Grady marks down some $4.09 pens to $3.59 for a week and then marks them back up to $4.09. Find the percent of increase and the percent of decrease to the nearest tenth. Are the percents of change the same for both price changes? If not, which is a greater change

Craig practiced 15 hours

Nicki practiced his drums for 11 hours, and considering Craig practiced 4 hours more than Nicki, Craig practiced his drums for 15 hours.

Let's start by figuring out how many hours Nicki practiced his drums. We know that Nicki practiced his drums 5 hours less than Marshal, and Marshal practiced his drums 16 hours. This means that Nicki practiced his drums for 16-5= 11 hours.

Next, we move on to figuring out how many hours Craig practiced his drums. The question tells us that Craig practiced his drums 4 hours more than Nicki. Since we now know that Nicki practiced his drums for 11 hours, this means that Craig practiced his drums for 11+4= 15 hours.

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C

G= - 4t + 100 ( add 4t to both sides )

G + 4t = 100 ( subtract G from both sides )

4t = 100 - G ( divide both sides by 4 )

t = [tex]\frac{100-G}{4}[/tex]

t=(G-100)/4 is the equation that correctly solves the given equation for t. So, option C is the correct answer.

Given that, the number of gallons of water in the pool changes with time t according to the equation.

The given equation is G = -4t + 100.

We need to solve the given equation for t.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Now, G = -4t + 100

⇒4t=G-100

⇒t=(G-100)/4

Therefore, t=(G-100)/4 is the equation that correctly solves the given equation for t. So, option C is the correct answer.

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first part: 5% of $94 is 0.05*94=$4.70

second part: 80% of 45 questions is .8*45 = 36

After investing $400 in an account with 3% interest compounded annually, the balance after one year will be $412.

The question is asking how much the balance will be after investing $400 in an account that pays 3% interest compounded annually after one year. The formula to calculate compound interest is [tex]A = P(1 +\frac{ r}{n})^{nt[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. As the interest is compounded annually, n is 1.

For this question, we substitute P with $400, r with 0.03 (3% as a decimal), n with 1 (since it's compounded annually), and t with 1 (since it's compounded for one year).

Now, our formula looks like this: [tex]A = 400(1 + \frac{0.03}{1})^{1*1[/tex] = 400(1 + 0.03) = 400 * 1.03 = $412.

Therefore, after one year, the balance in the account will be $412.

Answer:

Step-by-step explanation:

s=5?

t=5?

3(5) - 3(5) +3

(15) -15 = 0

0 + 3 = 3

The value of 3s - 3t + 3 given that s - t = 5 is 18.

In this problem, we are given that s - t = 5. Now we have to find the value of 3s - 3t + 3. What we can do is factor out the '3' from 3s - 3t, then we can see it as 3(s - t) + 3. Our equation becomes 3 * 5 + 3 which simplifies to 15 + 3, and then 18.

So, the value of 3s - 3t + 3 given that s - t = 5 is 18.

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To break even, the Waxmans need to make $5000 in profit. This can be achieved by selling 500 square yards of carpet, considering they make $10 profit per square yard.

In order for the Waxmans to break even, they will need to cover their startup costs through the profits they make selling carpet. The profit made per square yard of carpet sold is the selling price ($18) minus the cost per square yard ($8), which equals $10. Therefore, to break even, they would need to sell $5000 worth of profit. This means selling $5000/$10 = 500 square yards of carpet.

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Answer:

D. two possible amounts by which the dimensions were increased

Step-by-step explanation:

The solutions to the equation (6 + x)(9 + x) = 88 represent two possible amounts by which the dimensions of the rectangular patio were increased.

The solutions to the equation (6 + x)(9 + x) = 88 represent two possible amounts by which the dimensions of the rectangular patio were increased. The equation represents the area of the larger patio, which is found by multiplying the increased length (6 + x) by the increased width (9 + x), and setting it equal to 88. By solving the equation, you can find the possible values of x, which represent the amounts by which the dimensions were increased.

Let Upper Level = x

Middle level = 2x+40

Lower level = 3x-50

The sum of those 3 has to equal 15,002 seats.

X + (2x+40) + 3x-50) = 15, 002

Simplify the left side by combining the like terms:

6x - 10 = 15,002

Add 10 to each side:

6x = 15,012

Divide both sides by 6 to solve for x:

X = 15012 / 6

X = 2502

The upper level is X , so has 2,502 seats.

