(02.01 MC)
Eugene calculates how long it will take to earn his first million dollars if he earns an average gross pay of $975.00 per week. He
rounds his answer to 20 years. Is Eugene's answer viable?
Yes, Eugene can use traditional rounding rules to show the time required to earn the full million dollars.
No, Eugene would need to round down to show the time required to earn the full million dollars.
Not enough information to determine viability.
Yes, Eugene needs to round the years up to the nearest whole number to show the time required to earn the full million dollars.

Tameka can paint a house in 4 hours, and Rasheeda can paint the same house in 6 hours. If Tameka and Rasheed paint the house together, the can finish it in 2.4 hours.

This problem can be solved using unitary method.

Using this method, the required value is obtained by multiplying the quantity with the unit value.

Tamika can paint a house in 4 hours. It means:

In 1 hours Tamika can paint 1/4 house

Rasheeda can paint a house in 6 hours. It means:

In 1 hours Rasheeda can paint 1/6 house

If  Rasheeda and Tameka work together, they can paint 1/4 + 1/6 = 5/12 house in 1 hour.

It means, for 1 house, Rasheeda + Tameka need 12/5 = 2.4 hours

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Yes, because as x increases, y increases and because all of the pairs represent the same ratio.

When two sets of provided numbers change in proportion, the ratios are said to be directly proportional if they do so in the same direction.

If two ratios or fractions are equivalent, it may be shown using the proportion formula. By dividing the supplied numbers, we may determine the value that is missing. You may write the percentage formula as a: A and d are the extreme terms, and b and c are the middle terms, according to the formula b::c: d = a/b = c/d.

Yes, because as x increases, y increases.

Yes, because all of the pairs represent the same ratio.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 4000\left(1+\frac{0.04}{4}\right)^{4\cdot 10}\implies A=4000(1.01)^{40} \implies A \approx 5955.45[/tex]

Answer:

$5955.45

Step-by-step explanation:

We can use the formula to find the sum of the money, when we calculate the amount of money according to compound interest.

Before we getting ready to solve the sum, we have to keep these points in our mind.

Formula to find the sum of money after compound interest is:

[tex]\sf S = X ( 1 + r )^n[/tex]

Here,

S = Sum of money

X = Amount of money deposited

r = Interest rate

n = Time ( in years )

Let us solve it now.

[tex]\sf S = X ( 1 + r )^n\\\\\sf S = 4000 ( 1 + \frac{4}{100}*\frac{1}{4} )^4^0\\\\\sf S = 4000 ( 1 + \frac{4}{400} )^4^0\\\\\sf S = 4000 ( 1 + 0.01 )^4^0\\\\\sf S = 4000 ( 1.01 )^4^0\\\\\sf S = 5955.45[/tex]

Answer:

1.6 oz

Step-by-step explanation:

8 oz to spread into 5 bowls = 8/5

8/5=1.6

Answer:1.6

Step-by-step explanation: First your going to divide 8/5 but do it like this-8.0 divided by 5= 1.6 so that gonna be your answer. Hope it was helping you.

Answer:

B.  x <= -17 or x >= 15

Step-by-step explanation:

To solve this inequality, we need to split the absolute value expression into two separate cases, one for each possible sign of the expression within the absolute value bars.

For the case where the expression within the absolute value bars is positive, we can remove the absolute value bars and solve the resulting inequality as follows:

1/4(x+1) >= 4

(x+1) >= 16

x >= 15

For the case where the expression within the absolute value bars is negative, we can again remove the absolute value bars and solve the resulting inequality as follows:

-1/4(x+1) >= 4

-(x+1) >= 16

x <= -17

Combining these two cases, we get that the solution to the inequality is:

x <= -17 or x >= 15

So, the correct answer is B.

The principal sum refers to the amount payable in one sum in the case of accidental death and, in some cases, accidental dismemberment.

The amount paid in the case of accident or medical insurance in the event that the insured person dies, loses a limb, or loses sight is known to be as principal sum. It means that the principal sum amount is the maximum amount paid to the insured person for all injuries resulting from the accident.

Thus, the principal sum is the amount insured to be paid by the company to the beneficiary in the case of the insured individual's accidental death as well as in the loss of limb or sight.

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He drove 828 miles on the first day.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = distance Pete traveled on the second day

If on the first day, he traveled 1.5 times as far as he did the second day, then

distance Pete traveled on the first day = 1.5x

If Pete traveled 1,380 miles in two days, the the sum of the distance he traveled in two days is equal to 1380.

x + 1.5x = 1380

Simplify the equation and solve for the value of x.

x + 1.5x = 1380

2.5x = 1380

x = 552

distance Pete traveled on the second day = 552 miles

distance Pete traveled on the first day = 1.5(552) = 828miles

Therefore, he drove 828 miles on the first day.

