Arthur is building a rectangular sandbox for his son. The area of the sandbox is 17 23/32 square feet. If the length of the sandbox is 3 3/8 feet, what is the width of the sandbox?

The system of equations y = x + 3 and y = x² - 2x + 3 when solved for x and y is x = 0 and y = 3 & x = 3 and y = 6

From the question, we have the following parameters that can be used in our computation:

y = x² - 2x + 3

Using the graph to solve the equations

y = x + 3

y = x² - 2x + 3

We simply write out the point of intersection of y = x + 3 and y = x² - 2x + 3

When y = x + 3 is plotted, we have the intersection to be

(0, 3) and (3, 6)

Hence, the solutions are (0, 3) and (3, 6)

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The division equation that describes the situation here is as follows:

4 ÷ 2/3 = 6.

Together with addition, subtraction, and multiplication, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same number of items is known as division.

This operation is used by mathematicians to organise and evenly distribute resources.

As we can see in the question, that there are 6 groups.

Now 6 groups of 2/3 parts.

Now the whole part has been given as = 4.

This can also be stated as:

The whole part (4) has been divided into 2/3 small parts to get 6 equal parts.

Therefore, the expression as per division can be:

4 ÷ 2/3 = 6.

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a) Sample size 13:(43.614, 44.386)

b) Sample size 1300:(43.9663, 44.0337)

The weight of the screws is normally distributed and has a variance of 0.64g^2. In a sample, the mean of the screws was 44g. The following are the two-sided (symmetrical) confidence intervals with a 95 percent confidence level for the expected value of the weight:Option a) Sample size 13:For a sample size of 13, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(13) = 0.1772.The t-distribution should be used to calculate the confidence interval since the population's standard deviation is unknown.The t-value corresponding to the 95% confidence interval with 12 degrees of freedom (df = n – 1) is 2.179. Therefore, the confidence interval can be calculated as follows:44 ± 2.179(0.1772)= 44 ± 0.386= (43.614, 44.386)The expected weight of the screws in the population is estimated to be between 43.614 g and 44.386 g.Option b) Sample size 1300:For a sample size of 1300, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(1300) = 0.0172.The z-distribution should be used to calculate the confidence interval since the sample size is large enough to assume that the sample mean is approximately normally distributed.The z-value corresponding to the 95% confidence interval is 1.96. Therefore, the confidence interval can be calculated as follows:44 ± 1.96(0.0172)= 44 ± 0.0337= (43.9663, 44.0337)The expected weight of the screws in the population is estimated to be between 43.9663 g and 44.0337 g.

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After answering the given query, we can state that So, after 35 years, the amount account would have a value of $10,062.07.

aggregate attempting to determine the amount, total number, or duration needed. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how much you have, how much you need, or how much you get is its amount. He needs that much cash to get by.

a. We must first determine the quarterly interest rate in order to determine the account amount after five years:

r = 8% / 4 ≈ 2% every three months.

The amount after five years can then be determined using the compound interest formula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where P = $1,000 as the original investment

2% is the quarterly interest rate (r).

N = 4 times per year that interest is added (quarterly)

If t = amount of years, then 5

[tex]A = \$1000(1 + 0.02/4)^{(4*5)} = $1,221.50[/tex]

So, after five years, the account would have a total of $1,221.50.

b. We employ the same method as before to determine the account balance after 35 years:

[tex]A = \$1000(1 + 0.02/4)^{(4*35)} = $10,062.07[/tex]

So, after 35 years, the account would have a value of $10,062.07.

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Answer:

блина я сама не

Step-by-step explanation:

Answer: 32

Step-by-step explanation:

the min is 54 while the max is 86

86-54 is the range which is 32

Answer:

288π in³

Step-by-step explanation:

V-sphere = 4/3πr³

D = 12in   r = D/2 = 12/2 = 6 in

V = (4/3)(6)³π = (4/3)(216)π = 288π in³

If Dumisani earn $42480 per month and he splits his earnings in the ratio 7:5, then he saves $17,700 per month.

A ratio is a way of comparing two quantities or values. It expresses the relationship between two numbers or values in terms of their relative sizes or amounts.

To split Dumisani's earnings in the ratio 7:5, we need to divide his earnings into 7 + 5 = 12 equal parts.

Each part is therefore:

42480 ÷ 12 = 3,540

Dumisani saves the lesser amount, which is in the ratio of 5 parts to 7 parts.

