All categories

3 years ago

Select the correct answer from each drop-down menu.

Mathematics

1 answer:

zepelin [54]3 years ago

3 0

<h3>Answer:</h3>

y = 0.1x +1500

<h3>Explanation:</h3>

You need an equation that will give Gary a salary of $1500 even if he makes no sales (x=0). The only possible choice for the second item is then ...

... +1500

You are expected to know that Gary's commission of 10% of sales is computed by multiplying sales (x) by 10%. That is, if Gary sells $100 worth of items, his commission is ...

... 10% × $100 = $10

That is, the multiplier is 0.1.

Gary's salary (y) is then computed as

... y = 0.1x +1500

_____

<em>Comment on percentages</em>

The % symbol is a shorthand way to write /100. That is, 10% = 10/100, ten hundredths, or 0.10. (You might notice here that "percent" and "hundredths" can be used interchangeably.)

You might be interested in

Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage ea

garik1379 [7]

Answer:

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

Step-by-step explanation:

We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.26.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328$

The 95% confidence interval for the population proportion is (0.192, 0.328).

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

3 0

3 years ago

Substitue the expression 5-3x into the second equation

Rina8888 [55]

Answer:

Step-by-step explanation:

you substitute for y since you know what y equals.

so, it will then be

5x -4(5 -3x) = -3

you then multiply -4 by everything in the parenthesis

so then it will be

5x - 20 + 12x = -3

Then combine like terms

5x + 12x = 17x

then the new equation is

17x -20 = -3

the next step is to and 20 to both sides since it is negative you do the opposite.

17x - 20 = -3

17x = 17 divide 17 by both sides sice 17 is being multiplied by x you do the opposite and divide and you get 1.

4 0

3 years ago

An example problem in a Statistics textbook asked to find the probability of dying when making a skydiving jump.

MArishka [77]

Answer:

(a) 0.999664

(b) 15052

Step-by-step explanation:

From the given data of recent years, there were about 3,000,000 skydiving jumps and 21 of them resulted in deaths.

So, the probability of death is $\frac{21}{3000000}==0.000007$ .

Assuming, this probability holds true for each skydiving and does not change in the present time.

So, as every skydiving is an independent event having a fixed probability of dying and there are only two possibilities, the diver will either die or survive, so, all skydiving can be regarded as is Bernoulli's trial.

Denoting the probability of dying in a single jump by $q$ .

$q=7\times 10^{-6}=0.000007$ .

So, the probability of survive, $p=1-q$

$\Rightarrow p=1-7\times 10^{-6}=0.999993.$

(a) The total number of jump he made, n=48

Using Bernoulli's equation, the probability of surviving in exactly 48 jumps (r=48) out of 48 jumps (n=48) is

$=\binom(n,r)p^rq^{n-r}$

$=\binom(48,48)(0.999993)^{48}(0.000007)^{48-48}$

$=(0.999993)^{48}=0.999664$ (approx)

So, the probability of survive in 48 skydiving is 0.999664,

(b) The given probability of surviving =90%=0.9

Let, total $n$ skydiving jumps required to meet the surviving probability of 0.9.

So, By using Bernoulli's equation,

$0.9=\binom {n }{r} p^rq^{n-r}$

Here, r=n.

$\Rightarrow 0.9=\binom{n}{n}p^nq^{n-n}$

$\Rightarrow 0.9=p^n$

$\Rightarrow 0.9=(0.999993)^n$

$\Rightarrow \ln(0.9)=n\ln(0.999993)$ [ taking $\log_e$ both sides]

$\Rightarrow n=\frac {\ln(0.9)}{\ln(0.999993)}$

$\Rightarrow n=15051.45$

The number of diving cant be a fractional value, so bound it to the upper integral value.

Hence, the total number of skydiving required to meet the 90% probability of surviving is 15052.

3 0

3 years ago

Hannah and Dawson have both invested money in savings accounts with APYs of 3.2%. If Hannah's account has a balance of $31,000 a

9966 [12]

Answer:

$341.07

Step-by-step explanation:

Hanna and Dawson both invested at 3.2% = 0.032

Hannah has balance of 31,000 in account

Dawson has balance of 42000 in account

Interests earned by both are

1)Hannah -P(1+i)^-n

=31000(1+0.032)^-1

=31000(1.032)^-1

=31000(0.968992)

=$30038.752

=$30038.75

Interest earned by Dawson is $31,000 - $30038.75 = $961.25

2)Dawson- P(1+i)^-n

=42000(1+0.032)^-1

=42000(1.032)^-1

=42000(0.968992)

=$40697.664

=$$40697.664

Interest earned by Dawson is $42,000 - $40697.66= $1302.32

3) Hence the amount that Dawson earns than is:

=$1302.32-$961.25

= $341.07

3 0

3 years ago

Assume that y varies inversely with x. if y = 16 when x = 1/2, find y when x=32

MissTica

y varies inversely with x.

Example:

If we multiply x by 2 we need to divide y by 2 too.

So,

If y = 16 and x = 1/2, find y when x = 32

Lets see, from 1/2 to 32 e need to multiply 1/2 by 64, right? So let's divide 16 by 64.

16/64 = 8/32 = 4/16 = 2/8 = 1/4

So we can say that:

If y = 16 when x = 1/2, y = 1/4 when x = 32.

4 0

3 years ago