Today only, a sofa is being sold at a 32% discount. The sale price is $221.What was the price yesterday?

The percentage increase is about 16.66%.

What is a percentage increase?

The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in the percentage.

The initial amount was $18 and the final amount is $21.60.

By using the percentage increase formula, we can write

        Percentage increase = (final value - initial value)/|Final value| * 100

                                            = ((21.60 - 18)/21.60)*100

                                            = 16.66%

Hence, the percentage increase is about 16.66%.

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Answer:

B. (-2, 0)

Step-by-step explanation:

The solution of a system of equations is where the lines intersect.

Hope it helps!

Answer:The correct answer is 4 packages of hot dogs and 5 packages of hot dog buns

Explanation:

To find the least number of packages of each item the team has to buy, it is necessary to find the Least Common Multiple of the two numbers (10 and 8), which is the lowest integer that is multiple of both 10 and 8, and therefore represents the least number of hot dogs and hot dog buns the team has to buy to get the same number of the two items. Now, to find the LCM follow this process:

1. List the two numbers

10

8

2. Now, find the multiplies of each number

10 x 1 = 10 / 10 x 2= 20/ 10 x 3= 30 / 10 x 4 = 40...

8 x 1= 8/ 8 x 2 = 16 / 8 x 3 = 24 / 8 x 4 = 32 / 8 x5 = 40...

3. Notice the first common number in both, in this case, 40 because 10 x 4 = 40 and 8 x 5= 40.

This means the Least Common Multiple is 40, and therefore the team should buy 40 of each item. Additionally, this means they need to buy 4 packages of hot dogs (each package contains 10 units) and 5 packages of hot dog buns (each package contains 8 units).

Answer:

Any 4: 15

At least 4: 22

Explanation:

The number of ways to select x elements from a group of n is calculated as

So, the number of ways to select any 4 from a group of 6 is

On the other hand, the number of ways to select at least 4 is the sum of the number of ways to select 4, the number of ways to select 5, and the number of ways to select 6.

Since 6C5 and 6C6 is equal to

We get that the number of ways to select at least 4 is equal to

6C4 + 6C5 + 6C6 = 15 + 6 + 1 = 22

Therefore, the answers are:

Any 4: 15

At least 4: 22

Number of cupcakes with a baker = 24

Number of chocolate cupcakes with the baker:

\( =\tt \frac{1}{4} \: \: of \: \: 24\)

\( =\tt \frac{1}{4} \times 24\)

\( = \tt \frac{24}{4} \)

\( \color{plum}=\tt 6 \: cupcakes\)

Thus, the number of chocolate cupcakes the baker has = 6

Number of strawberry cupcakes with the baker :

\( = \tt \frac{4}{4} - \frac{1}{4} \: \: of \: \: 24\)

\( =\tt \frac{3}{4} \: \: of \: \: 24\)

\( =\tt \frac{3}{4} \times 24\)

\( = \tt \frac{72}{4} \)

\( \color{plum}=\tt 18 \: cupcakes\)

Thus, the number of strawberry cupcakes = 18

Therefore, the number of strawberry cupcakes with the baker = 18

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

the circumference is

answer: C.

Answer:

$0.04 per ounce

Step-by-step explanation:

To find the unit rate, divide $2.56 by 64 to find the price per ounce. 2.56/64 = 0.04

So, the unit rate is $0.04 per ounce

Answer:

$0.04/oz

Step-by-step explanation:

Unit rate means $ per unit, so here it would be $ per oz.

2.56/64

= (256/64)/100

= 4/100

= 0.04

So the unit price is $0.04/oz.

Answer:

28.0125 cm^2 rounded to 28.0 cm^2

Step-by-step explanation:

Area = a*b*sin(c)*1/2

Area = 7 * 13 * sin(38) * 1/2

Area = 91/2 * 0.61566...

Area = 28.0125...

Answer:

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

Area of the sphere:

\(S=4*\pi *r^2\)

Volume of the sphere:

\(V=\dfrac{4*\pi *r^3}{3}\)

\(\dfrac{S}{3} =\dfrac{V}{7} \\\\\dfrac{4*\pi *r^2}{3} =\dfrac{4*\pi *r^3}{3*7} \\\\1=\dfrac{r}{7} \\\\\\r=7\\\\great \ circle: 2*\pi* r=14*\pi\\\)

\(Volume=\dfrac{4*\pi *7^3}{3} =\dfrac{1372*\pi }{3} \approx{1436,7550...(cm^3)}\)

Answer:

Option C.  \(g(x)=(\frac{1}{3}x)^2\)

Step-by-step explanation:

Given a function to start with, extra operations that are done outside of the given function, cause vertical transformations, whereas operations that are done inside of the function cause horizontal transformations.

Transformations on the outside

Ex. \(g(x)=(x^2)-3\)  is subtracting 3 outside, so its transformation is vertical.

Transformations on the inside

Ex. \(g(x)=(x-7)^2\) is subtracting 7 inside, so its transformation is horizontal.

For any function, stretches or compressions occur by multiplying by positive numbers larger or smaller than 1.

Multiplying by numbers larger than one, quantities get larger, and multiplying by a positive number less than one, quantities get smaller.

For example, \(\$10*2 = \$20\), but \(\$10*\frac{1}{2} = \$5\)

For transformations, this intuition needs a small modification:

Multiplying on the outside

When multiplying outside of the function, things outside happen normally, and since it is happening outside, it is in a vertical direction.

Ex. Multiplying outside by 3, things get larger (stretch) vertically to 3 times as much as (300% of) normal (away from a height of zero).

Multiplying outside by \(\frac{1}{2}\) , things get smaller (compress) vertically down to \(\frac{1}{2}\) as much as (50% of) normal (toward a height of zero).

"g" is lower than "f", so it may have been compressed vertically (see alternative solution at end).

Looking at the only options with multiplication outside (A & B), option B multiplies by 3 (greater than 1), so it would stretch "f" even taller.

Option A, does compress "f" vertically (by 1/3), but doesn't compress it enough to arrive at the point (3,1) defined on function "g". Note ordered pair (3,1) on "g", meaning when you input "3", you get out "1".  

Putting 3 into the "f" function, f(3)=9.  Since one-third (the transformation in Option A) of 9 is 3, not 1, Option A doesn't compress "f" enough.

Multiplying on the inside

When multiplying inside, transformations happen horizontally, and inside things happen "backwards".

So, if multiplying inside by 4, (...normally things get bigger...) things actually get smaller (compressed) horizontally, reduced to 1/4 (the reciprocal of 4) the size (toward a horizontal distance of zero).

If multiplying by a number less than one (but positive), like \(\frac{1}{3}\) , (...things normally get smaller...) things will actually get larger (stretch) in the horizontal direction out to triple (the reciprocal of \(\frac{1}{3}\)) as much as normal.

Looking options C & D (where multiplication happens inside), both have multiplication by a positive number less than one (... normally would make things smaller...), which will stretch "f" out horizontally.

Looking at the red point (3,1), the blue function does have a height-matched point at (1,1).

Measuring horizontal distances, (3,1) is 3-units from the y-axis, whereas (1,1) is only 1-unit away.  Thus, the "g" is 3 times as far as "f", meaning a horizontal stretch outward by 3.

Answer C multiplies inside by \(\frac{1}{3}\), so it actually makes things 3 times bigger horizontally.

The correct answer is option C.

To verify, from (3,1), put 3 into the option C g(x) --  it gives "1" as an output.

\(g(x)=(\frac{1}{3}x)^2\\g(3)=(\frac{1}{3}(3))^2\\g(3)=(1)^2\\g(3)=1\\\)

This function could have been compressed vertically to obtain the red graph.

Note that f(3)=9.

The point (3,1), on the red function, is only at a height of 1 ... 1/9th the height of the blue function.  We could compress the "f" vertically by 1/9th to transform the blue function into the red function.

Vertical transformations come from operations outside, and outside things behave "normally", so to vertically compress by 1/9th, just multiply on the outside by 1/9th.

Thus, an alternative answer to transform f(x) to g(x) is \(g(x)=\frac{1}{9}(x^2)\)

Two last things:

Simplifying this function we just obtained we get \(g(x)=\frac{1}{9}x^2\)

Returning to the function that we chose for our answer in option C, \(g(x)=(\frac{1}{3}x)^2\)

\(g(x)=(\frac{1}{3}x)(\frac{1}{3}x)\)

\(g(x)=\frac{1}{9}x^2\)

Note that the transformation answer for this problem (Option C) and our alternative solution both simplify and match perfectly, so they both represent the same end result.

The range of the graphed function in this problem is given as follows:

[-9, 9].

The values of y in this function are between -9 and 9, inclusive, hence the range of the function is given as follows:

[-9, 9].

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Answer: 1.05 dollars

Step-by-step explanation:

Since an 8 minute phone call is 1.20 dollars, we divide 1.2 by 8 to get the price per minute of .15. This means we now multiply by seven to get 1.05 dollars.

Answer:

If they can be the same fraction, like 2/3 + 2/3, then yes. If they can have different denominators, like 4/5 + 1/2, then yes. Any other way is no.

Step-by-step explanation:

The same fraction (2/3 + 2/3) will equal 4/3, which is more than 1.

Different denominators (4/5 + 1/2) will equal 13/10, which is more than 1.

Nd if I'm wrong, my bad. I really tried.