Middle level = 2x +40 = 2(2502) +b40 = 5004 + 40 = 5,044 seats

Lower level = 3x-50 = 3(2502) -50 = 7506 - 50 = 7,456 seats

The number of seats in the upper level is required.

The number of seats the upper level has is 2502.

Let the number of upper level seats be [tex]x[/tex]

The lower level seats are [tex]3x-50[/tex]

The middle level seats are [tex]2x+40[/tex]

The total number of seats are 15002

So,

[tex]x+3x-50+2x+40=15002\\\Rightarrow 6x-10=15002\\\Rightarrow x=\dfrac{15002+10}{6}\\\Rightarrow x=2502[/tex]

The number of seats the upper level has is 2502.

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Answer:

Option C.

Step-by-step explanation:

A polynomial is defined as

[tex]P(x)=ax^n+bx^{n-1}+...+c[/tex]

where, [tex]ax^n[/tex] is leading term.

If n is even and a is positive, then the end behavior is up and up.

If n is even and a is negative, then the end behavior is down and down.

If n is odd and a is positive, then the end behavior is down and up.

If n is odd and a is negative, then the end behavior is up and down.

The given polynomial is  

[tex]P(x)=2x^7-8x^6-3x^5-3[/tex]

In this polynomial leading term is [tex]2x^7[/tex].

a=2 and n=7, which is odd.

Since n is odd and a is positive, therefore the end behavior is down and up.

We want to analyze the end behavior of a graph of a given polynomial by the degree and leading coefficient.

The correct option is C: "The leading term is 2x^7. Since n is odd and a is positive, the end behavior is down and up."

The general rule to know this is:

If the degree is even, then the two arms of the polynomial go in the same direction, then if the leading coefficient is positive, both ends go up.

If the leading coefficient is negative, both ends go down.

In the case where the degree is odd, each end go in a different direction.

If the leading coefficient is positive, the first end (the one for the negative values) go down, and the other end goes up.

When the leading coefficient is negative the inverse happens.

Here we have the polynomial:

p(x) = 2*x^7 - 8*x^6 - 3*x^5 - 3

We can see that the degree is 7, so it is odd, and the leading coefficient is positive (is equal to 2).

Then the first end goes down and the second goes up, thus the correct option is C.

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Trisha has 18 nickels and 14 dimes in her bag worth $2.80. The solution involves solving equations simultaneously to find the number of each coin.

Trisha has 18 nickels and 14 dimes. Let's break it down:

Let N represent the number of nickels and D represent the number of dimes.

We know that N + D = 32 (the total number of coins).

We also know that 0.05N + 0.10D = 2.80 (the total value in dollars).

Solving these two equations simultaneously gives N = 18 and D = 14.

Therefore, Trisha has 18 nickels and 14 dimes.

Answer:

180%

Step-by-step explanation:

Answer:

160piein^3

Step-by-step explanation:

Answer: The correct option is (B) [tex]\left(5,\dfrac{1}{2}\right).[/tex]

Step-by-step explanation: We are given to find the midpoint of the line segment shown in the figure.

From the figure, we see

a line segment with co-ordinates of the endpoints (5, 4) and (5, -3).

We know that

the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) is given by

[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]

Therefore, the co-ordinates of the line segment shown is given by

[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right)=\left(\dfrac{5+5}{2},\dfrac{4-3}{2}\right)=\left(5,\dfrac{1}{2}\right).[/tex]

Thus, (B) is the correct option.

Answers

1.  1,364

2. x⁴ + 2x - 6

3.  x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4.  x⁴ - 7x³  - 21x² + 63x -108

5.  a(n-1) + 1.4

6. 3/(2× 2ⁿ⁻¹)

Explanation

Q1

Σ4ⁿ = 4¹ + 4² + 4³ + 4⁴ + 4⁵

      = 4 + 16 + 64 + 256 + 1024

       = 1,364

Q2. What is (f−g)(x)?

f(x)=x4−3x2+5x−7

g(x)=x3−3x2+3x−1

(f−g)(x) = (x⁴−3x²+5x−7

) - (x³−3x²+3x−1)

             =x⁴ + 2x - 6

3. What is (f⋅g)(x)?

f(x)=x2−5x+4

g(x)=x3−1

(f⋅g)(x) = (x³−1)(x²−5x+4

)

           = x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4. Let f(x)=x2−9 ​ and g(x)=x2−7x+12 .