The problem seems incomplete. The question must be

"Pete traveled 1,380 miles in two days. The first day, he traveled 1.5 times as far as he did the second day. How many miles did he drive on the first day?"

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The solution set for the expression is {0,  π/2,  π}.

According to the question,

Here we have the expression:

tan([tex]\frac{3\pi }{4}[/tex] - 2x) = -1

First, we know that:

tan([tex]\frac{3\pi }{4}[/tex]) = -1

So, if x = 0, the equation is true and it means that x = 0 is a solution.

And the tangent function is defined as a period of pi.

This means that:

tan(x) = tan(x -  π) = tan(x - 2*π) etc.

Then if x = π/2 and x = π also are solutions, so we conclude that the solution set for the given expression is: {0,  π/2,  π}.

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The following are the value of angles in the rectangle:

m∠HMJ and m∠JMK lie on the straight line HK

126° + m∠JMK = 180° {sum of angles on a straight line}

m∠JMK = 180° - 126°

m∠JMK = 54°

∆JMK is an Isosceles triangle so; m∠JKH = m∠JKM = m∠KJM

2m∠JKH + 54° = 180° {sum of interior angles of a triangle}

m∠JKH = (180° - 54°)/2

m∠JKH = 63°

m∠HLK = 90° one interior angle of rectangle

m∠HJL and m∠KJM are complimentary which implies they sum up to 90°

m∠JKH = m∠KJM = 63° so;

m∠HJL = 90° - 63°

m∠HJL = 27°

m∠LHK and m∠JKH are alternate angles and they are equal so;

m∠LHK = 63°

m∠JLK and m∠HJL are also alternate angles so;

m∠JLK = 27°

In conclusion, we have the angles of the rectangle as m∠JMK = 54°, m∠JKH = 63°, m∠HLK = 90°, m∠HJL = 27°, m∠LHK = 63°, and m∠JLK = 27°.

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Answer:

Original: 0.24958333333... | Rounded Up: 0.25

Step-by-step explanation:

unit price = total price divided by quantity
5.99 divided by 24 = 0.24958333333...
We can round this to 0.25

2 1/2 = 5/2 = 2.5

Its 2.5 in decimals

The composition of the 8.5 cm diameter, 7 mm thick medal metal alloy, which is composed of gold silver and bronze are as follows;

1) The mass of the gold in the alloy is 0.81% × 39.72 cm³ × 19.3 g/cm³ ≈ 6 g

2) The total cost of the medal is about €540.95

An alloy is made by combining two or more different metals to produce a metal of desired qualities such as strength, durability or to prevent corrosion.

1) The percentage of silver by volume = 92.5%

Percentage of copper = 6.69%

Percentage of gold = 0.81%

Volume of the medal = π × (8.5 cm)²/4 × 7 mm ≈ 39.72 cm³

Volume of the gold ≈ 0.81% × 39.72 cm³ ≈ 0.32 cm³

Mass = Density × Volume

Mass of the gold ≈ 19.3 g/cm³ × 0.32 cm³ ≈ 6 grams

2) The mass of the silver in the medal is found as follows;

Mass = 92.5% × 39.72 cm³ × 10.5 g/cm³ ≈ 385.78 g

Mass of the copper is found as follows;

Mass = 6.69% × 39.72 cm³ ×8.9 g/cm³ ≈ 23.65 g

The total cost of the medal is therefore;

Total cost ≈ 6 × 42.55 + 385.78 × 0.74 + 23.65 × 0.0075 ≈ 540.95

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The equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday is C = 24 - 4t

Number of chocolate violet eats each night = 4

Number of chocolate originally in the box = 24

Number of chocolate remaining = C

Number of days after violet birthday = t

Number of chocolate remaining = Number of chocolate originally in the box - (Number of chocolate violet eats each night × Number of days after violet birthday)

C = 24 - (4 × t)

C = 24 - 4t

In conclusion, the equation which represents violet's remaining chocolate after her birthday is C = 24 - 4t

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Answer:

Isha Chawla the viewer's attention to detail and the game name is the viewer's of the viewer's the viewer's of math and science and time of year for you are interested please contact me homework for the same to the viewer's attention to the seller if

The relation to each other on the vertical number line,

For any two numbers x, y where y>x.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.

According to the questions,

In vertical number line,

x is placed in the bottom and is y placed on the top on vertical

number line.

⇒ y>x

For example,

If x = 3 and y = 4.

Then, y>x.

Hence the required relation is y>x.

