The area of a rectangle is 44 ft2 , and the length of the rectangle is 3 ft less than twice the width. find the dimensions of the rectangle.

To find the two numbers with the sum of 226 and a difference of 200, set up two equations, add them to find one number, and then substitute it into one of the equations to find the other. The two numbers are 213 and 13.

The sum of two numbers is 226, and their difference is 200. To find the two numbers, we can set up two equations based on the given information:

Add both equations to eliminate y:

Substitute x in one of the equations to find y:

The two numbers are 213 and 13.

Answer:

271.3 mm^3

Step-by-step explanation:

Volume of a cylinder = πr^2h

To find the answer, we need to find the difference between the large cylindrical and small cylindrical  pipes.

V = π h (R^2 – r^2)

Given: h= 10, R is outer radius = 8.4/2 = 4.2, r is inner radius = 6/2 = 3

V = π (10) (4.2^2 – 3^2)

V= 3.14*10(17.64 - 9)

V = 31.4(8.64)

V = 271.3 mm^3

The volume of metal in the pipe 271.3 mm^3

Hope this will helpful.

Thank you.

The volume of the metal in the pipe is 271.3 mm³.

A cylinder is a three-dimensional shape. It is a prism with a circular base.

Volume of a cylinder = πr²h

Where:

π = 3.14 = PI

r = radius = diameter / 2

The volume of the metal in the pipe = volume of the metal pipe - volume of the hole

3.14 x 10 x [(8.4/2)² - (6/2)²]

3.14 x 10 x [17.64 - 9}

3.14 x 10 x 8.64

= 271.3 mm³

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Answer:

[tex]64\ units^{3}[/tex]

Step-by-step explanation:

we have

[tex]V=s^{3}[/tex]

This is the formula to calculate the volume of a cube

where

s is the length side of the cube

In this problem we have

[tex]s=4\ units[/tex]

substitute

[tex]V=4^{3}=64\ units^{3}[/tex]

Let us say that:

K = age of Kristen

B = age of Ben

From the problem, we make the equations:

eqtn 1: K + B = 32

eqtn 2: (K – 4) = 2 (B – 4)

Simplifying eqtn 2:

K – 4 = 2 B – 8

K = 2 B – 4

Plugging in this to eqtn 2:

(2 B – 4) + B = 32

3 B – 4 = 32

3 B = 36

B = 12

From eqtn 2:

K = 2 B – 4 = 2 (12) – 4 = 20

So Kristen is 20 while Ben is 12.

Final answer:

By translating the given information into a system of equations and solving them step-by-step, we found that Kristen is 20 years old and Ben is 12 years old.

Explanation:

The question asks us to solve a system of equations based on the ages of Kristen and Ben. The total sum of their ages is 32, and four years ago, Kristen's age was twice that of Ben. Let's denote Kristen's age as K and Ben's age as B. The given information can be translated into two equations:

K + B = 32

K - 4 = 2(B - 4)

To solve these equations, first simplify the second equation:

K - 4 = 2B - 8

K = 2B - 4

Now substitute the value of K from the second equation into the first equation:

2B - 4 + B = 32

3B = 36

B = 12

Now that we know Ben's age (12), we can find Kristen's age by substituting the value of B into any of the initial equations. Using K + B = 32:

K + 12 = 32

K = 20

Therefore, Kristen is 20 years old and Ben is 12 years old.

Answer:

Option B - right angle

Step-by-step explanation:

We have Given statement : To trisect a(n) ____ angle, you first construct an equilateral triangle.

Solution: Option B is correct because,  a right angle is 90 degrees and an equilateral triangle has a 60 degree corner.

So, if you construct the equilateral you have one 60 and one 30, now bisect the 60.  

The  17/4 as a mixed number can be written as  4 1/4.

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.

In order to make 17/4 as a mixed number, we would have to do 17 divided by 4.

17/ 4 = 4.25

Then just put that decimal into a fraction.

That would be 4.25 = 4 1/4

Therefore, the  17/4 as a mixed number can be written as  4 1/4.