So he saves:

5 × 3,540 = $ 17,700

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Answer:

Total profit after 10 years = [tex]\$5,277,064[/tex]

Step-by-step explanation:

Let [tex]a_n[/tex]  represent the profit in the nth year

Then [tex]a_{n+1}[/tex]  represents the profit in year  [tex]n+[/tex]1

[tex]\text{Common ratio } r = \dfrac{a_{n+1}}{a_n}[/tex]

The sum of a geometric sequence is given by
[tex]S_n = a_1 \cdot \dfrac{1 - r^n}{1-r}[/tex]

where
[tex]a_1 =[/tex] first term
[tex]r =[/tex] common ratio
[tex]n =[/tex] number of terms

Calculation of r

To calculate r we see that the profit increases by 16% every year

16% = 16/100 = 0.16

If profit increases by 0.16, then next year's profit
= this year's profit(1 + 0.16)

= this year's profit x 1.16

r = 1.16 the ratio of a term to the previous term

In this problem we are given the first term as
[tex]a_1 = 247,500[/tex] [tex]\text{ = profit in first year}[/tex]
[tex]n = 10 =[/tex] number of years

[tex]r = 1.16[/tex]

Plugging these values into equation [1] for the sum we get
[tex]\begin{aligned}S_n &= a_1 \cdot \dfrac{1 - r^n}{1-r}\\\\&= 247500 \cdot \dfrac{1-1.16^{10}}{1-1.16}\\\\& = 247500 \cdot \dfrac{-3.41143}{-0.16}\\& = 247500 \cdot 21.3215\\& = 5277064\end{aligned}[/tex]

Therefore the total profit after 10 years
= $5,277,064

5??????????????????????

Answer:

x = y = 4.24

Step-by-step explanation:

sin45 = x/6

x = 6(sin45) = 4.24

y = 6(cos45) = 4.24

Because this is a 45-45-90 isosceles triangle, x=y

Answer:

-128.31

First choice

Step-by-step explanation:

Using a calculator:

7.05(−18.2) = 7.05 x -18.2 = -128.31

Answer: To solve the inequality x − (5 − 3x) ≤ 2x − 1, we need to simplify it by first distributing the negative sign in front of the parentheses, and then combining like terms. This gives us:

x - 5 + 3x ≤ 2x - 1

4x - 5 ≤ 2x - 1

Next, we can isolate the variable on one side of the inequality by subtracting 2x from both sides:

4x - 2x - 5 ≤ -1

2x - 5 ≤ -1

Finally, we can isolate x by adding 5 to both sides and dividing by 2:

2x ≤ 4

x ≤ 2

So the solution to the inequality is x ≤ 2.

To graph this solution on a number line, we can put a closed dot at 2 and shade to the left of it, since all values less than or equal to 2 satisfy the inequality. Therefore, the correct graph is A, a number line with a closed dot at 2 shaded to the left.

Step-by-step explanation:

Answer:

5 cubed is 5 x 5 x 5 = 125.

10 squared is 10 x 10 = 100.

So, 5 cubed - 10 squared = 125 - 100 = 25.

We can also express 25 as a power of 5 by noting that 25 = 5 squared. Therefore:

5 cubed - 10 squared = 5 squared x 5 - 10 squared = 5^(2+1) - 10^(2) = 5^3 - 10^(2) = 125 - 100 = 25.

So, the answer is 5 squared or 5^2.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5 cubed - 10 squared

[tex]5^{3} - 10^{2} \\ = 125 - 100\\= 25[/tex]

Hope this helps!

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The figures converted from fraction to decimal to percent (Questions 9-14) are given as follows:

       Percent                             Decimal                              Fraction

9)      316.2%.                            3.162                                   3 4861/30000

10)    6.94%.                              0.0694                                347/5000.
11)     15.27%.                             0.1527                                 1527/10000

12)    217 2761/3367%              2.178                                    1089/500

13)    723 12/21%                       7.236                                  1809/250
14)    87%                                  0.87                                     87/100

9) Given the compound fraction:   3 4861/30000

To convert 3 4861/30000 to a decimal, we first need to convert the mixed number to an improper fraction:

3 4861/30000 = (30000*3 + 4861)/30000

= 94861/30000

To convert this fraction to a decimal, we divide the numerator by the denominator:

94861/30000 ≈ 3.162

To convert 3 4861/30000 to a percentage, we multiply the decimal by 100:

3.162 x 100 ≈ 316.2%

So, 3 4861/30000 as a percentage is approximately 316.2%

10)  Given the decimal 0.0694
To convert 0.0694 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.0694 = 694/10000

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

694/10000 = (3472)/(50002) = 347/5000

So, 0.0694 as a fraction is 347/5000.


