The price of a pair of shoes after 8% sales tax was added was $77.76. Find the original price before sales tax

After solving the equation, the value obtained for x will be equal to 1.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

4 times x plus one-half equals one-half times x plus 4.

Let's write it in mathematical form,

4x + 1/2 = 1/2x + 4

Now, solve the equation for x,

4x - 1/2x = 4 - 1/2

(8x - x)/2 = (8 - 1)/2

7x/2 = 7/2

x = (7 × 2)/(2 × 7)

x = 14/14

x = 1

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Answer: The Tri-State Pick 3 lottery game offers a choice of several bets, including a "box" bet where you choose a three-digit number and win if the number you choose has the same digits as the winning number, in any order. The expected payoff for a $1 bet on the box is $83.33.

To find this expected value, we need to consider all the possible ways that the winning number could be chosen and calculate the probability of each outcome. Since the winning number is chosen at random, each of the 10 possible digits (0 through 9) is equally likely to be chosen for each of the three positions in the winning number.

Since the box bet pays off if the digits of your chosen number match the digits of the winning number, regardless of their order, the number of winning combinations is equal to the number of ways to arrange the three digits of the winning number. This is equal to 3! (3 factorial), which is equal to 6.

Since there are a total of 10 possible digits for each position and the winning number has three positions, there are a total of 10 x 10 x 10 = 1000 possible winning numbers. Of these, 6 will pay off for a box bet, so the probability of winning a box bet is 6/1000 = 0.006.

Since the expected value of a bet is equal to the probability of winning multiplied by the payoff, the expected value of a $1 bet on the box is 0.006 x $83.33 = $0.05. Therefore, the expected payoff for a $1 bet on the box is $0.05.

Answer: [tex]2^4 \times 5[/tex]

Step-by-step explanation:

[tex]80=2 \times 40\\\\80=2 \times 2 \times 20\\\\80=2 \times 2 \times 2 \times 10\\\\80=2 \times 2 \times 2 \times 2 \times 5\\\\80=2^4 \times 5[/tex]

When Ms. Hall is buying Ms. Ward some gifts for Christmas as described in the problem,

the Constant: $90 and $7

the Coefficient: $7

the Equation:  $90 + $7x

Information form the problem shows that

one big gift that will cost $90

some small gifts that cost $7 each

the constant in this case is the price of the gifts

$90 and $7

the coefficient is $7

the equation is

$90 + $7x

where x is the number of the small gifts

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Fátima tiene un total de $ 160, Gabriel tiene un total de $ 690 y José tiene un total de $ 230.

En este problema tenemos a tres personas, Fátima, Gabriel y José, que reúnen un total de $ 1.080. A continuación, traducimos las variables y ecuaciones asociadas a la situación:

x - Cantidad de dinero de Fátima.

y - Cantidad de dinero de Gabriel.

z - Cantidad de dinero de José.

Ecuaciones: Fátima, Gabriel y José tienen un total de $ 1080.

x + y + z = 1080

Gabriel tiene 3 veces lo que José tiene.

y = 3 · z

Fátima tiene $ 70 menos que José.

x = z - 70

A continuación, resolvemos el sistema de ecuaciones lineales:

x + y + z = 1080

(z - 70) + 3 · z + z = 1080

5 · z - 70 = 1080

5 · z = 1150

z = 1150 / 5

z = 230

x = z - 70

x = 230 - 70

x = 160

y = 3 · z

y = 3 · 230

y = 690

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Answer: $16 = 4s + 3g

Step-by-step explanation:

s = shoes

g = games

TRUE: The given contrapositive statement are correct,

If m ≤ 3, then, m < 5.

For the stated conditional statement -

If m ≤ 3, then, m < 5.

Then, contrapositive statement for the given statement will be

(m < 5)' ⇒ (m ≤ 3)'

That is;

(m > 5) ⇒ (m > 3)

That is, if m> 5 then, m > 3, which is true.

Thus, the contrapositive statement for the given conditional statement is true.

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Answer: 68600

hope it helps!

Answer:

Step-by-step explanation:

The statements that are true regarding undefined terms are;

The reason these statements above are true are as follows:

Examples of undefined terms includes a point, a plane, a line and a set

A point is for representing a position in space. It has no dimensions

Therefore, the statement, A point has no length or width is true

A plane is defined as an interconnected set of points that lay on the same flat surface, and extends infinitely along the surface in all directions

A line is defined as an infinite set of points that are arranged in straight path and extends without end in opposite directions

Therefore, the statement, a line consists of an infinite number of points is true

Therefore, a plane can be considered as being made up of an infinite set of lines that are located on a flat surface

Therefore, the statement, a plane consists of an infinite set of lines is true

Net profit is a company's profit after all expenses have been deducted. What remains after deducting fixed costs from gross profit is the net profit.

Subtracting the cost function from the revenue function yields the profit function. Assume that the profit is denoted by P(x), the revenue is denoted by R(x), the cost is denoted by C(x), and x is the quantity of goods sold. Consequently, the profit function is denoted by P(x) = R(x0 - C) (x).

Total Revenue - Total Expenses = Net Profit

A company that sells online has a $350,000 revenue and a $50,000 cost of products sold.The net income formula is defined as the difference between the total revenue earned and the total costs.Total revenue minus all costs equals net income.

The money a corporation makes after deducting interest, operational costs, and taxes over a specific time period is known as net profit.Profit After Tax is another name for Net Profit (PAT).

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Examples of unit rates are Dollars per pound calories and earnings per hour. The rest is not the unit rate.

What is the unit rate?

An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. 70 yards in 10 seconds and 7 yards in 1 second are both ratios, although only the latter is a unit rate.

Earnings per hour are a unit rate since it is calculated for an hour.

Dollars per pound calories is a unit rate.

Serving $25.50 for 5 gallons is not a unit rate, the cost is for 5 gallons. If the cost is for 1 gallon then it will unit rate.

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Answer:  A= 52cm  B= 94mm  C= 9m  D= 17cm

Step-by-step explanation:

A) You first need to find the missing sides by doing

11-9= 2

and 15-9= 6

you then add it all together

6+2+9+9+15+11=52cm

B) You first need to find the missing sides by doing

25-18=7

and 22-6= 16

you then add it all together

25+22+18+16+7+6=94mm

C) You first need to find the missing sides by doing

0.5+1=1.5 then 2.5-1.5=1

and 1.2+0.8=2 then 2-0.5=1.5

you then add the numbers all together

1+1.5+0.8+1+0.5+0.5+1.2+2.5=9m

D) You first need to find the missing sides by doing

2.5+1= 3.5 then 3.5-2=1.5

and 1.5+2.5=4 then 5-4=1

you then add all the numbers together

2.5+2.5+1.5+1+5+2+1+1.5=17cm

Answer:

D

Step-by-step explanation:

if you move the preimage on the image you can see that the two figures are equals

Answer:

Step-by-step explanation:

the answer is 11/12

we conclude at the 1% level of significance that the claim is true by accepting H₀

What is Hypothesis?

A hypothesis outlines your expectations for the results of your investigation. It is a speculative, untested response to your research question.

Given,

n = 81

x bar = 7

s= 2

Here, a doctor claims that people are atmost 6 pound over weight

H₀ : μ ≤ 6 versus

H₀ : μ > 6 versus

Now,

The Test Stastistic is

t = x bar - μ / s√n

t = 7-6/2√81

t = 4.5

let ∝ = 0.10, then p value = 0.000

p value >∝

yes, conclude the claim is true by accepting H₀

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Answer:

x = 98

Step-by-step explanation:

Solve for x:

(x - 14)/7 = 12

Multiply both sides of (x - 14)/7 = 12 by 7:

(7 (x - 14))/7 = 7×12

(7 (x - 14))/7 = 7/7×(x - 14) = x - 14:

x - 14 = 7×12

7×12 = 84:

x - 14 = 84

Add 14 to both sides:

x + (14 - 14) = 14 + 84

14 - 14 = 0:

x = 84 + 14

84 + 14 = 98:

Answer:  x = 98

a) The value of P(Y∩P) =0.23

b) The value of (Y|P) = 0.34

c)  The value of (P|Y) = 0.27

d) The value of P(Y/P') = 0.68

What is Venn diagram?