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Answer: The factorized form of [tex]n^2-25[/tex] will be

[tex](n-5)(n+5)[/tex]

Explanation:

Since we have given that

[tex]n^2-25[/tex]

Now, we need to factorize the expression,

We know the formula for "difference of squares" which is given by

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Using the formula, we get

[tex]n^2-25=n^2-5^2=(n-5)(n+5)[/tex]

Hence, the factorized form of [tex]n^2-25[/tex] will be

[tex](n-5)(n+5)[/tex]

The number of years will the population reach 14,652 will be 500 years.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The growth in the population of a city can be seen using the formula given below.

[tex]\rm P(t) = 9768 \times e^{0.003 \times t}[/tex]

Where t is the number of years.

The number of years will the population reach 14,652 will be given as,

[tex]\rm 14652 = 9768 \times e^{0.003 \times t}\\\\e^{0.003 \times t} = 1.5[/tex]

Take natural log on both sides, then we have

0.003 × t = 1.5

t = 1.5 / 0.003

t = 500 years

The number of years will the population reach 14,652 will be 500 years.

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The domain of the function is restricted to the altitude of the plane, and the plane cannot exceed its absolute ceiling. The graph of the function will have a vertical asymptote at the absolute ceiling. As the plane approaches its absolute ceiling, the time required to further increase its altitude increases significantly. To find the time it will take for the plane to climb to a specific altitude, substitute the altitude into the equation and solve for time.

a. The domain of the function is determined by the restrictions given in the problem. In this case, the domain represents the altitude of the plane. Since the plane's absolute ceiling is 18,000 feet, the altitude cannot exceed 18,000 feet. Therefore, the domain is 0 ≤ h ≤ 18,000.

b. To graph the function, we can plot points by substituting different values of h into the function and calculating the corresponding values of t. This will result in a smooth curve. Asymptotes occur when the function approaches certain values of h or t. In this case, the function has a vertical asymptote at h = 18,000, because the plane cannot climb beyond its absolute ceiling.

c. As the plane approaches its absolute ceiling of 18,000 feet, the time required to further increase its altitude increases significantly. This is because the logarithmic function in the equation has a slower growth rate as h approaches its limit.

d. To find the time it will take for the plane to climb to an altitude of 4000 feet, we can substitute h = 4000 into the equation t = 50 log10 (18000/(18000-h)) and solve for t.

To multiply 1.3 x 10^-2 and 0.05 in scientific notation, convert 0.05 to 5 x 10^-2. Multiply 1.3 by 5 to get 6.5, then add the exponents to get 6.5 x 10^-4, which is the final answer in scientific notation.

The question asks to calculate the multiplication of 1.3 x 10^-2 and 0.05 and express the result in scientific notation. To solve this arithmetic with numbers in scientific notation, you should multiply the decimal numbers and add the exponents of the ten's powers. The decimal multiplication is 1.3 multiplied by 0.05, which equals 0.065. Since 0.05 is not in scientific notation, it can be written as 5 x 10^-2 to simplify the calculation. Thus, the multiplication becomes (1.3 x 10^-2) x (5 x 10^-2). The next step is to multiply the decimal parts, 1.3 and 5, getting 6.5. The exponents of ten are then added together: -2 + (-2) = -4. The final multiplication gives us 6.5 x 10^-4. However, for true scientific notation, the leading number must be between 1 and 10, so we rewrite 6.5 as 6.5 x 10^0. The final scientific notation is therefore 6.5 x 10^-4.

The value of x with a z-score of -0.74 is -0.22.

To find the value of x that has a z-score of -0.74, we can use the formula:

x = mean + (z-score * standard deviation)

Given that the mean (mean) is 2 and the standard deviation (standard deviation) is 3, we can substitute these values into the formula:

x = 2 + (-0.74 * 3)

Simplifying the equation, we get:

x = 2 - 2.22

x = -0.22

Therefore, the value of x that has a z-score of -0.74 is -0.22.

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The total amount repaid by Melvin for the specified case is given by: Option C. $1,440

For finding the total amount repaid, we need to find how repeated addition can be evaluated using multiplication.

