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LUCKY_DIMON [66]

3 years ago

8

A pair of pants was 40% off the original price. The sale resulted in a $36 discount. What was the original price before the sale

?

1 answer:

Mama L [17]3 years ago

8 0

Answer:

$90.00

Step-by-step explanation:

40% of What is 36?

40/4 = 10 (10%)

36/4 = 9 (9 is 10% of the answer we are looking for)

Multiply both answers (9 and 10) by each other.

You get 90

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Identify the standard form of the equation by completing the square.

OLEGan [10]

Answer:

$\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Step-by-step explanation:

<u>Given equation</u>:

$4x^2-9y^2-8x+36y-68=0$

This is an equation for a horizontal hyperbola.

<u>To complete the square for a hyperbola</u>

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

$\implies 4x^2-8x-9y^2+36y=68$

Factor out the coefficient of the x² term and the y² term.

$\implies 4(x^2-2x)-9(y^2-4y)=68$

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

$\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2$

$\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36$

Factor the two perfect trinomials on the left side:

$\implies 4(x-1)^2-9(y-2)^2=36$

Divide both sides by the number of the right side so the right side equals 1:

$\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}$

Simplify:

$\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Therefore, this is the standard equation for a horizontal hyperbola with:

center = (1, 2)
vertices = (-2, 2) and (4, 2)
co-vertices = (1, 0) and (1, 4)
$\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}$
$\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)$

4 0

2 years ago

An experiment is performed where a 4-sided die is rolled and then a 3-color spinner is spun. The possible outcomes for each even

Mrac [35]

1,R 2,R 3,R 4,R 1,B 2,B 3,B 4,B 1,Y 2,Y, 3,Y

6 0

4 years ago

(a) A poll of 2,298 likely voters was conducted on the president’s performance. Approximately what margin of error would the app

SashulF [63]

Answer:

a.d= 0.0204

b.[0.4728;0.5072]

c.A.Yes, the confidence interval contains .50.

Step-by-step explanation:

Hello!

you have a sample of 2298 voters and the sample proportion of voters that agree with the president's performance is 49%, which means that the sample proportion of voters that oppose the president will be 51%.

a) The margin of error for a 95% CI to estimate the proportion of voters that approve the president.

The formula for the CI for the proportion is:

^ρ± $Z_{1-\alpha/2}$ *√(^ρ(1-^ρ))/n

The margin of error "d" is half the amplitude of the interval (or, to put it simply, is what you subtract and add to the sample proportion)

d= $Z_{0.975}$ *√(^ρ(1-^ρ))/n

d= 1.96*√(0.49(1-0.49))/2298

d= 0.0204

b) Construct a 90% CI for the true proportion

[^ρ± $Z_{1-\alpha/2}$ *√(^ρ(1-^ρ))/n]

[0.49±1.648*√(0.49(1-0.49))/2298]

[0.4728;0.5072]

c) The CI interval I've made in b. is for the voters that agree with that president, but since you want to see if the proportion of people on favor/opposing is 0.50 whether the interval is made with the information of the people who agree or oppose doesn't change the answer.

The interval contains 0.50 if you were to make the hypothesis that the proportion of people who agree with the president H₀:ρ=0.50, at complementary confidence level α: 0.10, you can say that the proportion of people who agree with the president is 50%. Then you can also say that the proportion of opposition voters is 50%.

I hope you have a SUPER day!

8 0

4 years ago

La diferencia entre 4 veces un numero y 158 es 36 encontrar el numero

guajiro [1.7K]

Datos a considerar

el numero = x

la diferencia entre el numero y 158 = x - 158

4 veces un numero = 4x

entonces 4x - 158 = 36 -----------> 4x = 36 + 158 ----> x = 194 div 4

x = 48,5

8 0

3 years ago

Mademuasel [1]

DB is a median (given). It goes from vertex point D to midpoint B.

The point B is the midpoint of segment AC. So B cuts AC into two equal halves: AB and AC
Meaning AB = AC

AC = AB+BC ... segment addition postulate
AC = AB+AB ... substitution; replace BC with AB (valid because AB = AC)
AC = 2*AB
2*AB = AC
2*AB = 50 ... substitution; replace AC with 50
2*AB/2 = 50/2 ... divide both sides by 2
AB = 25 which is the answer

6 0

3 years ago