A shirt originally cost $50.97, but it is on sale for $40.78. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent.

Answer:

5

Step-by-step explanation:

When you are dividing fractions you must flip the second digit and the sign should be changed to multiplication sign.

So in this equation it will be

2 / 4/10 =

2 * 10/4=

20/4=

5

Hope you found this answer helpful

Answer:

Either [tex]-4\sqrt{6}[/tex] or [tex]4\sqrt{6}[/tex], depending on whether [tex]\alpha[/tex] is larger than [tex]\beta[/tex].

Step-by-step explanation:

The two roots (might necessarily be distinct or real) of the quadratic equation

[tex]ax^{2} + bx + c = 0[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants and [tex]a\ne 0[/tex] are

The difference between the two will be either:

[tex]x_1 - x_2 = 2\sqrt{b^{2} - 4ac}[/tex] or

[tex]x_2 - x_1 = -2\sqrt{b^{2} - 4ac}[/tex].

For this question,

[tex]x_1 - x_2 = 2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = 4\sqrt{6}[/tex], or

[tex]x_1 - x_2 = -2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = -4\sqrt{6}[/tex].

An expression is defined as a set of numbers, variables, and mathematical operations. The order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The total weight of the five cars each weighing 3,000 pounds is,

Total weight = Number of cars × Weight of each car

= 5 × 3,000 pounds

= 15,000 pounds.

= 1.5 × 10⁴ pounds

Hence, the order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.

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Answer:

$40.35

Step-by-step explanation:

First, solve for the sales price. Change the percentage into a decimal:

60% = 60/100 = 0.60

Next, multiply 0.60 with the original price, 97:

97 x 0.60 = 58.2

Subtract 58.2 from the original price:

97 - 58.2 = 38.8

Now, change the tax percentage into a decimal.

4% = 4/100 = 0.04

Multiply 0.04 with the sales price:

38.8 x 0.04 = 1.552

Add the sales price (rounded to nearest hundredth) to the sales price:

1.55 + 38.8 = 40.35

$40.35 is your answer.

~

Answer:

40.35

Step-by-step explanation:

First find the discount

97 * 60%

97 *.6 = 58.2

Subtract the discount to find the new price

97-58.20 =38.80

Next find the tax

38.80 * 4%

38.80 * .04

1.55

We add the tax to the sales price

38.8+1.55

40.35

Answer:

* The value of a1 = 945.65 ⇒ answer c

Step-by-step explanation:

* Lets revise the geometric series

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Progression:

- U1 = a  ,  U2  = ar  ,  U3  = ar²  ,  U4 = ar³  ,  U5 = ar^4

- Un = ar^n-1, where a is the first term , r is the constant ratio

 between each two consecutive terms, n is the position

 of the term

- The sum of first n terms of a Geometric series is calculate

  from Sn = [a1 (1 - r^n)]/(1 - r) , where a1 is the first term, r is the

  common ratio and n is the number of the terms

* Lets solve the problem

∵ Sn = 88,560

∵ r = 2.2

∵ n = 6

∵ Sn = [a1 (1 - r^n)]/(1 - r)

∴  88,560 = [a1 (1 - 2.2^6)]/(1 - 2.2) ⇒ simplify up and down

∴ 88,560 = [a1 (-112.379904)]/(-1.2) ⇒ simplify the fraction

∴ 88,560 = a1 (93.64992) ⇒ divide both sides by 93.64992

∴ a1 = 945.6494998 ≅ 945.65

* The value of a1 = 945.65

Answer:

2log5(x) - 2log5(4)

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression log₅(x/4)² can be expressed as,

log₅(x/4)²

= 5log(x/4)  {∵ log(aᵇ) = b log(a) }

=5[log(x) - log(4)]

= 5log(x) - 5log(4)

Hence, the expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).

