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3 years ago

Solve the following equations below by showing all the steps. - 1. 9(4 - 2x) – 3 = 4 - 6(3x – 5)

Mathematics

1 answer:

In-s [12.5K]3 years ago

6 0

Answer:

No real solution

Step-by-step explanation:

First off I'm assuming that the 1 or -1 at the begging is just the problem number:

First you distribute on both sides

36 - 18x - 3 = 4 - 18x + 30

Then combine like terms

33 - 18x = 34 - 18x

Then rearrange the terms by adding 18x to both sides and subtracting both sides by 33. You should get:

0 = 1

When you add positive 18x it cancels the -18x out. And 34 - 33 is 1. Obviously, zero cannot equal 1 so there is no real solution

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The Kirkland family is buying a new living room set that costs $1,495.

never [62]

<h3>Answer: 173.04 dollars</h3>

======================================================

Explanation:

The down payment is $400, so that means they must pay back 1495-400 = 1095 dollars. Let L = 1095 be the amount loaned

The annual interest rate is 28% which means r = 0.28; the monthly interest rate is i = r/12 = 0.28/12 = 0.02333 approximately

There are 12 months in a year, so n = 12 is the number of payment periods

----------------------------------------

In summary so far, we have

L = 1095
i = 0.02333 (which is approximate)
n = 12

Those values will be plugged into the monthly payment formula below

M = L*( i*(1+i)^n )/( (1+i)^n - 1 )

M = 1095*( 0.02333*(1+0.02333)^12 )/( (1+0.02333)^12 - 1 )

M = 105.671914631108

M = 105.67

The monthly payment is $105.67

If they have a monthly payment of $105.67, and they pay that for 12 months, then 12*105.67 = 1,268.04 dollars is the amount of money they pay back to the credit card company.

The total amount of interest would be 1,268.04 - 1,095 = 173.04 dollars

Side note: the formula is a complicated ugly mess, so it's understandable to use calculators that already have the formula built in. Many websites offer free calculators that do this.

7 0

3 years ago

In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of

Phoenix [80]

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean number of chocolate chips = $\frac{\sum X}{n}$ = 1238.2

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 94.3

n = sample of car drivers = 16

$\mu$ = population mean number of chips in a bag

<em>Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.</em>

<u>So, 95% confidence interval for the population mean, </u> $\mu$ <u> is ;</u>

P(-2.131 < $t_1_5$ < 2.131) = 0.95 {As the critical value of t at 15 degrees of

freedom are -2.131 & 2.131 with P = 2.5%}

P(-2.131 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.131) = 0.95

P( $-2.131 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.131 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

<u>95% confidence interval for</u> $\mu$ = [ $\bar X-2.131 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.131 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }$ , $1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }$ ]

= [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

7 0

3 years ago

Sam owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many sto

yawa3891 [41]

Answer:

370 stores

Step-by-step explanation:

Given data

initial number of stores P= 200

r= 8%

t= 1999-2007= 8 years

Let us apply the compound interest expression to find the final amount of stores

A= P(1+r)^t

A= 200(1+0.08)^8

A= 200(1.08)^8

A= 200*1.85

A=370

Hence the number of stores in 2007 is 370 stores

4 0

2 years ago

A group of climbers begin climbing at an elevation of 5000 feet and ascend at a steady rate of 1500 vertical feet per hour. This

KatRina [158]

Answer:

Linear function: $y=1500x+5000$

x- Independent variable

y- Dependent variable

Step-by-step explanation:

We are given that

Climbers start climbing at an elevation of height =5000 ft

The steady rate at which climbers start climbing=1500 ft/h

We have to find the independent variable and dependent variable.

Let time taken by climbers=x hours

In 1 hour, climbers cover distance =1500 ft

In x hours , climber cover distance=1500x ft

According to question

The total distance y covered by climber in x hours

$y=1500x+5000$

This is required linear function.

We can see that

x does not depend on any other quantity.Therefore, x is independent variable .

When the value of x changes then the value of y is also change.

It means the value of y depends on the value of x.

Therefore, y is dependent variable.

8 0

3 years ago

Convert -450° from degrees to radians. (5 points)

ValentinkaMS [17]

Negative five pi divided by two

4 0

2 years ago