What is (fg)(x)?

(fg)(x) = (x²−9)(x²−7x+12)

           = x⁴ - 7x³  - 12x² - 9x² + 63x -108

            =  x⁴ - 7x³  - 21x² + 63x -108

5. What is the recursive rule for the sequence?

4.4, 5.8, 7.2, 8.6, 10, …

5.8 = 4.4 = 1.4,     10 - 8.6 = 1.4  The sequence is an AP where the common difference is 1.4 and the first term a is 4.4.

We and 1.4 to the previous term in order to get the next term.

an = a(n-1) + d

     = a(n-1) + 1.4

6. Enter the explicit rule for the geometric sequence.

3/2, 3/4, 3/8, 3/16, 3/32, …

common ratio r, = 4/3 ÷3/2 = 1/2

First term a, = 3/2

an =  arⁿ⁻¹

     = (3/2)(1/2)ⁿ⁻¹

      = 3/(2× 2ⁿ⁻¹)

If s, r and t are given right lines in the same plane and with condition

s⊥t  and r⊥t we can conclude that s║r ( s and r are parallel).

Good luck!!!

The conclusion is;

line r and s are parallel lines.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

We have lines r, s and t in the same plane.

And s⊥t and r⊥t.

That means,

The conclusion is line r and s are parallel lines.

Therefore, r and s are parallel lines.

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The values are always interpreted as (x1, y1) and (x2, y2) in order from left to right, so in this case, (7,2) are (x1, y1) and (15, 8) are (x2, y2)

X1 = 7

Y1 = 2

X2 = 15

Y2 = 8

a = 0.19

0.38/2 = 0.19

Look at the pictures (examples)

m∠1 = m∠6 → answer: none

m∠2 = m∠3 → answer: none

m∠2 = m∠C → answer: none

D. 27.6 is your answer

c or a !!!!!!!!!!!!!!!!!!!

14/25 , 29/50 , 53/100 , 13/20 and 3/5

Solution:

Put your numbers first in decimal form;

0.56 , 0.58 , 0.53 , 0.65 and 0.60

Then arrange them from the least to greatest;

0.53 , 0.56 , 0.58 , 0.60 and 0.65

Then revert your values to fraction form to give a final answer:

53/100 , 14/25 , 29/50 , 3/5 , 13/20

Answer:

The correct answer is C. $5.07

Step-by-step explanation:

Answer:

5.07

Step-by-step explanation:

the correct answer should be (b) 6 is extraneous.

If you look at the second row of the solution you see (x-6) as a factor in one of the denominators. That's a problem: if 6 were a solution this denominator would become 0. But denominators being 0 is bad (undefined), so while 6 comes out of the algebraic manipulation as a solution, it is invalid, or extraneous.

-3 is a fine solution.

The correct statement is B that is "6 is an extraneous solution because it creates a zero in the denominator" as the step 2 has x-6 as a term of denominator of the RHS.

The lower number in a fraction is known as the denominator. It demonstrates the equal division of something into parts. Four would be the denominator, for instance, if the fraction was 3/4. For instance, the fraction bar is the line that separates the numbers 4 and 5, and 4/5 is a fraction. Here, the numerator is the number above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or number of parts out of the whole, is represented by a numerator. The bottom number alone serves as the denominator.

Here,

The right option is B, which means that "6 is an extraneous solution because it creates a zero in the denominator," since the RHS's step 2's denominator term is x-6.

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Answer:

B

Step-by-step explanation:

The two points going to the left that are roots are

(-3,0) and (-1,0)

So the factors are (x + 3)(x + 1)

The points going to the right are

(2,0)(3,0)

So the factors are (x - 2)(x - 3)

The answer is B

the answer to your question is B

To find the number, divide 34,400 by 344%

To solve this problem, we need to translate the phrase into an equation and solve for the unknown number.

The phrase "344% of what number is 34,400" can be translated as 344% * x = 34,400.

To solve for x, we divide 34,400 by 344% or 3.44.

Therefore, the number is 10,000.

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To find the number, divide 34,400 by 344% (or 3.44), resulting in the number 10,000.

