A) 12<br> B) 7<br> C) -11<br> D) 8<br> 6x+4

Nika earns a gross pay of $73,000. Her total employee benefits are 22% of her gross pay and she has no job expenses. If Nika get

mihalych1998 [28]

Total compensation $94060. First, establish the value of the benefit package by calculating 22% X 73000 = 16060. Next, add the benefits to the salary 73000 + 16060 = 89060 and now add the $5000 raise for a new total of 94060 in total compensation.

3 0

3 years ago

Read 2 more answers

A lottery game requires that a person select in uppercase or lowercase letter followed by two different two-digit numbers (where

Irina-Kira [14]

Using the Fundamental Counting Theorem, it is found that there are 416,520 ways to fill out a lottery ticket.

<h3>What is the Fundamental Counting Theorem?</h3>

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

First, one uppercase or lowercase letter is chosen, there are 26 of each, hence $n_1 = 52$ .

Then, two different two-digit numbers are chosen, and there are 90 of them, hence $n_2 = 90, n_3 = 89$ , as the third digit has to be different of the second.

Then:

$N = n_1n_2n_3 = 52(90)(89) = 416520$

There are 416,520 ways to fill out a lottery ticket.

To learn more about the Fundamental Counting Theorem, you can take a look at brainly.com/question/24314866

5 0

3 years ago

What is the sum of the roots of the quadratic equation x²+6x-14=0?

aivan3 [116]

Answer:

<h3>Sum of Roots =<u> (-8)</u><u> </u><u> </u></h3><h3>Product of Roots = <u> </u><u> </u><u>(-84)</u><u> </u><u> </u></h3>

Step-by-step explanation:

${x}^{2} + 6x - 14 = 0$

Roots :- 6 and -14

Sum of the roots :

[6 + (-14)]

= (-8)//

Product of the roots :

[(6)(-14)]

= (-84)//

8 0

3 years ago

A metallurgist has one alloy containing 32% copper and another containing 65% copper. How many pounds of each alloy must he use

kompoz [17]

Answer:

<h2>30.67 pounds of 32% copper alloy and 10.33 pounds of 65% copper alloy</h2>

Step-by-step explanation:

First alloy contains 32% copper and the second alloy contains 65% alloy.

We wish to make 44 pounds of a third alloy containing 42% copper.

Let the weight of first alloy used be $x$ in pounds and the weight of second alloy used be $y$ in pounds.

Total weight = $44\text{ }pounds=x+y$ $-(i)$

Total weight of copper = $42\%\text{ of 44 pounds = }32\%\text{ of }x\text{ pounds + }65\%\text{ of }y\text{ pounds }$

$\dfrac{42\times 44}{100}=\dfrac{32x}{100}+\dfrac{65y}{100}\\\\ 32x+65y=1848$ $-(ii)$

Subtracting 32 times first equation from second equation,

$32x+65y-32x-32y=1848-32\times44\\33y=440\\y=13.333\text{ }pounds \\x=30.667\text{ }pounds$

∴ 30.67 pounds of first alloy and 13.33 pounds of second alloy were used.

4 0

3 years ago

A study conducted in June 2015 examines ownership of tablet computers by US adults. A random sample of people were surveyed, and

Tatiana [17]

Answer:

a) The null hypothesis

H₀: P₁ = P₂

The alternative hypothesis

Hₐ: P₁ ≠ P₂

The proportion of the women population that own a tablet is P₁

And the proportion of the men population that own a tablet is P₂

b) The sample statistics are p₁ and p₂ for women and men sample proportions that own a tablet respectively.

p₁ = 0.4663

p₂ = 0.4330

The difference in sample proportion of tablet owners = p₁ - p₂ = 0.4663 - 0.4330 = 0.0333 (not 0)

Hence, the alternative hypothesis is true.

Step-by-step explanation:

The null hypothesis is the one that predicts no difference in tablet ownership.

The alternative hypothesis is the one that proves the initial theory of the survey that there is a difference in the proportion of men and women populations that own a tablet.

If the proportion of the women population that own a tablet is P₁

And the proportion of the men population that own a tablet is P₂

Then, the sample proportion of women that own a tablet = p₁

Sample proportion of men that own a tablet = p₂

The null hypothesis, H₀, stated mathematically, is

H₀: P₁ = P₂

The alternative hypothesis, Hₐ, stated mathematically, is

Hₐ: P₁ ≠ P₂

b) Like I stated in (a) the sample statistics are p₁ and p₂ for women and men sample proportions that own a tablet respectively.

From the data given,

p₁ = (235/504) = 0.4663

p₂ = (197/455) = 0.4330

In the sampled group, the women group have a higher proportion of tablet owners.

The difference in sample proportion of tablet owners = p₁ - p₂ = 0.4663 - 0.4330 = 0.0333

Hence, the alternative hypothesis is true.

Hope this Helps!!!

3 0

4 years ago

A) 12 B) 7 C) -11 D) 8 6x+4