end semicircles?

Two semicircles = 1 whole circle

Area of any circle = pi * r^2

Step Three

Find the area of the circle

r = the width / 2     This may not be true. You need the diagram. If the circles are drawn on the length then use r = the length / 2

r = 70/2  = 35 cm

Area of circle = pi * r^2

Area of circle = 3.14 * 35^2

Area of circle = 3846.5

Step Four

Find the total area

The total area = Area of the rectangle + area of circle

The total area = 6230 + 3846.5

The total area = 10076.5 cm^2 <<<< Answer

To find segment AD given HD = 24 when H is the centroid, you would use the property of the centroid that divides medians in a 2:1 ratio. Since HD is the shorter part, multiply 24 by 2 to get AD = 48 units.

You're asking how to find the length of segment AD given HD = 24 in a geometric context involving a centroid. To find AD, we must understand the properties of the centroid, which is the point where the three medians of a triangle intersect. A median connects a vertex of a triangle to the midpoint of the opposite side, and in every triangle, the centroid divides each median in a 2:1 ratio, with the longer segment being closest to the vertex.

Given that HD = 24 and D is the midpoint of AH (because H is the centroid), according to the centroid properties, the length of AD must be twice the length of HD. Therefore:

AD = 2 * HD

AD = 2 * 24

AD = 48

The length of segment AD is 48 units.

Let the weight of triangle be x units. You are given that the weight of square is 1 unit.

1) On the left side of the balanced beam you can see 3 triangles and 5 squares. The weight on left side is 3·x+5·1=3x+5 units.

2) On the right side of the balanced beam you can see 2 triangles and 7 squares. The weight on right side is 2·x+7·1=2x+7 units.

3) If the whole system is balanced, then the weights on left and right sides are equal:

3x+5=2x+7.

Solve this equation:

3x-2x=7-5,

x=2 units.

Answer: option A

The correct product of 27 and 600 is:

[tex]\[ \boxed{16200} \][/tex]

"The correct answer to find the product of 27 and 600 is not obtained by simply adding 27 six times and then appending zeros. The correct method to calculate 27 x 600 is as follows:

 First, multiply 27 by 6 to get the hundreds place value correct:

[tex]\[ 27 \times 6 = 162 \][/tex]

Next, since we are multiplying by 600, we need to account for the additional zeros. Each zero represents a factor of 10, so we multiply 162 by 100 (since there are two zeros in 600):

[tex]\[ 162 \times 100 = 16200 \][/tex]

Therefore, the correct product of 27 and 600 is:

[tex]\[ \boxed{16200} \][/tex]

The method described in the question is incorrect because it does not properly account for the place value of the digits in the multiplication. When multiplying by a number with zeros, each zero represents a power of ten and must be considered in the multiplication process. The correct method involves multiplying the numbers and then adjusting the final product's place value by adding zeros according to the multiplier's zeros."

The slope of the Line is 3

What is the slope of a line?

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) may be easily determined by finding the difference among the coordinates of the points. The slope is normally represented by the letter 'm'.

Conclusion: The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

The general equation of a line having a slope is y = mx + c

we have to arrange the equation 6x - 2y = 10 in y = mx + c form

6x -2y = 10

2y = 6x - 10

y = 3x - 5

The slope of the line is represented by m, the value of m in equation y = 3x - 5 is 3

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i DON;T KNOW MAYBE 10+9=21 is the correct answer. let me know if it right! hope u have a grate day

the last statement is true, that is

the table represents a function because each input has exactly one output assigned to it.