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ANSWER

[tex]{(3a + 4b)}^{2} [/tex]

EXPLANATION

The given function is:

[tex] 9{a}^{2} + 24ab + 16 {b}^{2} [/tex]

This can be rewritten as

[tex]{(3a)}^{2} + 2(3 \times 4)ab + {(4b)}^{2} [/tex]

Recall that:

[tex] {x}^{2} + 2xy + {y}^{2} = {(x + y)}^{2} [/tex]

Let x=3a and y=4b,

Then,

[tex]{(3a)}^{2} + 2(3 \times 4)ab + {(4b)}^{2} = {(3a + 4b)}^{2} [/tex]

Hence the fully factored form is:

[tex]{(3a + 4b)}^{2} [/tex]

Answer:

The correct answer is (3a + 4b)^2

Step-by-step explanation:

Answer: Option C

[tex]AC = 2\pi[/tex]

Step-by-step explanation:

The arc length is calculated as

[tex]L = \theta * R[/tex]

Then

[tex]AC = \theta * R[/tex]

We know that

[tex]BC = 24\ ft[/tex]

If BC is the diameter of the circumference then the radius R is:

[tex]R = \frac{BC}{2}[/tex]

[tex]R = \frac{24}{2}[/tex]

[tex]R = 12\ ft[/tex]

Now we convert the anglo from degrees to radians[tex]\theta= 30\° * \frac{\pi}{180\°}\\\\\theta=\frac{1}{6}\pi[/tex]

Finally

[tex]AC = \frac{1}{6}\pi * 12[/tex]

[tex]AC = 2\pi[/tex]

Answer:

The length of the arc AC is 2π ⇒ answer C

Step-by-step explanation:

* Lets revise some facts in the circle

- The length of the arc is depends on the measure of the arc and the

  radius of the circle

- The length of the arc is a part of the length of the circle

- The length of the circle is 2πr

- The rule of the length of the arc = [tex]\frac{\alpha }{360}*2\pi r[/tex],

  where α is the measure of the arc

* Now lets solve the problem

- In circle P

∵ BC is a diameter

∵ BC = 24 ft

∵ The length of the radius of the circle is 1/2 the length of the diameter

∴ The length of the radius = 1/2 × 24 = 12 ft

- Ac is an arc in the circle

∵ The measure of the arc = 30°

∵ The length of the arc = [tex]\frac{\alpha }{360}*2\pi r[/tex] ,

  where α is the measure of the arc

∴ α = 30°

∵ r = 12 ft

∴ The length of the arc = [tex]\frac{30}{360}*2(12)\pi=\frac{1}{12}*(24)\pi=2\pi[/tex]

∴ The length of the arc AC is 2π

Answer:

= 15x +30y -220

Step-by-step explanation:

We can easily get another expression if we multiply each individual term, and

add together the result

30(1/2x-2)+40(3/4y-4)

= 15x-60 +30y-160

= 15x +30y -220

See attached picture below

To calculate the year in which the population of the country is expected to reach 300 million, set up and solve the provided equation involving the population function. By following the steps of solving for x, you can identify the specific year when the population is estimated to reach 300 million.

To find in what year the population can be expected to reach 300 million, we can set up the equation:

P(x) = 100 * 1.02^x = 300

Now, solve for x:

Answer: 400<=25m-85

Step-by-step explanation: 400 is how much he wants to AT LEAST make so it’ll be more than or equal to four hundred. Then he gets payed 25 dollars per law. Number of laws are unknown so its m making 25m. Lastly he has to pay 85 dollars for the law mower so that subtracts his from his pay making it 25m-85.

Answer:

slope= -2

Step-by-step explanation:

using [tex]\frac{y2-y1}{x2-x1}[/tex] you plug in the values of (-2,4) and (0,0)

=[tex]\frac{0-4}{0-(-2)}[/tex]

=[tex]\frac{-4}{2}[/tex]

= -2

Answer:

The slope is -2

Step-by-step explanation:

(4 - 0)/(-2 - 0) = 4/(-2) = -2

Answer:

Mitochondria

Step-by-step explanation:

Mitochondria is the cell organelle responsible for ATP synthesis.

Hope this helps!

Feel free to ask if you have anymore questions!

Answer: the mitochondria

Step-by-step explanation: it’s the power source of the cell. Hope this helps! :)

Answer:

10y^7

Step-by-step explanation:

Do 2(5) and do y^4 times y^3!

2(5)=10

if you have to write out what y^4 means and y^3...

How many factors of y do you have 7... so y^4*y^3=y^7

The answer is 10y^7

Answer:

A. The slope is 4.

B. The y-intercept is 8.

C. The equation is y = 4x + 8

Step-by-step explanation:

We know that there is a flat $8 cost in addition to $4 per ride. We can express this by using:

y = 8 + 4x.

y is the total cost

x is the number of rides

The question wants the equation in slope-intercept form.

Slope-intercept form of a line: y = mx + b

m = slope

b = y-intercept

y = 8 + 4x ➵ y = 4x + 8

Now that we have the slope-intercept form of the line, we can answer the problems.

A. The slope is 4.

B. The y-intercept is 8.

C. The equation is y = 4x + 8

Answer:

4.5 mg per ounce

Step-by-step explanation:

To find the average caffeine content per ounce of Pepsi, take the caffeine and divide by the ounces

54 mg/12 ounces

4.5 mg per ounce

Answer:

The average caffeine content per ounce of Pepsi is 4.5 gm

Step-by-step explanation:

Given :A 12-ounce Pepsi contains 54 mg of caffeine

To Find : What is the average caffeine content per ounce of Pepsi? Round your answer to the nearest tenth, if needed.

Solution :

A 12-ounce Pepsi contains 54 mg of caffeine.

We are supposed to find the average caffeine content per ounce of Pepsi

Amount of caffeine in 12 ounces of Pepsi = 54 mg

Amount of caffeine in 1 ounce of Pepsi = [tex]\frac{54}{12}[/tex]

                                                             = [tex]4.5[/tex]  

Hence the average caffeine content per ounce of Pepsi is 4.5 gm

Answer:

A

Step-by-step explanation:

note that the exact value of

sin ( [tex]\frac{\pi }{4}[/tex] ) = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ← the value of the x- coordinate

874.890 i think, sorry if im wrong

Answer:

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\=============================[/tex]

[tex]f(x):\\\\given:\ (-1,\ -5),\ (0,\ -1),\ (1,\ 3)\\\\m=\dfrac{3-(-5)}{1-(-1)}=\dfrac{8}{2}=4\\\\(0,\ -1)\to b=-1\\\\f(x)=4x-1\\\\---------------------------\\\\g(x)=2x-7\to m=2,\ b=-7[/tex]

Answer:

Part A: The slope of F(x) is greater than the slope of g(x)

Part B: The Y-intercept of f(x) is greater than that of g(x)

Step-by-step explanation:

To calculate the slope on f(x) we just have to take two points from the table and use the formula for slope:

[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]

Now the points to use will be:

P1:(0,-1)

P2:(1,3)

Now we just put this values into the formula:

[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]

[tex]m=\frac{3-(-1) }{1- (0)} }[/tex]

[tex]m=\frac{4}{1}\\ m=4[/tex]

Now to know the slope of g(x) we just have to remember that in the function form y=mx+c the "m" represents the slope, so if g(x)=2x-7 the slope would be "2".

Now we know that f(x) has a greater slope.

To know the greater Y intercept we just take the point in the table where x is "0" since it´s where the Y intercepts with the Y axis, and in f(x) that point is (0,-1), now in g(x) we just evaluate the function to x=0.

[tex]g(x)=2x-7\\g(x)=2(0)-7\\g(x)=-7[/tex]

The Y intercept in g(x) would be in (0,-7), since -1 is greater than -7, we can say that f(x) has the greatest Y-intercept.

