gretchen buys a sweater at a clearance sale for $35.74. The original price of the sweater was $59.99. Find the percent discount.

The total cost of the item after the sales tax of 8 % is given by the equation t = 1.08p , where p is the initial price of the item

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost price of the item be represented as t

Let the initial cost price of the item be represented as p

Now , the sales tax percentage = 8 %

So , the equation will be

The total cost price of the item t = sales tax percentage ( initial cost price of the item ) + initial cost price of the item

Substituting the values in the equation , we get

The total cost price of the item t = 8 % ( p ) + p

On simplifying the equation , we get

The total cost price of the item t = ( 8/100 ) p + p

The total cost price of the item t = 0.08p + p

The total cost price of the item t = 1.08p

Hence , the equation is t = 1.08p , where p is the initial price of the item

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The required first five terms of the sequence are 2, 10, 50, 250, and 1250.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The first five terms of the sequence, a(n), defined by the recurrence relation a(n+1) = 5a(n) and a(1) = 2, are as follows:

a(1) = 2

a(2) = 5a(1) = 5 × 2 = 10

a(3) = 5a(2) = 5 × 10 = 50

a(4) = 5a(3) = 5 × 50 = 250

a(5) = 5a(4) = 5 × 250 = 1250

Therefore, the first five representations of the sequence are 2, 10, 50, 250, and 1250.

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Barren's net worth statement exists shown to the right.

Your total worth, including both financial and non-financial assets, equals your net worth less any outstanding obligations.

Using a net worth statement, you can view your financial situation at any given time. It is comparable to a "financial snapshot," showing the dollar amounts of your assets and liabilities (liabilities or debts).

Assets - Liabilities = Net Worth is the equation for calculating net worth.

The total of Lauren Juliana's debts will be subtracted from the total of her assets to determine her net worth (cash and jewelry).

= ($ 14,692 + $ 2,575) - ($ 10,981 + $ 1,682 + $ 787)

simplifying the equation, we get

= $ 3,817

barren's net worth statement is shown to the right.

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The required total net worth of Lauren Juliana is $ 3,817.

Your all out worth, including both monetary and non-monetary resources, rises to your total assets less any remaining commitments.

Utilizing a total assets proclamation, you can see what is going on at some random time. It is equivalent to a "monetary preview," showing the dollar measures of your resources and liabilities (liabilities or obligations).

Resources - Liabilities = Total assets is the condition for working out total assets.

The complete of Lauren Juliana's obligations will be deducted from the absolute of her resources for decide her total assets (money and adornments).

= ($ 14,692 + $ 2,575) - ($ 10,981 + $ 1,682 + $ 787)

working on the situation, we get

= $ 3,817

desolate's total assets articulation is displayed to one side.

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By using the formula for the perimeter, we will get that the width of the pool is 20 meters.

Remember that for a rectangle of length L and width W, the perimeter is given by the formula:

P = 2*(L + W)

In this case, we know that the perimeter is 90m, and the length is 25m, then we know that:

P = 90m

L = 25m

Replacing that in the formula above we will get:

90m = 2*(25m + W)

now we can solve this for W.

90m/2 = 25m + W

45m - 25m = W

20m = W

The width of the pool is 20 meters.

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The equation of the least squares regression line for the data set is (b) ŷ = -2.984x + 112.38

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

Volunteer 15 11 22 35 18 41 27 18

Trees 77 99 4 11 44 14 2 90

Using a graphing calculator, we have the following calculation summary

The regression equation is represented as

ŷ = bX + a

Where

b = SP/SSX = -2213.88/741.88 = -2.98416

a = MY - bMX = 42.63 - (-2.98*23.38) = 112.37978

So, we have

ŷ = -2.98416X + 112.37978

Approximate

ŷ = -2.984x + 112.38

Hence, the equation  is ŷ = -2.984x + 112.38

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Radical form is rather simple. It refers to the form of a number or algebraic expression where the number or expression is contained under a radical. The answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].

Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

A radical notation is an expression that makes use of a root, such as the square or cube root.

The fundamentals of radical form are simple. When a numerical or algebraic expression is under a radical, the term refers to that version of the expression. To improve that, we can manipulate a number or an algebraic expression in radical form to convert it to simplest radical form.

[tex]\text { Simplify }-x \sqrt{2} 8+10 \sqrt{6} 3 x^2:-\\\\8 \sqrt{2} x+30 \sqrt{6} x^2 -x \sqrt{2} \cdot 8+10 \sqrt{6} \cdot 3 x^2 \\\\& =-8 \sqrt{2} x+30 \sqrt{6} x^2\end{aligned}$$[/tex]

Therefore, the answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].

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Answer:

If she played on the swings for 24 minutes and on the slide for 13, then she was at the playground for 37 minutes.

If she left the playground at 4:28, then you want to subtract 37 minutes from 4:28.

4:28 - :37 = 3:51.

She arrived at the playground at 3:51

Step-by-step explanation:

Hope it helps! =D

Answer:

3:51 p.m.

Step-by-step explanation:

Add the two amounts of time:

24 minutes + 13 minutes = 37 minutes

She was at the park for 37 minutes. She arrived at the park 37 minutes before 4:28 p.m.

Now we subtract 37 minutes from 4:28 p.m.

Remember that 1 hour = 60 minutes, so when you borrow 1 hour to do the subtraction, you add 60 minutes to the minutes of the time of day.

Borrow 1 hour from 4 hours as 60 minutes. You end up with 3 hours. Then add the 60 minutes to the 28 minutes to get 88 minutes.

4:28 p.m. is the same as 3:88 p.m.

     4:28 p.m.                             3:88 p.m.

-     0:37                 ----->         -  0:37

-------------------                       -------------------

                                                  3:51 p.m.

Answer: 3:51 p.m.

The 3 year simple interest at 4% will be $38,192.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

The principal amount = $34,100

Interest rate = 4%

Time = 3 years Now,

Since, We know that;

Where, A is final amount.

P is principal amount.

r is interest rate.

t is time.

Substitute all the values, we get;

A = $34,100 (1 + 4/100)³

A = $34,000 (104/100)³

A = $34,000 × 104/100 × 104/100 × 104/100

A = $38,192

Thus, The Simple interest will be $38,192.

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Answer:

Step-by-step explanation:

3:12 7:28

The means are the second and third terms in the proportion.

The extremes are the two outside terms.

12 and 7 are the means.

(3 and 28 are the extremes.)

So thre answer is D.  12 and 7.

Answer:

Step-by-step explanation:

Answer:

  See attached

Step-by-step explanation:

You want the solution to the inequality -12x < -48 shown on a number line.

The solution to the inequality is found by dividing by the x-coefficient

  -12x < -48

  x > 4 . . . . . . . divide by -12

When working with inequalities, you need to know that multiplying or dividing by a negative number reverses the inequality symbol.

The value x=4 is not included in the solution set, so an open circle is plotted at that point. All values of x greater than x=4 are included in the solution set, so the number line is shaded to the right of the open circle.

The graph of the solution is shown in the attachment.

__

Additional comment

Often, you can avoid multiplying or dividing an inequality by a negative number by rearranging it. Here, adding 12x+48 to both sides makes it be ...

  48 < 12x

Now, you can divide by 12 without worrying about the inequality symbol:

  4 < x . . . . . same as above

Therefore , the solution of the problem of expression comes out to be

9.12 x 10 ^-2.

An algebraic expression must be checked via replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is comparable to 6, since 6 + 6 equal 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Given : 0.0912 in scientific notation

=> 9.12 /100

By using scientific notation

=> 9.12 × 10^-2

=> 9.12 x 10 ^-2

So, we get 9.12 x 10 ^-2 as the scientific notation for the given expression

Therefore , the solution of the problem of expression comes out to be

9.12 x 10 ^-2.

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The 95% confidence interval for the proportion of people who prefer Candidate A is given as follows:

(0.438, 0.522).

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The parameters for this problem are given as follows:

[tex]n = 550, \pi = \frac{264}{550} = 0.48[/tex]

Hence the lower bound of the interval is obtained as follows:

[tex]0.48 - 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.438[/tex]

The upper bound of the interval is obtained as follows:

[tex]0.48 + 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.522[/tex]

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Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b.  For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).

Given the equation 17v = 62, we can take the logarithm base 17 of both sides:

log(17^v) = log(62)

v*log(17) = log(62)

Dividing both sides by log(17) gives us:

v = log(62) / log(17)

This is the solution for v, the unknown variable in the equation.

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Therefore ,answering the offered question, we can state that the figure's surface area is SA = 2(9 11+11 9+11 * 11), which equals SA = 638 in2.

Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional shape. You may compute the contact area of a cube with six square faces by adding together their individual areas. Alternatively, you can use the following formula to name the box's dimensions: Surfaces (SA) = 21 h + 2 lw + 2 hw. A tri shape's surface area is calculated as the total amount of space it occupies.

Here,

Front = rear = 11*11

top = bottom = 9*11

sides = 11*9;

SA= 2(911+119+1111)

SA=2(9999 +121)

SA = 2(319) (319)

SA = 638 in²

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It's a good idea to utilize the 13 cm measurement that Martha used for her scale illustration. This is because it would be simpler to measure the flag's stripes. The American flag has 13 stripes, thus each one is 1 centimeter wide.

Flags can be as big as 20 feet by 38 feet, although most are between 3 feet by 5 feet and 5 feet by 8 feet in size. The standard size for an American flag flown outside a home is 3 x 5.

A flag's rectangular design assures that even a moderate breeze would cause it to move, making it readily apparent to everyone else. Additionally, the shape is efficient in terms of production costs, according to a number of flag designers.

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Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25[tex]b^{2}[/tex] + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25[tex]b^{2}[/tex]  = -(5)(5) * [tex]b^{2}[/tex]

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * [tex]b^{2}[/tex] +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

To rewrite the radical expression "the seventh root of x to the thrid power" as an expression with a rational exponent, we need to use the property that allows us to rewrite a root of a power as a power with a rational exponent. This property states that "the nth root of x to the mth power" is equal to "x to the m/nth power".