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If j(x) = 5^(x - 3), using laws of exponents to solve the given expression [j(x + h) - j(x)]/h gives; [j(x + h) - j(x)]/h =  [(5^(x - 3))(5^(h) - 1)]/h

We are given the function as;

j(x) = 5^(x - 3)

Now, we want to solve the expression;

[j(x + h) - j(x)]/h

This gives us;

j(x + h) = 5^(x - 3 + h)

Thus, our expression is now;

[j(x + h) - j(x)]/h = [5^(x - 3 + h) - 5^(x - 3)]/h

Now, according to laws of exponents, we know that;

y³ × y² = y³ ⁺ ²

Thus;

5^(x - 3 + h) = 5^(x - 3) × 5^h

Therefore;

[5^(x - 3 + h) - 5^(x - 3)]/h = [(5^(x - 3))(5^(h) - 1)]/h

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The expression that represents the total amount that Ellie paid is 1.2614x

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

Bill = x

Tax applied to bill = 6%

Tip = 19%

The expression that represents the total amount that Ellie paid is then represented as

Expression = Bill * (1 + Tax applied to bill) * (1 + Tip)

Substitute the known values in the above equation, so, we have the following representation

Expression = x * (1 + 6%) * (1 + 19%)

So, we have

Expression = x * 1.2614

This gives

Expression = 1.2614x

Hence, the expression is 1.2614x

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The mean of the distribution is 61.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given, the median and mode of a dataset are 45 and 13 respectively

They have given that the median of the distribution is 45

They have given that the mode of distribution is 13

To find the mean of the distribution, let's consider

The relationship between the mean, mode, and the median is given by

Mode = 3 Median - 2 Mean

Mean = (3* 45 - 13)/2

Mean = 122/2

Mean = 61

Therefore, the mean of a distribution if its median and mode are 45 and 13 respectively is 61.

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The equation of the exponential function is 2ˣ with the given properties.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

An exponential function of base e has the form f(x) = [tex]ae^{(bx)}[/tex], where a and b are constants.

The horizontal asymptote of this function is at y=1, which means that a=1.

The y-intercept is the point where the graph crosses the y-axis, which is at x=0. The value of f(0) is the y-intercept of the graph, and since it is less than 2, we have [tex]f(0) = 1\times e^{(b\times0)}[/tex] = 1 < 2.

The graph also contains the point (-1, 2), which means that f(-1) = 2. Substituting the values we have found for a and f(0) into the equation for f(x), we get [tex]f(-1) = 1\times e^{(b\times(-1))}[/tex] = 2.

Solving this equation for b, we find that b = ln(2).

Substituting this value for b into the equation for f(x), we get f(x) = [tex]e^{(ln(2)x)} = 2^x[/tex].

This is the equation of the exponential function with the given properties.

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Answer:

The Chinese traditional culture should first include thought, writing and language, and then the six arts, namely, rites, music, archery, imperial skills, calligraphy and mathematics, and then the calligraphy, music, martial arts, quyi, chess, festivals and folk customs derived from the rich life. Traditional culture is something that is closely related to our lives, integrated into our lives, and we enjoy it without knowing it.

Chinese traditional culture should include: ancient Chinese literature, ancient poetry, words, music, Fu, folk music, folk drama, quyi, Chinese painting, calligraphy, couplets, lantern riddles, shooting, wine, Xiehouyu, etc.; Traditional festivals (according to the lunar calendar) are: the first day of the first lunar month the Spring Festival (lunar New Year), the fifteenth day of the first lunar month the Lantern Festival, April 5 Qingming Festival, Qingming Festival before and after the cold food Festival, May 5 Dragon Boat Festival, July 7 Qixi Festival, August 15 Mid-Autumn Festival, the twelfth Lunar month thirty New Year's Eve and various folk activities; Ancient Chinese natural sciences, including the traditional calendar, and the traditional cultures of various regions and ethnic minorities living in China are also part of traditional Chinese culture.

Answer:

1/3

Step-by-step explanation:

This equation is in slope-intercept form, which describes the slope and y-intercept of a linear equation.

[tex]y=mx+b[/tex] is how we describe such equations where "m" is the slope and "b" is the y-intercept. In this case, the slope is 1/3 because that is equivalent to the value of "m".

There are 125 four-digit even numbers that can be formed using the digits 2, 3, 5, 17, and 9.

To calculate the number of 4-digit even numbers that can be formed with the given digits, we can use the formula n^r, where n is the number of digits and r is the number of digits in the number. In this case, n = 5 and r = 4, so we can calculate 5^4 = 625.

Since we are looking for even numbers, we must eliminate any numbers that end in an odd digit.  This means that we must eliminate the numbers with the digits 3 and 5 as the last digit. Therefore, 625 - (3*25) - (5*25) = 625 - 75 - 125 = 425.