To solve this problem, we need to find what number 344% of is equal to 34,400. Here's how we can do it step by step:

Step 1:

Translate the problem into a mathematical equation.

Let's denote the unknown number as [tex]\( x \)[/tex]. The problem translates to:

[tex]\[ 344\% \text{ of } x = 34,400 \][/tex]

Step 2:

Rewrite the percentage as a decimal.

[tex]\[ 344\% = \frac{344}{100} = 3.44 \][/tex]

Step 3:

Write the equation using the decimal form of the percentage.

[tex]\[ 3.44 \times x = 34,400 \][/tex]

Step 4:

Solve for [tex]\( x \).[/tex]

[tex]\[ x = \frac{34,400}{3.44} \][/tex]

Step 5:

Perform the division.

[tex]\[ x = 10,000 \][/tex]

So, 344% of 10,000 is 34,400. Thus, the unknown number is 10,000.

The area of a circle with a radius of 7.5 cm is 176.81 cm² to two decimal places, and the area of a semicircle with a radius of 8.2 cm is 104.8 cm² to one decimal place.

To work out the area of a circle with a radius of 7.5 cm using π (pi) as 3.142, we use the formula A = πr².

First, square the radius: 7.5 cm × 7.5 cm = 56.25 cm².
Then multiply by π: 56.25 cm² × 3.142 = 176.8125 cm².
The area to 2 decimal places is 176.81 cm².

For the area of a semicircle with radius 8.2 cm, we first calculate the area of a full circle and then divide by 2.
Full circle area: 8.2 cm × 8.2 cm × 3.142 = 209.5852 cm².
Area of the semicircle: 209.5852 cm² ÷ 2 = 104.7926 cm², which rounds to 104.8 cm² to 1 decimal place.

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The area of the circle is [tex]177.16[/tex] [tex]cm^2[/tex] and the area of semicircle is [tex]105.0[/tex] [tex]cm^2[/tex].

The area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.

1. For the first question, the radius [tex]\( r \)[/tex] is given as 7.5 cm. Using the formula for the area of a circle:

[tex]\[ A = \pi r^2 \][/tex]

[tex]\[ A = 3.142 \times (7.5 \text{ cm})^2 \][/tex]

[tex]\[ A = 3.142 \times 56.25 \text{ cm}^2 \][/tex]

[tex]\[ A = 177.1625 \text{ cm}^2 \][/tex]

Rounded to two decimal places, the area of the circle is [tex]\( A = 177.16 \text{ cm}^2 \)[/tex].

2. For the second question, the figure is a semicircle with a radius of 8.2 cm. The area of a semicircle is half the area of a full circle.

Therefore, using the formula for the area of a circle and then dividing by 2:

[tex]\[ A_{\text{semi}} = \frac{1}{2} \pi r^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times (8.2 \text{ cm})^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times 67.24 \text{ cm}^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 210.0944 \text{ cm}^2 \][/tex]

[tex]\[ A_{\text{semi}} = 105.0472 \text{ cm}^2 \][/tex]

Rounded to one decimal place, the area of the semicircle [tex]\( A_{\text{semi}} = 105.0 \text{ cm}^2 \)[/tex].

Answer: [tex]4\frac{1}{7} ft[/tex]

Step-by-step explanation:

Area (A): [tex]36\frac{1}{4} = \frac{4(36)+1}{4} = \frac{144+1}{4} = \frac{145}{4}[/tex]

Length (L): [tex]8\frac{3}{4} = \frac{4(8)+3}{4} = \frac{32+3}{4} = \frac{35}{4}[/tex]

width (w): W

A = L x W

[tex]\frac{145}{4}[/tex] = [tex]\frac{35}{4}[/tex] x W

[tex](\frac{4}{35})[/tex][tex]\frac{145}{4}[/tex] = [tex](\frac{4}{35})[/tex][tex]\frac{35}{4}[/tex] x W

[tex]\frac{4(145)}{35(4)} = \frac{145}{35} = \frac{5(29)}{5(7)} = \frac{29}{7} = W[/tex]

[tex]\frac{29}{7} = \frac{7(4) + 1}{7} = 4\frac{1}{7}[/tex]

[tex]x^2+52=\\\\x^2-(-52)=\\\\(x-\sqrt{-52})(x+\sqrt{-52})=\\\\(x-2\sqrt{13}i)(x+2\sqrt{13}i)[/tex]