To convert 0.0694 to a percentage, we multiply the decimal by 100:

0.0694 x 100 = 6.94%

So, 0.0694 as a percentage is 6.94%.


11) Given the decimal - 0.1527

To convert 0.1527 to a percentage, we multiply the decimal by 100:

0.1527 x 100 = 15.27%

So, 0.1527 as a percentage is 15.27%.

To convert 0.1527 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.1527 = 1527/10000

12) Given the compound percentage - 217 2761/3367%

To convert 217 2761/3367% to a decimal, we first need to convert the mixed number to an improper fraction:

217 2761/3367% = (3367*217 + 2761)/3367% = 733400/3367%

743032/3367% = 217.82001782%
217.82001782% = 2.1782001782
220.680724681% [tex]\approx[/tex] 2.178

Thus, in fraction:

2.178 = 2.178/1

Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000

= 2.178/1 x 1000/1000

= 2178/1000

= 1089/500


13) Given the compound fraction - 723 12/21%


To convert 723 12/21% to a decimal, we first need to convert the mixed number to an improper fraction:

723 12/21% = (21*723 + 12)/21% = (15195/21)%

(15315/21)% = 7.23571428571
15315/21%  [tex]\approx[/tex] 7.236


Converting 7.236 to fraction:

7.236 = 7.236/1


Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000


= 7.236/1 x 1000/1000

= 7236/1000: Divide numerator and denominator by 4

= (7236÷ 4)/(1000÷4)

= 1809/250


14) Given 0.87:

To convert 0.87 to a percentage, we multiply the decimal by 100:

0.87 x 100 = 87%

So, 0.87 as a percentage is 87%.

To convert 0.87 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:

0.87 = 87/100

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The y-intercept of the graph is located at (0, 0). So, the value of c is 0.

What is graph?

A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. The vertices represent the variables, while the edges represent the relationship between them.

To find the y-intercept of the graph of y = -7x + 140y, we need to substitute x = 0 into the equation and solve for y. This will give us the y-coordinate of the point where the graph intersects the y-axis.

Substituting x = 0, we get:

y = -7(0) + 140y

y = 140y

Simplifying the equation, we get:

139y = 0

Dividing both sides by 139, we get:

y = 0

Therefore, the y-intercept of the graph is located at (0, 0). So, the value of c is 0.

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Using Pythagorean theorem, the triangle is an acute triangle.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental result in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle.

In equation form, this can be written as:

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (also known as the legs) of the right-angled triangle.

If the triangle is not a right triangle, then the inequality [tex]c^2 < a^2 + b^2[/tex]holds for an acute triangle and [tex]c^2 > a^2 + b^2[/tex] holds for an obtuse triangle.

Using this formula, we can check if the given triangle is right, acute, or obtuse:

a = 43, b = 96, and c = 89

[tex]c^2 = 89^2 = 7921[/tex]

[tex]a^2 + b^2 = 43^2 + 96^2 = 1849 + 9216 = 11065[/tex]

Since [tex]c^2 < a^2 + b^2[/tex], we can see that:

[tex]c^2 < a^2 + b^2[/tex]

So the triangle is an acute triangle.

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Answer:

Step-by-step explanation:

1. 500

2. 10

3. 25000

the volume of the cylinder is approximately 30.19 cubic feet.

To find the volume of a cylinder, we use the formula:

V = πr²h

where V is the volume, r is the radius of the circular base, h is the height, and π is a constant that approximates the ratio of the circumference of a circle to its diameter, which is approximately 3.14.

In this case, we're given that the cylinder has a height of 3.8 feet, and a segment from one point on the circular base to another point on the base through the center labeled 3.2 feet. This segment is the diameter of the circular base, which means that the radius of the base is half of that, or 3.2/2 = 1.6 feet.

Plugging these values into the formula, we get:

V = πr²h

V = 3.14 x (1.6 feet)² x (3.8 feet)

V = 3.14 x 2.56 square feet x 3.8 feet

V = 30.1864 cubic feet

Rounding to the nearest hundredth, we get:

V ≈ 30.19 cubic feet

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The percentage interest rate added to the account at the end of the year is 1.3%

Tax is the compulsory levy paid by citizens to the government for buying goods and services.

