The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?

w ≤ 10 – l
2l + 2w ≥ 62
w ≤ 10 – l
2l + 2w > 62
w ≤ l – 10
2l + 2w ≥ 62
w ≤ l – 10
2l + 2w > 62

Answer:

Step-by-step explanation:

To check for 6 - Number should be Divisible by 2 and 3

4186650 is divisible by 2 % 3

To check for 8 - Las Three digits should be taken as a number and be checked if its divisible my 8

4186650 / 4 = 165.5

So the number is not divisible by 8

To check for 11 - we need to add the odd places and the even places and then subtract them both. if the answer is 11 or 0 then its divisible

4 + 8 + 6 + 0 = 19

1 + 6 + 5 = 12

19 - 12 = 7

So the number is not divisible by 11

Hope you are clear

Using relations in a right triangle, we have that the height of the tree is of 91.6 meters.

The relations in a right triangle are given as follows:

The graph for this problem is given at the end of the answer, and using it and the relations, we can build two equations involving x and the height h, and solve the system of equations for h.

From the triangle involving point G(angle of 43º), we can build the following relation:

tan(43º) = h/x

0.9325 = h/x

x = (1/0.9325)h.

x = 1.0724h (because we want to find h, hence we write x as a function of h).

From the larger triangle, that has the angle of 38º, we have the following relation.

tan(38º) = h/(x + 19).

tan(38º) = h/(1.0724h + 19). (considering that x is a function of h, as we found above).

0.7813 = h/(1.0724h + 19).

Hence, we apply cross multiplication to solve for h, as follows:

h = 0.7813(1.0724h + 19).

h = 0.8379h + 14.8447.

0.1621h = 14.8447

h = 14.8447/0.1621

h = 91.6 meters.

Hence:

The height of the tree is of 91.6 meters.

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If a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub

Given,

The total quantity of water in the tub = 8 gallons

The quantity of water draining for every 5 minutes = 6 gallons

The quantity of water draining for every 1 minutes = [tex]\frac{6}{5} =1.2[/tex] gallons

Consider the number of minutes as x

Then the equation for the amount of water in the tub

f(x)= 8 - 1.2x

The number off minutes take to empty the tub = Total quantity of water / Quantity of water draining per minute

=[tex]\frac{8}{1.2}=6.67[/tex] minutes

Hence, if a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub.

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The simplest form of product is, 28c¹³.

⇒ -7c⁷ * (-4c⁶) = 28 c¹³

The given expression can be simplified as;

The given product is;

-7c⁷ * (-4c⁶)

We have to simplify the given product.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, The given expression can be simplified as;

The product is given as;

-7c⁷ * (-4c⁶)

We can simplify by the rule of exponent as;

-7c⁷ * (-4c⁶)

= 28 c⁷⁺⁶

= 28 c¹³

So, -7c⁷ * (-4c⁶) = 28 c¹³

Hence, The simplest form of product is find as 28c¹³.

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The length of the segment to the nearest tenth of a centimeter is 105.0 cm

The given parameter is the line segment

When the line segment is measured by a meter rule, we have the length to be

Length = 105 cm

When approximated to the nearest tenth, we have:

Length = 105.0 cm

Hence, the length of the segment to the nearest tenth of a centimeter is 105.0 cm

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Answer:

0.522

0.063

Step-by-step explanation:

6 x 8.7 = 52.2

6 x 1.05 = 6.3

If we move them both two decimal places then...

0.522

0.063

She will need 1.34 pounds of salt for a full of bucket of water.

It is given that, Kayke mixes 1/6 pound of salt with 1/8 bucket of water to make a saline solution.

With 1/8 bucket of water she mixes 1/6 pound of salt.

1/8 bucket of water = 1/6 pounds of salt

Now, using unitary method to find salt needed to use for a full bucket of water.

So,

1 bucket of water = 8/6 pounds of salt

= 1.34 pounds of salt.  

She will need 1.34 pounds of salt for a full of bucket of water.