Now we must eliminate any numbers that do not begin with an even digit. This means that we must eliminate the numbers with the digits 3 and 9 as the first digit. Therefore, 425 - (3*25) - (9*25) = 425 - 75 - 225 = 125. Therefore, there are 125 four-digit even numbers that can be formed with the given digits.

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Answer:

x=-1

Step-by-step explanation:

2*2x =4x and 2*-4=-8

now we have 4x-8=-10x+6

To solve for x we can first subtract 8 from both sides of the equation to isolate the x terms on one side. This gives us 4x = -10x + 14. Then, we can add 10x to both sides to isolate the x term on one side and get 14x = 14. Finally, dividing both sides by 14 will give us the value of x as -1.

Hope this helps!

Answer:

x = 1

Step-by-step explanation:

2(2x-4)=-10x+6

expand the bracket

4x-8 = -10x+6

collect like terms

4x+10x = 8+6

14x = 14

divide by the coefficient of x

14x÷14 = 14÷14

x = 1

In the first row there are 7 chairs, and common difference is 2 implies that, the sequence in increasing order.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

Given that,

The definition of the arithmetic sequence is given by,

an = a₁ + (n-1) d       (1)

Also, in first row, there are 7 chairs.

And after that row two more chairs are behind the first row.

Implies that, a₁ = 7 and d = 2.

Substitute this value in equation (1),

aₙ = 7 + (n - 1) 2

aₙ = 7 + 2n - 2

an = 5 + 2n

For the value of n the number of chairs can be found.

Hence, the arithmetic sequence is in increasing order.

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Answer:

d

Step-by-step explanation:

Answer:

The error occurred in the second step

Step by step answer:

In order of operations the power or the exponentials before the the addition

Answer:

y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

The slope is the change in y over the change in x.

[tex]\frac{0-8}{1 - -2}[/tex] = [tex]\frac{-8}{1+2}[/tex] = [tex]\frac{-8}{3}[/tex]

The slope (m) is [tex]\frac{-8}{3}[/tex]

Use the slope and one of the points to find the y intercept

I will use the point (1,0)

x = 1

y = 0

m = [tex]\frac{-8}{3}[/tex]

y = mx + b  Substitute in what you know and solve for b

0 = [tex]\frac{-8}{3}[/tex](1) + b

0 = [tex]\frac{-8}{3}[/tex] + b  Add [tex]\frac{8}{3}[/tex] to both sides

[tex]\frac{8}{3}[/tex] = b

The y-intercept (b) is [tex]\frac{8}{3}[/tex]

y = mx + b

y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]

The graph of the function y = - (5/3)x² is a parabola openning downwards

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, A function y = - (5/3)x².

Its parent function is y = x², which is a parabola opening upwards having a vertex at (0, 0).

Now, The graph of the function y = - (5/3)x² is a parabola that opens downwards having a vertex at (0, 0) but a bit steeper as the value of a is less than - 1.

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The value of x is x = 36.

What is similar triangles?

Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects include all equilateral triangles and squares with any side length. To put it another way, if two triangles are similar, then their corresponding angles and sides are congruent and equal in size.

Given:

ΔLMN ∼ ΔPON

We have to find the value of x.

As the triangles ΔLMN and ΔPON are similar, so the sides of the triangles are in proportion.

⇒  LM / PO = MN / ON

⇒    42 / 14 = x / 12

⇒            3 = x / 12

⇒            x = 36

Hence, the value of x is x = 36.

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The area of the path is A(x) = 459 + 88x + 4x²

The area of a rectangle can be found by multiplying the length and width of the rectangle.

This can be done as shown below:

Area = length*width

We can find the width of the path as shown below:

Let the width of the path be x.

The length of the pool is 27 meters.

The width of the pool is 17 meters.

The area of the pool including the path is given as:

A(x) = (27 + 2x)(17 + 2x)

A(x) = 459 + 54x + 34x + 4x²

A(x) = 459 + 88x + 4x²

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The function g(x) for the input values are g(-2) = -19, g(0) = -5 and g(3) = -14

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

A function and a set of input values

The equation of the function is given as

g(x) = –2x2 + 3x – 5

Express properly

So, we have

g(x) = –2x² + 3x – 5

The input values are given as

–2, 0, and 3.

Substitute  –2, 0, and 3 in g(x) = –2x² + 3x – 5

So, we have the following representations

g(-2) = –2(-2)² + 3(-2) – 5

Evaluate

g(-2) = -19

Next, we have

g(0) = –2(0)² + 3(0) – 5

g(0) = -5

Lastly, we have

g(3) = –2(3)² + 3(3) – 5

g(3) = -14

Hence, the values are g(-2) = -19, g(0) = -5 and g(3) = -14

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