Amount Samia invest = £3,000

Amount of interest = x

Rate of tax = 20%

Amount of tax = £7.80

So,

20% of x = £7.80

0.2x = £7.80

x = £7.80/0.2

x = £39

Percentage of interest rate:

x% of £3000 = £39

x% × 3000 = 39

x% = 39/3000

x% = 0.013

x% = 1.3%

Hence, 1.3% is the percentage of Samia investment added to the account.

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There are four numbers: 8, 15, 100 and 123.

Number is a mathematical object used to count, measure, and label. It is used in many different contexts, from everyday life to scientific research. Numbers can be represented in various forms, such as symbols, digits, and words. They are used to represent quantities, distances, time, and other concepts. Numbers can also be used to represent relationships, such as equations, which are statements that describe how two or more things are related.

To solve this problem, it is best to line the numbers up on the y axis or x axis. To multiply the numbers, start by multiplying the numbers on the y axis first. So, 8 x 15 = 120. Then, multiply the result by the number on the x axis which is 100. 120 x 100 = 12,000. Finally, multiply 12,000 by the last number on the x axis which is 123. 12,000 x 123 = 1,476,000. Therefore, the answer to the problem is 1,476,000.

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Answer:

y=30x+50

Step-by-step explanation:

3x30+50=140

5x30+50=200

The slope of the line that passes through the points (6,10) and (6,−2) is undefined.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Now, let's apply this formula to the given points (6, 10) and (6, -2). Here, x₁ = 6, y₁ = 10, x₂ = 6, and y₂ = -2. Substituting these values in the formula, we get:

slope = (-2 - 10) / (6 - 6)

Notice that the denominator is zero, which means that the line is a vertical line. In this case, the slope is undefined.

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Answer:

Step-by-step explanation:

I think y ≤ 3 - 3x

To calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

What is rate ?

In mathematics, a rate is a ratio that compares two quantities with different units. It is typically expressed as the amount of change of one quantity with respect to another quantity. Rates are often used in the context of describing how quickly or slowly something changes over time or space.

To calculate a rate, we need to divide two quantities that have different units. For example, if we want to find the rate of a car's speed, we divide the distance traveled (in miles) by the time taken to travel that distance (in hours).

The formula for rate is:

rate = quantity / time

To calculate a unit rate, we need to divide a rate by the quantity being measured. For example, if the rate is the number of miles traveled per hour, the unit rate would be the number of miles traveled in one hour. To find the unit rate, we divide the rate by 1 hour.

The formula for unit rate is:

unit rate = rate / 1

When calculating rates or unit rates, it is important to make sure that the units of the quantities being divided are consistent. If the units are not the same, we need to convert them to the same unit before performing the division.

Therefore, to calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

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Answer:

A

Step-by-step explanation:

we know that

tan x=sin x/cos x

if  

then

x belongs to the II quadrant or IV quadrant

sin 30°=

cos 30°=

therefore

tan 30°=

the angle theta has a 30-degree reference angle and is located in Quadrant II or IV

Answer:

A

Step-by-step explanation:

Based on the angles, a triangle can be classified as either acute, right, or obtuse and based on the sides, a triangle can be classified as either equilateral, isosceles, or scalene.

To classify a triangle, we need to consider both its angles and sides. Based on the angles, a triangle can be classified as either acute, right, or obtuse.

An acute triangle has all three angles measuring less than 90 degrees. A right triangle has one angle measuring exactly 90 degrees. An obtuse triangle has one angle measuring greater than 90 degrees.

Based on the sides, a triangle can be classified as either equilateral, isosceles, or scalene.

An equilateral triangle has all three sides equal in length. An isosceles triangle has two sides of equal length. A scalene triangle has all three sides of different lengths.

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The value of distance between city B to city C given by 'x' is found as: 41 miles.

Distance in air miles from city A to each city B and city C are-

City A to City B= 11

City A to city C= 29

City B to City C= X

Then,

Distance between city B to city C = distance between city A to city B +  between city A to city C

x = 29 + 11

Solving the linear equation:

x = 41

Thus, the value of distance between city B to city C given by 'x' is found as: 41 miles.

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Answer:

Step-by-step explanation:

So first you would combine like terms which in this case are 9x, -6x, y, and y

So: 9x+y-6x+y

(9x-6x)+(y+y)

3x+2y is the final answer

hope this helped

Answer:

Step-by-step explanation: