-1/2(7z+4)+1/5(5z-15)

What is the value of f(-4) in the piecewise function f(x)= -x-5 for -5<= x <= -2; -x^2+1 for -2<=x<=2; (x-3)^2+2 for

Alik [6]

We first need to pick the correct piece to use. In this case, we will use f(x) = -x-5 because -5<=-4.

Then, we use direct substitution:
f(-4) = -(-4) - 5
f(-4) = -1

5 0

3 years ago

Read 2 more answers

Which of these ratios are equivalent ratio<br> 1:4 2:8 3:6 7:28

Harrizon [31]

Answer:

1:4

2:8

7:28

Step-by-step explanation:

1:4
2:8 , 1:4
7:28, 1:4

5 0

2 years ago

You must calculate the number of sheets of plywood needed for subflooring. Each sheet of plywood measures 4'by 8. The measuremen

snow_lady [41]

Answer:

25 sheets of plywood will be needed

Step-by-step explanation:

Each sheet of plywood measures $4ft*8ft=32ft^{2}$ .

We have to cover the surface of the house, minus the surface of the hole of the stairs.

$Surface _{to cover} = Surface _{house} -Surface _{hole}= (28ft*30ft)-(12ft*4ft)= 840ft^{2}-48ft^{2}=792ft^{2}$

To know how many sheets will be needed, we divide the surface to be covered by the surface of each sheet

$Sheets_{needed} =\frac{Surface _{house}}{Surface _{sheet}} =\frac{792ft^{2}}{32\frac{ft^{2}}{sheet} } = 24,75 sheets$

As we can't buy 0,75 of a sheet, we round it up, i.e. we will need 25 sheets of plywood for subflooring.

8 0

3 years ago

Todd wants to buy a new video game for $43.31. He has $55.50. The sales tax is 8.5% of the total purchase. Does Todd have enough

sammy [17]

Answer:

yes

Step-by-step explanation:

We can estimate* that the total price including tax of the game will be less than ...

$43.31 +10% of 43.31 = $43.31 +4.33 = $47.61

Todd easily has enough to pay for the game, including tax.

_____

You can work this more exactly a couple of ways.

1. Price + tax = 1.085×$43.31 = $46.99 . . . less than Todd's budget

2. Most Todd can afford: $55.50/1.085 = $51.15 . . . more than the game price

_____

* For estimating purposes, we like to use numbers that are easy to compute with. 10% is one such number, as it only requires moving the decimal point.

7 0

3 years ago

The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4. Suppose 64 golfers play

Vilka [71]

Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .