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3 years ago

A 2 pound box of salt sells for $.89 and a 5 pound box sells for 2.09. What is the linear equation for this?

1 answer:

4 0

Y = ax + b;

0.89 = a * 2 + b and 2.09 = a * 5 + b =>
=> 2.09 - 0.89 = a * 5 + a * 2 + b - b => 1.20 = 3 * a => a = 1.20 / 3 => a = 0.40;
b = 0.89 - 0.40 * 2 => b = 0.89 - 0.80 => b = 0.09;

y = 0.40x + 0.09 => 0.40x - y + 0.09 = 0 is the linear equation.

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Jans account balance is $2800. She pays $750 for rent. Jan wants to go on vacation but she wants to keep a balance of at least $

joja [24]

Answer:

Step-by-step explanation:

$2800 - $750 = $2050

$2050 - $500 = $1550

$750 rent

$500 vacation savings

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4 years ago

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3 years ago

Heather received $100 for her 13th birthday if she saves it in a bank with 3% interest compounded quarterly how much money will

ololo11 [35]

Answer:

109.38

Step-by-step explanation:

Recall the formula for compound interest is as follows:

A = P·(1 + r/n)nt , where

P = principal amount (initial amount deposited)

r = annual rate of interest (in decimal form)

t = # of years amount is deposited for

n = # of times interest is compounded per year

A = amount accumulated after t years, including interest

The problem asks how much money Heather will have in the bank by her 16th birthday when she deposited $100 on her 13th birthday in a bank with 3% interest compounded quarterly. From this, we have the following information:

P = $100

r = 0.03 ==> 3%/100% = 0.03

t = 3 years ==> 16 - 13 = 3

n = 4 ==> since there are 12 months per year and 12/4 = 3 months,

then interest is compounded every 3 months which is a total of 4 times per year

Therefore,

A = P(1 + r/n)nt

= 100(1 + 0.03/4)4·3

= 100(1 + 0.0075)12

= 100(1.0075)12

= 109.38069

≈ 109.38

Thus, Heather will have $109.38 in the bank by her 16th birthda

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3 years ago

Data were collected on the amount spent by 64 customers for lunch at a major Houston restaurant. These data are contained in the

galina1969 [7]

Answer:

a. The margin of error is 2.29.

b. 19.23 to 23.81

Step-by-step explanation:

The sample size is n=64.

We start by calculating the sample mean and standard deviation with the following formulas:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}$

The sample mean is M=21.52.

The sample standard deviation is s=6.89.

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{6.89}{\sqrt{64}}=\dfrac{6.89}{8}=0.861$

The degrees of freedom for this sample size are:

$df=n-1=64-1=63$

The t-value for a 99% confidence interval and 63 degrees of freedom is t=2.656.

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

$MOE=t\cdot s_M=2.656 \cdot 0.861=2.29$

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

LL=M-t \cdot s_M = 21.52-2.29=19.23\\\\UL=M+t \cdot s_M = 21.52+2.29=23.81

The 99% confidence interval for the mean is (19.23, 23.81).

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3 years ago

Find the area of a triangle with base of 4 and height of 3x-5

jok3333 [9.3K]

Answer:

Area of a triangle is 1/2B x H

In this case, BH = 0.5(3x-5)·4x

A = 4/2 · (3x²-5x)

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3 years ago