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2 years ago

5

While shopping at a clearance sale, Samantha finds a $60.00 dress on sale for 25% off. Samantha also has a 50% off coupon. Which

statement correctly summarizes her savings?

1 answer:

aksik [14]2 years ago

8 0

Answer:

Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction

Step-by-step explanation:

Samantha will be offered the choice of using the coupon or the sale discount. If she chooses tht 50% coupon, her savings will be $30. If she chooses the marked sale discount, her savings will be $15.

The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.

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2 years ago

F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find <em>a</em>, compare the coefficients of x³:

$\implies a=3$

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

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To find <em>c</em>, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

<u>Zero Product Property</u>

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

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9 months ago

You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. As part of your study, you r

Alenkasestr [34]

Answer:

90% confidence interval for the population mean is between a lower limit of $92.18 and an upper limit of $107.82.

Step-by-step explanation:

Confidence interval for a population mean is given as mean +/- margin of error (E)

mean = $100

sd = $25.20

n = 30

degree of freedom = n-1 = 30-1 = 29

confidence level (C) = 90% = 0.9

significance level = 1 - C = 1 - 0.9 = 0.1 = 10%

critical value (t) corresponding to 29 degrees of freedom and 10% significance level is 1.699

E = t×sd/√n = 1.699×25.20/√30 = $7.82

Lower limit of population mean = mean - E = 100 - 7.82 = $92.18

Upper limit of population mean = mean + E = 100 + 7.82 = $107.82

90% confidence interval is ($92.18, $107.82)

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Answer: $1,007.00

<em>I hope this helps, and Happy Holidays! :)</em>

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