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59265 divided by a number raised to the 8th power × 596 × 427 is presented as follows;

[tex]15082468380 \times {x}^{ - 8} [/tex]

The given number to be divided is 59265

Let x represent the number that is raised to the 8th power, we have;

The number by which 59265 is divided = x⁸

The number by which the result is multiplied = 596 × 427

Therefore, we have;

[tex] \frac{59265}{x^8} \times 596 \times 427 = \frac{59265}{ {x}^{8} } \times 254492 [/tex]

The above expression can be expressed using the rules of indices as follows;

[tex]\frac{59265 \times 254492}{ {x}^{8} } =15082468380 \times {x}^{ - 8} [/tex]

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The slope of graph is 4.17 (a+1). It represents the annual rise in dose a.

Excellent understanding of medications, their mechanisms of action, side effects, interactions, mobility, and toxicity are prerequisites for practicing pharmacy. Thus, pharmacists are the key healthcare professionals who maximize the use of medicine for the benefit of patients. They are also the world's foremost authorities on drug therapy.

The pharmacist use equation C= 0.0417 d (a+1)

Applying in (mg)

So d = 100 mg

Therefore c = 0.0417×100 (a+1)

C= 4.17 (a+1)

4.17 (a+1) is the slope for the graph of c, which reflects the annual rise in dose a.

kid requires. Given that a newborn is age 0, the appropriate dosage is

c(0) = 4.17 (a+1)

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417D(a + 1). Suppose the dosage for an adult is 200 mg.

(a) Find the slope of the graph of c. What does it represent?

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Correct answer is C. y = x2 - 8x + 16 is the quadratic equation.

The answer to the question is:

x = 4

The graph has a multiplicity of 2 at x = 4 since it only touches this value and does not cross it.

The equation is then shown as follows:

y = (x - 4)^2

Expand

y = x^2 - 8x + 16

The quadratic equation is y = x2 - 8x + 16 as a result.

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Answer: last one

Step-by-step explanation:

Answer: 10.5

Step-by-step explanation:

The mean is all of the numbers in a system added together then divided by the amount of numbers in a system.

3 + 6 + 9 + 12 + 15 + 18 = 63

63 / 6 = 10.5

Answer: 2.2 miles per hour

Step-by-step explanation:

Since we are given his speed in one third of an hour, we can simply triple his speed to get his miles per hour.

[tex]\frac{11}{15} * 3\\= \frac{33}{15}\\\\= 2 \frac{1}{5}[/tex]

or, 2.2 miles per hour

Answer:

2.2mph!

Step-by-step explanation:

The cost of the guitar after expansion will be $144.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The price of guitars from universal guitar company increased by 60% when the business expanded. If a guitar cost $90 before the expansion.

Then the cost of the guitar after expansion will be

Cost = (1 + 0.60) x $90

Cost = 1.60 x $90

Cost = $144

The cost of the guitar after expansion will be $144.

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1/100 < 0.2 < 1/4 is the correct order of the given numbers arranged from least to greatest.

Given that, 1/100, 1/4 and 0.2 and we have to arrange them from least to greatest. So, basically we have to arrange them in ascending order.

1/100 can be written in decimal form as 0.01

1/4 can be written in the decimal form as 0.25

and 0.2 is already in the decimal form.

Now, we have 0.01, 0.25 and 0.2 and we have to arrange them from least to greatest.

Out of 0.01, 0.25 and 0.2, 0.01 is the smallest and 0.25 is the greatest.

0.01 < 0.2 < 0.25

This is the arrangement of the given number in decimal form.

1/100 < 0.2 < 1/4

This is the correct order of 1/100, 1/4 and 0.2 arranged in ascending order.

Therefore, 1/100 < 0.2 < 1/4 is the required answer.

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The required solutions are,
1) point A on the triangle is the center of dilation.
2) Triangle ABC is the original triangle.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
1) As shown in the figure, after dilation the only initial point that does not change points A. So it could be concluded that point A is the center of dilation.
2) since the scale factor is of 1/2 implies that the dilated figure is lower than the size of the original figure hence, triangle ABC is the original triangle.

Thus, the required solutions are,
1) point A on the triangle is the center of dilation.
2) Triangle ABC is the original triangle.

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Answer:

42.7

Step-by-step explanation:

What percent of 61 is 70?

61 --> Base number

0.7 --> Percent

61 x 0.7 = 42.7

Answer:

61/70 as a percentage is 87.1429%

Step-by-step explanation:

The two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

We are given that a study of a very large number of pregnant women in Arkansas reports that the women gained, on average, 14 pounds during their pregnancy and that 18% of the women smoked.