A. The consumers interviewed in this manner can be considered a random sample of the population as a whole.

B. The sample is a random sample of people who go to malls.

C. It should be noted that the sample applies for just for people who go to that mall.

It should be noted that in a random sample, everyone has an equal chance of being selected.

In this case, the consumers interviewed in this manner can be considered a random sample of the population as a whole. Here, everyone had an equal chance of being picked.

In this case, the sample is a random sample of people who go to malls.

It should be noted that 95% of American households shop at malls at least once a year and that two-thirds shop at malls at least once every 2 weeks. This will give the random sample of the people.

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Answer:

2.4

Step-by-step explanation:

Use formula y2-y1/x2-x1

Points = (-2,-7) and (3,5)

5 - (-7)/3 - (-2)

NB: Negative times negative gives positive.

5 + 7/3 + 2

12/5

2.4

Slope = 2.4.

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ANSWER

Students = 110

Teachers = 22

EXPLANATION

Let the number of students be s.

Let the number of teachers be t.

There are 5 times as many students as teachers. This means that:

The sum of students and teachers is 132. This means that:

We can solve this by substitution. To do this, substitute the first equation into the second.

That is:

Recall that:

Therefore, there are 110 students and 22 teachers.

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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Answer:

25 + 5√29

Step-by-step explanation:

(I added a photo below)

First, let's find BC using the Pythagorean theorem (from ∆BCD):

\( {bc}^{2} = {25}^{2} + {10}^{2} = 625 + 100 = 725\)

\(725 > 0\)

\(bc = \sqrt{725} =5 \sqrt{29} \)

Then we see, that AB = 25 + x

So, now we can find AC:

\( {ac}^{2} = ({25 - x})^{2} - ({5 \sqrt{29} })^{2} = 625 - 50x + {x}^{2} - 25 \times 29 = 625 - 50x + {x}^{2} - 725 \)

Now we have a quadratic equation:

\( {x}^{2} - 50x - 100 = 0\)

\(d = {b}^{2} - 4 \times a \times c = ({ - 50})^{2} - 4 \times 1 \times ( - 100) = 2500 + 400 = 2900 > 0\)

\(x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{50 - 10 \sqrt{29} }{2} = 25 - 5 \sqrt{29} \)

This is a negative number and we cannot use it, since x has to be a natural number

\(x2 = \frac{ - b + \sqrt{d} }{2 a} = \frac{50 + 5 \sqrt{29} }{2} = 25 + 5 \sqrt{29} \)

Answer:

2nd option bro

Step-by-step explanation:

Answer:

3+2i

Step-by-step explanation:

just did it

Answer:

Step-by-step explanation:

Answer:

37.5mph

Step-by-step explanation:

speed= distance/time

So, 25/2/3

simplify

25*3/2

37.5.

I don't think anybody can answer your question without the full question and answers.

Nate's work to solve a math problem is shown below problem leona traveled 25 miles into 2/3 of an hour what was her average speed in miles per hour.

Step-by-step explanation: step 1 . 25 divided by 2/3 step 2 1/25 * 2/3

Answer 2/75

What was Nate's first error? he used to vision instead of multiplication tomorrow in the first piecehe also switched the divisor and the division when creating an equation to the model problem and step one he also placed the wrong term with the receptacle and step two he should not have changed division to multiplication and step two.

This is the full question for you guys to answer if it's not your full question well it was mine.

Answer:

22 1/2

Step-by-step explanation:

Approximately 17.65% of Ana's salary is withheld for taxes.

To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.

Number of hours worked per week (H) = 25 hours

Hourly wage (W) = $10

Net salary (S) = $212.50

Calculate the total earnings before taxes:

Total earnings = Hours worked * Hourly wage

Total earnings = 25 hours * $10/hour

Total earnings = $250

Determine the amount of tax withheld:

Tax withheld = Total earnings - Net salary

Tax withheld = $250 - $212.50

Tax withheld = $37.50

Calculate the percentage of salary withheld for taxes:

Percentage withheld = (Tax withheld / Net salary) * 100

Percentage withheld = ($37.50 / $212.50) * 100

Percentage withheld ≈ 17.65%

Therefore, approximately 17.65% of Ana's salary is withheld for taxes.

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Answer:

If they are parallel then the answer should be 28m

Step-by-step explanation:

Answer:

98 m

Step-by-step explanation:

105/30 = 3.5

3.5 x 28 = 98

The meaning of the absolute value in this problem is given as follows:

The temperature decreased 1.2 degrees.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

The number for this problem is -1.2, hence:

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Answer:

-4/3

Step-by-step explanation:

Moving from C(-4, 4) and D(5, -8) we see that x (the 'run') increases by 9 and that y (the 'rise') decreases by 12.  Thus, the slope m is rise/run, or

m = -12/9 = -4/3

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.