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2 years ago

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

Mathematics

1 answer:

m_a_m_a [10]2 years ago

3 0

Answer:

see below

Step-by-step explanation:

Part A

We can shift f(x) to the left or shift it up

Part B

f(x+k) for a shift to the left

f(x) + k for a shift up

Part C

Looking at shifting f(x) to g(x) by going left, we are shifting 6 units to the left

f(x+6) will shift f(x) 6 units to the left

g(x) = f(x+6)

We can all shift f(x) up, we can shift up 18 units

f(x) +18 will shift the function up 18 units

g(x) = f(x) +18

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Suppose the true proportion of voters in the county who support a restaurant tax is 0.54. Consider the sampling distribution for

Eva8 [605]

Answer:

The correct answer is:

(a) 0.54

(b) 0.0385

Step-by-step explanation:

Given:

Restaurant tax,

p = 0.54

Sample size,

n = 168

Now,

(a)

The mean will be:

⇒ μ $\hat{p}= p$

$=0.54$

(b)

The standard error will be:

$\sigma \hat{p}$ = $\sqrt{[\frac{p(1-p)}{n} ]}$

= $\sqrt{[\frac{(0.54\times 0.46)}{168} ]}$

= $\sqrt{[\frac{(0.2484)}{168} ]}$

= $0.0385$

6 0

2 years ago

A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a 2 feet

Ksivusya [100]

Answer:

The width and the length of the pool are 12 ft and 24 ft respectively.

Step-by-step explanation:

The length (L) of the rectangular swimming pool is twice its wide (W):

$L_{1} = 2W_{1}$

Also, the area of the walkway of 2 feet wide is 448:

$W_{2} = 2 ft$

$A_{T} = W_{2}*L_{2} = 448 ft^{2}$

Where 1 is for the swimming pool (lower rectangle) and 2 is for the walkway more the pool (bigger rectangle).

The total area is related to the pool area and the walkway area as follows:

$A_{T} = A_{1} + A_{w}$ (1)

The area of the pool is given by:

$A_{1} = L_{1}*W_{1}$

$A_{1} = (2W_{1})*W_{1} = 2W_{1}^{2}$ (2)

And the area of the walkway is:

$A_{w} = 2(L_{2}*2 + W_{1}*2) = 4L_{2} + 4W_{1}$ (3)

Where the length of the bigger rectangle is related to the lower rectangle as follows:

$L_{2} = 4 + L_{1} = 4 + 2W_{1}$ (4)

By entering equations (4), (3), and (2) into equation (1) we have:

$A_{T} = A_{1} + A_{w}$

$A_{T} = 2W_{1}^{2} + 4L_{2} + 4W_{1}$

$448 = 2W_{1}^{2} + 4(4 + 2W_{1}) + 4W_{1}$

$224 = W_{1}^{2} + 8 + 4W_{1} + 2W_{1}$

$224 = W_{1}^{2} + 8 + 6W_{1}$

By solving the above quadratic equation we have:

W₁ = 12 ft

Hence, the width of the pool is 12 feet, and the length is:

$L_{1} = 2W_{1} = 2*12 ft = 24 ft$

Therefore, the width and the length of the pool are 12 ft and 24 ft respectively.

I hope it helps you!

8 0

2 years ago

Using the table below showing median income by year, how many years did it take for the annual household income to double from i

frozen [14]

Answer:

2006

Step-by-step explanation:

Trust

8 0

3 years ago

Input the equation of the given line in standard form.

noname [10]

Answer:

y = 2/3x + 1/3

Step-by-step explanation:

Standard form of a line looks like y=mx+b. We already know that m is 2/3, but we don't know b. b is our y-int. With the given information, we can write this equation is point-slope form. That looks like y - y1 = m(x-x1). (x1, y1) = (1, 1) - the point given to us. So if you plug in that point to the equation, and the slope - m, it'll look like y - 1 = 2/3 (x - 1).

From here, you can just solve for y, and it'll be in standard form. I would distribute 2/3 first.

y - 1 = 2/3x - 2/3

Then, add 1 to both sides.

y = 2/3x + 1/3

4 0

3 years ago

4th grade math the 8s in 88,000 answers

Tomtit [17]

Explain more are you trying to figure out how much the 8s are worth in the number

7 0

3 years ago

Read 2 more answers