A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.

Given that there are two events Y and P.

P(Y) = 0.57

P(P) = 0.5

P(Y∪P) = 0.84

The formula of intersection is  P(Y∩P)  = P(P) + P(Y) - P(Y∪P)

Putting P(Y) = 0.57, P(P) = 0.5, P(Y∪P) = 0.84

P(Y∩P)  = 0.5 + 0.57 - 0.84

P(Y∩P) = 0.23.

b)

P(Y|P) = P(Y) - P(Y∩P)

P(Y|P) = 0.57 - 0.23

P(Y|P) = 0.34

c)

P(P|Y) = P(P) - P(Y∩P)

P(P|Y) = 0.5 - 0.23

P(P|Y) = 0.27

d) P(Y/P') = P(Y∩P') / P(P')

P(Y/P') = P(Y|P)/[1 - P(P)]

P(Y/P') = 0.34/(1- 0.5)

P(Y/P') = 0.68

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Answer:

Answers below

Step-by-step explanation:

1. The value 550 represents the initial balance in the account, which means the account started with $550.

2. 528.28

425.00 x  2.7% x 9 = 103.275

Then we add 103.275 to the initial deposit of $425.00

425.00 + 103.275 = 528.275

Therefore the answer is $528.28

3. The answer for this one is  f(n) = 56 + 3(n − 1)

So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex]

Therefore, its 56 + 3(n − 1)

4. For this one we solve for r and using a calculator its r = 0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

1) The given equation is 687.5=550(1+0.05t)

Here, amount=$687.5, principal (initial balance)=$550 and rate of interest =0.05×100 =5%

So, the value 550 represents the initial balance in the account, which means the account started with $550.

2) Given that, principal=$425.00, time period=9 years and rate of interest=2.7%

We know that, S.I=(P×T×R)/100

= (425×9×2.7)/100

= 103.275

Amount=103.275+425

= 528.275

≈ $528.28

3) The given arithmetic sequence is 56, 59, 62, 65, 68,.…

Here, first term (a)=56 and common difference=59-56=3

We know that, general form of arithmetic sequence is aₙ=a+(n-1)d

Now, f(n)=56+(n-1)3

4) The given equation is 816=600(1+9r)

1+9r =816/600

1+9r =1.36

9r=0.36

r=0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

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Answer: y = 5x

Step-by-step explanation:

Answer:

24 Inches

Step-by-step explanation:

The length of a piece of wood that uses 8 nails as required in the task content is; 24 inches.

What is the length of a piece of wood that uses 8 nails?

It follows from the task content that the length of a piece of wood that uses 8 nails is to be determined from the task content.

Answer:

should be angle 7, 1, and 3

hope i could helpppp

Answer: 1 , 7 , 3

Step-by-step explanation:

The angles that habe the same measurement of angle 5 are;

1 , 7 , 3

Because the lines are parallel, these angles correspond to angle 5.

Answer:

5

Step-by-step explanation:

2 +3 = 5    

The odds ratio for the association between exposure to emf's and breast cancer would be (11/5) / (108/436) = 2.2.

1. Calculate the odds of exposure for cases: 11/5 = 2.2

2. Calculate the odds of exposure for controls: 108/436 = 0.25

3. Divide the odds of exposure for cases by the odds of exposure for controls: 2.2/0.25 = 8.8

4. Finally, the odds ratio for the association between exposure to EMF's and breast cancer is 2.2.

The odds ratio for the association between exposure to EMF's and breast cancer can be calculated by dividing the odds of exposure for cases by the odds of exposure for controls. To calculate this, first take the number of cases exposed (11) and divide it by the number of cases not exposed (5). This will give the odds of exposure for cases (2.2). Second, take the number of controls exposed (108) and divide it by the number of controls not exposed (436). This will give the odds of exposure for controls (0.25). Finally, divide the odds of exposure for cases (2.2) by the odds of exposure for controls (0.25). This will give the odds ratio for the association between exposure to EMF's and breast cancer (2.2).

Odds ratio = (11/5) / (108/436) = 2.2

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The value of y₂, y₃ and y₄ in the linear function are -21, -26 and -31 respectively.

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, to find the missing values in the table we have to use the equation of the linear function.

y = mx + b

let's find m.

using (4, -16) and (8, -36)

m = slope = -36 + 16 / 8 - 4

m = -20 / 4

m = -5

Hence, let's find y-intercept using (4, -16).

y = -5x + b

-16 = -5(4) + b

-16 + 20 = b

b = 4

Therefore, the equation is y = -5x + 4.

Let's find y₂, y₃ and y₄

y₂ = -5(5) + 4 = -25 + 4 = - 21

y₃ =  -5(6) + 4 = -30 + 4 = -26

y₄ =  -5(7) + 4 = -35 + 4 = - 31

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By solving a linear equation, it can be calculated that

Each club can order 21.1 cupcakes if they both have the same amount of

money to spend

What is a linear equation?

Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign

A one degree equation is called linear equation

Let the number of cupcakes ordered by each club be c

The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee

Total amount spent = $(13 + 3.35c)

The orchestra would like to order cupcakes from Publix at $2.90 each

and a $22.50 order fee

Total amount spent = $(22.5 + 2.90c)

By the problem,

The linear equation is

13 + 3.35c = 22.5 + 2.90c

3.35c - 2.90c = 22.5 - 13

0.45c = 9.5

c = 21.1

This solution is not viable as the number of cupcakes must be an integer not a decimal.

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The length of BC is approximately 5.72 miles and the length of AC is approximately 12.67 miles.

Let's represent the length of the side opposite angle A "BC" and the length of the side adjacent to angle A "AC". We can then use the sine function to find BC:

sin(A) = BC / AC

Substituting the given values, we get:

sin(24°) = BC / 14

We can use a calculator or look up the value of sin(24°) to get:

sin(24°) ≈ 0.406

Solving for BC, we get:

BC = 14 * sin(24°) ≈ 5.72

To find AC, we can use the cosine function:

cos(A) = AC / AC

Substituting the given values, we get:

cos(24°) = AC / 14

We can use a calculator or look up the value of cos(24°) to get:

cos(24°) ≈ 0.913

Solving for AC, we get:

AC = 14 x cos(24°) ≈ 12.67

Thus, BC is about 5.72 miles long while AC is about 12.67 miles in length.

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A line passes through point (1, 6) and has a slope is y=8x-14 We want to write the equation of the line that passes through (1, -6) and has a slope of 8 in slope-intercept form

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope (8), we can immediately plug that into the equation

So far, the equation of the line is:

y=8x+b

Now we need to find b

The line passes through the point (1, -6), which means that the point is a solution to the equation; when plugged into the equation, it'll create a true statement. This can help us find unknown variables, like b

Substitute 1 as x and -6 as y in the equation to solve for b

-6=8(1)+b

Multiply

-6=8+b

Subtract 8 from both sides

-14=b

Substitute -14 as b into the equation

y=8x-14

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The numbers of the atoms of each element are;

6 atoms of carbon, 12 atoms of oxygen

12 atoms of hydrogen, 6 atoms of oxygen

6 atoms of carbon, 12 atoms of hydrogen, 6 atoms of oxygen

12 atoms of oxygen

In a chemical reaction, there is the combination of the atoms of the reactants and a consequent recombination as the products are formed. In accordance with the law of the conservation of mass, we know that the number of atoms before reaction must be equal to the number of atoms after reaction.

Now we have to look at the atoms and count up the number of atoms of each element in each of the compounds and this is how we are able to obtain the number of each atom as shown above.

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From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.

A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.

Given, linear equation is

[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]

Hence, the x equals to -8.

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