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3 years ago

When a number is increased by 2.8%, the result is 56. What is the original number to

Mathematics

1 answer:

Sever21 [200]3 years ago

6 0

Answer:

The original number was 54.5.

Step-by-step explanation:

If a number is increased by 2.8%, then it is 102.8% of it's original number.

In mathematics, "of" in virtually all cases means "multiplied by".

Therefore, we do the opposite:

1. Convert to a decimal.

102.8% = 1.028

2. Divide by the decimal.

$56 \div 1.028 = 54.47$

3. Round it to the nearest tenth.

54.47 rounds to 54.5.

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Rewrite the expression ln(33^3)+ln(9^4) so that it includes the expressions ln(3) and 33 and 9 do not appear inside a natural lo

krok68 [10]

Answer:

In Section 6.1, we introduced the logarithmic functions as inverses of exponential functions and

discussed a few of their functional properties from that perspective. In this section, we explore

the algebraic properties of logarithms. Historically, these have played a huge role in the scientific

development of our society since, among other things, they were used to develop analog computing

devices called slide rules which enabled scientists and engineers to perform accurate calculations

leading to such things as space travel and the moon landing. As we shall see shortly, logs inherit

analogs of all of the properties of exponents you learned in Elementary and Intermediate Algebra.

We first extract two properties from Theorem 6.2 to remind us of the definition of a logarithm as

the inverse of an exponential function.

Step-by-step explanation:

Hope this helps

4 0

3 years ago

Find the equation of a line that passes through the point (0,-4) and has a gradient of 2. Leave your answer in the form y=mx+c

OLga [1]

Answer:

y=2x-4

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=2(x-0)

y+4=2x-0

y=2x-0-4

y=2x-4

3 0

1 year ago

2. Alicia is writing the program for a video game. For one part of the game she uses the rule (x,y) ->(x-3,y+4) to move point

Taya2010 [7]

Given rule (x,y) ->(x-3,y+4) to move points on the screen.

a) We are given first input (-6,0).

(-6,0) represents x=-6 and y=0.

Plugging values of x and y in given rule (x,y) ->(x-3,y+4), we get

(-6,0) --> (-6-3, 0+4). It would give us (-9,4)

So, first output is (-9,4).

b) We are given second input (3,-4).

(-6,0) represents x=3 and y=-4.

Plugging values of x and y in given rule (x,y) ->(x-3,y+4), we get

(-6,0) --> (3-3, -4+4). It would give us (0,0).

So, second output is (0,0).

7 0

3 years ago

We would like to construct a 99% confidence interval for the mean, based on a sample of 50 observations. The sample standard dev

Sloan [31]

Answer:

Lower confidence limit = 20.191

Step-by-step explanation:

Sample mean; x' = 22

Sample standard deviation; s = 5.5

Sample size; n = 50

Confidence interval = 99%

Since sample size > 30, we will use the formula;

CI = x' ± zs/√n

Where;

x' is sample mean

s is sample standard deviation

n is sample size

z is z-value of the confidence interval

From the table attached, z for 99% = 2.3263

Thus;

CI = 22 ± (2.3263 × 5.5)/√50

CI = 22 ± 1.809

CI = 23.809 or 20.191

Lower confidence limit = 20.191

3 0

3 years ago

An automobile manufacturer claims that its van has a 27.6 miles/gallon (MPG) rating. An independent testing firm has been contra

user100 [1]

Answer:

2.52

Step-by-step explanation:

An automobile manufacturer claims that its van has a 27.6 miles/gallon (MPG)

So, $\mu = 27.6 miles/gallon$

n = 210 vans

x = 28

$\sigma= 2.3$

Formula of test statistic = $z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{28-27.6}{\frac{2.3}{\sqrt{210}}}$

$z=2.5202$

Hence the value of the test statistic is 2.52

8 0

3 years ago