Answer:

Part 1) [tex]x=6.6\ units[/tex]

Part 2) [tex]DE=16.2\ units[/tex]

Step-by-step explanation:

Part 1) Find the value of x

we know that

Triangles CDF and FDE are similar

therefore

The ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

[tex]CD/FD=FD/DE[/tex]

[tex]\frac{5}{9}=\frac{9}{2x+3} \\ \\5*(2x+3)=9*9\\ \\10x+15=81\\ \\10x= 81-15\\ \\10x=66\\ \\ x=6.6\ units[/tex]

Part 2) Find the length of DE

[tex]DE=2x+3[/tex]

substitute the value of x

[tex]DE=2(6.6)+3=16.2\ units[/tex]

Answer:

x = 6.6

Length of  =  16.2 units

Answer:

Step-by-step explanation:

By the distributive property of multiplication, 2x(x-4) = 2x^2 - 8x.  This could be re-written as 2(x^2 - 8).

Answer:

B. 2x^2-8

Step-by-step explanation:

Got Correct On MyPath.

Answer:

Step-by-step explanation:

Book A:  Mass is 1000 g + 700g + 10 g, or 1720 g.

Book B:  Mass is 1500 g + 100 + 80, or 1680 g.

Book A has the greater mass:  1720 g versus 1680 g.

The difference in mass is 1720 g - 1680 g, or 40 g

Answer:

Book A has the greater mass:  1720 g versus 1680 g.

The difference in mass is 1720 g - 1680 g, or 40 g

Step-by-step explanation:

Book A:  Mass is 1000 g + 700g + 10 g, or 1720 g.

Book B:  Mass is 1500 g + 100 + 80, or 1680 g.

Answer:  [tex]\bold{a.\quad \dfrac{1}{4}}[/tex]

Step-by-step explanation:

Since it is already given that the number is a 4 and each of the four colors only has one 4, then the probability for green is:

[tex]P=\dfrac{\text{number of green 4's}}{\text{total number of 4's}}=\dfrac{1}{4}[/tex]

If you wanted to find the probability that it is a four and it is green then you would calculate the probability as:

[tex]P=\dfrac{\text{number of 4's}}{\text{total number of numbers}}\times \dfrac{\text{number of greens}}{\text{total number of colors}}\\\\\\.\ =\dfrac{4}{40}\times\dfrac{1}{4}\\\\\\.\ =\dfrac{1}{40}[/tex]

Answer: 28

Step-by-step explanation:

7/8 = m/32

cross multiply the expression

8m = 224

m = 224/8 = 28

Hope it helped!

[tex]\huge{\boxed{m=28}}[/tex]

[tex]\frac{7}{8}=\frac{m}{32}[/tex]

Since [tex]8[/tex] is multiplied by [tex]4[/tex] to get 32, you also multiply [tex]7[/tex] by [tex]4[/tex] to get [tex]m[/tex].

[tex]7*4=28[/tex]

Answer:

Perimeter  = 2 * (x + 15)

Step-by-step explanation:

Rectangle:

l = 2/3x + 10

b = 1/3x + 5

Perimeter  = 2 * (l + b)

                 = 2 * ( 2x/3 + 10 +  1x/3 + 5)

                 = 2 * (3x/3 + 15)

                  = 2 * (x + 15)

Answer:

answer

Step-by-step explanation:

f(x) = 4x² + 1

g(x) = x² - 5

Then

(f + g)(x) = 4x² + 1 + x² - 5

             = 5x² - 4

Answer: 5x² - 4

Answer:

The correct option is B.

Step-by-step explanation:

The correct option is net.

A geometric net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or you can say that  a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.

The basic steps to determine whether a net forms a solid: are:

1. Make sure that the solid and the net have the same number of faces and that the shapes of the faces of the solid match the shapes of the corresponding faces in the net.  

2. Visualize how the net is to be folded to form the solid and make sure that all the sides are properly fit together.

Nets are helpful when we need to find the surface area of the solids....

Answer:

the answer C) 3pi/2 semoga membantu

Answer: about 34.6

Step-by-step explanation: 11 is the radius, but you need the diameter which is 22. multiply 22 by pi and divide that number by 2 since it is half a circle.