Now, we need to tell the two variables of the study.

Now, we can see that the independent variable is pregnant women.

Also, the two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

Therefore, the two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

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Answer:

Step-by-step explanation:

Discussion

Note: I think the length is supposed to be the height of 1 cookie.

The volume of the 12 cookies (1 dozen=12) is 176,715 in^3

The area of 1 cookie is 5 in

Area = pi * r^2

Area  of one cookie = 3.14 * 5^2

Area of one cookie = 78.5 in ^2 Note this is also the area of the base of the container.

Height of the 12 cookies = Volume / Area of one cookie

Height of the 12 cookies = 176.715/78,5

Height of the 12 cookies = 2.25 inches.

Answer

Thickness (height) of one cookie = 2.25/12

Thickness (height) of one cookie = .188 inches.

this picture is not clear

that traingle

Answer:

2+x/6=w

step by step

If a road repair crew spread 13 1/4 tons of gravel evenly over 4.5 feet of road then 2.39 tons of gravel is spread by them on each foot of road.

This is solved by using unitary method

4.5 feet of road is getting covered by 13 1/4 tons of gravel

Then 1 foot of road will be covered by (13 1/4) /4.5 tons of gravel

= (43/4) / 4.5 tons of gravel

= 2.388 tons of gravel

2.39 tons of gravel is required to cover 1 foot

If a road repair crew spread 13 1/4 tons of gravel evenly over 4.5 feet of road then it requires 2.39 tons of gravel is spread by them on each foot of road.

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Answer:

multiply input number by 2

Step-by-step explanation:

So, this is our function

y=2x===>

(3, 6), (4, 8), (5, 10), (6, 12), (7, 14)

so according to this functionality the output part is equal to input part multiplied by 2

If the first two spaces are for letters and the remaining five are for numbers, then 67,600,000 distinct seven-plate license plates are possible.

Putting things or numbers in order is known as a permutation. Combinations are a way to choose items or numbers from a collection of items or groups of items without regard to their order.

We can count the number of ways an item set can be rearranged using permutations. When counting combinations, we look at how many options we have from a larger pool of available items. Important statistical concepts include combinations and permutations.

We know that :

It consists of 10 digits and 26 letters.

Due to the repetition of letters and numbers. Since the first two positions are letters, first can be filled in.

26 * 26 = 676 ways.

Five more spots may then be filled.

10 * 10 * 10 * 10 * 10 = 100000ways

If the first two spaces are really for letters and the remaining five spaces are for numbers, then there are a variety of 7-place license plates that can be made.

26 * 26 * 10 * 10 * 10 * 10 * 10 = 67,600,000ways.

If the first two spaces are for letters and the remaining five are for numbers, then 67,600,000 distinct seven-plate license plates are possible.

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The subway car passes through 48 stations in 2hours

It is given that a subway car passes 4 stations every 10 mins.

Subway car is being referred to the metro system of New York city

It is known to us that an hour has 60 mins

We are given that subway car passes 4 stations every 10 mins

Therefore number of stations passed by subway car in 1 hour

= 60/10 x 4 = 24 stations

We are required to find the number of stations crossed by subway car in 2 hours

Therefore, number of stations crossed by subway car in 2 hours= 24 x 2

= 48  stations

Therefore, the subway car passes 48 stations in 2 hours

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Answer:

In fact, they're called equivalent ratios, which are ratios that express the same relationship between two numbers. The ratios 60/1 and 120/2 are equivalent because the relationship between the two parts of the ratios didn't change. According to the ratio 60/1, you travel 60 miles for every hour you drive.14 Oct 2021

y = 30x

Calculate  the number of gallos of water used to water trees i'd 30 times the number of trees.

Let's take,

Number of gallons = y

Number of trees = x

Then, according to the problem,

Number of gallons = 30*(Number of trees)

So….. y = 30*x

y = 30x

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The measure m<D is 26

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

m<ABE = 52

<EBD = <CBD

Now,

<ABE + <EBD + <DBC = 180 (linear pair)

52 + 2<EBD = 180

2<EBD = 128

<EBD = 128/2

<EBD = 64

Now, In ΔDEB using angle sum property

<DEB + <EDB + <DBE = 180

90+ <EDB + 64=180

<EDB = 26

Hence, the measure of <D is 26 degree.

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