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You buy the same number of brushes, rollers and paint cans. Write an expression in simples form that represents the total amount

jeyben [28]

T= 21.79x + 3.99x + 6.89x where t is the total cost and x is the number of brushes/rollers/paint cans you buy. You don't need a different variable for each item because you buy the same amount of each.

4 0

3 years ago

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/// WORTH 70 points /// ASAP ////

belka [17]

A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

$y = (x+25)(x+9)$

Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)

$y = x^2 + 9x + 25x + 9(25)$

$y = x^2 +34x + 225$

Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)

$y-225 = x^2 +34x$

$y-225 + 17^2 = x^2 +34x + 17^2$

$y-225 + 289 = (x+17)^2$

$y = (x+17)^2 - 64$

What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

The vertex is where the squared term is zero, x=-17 , y =-64, (-17,-64)

The y intercept is y at x=0, so (0,225)

The x intercepts are the zeros; so at x=-25 and x=-9, aka (-25,0), (-9,0)

Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)

[Plot the points we generated and connect the dots. I'll leave the graphing to you]

In this problem, only positive values of x make sense. Why? (1 point)

x is the width of the pool edge; it must be positive.

What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)

x=0, y=225 i.e. (0,225)

The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)

(9+6)(25+6)=15(31)=465

Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)

$y=(x+6)(x+6)=(x+6)^2$

Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)

169 = (x+6)^2

Step 3: Solve your equation from Part b for x. (3 points)

$x + 6 = \pm \sqrt{169}$

$x = -6
 \pm 13$

$x= 7 \quad \textrm{ or } \quad x= -19$

Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)

Only the positive root works,

x=7 feet

5 0

3 years ago

The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a n

xz_007 [3.2K]

Answer:

(15,595, 16,805)

Step-by-step explanation:

We have to:

m = 16.2, sd = 3.75, n = 150

m is the mean, sd is the standard deviation and n is the sample size.

the degree of freedom would be:

n - 1 = 150 - 1 = 149

df = 149

at 95% confidence level the t is:

alpha = 1 - 95% = 1 - 0.95 = 0.05

alpha / 2 = 0.05 / 2 = 0.025

now well for t alpha / 2 (0.025) and df (149) = t = 1,976

the margin of error = E = t * sd / (n ^ (1/2))

replacing:

E = 1,976 * 3.75 / (150 ^ (1/2))

E = 0.605

The 95% confidence interval estimate of the popilation mean is:

m - E <u <m + E

16.2 - 0.605 <u <16.2 + 0.605

15,595 <u <16,805

(15,595, 16,805)

5 0

3 years ago

Which is greater 12/12 10/11

nexus9112 [7]

12/12 is greater because it is the same thing as 1 whole, whereas 10/11 is still considered a fraction of a whole number.

4 0

3 years ago

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Estimate the quotient: 1628 ÷ 8 answer choices 168 162 160 260 106

slega [8]

Answer:

203.5 so you can pick 168 because it's closer to the answer

Step-by-step explanation:

5 0

3 years ago