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b

Then, their multiplication can be interpreted as:

[tex]a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}[/tex]

For example,

[tex]5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}[/tex]

Since Melvin paid $60 for 24 months, so the amount he paid is $60 added 24 times, or:

Total amount paid by Melvin for furniture buying = 60  + 60 + ... + 60 (24 times) = [tex]24 \times 60 = 1440 \text{\: (in dollars)}[/tex]

Thus, the total amount repaid by Melvin for the specified case is given by: Option C. $1,440

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Inequalities describe a range of possible values and are useful in fields like business, economics, and physical sciences. They allow for decisions based on a range of results, like determining minimum product sales for profit. However, they don't provide specific values, which is a limitation in some contexts.

Many people would be interested in using inequalities in a range of fields, including business, engineering, economics, physical sciences, and mathematics. The use of inequalities provides benefits when you need to understand a range of possible values rather than a specific number. This allows decisions to be made based on a range of acceptable outcomes.

For example, in a business setting, inequalities can be used to determine the minimum number of products that need to be sold to achieve a certain profit. If the goal is to earn at least $500, the inequality would be nx > 500, where n is the price per unit and x is the number of units sold.

However, inequalities have their limitations. They provide a range of answers, not specific solutions. Thus, they may not be suitable in situations where precise values are needed. They also imply that all values within the range are equally acceptable, which might not always be the case.

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The probability of drawing a red marble first and a green marble second (without replacement) from a box containing 5 red, 8 green, 4 blue, and 3 yellow marbles is 2/19.

In the scenario you've described, you would first calculate the probability of selecting a red marble from the box. You have 5 red marbles and a total of 20 marbles (5+8+4+3), so the probability of drawing a red marble first is 5 out of 20, or 1/4.

When you draw a second marble without replacing the first, you have a slightly altered situation - the total number of marbles in the box now comes down to 19. We are interested in the probability of drawing a green marble now. As there are 8 green marbles, probability of drawing a green marble is 8 out of 19, or 8/19.

Probability of a red marble being picked first and then a green marble without replacement is calculated as: P(Red and then Green) = P(Red) * P(Green | Red is already picked). This equals 1/4 * 8/19 = 8/76 = 2/19.

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multiply 40 by 30% to find the discount then subtract

40 * 0.30 = 12

40-12 = 28

they would cost $28

Answer:

[tex]i^{12}=1[/tex]

Last option is correct.

Step-by-step explanation:

We have to simplify the expression [tex]i^{12}[/tex]

We can rewrite this expression using the properties [tex](a^m)^n=a^{mn}[/tex]

[tex](i^4)^{3}[/tex]

Now, we know that [tex]i^4=1[/tex]

Hence, we have

[tex](1)^{3}[/tex]

On simplifying, we get

[tex]1[/tex]

Thus, the simplified form is 1.

Last option is correct.

Answer:

it's 1

Step-by-step explanation:

a. at r = 2

P = [10! / (10 – 2)! 2!] * 0.33^2 * 0.67^(10 – 2)

P = 0.1989 ~ 0.20               (answer)

b. We deduct the values of P when r = 0, r = 1, r = 2 from 1 to get all values when r > 2

at r = 0

P = [10! / (10 – 0)! 0!] * 0.33^0 * 0.67^(10 – 0)

P = 0.0182

at r = 1

P = [10! / (10 – 1)! 1!] * 0.33^1 * 0.67^(10 – 1)

P = 0.0898

so for r > 2, the probability is:

P = 1 – (0.1989 + 0.0182 + 0.0898)

P = 0.6931            (answer)

c. at r = 3

P = [10! / (10 – 3)! 3!] * 0.33^3 * 0.67^(10 – 3)

P = 0.2614

at r = 4

P = [10! / (10 – 4)! 4!] * 0.33^4 * 0.67^(10 – 4)

P = 0.2253

at r = 5

P = [10! / (10 – 5)! 5!] * 0.33^5 * 0.67^(10 – 5)

P = 0.1332

So when r is between 2 and 5 inclusive, the probability is:

P = 0.1989+ 0.2614 + 0.2253 + 0.1332

P = 0.8188            (answer)