Using this property, we can rewrite "the seventh root of x to the thrid power" as "x to the 3/7th power". Therefore, the correct answer is "x to the 3/7th power".

The other answer choices are not equivalent to the original expression. "x to the seven thirds power" is not a valid expression because "thirds" is not a unit of measurement. "x^21" is not equivalent to the original expression because the base and exponent are not related in the same way as in the original expression. "x^4" is not equivalent to the original expression because the base is the same but the exponent is not.

Answer: x to the 3/7th power

Step-by-step explanation:

so you dont have to read a essay to get the answer lol

Answer:

Below

Step-by-step explanation:

(27500 - 8700) >= 150 x       where x is the number of 150 kg containers

a. The model represents exponential growth.

b. The annual percentage increase is 3%.

c. After 2390 decades the population was about 590000.

The formula for exponential growth is [tex]y = y_₀.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_₀.e^{(-kt)}.[/tex]

Given, The population P(in thousands) of Austin Texas during a recent decade is approximated by [tex]y = 492(1.03)^t[/tex].

The model represents exponential growth as time can not be negative.

The annual percentage increase in the model [tex]y = 492(1.03)^t[/tex] is 3%

as 1.03×100% = 103%.

The time when the population was about 590000 since the beginning of a decade is,

[tex]590000 = 492(1.03)^t[/tex].

[tex](1.03)^t = 590000/492[/tex].

[tex](1.03)^t = 1199.1869[/tex].

[tex]log_{1.03}1.03^t = log_{1.03}1199.1869[/tex].

t = 2389.84 Or 2390 decades.

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The range of the function will be;

⇒ { 4, 2, 0, - 2, - 4 }

or, { - 4, - 2, 0, 2, 4 }

A relation between a set of inputs having one output each is called a function.

Given that;

The relation is,

⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)

Now,

Since, The relation is,

⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)

We know that;

The range of relation is the value of y.

Hence, The range of relation = { 4, 2, 0, - 2, - 4 }

Thus, The range of the function will be;

⇒ { - 4, - 2, 0, 2, 4 }

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A single fraction will be;

⇒ 1/(y + 12)

And, Domain of this expression is,

⇒ Domain = (-∞, ∞) - { 12 }

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)

Now,

Since, The expression is,

⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)

Simplify the expression as;

⇒ 4 (y - 2) - 3 (y + 2) / (y-2) (y+2) + 12 / (y² - 4)

⇒ 4y - 8 - 3y - 6 / (y² - 4) + 12 / (y² - 4)

⇒ (y - 14) / (y² - 4) + 12 / (y² - 4)

⇒ (y - 14 + 12) / (y² - 4)

⇒ (y - 12) / (y- 12) (y + 12)

⇒ 1/(y + 12)

Hence, A single fraction will be;

⇒ 1/(y + 12)

And, Domain of this expression is,

⇒ Domain = (-∞, ∞) - { 12 }

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Answer: The function G(x) = [x] returns the greatest integer less than or equal to x. This means that for any value of x, G(x) will be the largest integer that is less than or equal to x. For example, G(3.5) = 3 and G(5) = 5.

The function R(x) = x/+2, x is any real number, this function returns the value of x incremented by 2. In other words, it is the result of adding 2 to x.

On the other hand, the graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1, this means that for every change of 1 unit in the x-axis, the y-axis will change by 1 unit as well.

When we compare the two graphs, we can see that the graph of R(x) is shifted up 2 units from the graph of G(x) . If the graph of G(x) is thought of as the "ground", the graph of R(x) is "floating" two units above it. Also, the graph of R(x) is continuous while the graph of G(x) is not.

To sum up:

-The graph of G(x) is a step function, which start at the negative infinity and jumps up to the next integer at every point.

The graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1

-R(x) is always two units above G(x) , and is a continuous function, while G(x) is not.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step: Solve−3x−4y=15for x:

−3x−4y=15

−3x−4y+4y=15+4y(Add 4y to both sides)

−3x=4y+15

−3x

−3

=

4y+15

−3

(Divide both sides by -3)

x=

−4

3

y−5

There were 8 roses on each bushes

Gemma has 3 rose bushes

Each bush has the same number of roses

She picks 4 of the roses

After picking the roses, there are 20 left in the bushes

Therefore the number of rose on each bush can be calculated as follows

20 + 4

= 24

24/3

= 8

Hence there are 8 roses in each bush

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ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.

There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.

X now has 300 mg of sodium in it.

[tex]x = 300[/tex]

Y also has 450 mg of sodium in it.

[tex]y = 450[/tex]

Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.

Let the number of frozen dinners be "b," and the number of soup cans be "a."

ax + by = 6000

a(300) + b(450) = 6000 .

Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation

[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]

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Answer:

Domain is all real numbers (basically any number)

Step-by-step explanation:

Step 1: Simplify the expression first

y = 2(x+1)-(3x-2)

y = 2x + 2 -3x + 2

y = -x + 4

Step 2: Observe the graph

y = -x + 4 is simply a linear graph with a negative fixed gradient of -1, with a y-intercept of 4.

Step 3: Identify the domain

For linear graphs, domain is all real numbers.

(No restrictions on the graph according to question)