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2 years ago

How do you simplify 15/40

Mathematics

1 answer:

Katyanochek1 [597]2 years ago

3 0

Answer:3/8

Step-by-step explanation:

The simplest form of

15 /40 is 3 /8 .

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 15 and 40 is 5

Divide both the numerator and denominator by the GCD

15 ÷ 5

40 ÷ 5

Reduced fraction:

3 /8

Therefore, 15/40 simplified to lowest terms is 3/8.

You might be interested in

If f(x) = x ^ 2 is vertically compressed by a factor of 9 to g(x) , what is the equation of g(x) ?

Maslowich

Answer:

$g(x) = \frac{1}{9} \,x^2$ which agrees with option A in the list of possible answers

Step-by-step explanation:

A vertical compression by a factor 9 is represented by the transformation:

$\frac{1}{9} \,f(x) = \frac{1}{9} \,x^2$

Therefore the answer to the problem is:

$g(x) = \frac{1}{9} \,x^2$

6 0

2 years ago

Explain why any of the four operations placed between two terms 5 and -3 sqrt (8) will result in an irrational number

Gnoma [55]

Sum/difference:

Let

$x = 5 + (-3\sqrt{8}) = 5-3\sqrt{8}$

This means that

$3\sqrt{8} = 5-x \iff \sqrt{8} = \dfrac{5-x}{3}$

Now, assume that $x$ is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that $x$ was rational, which proves that the sum/difference of the two given terms was irrational

Multiplication/division:

The logic is actually the same: if we multiply the two terms we get

$x = -15\sqrt{8}$

if again we assume x to be rational, we have

$\sqrt{8} = -\dfrac{x}{15}$

But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.

7 0

2 years ago

A toy maker claims his best product has an average lifespan of exactly 14 years. A skeptical quality control specialist asks for

slamgirl [31]

Answer:

interval = [17.3948 , 20.6052]

Step-by-step explanation:

given,

random sample (n) = 45

average product lifespan = 19 years

standard deviation = 4 years

confidence interval of 99 % = ?

we know,

t* = qt(1.99/2 + 44 ) = qt(0.995,44)

t* = 2.692

so,

interval

$x = 19 \pm t* \times (\dfrac{s}{\sqrt{n}})$

$x = 19 \pm 2.692 \times (\dfrac{4}{\sqrt{45}})$

$x = 19 \pm 2.692 \times 0.5963$

$x = 19 \pm 1.6052$

interval = [19 - 1.6052 , 19 + 1.6052]

interval = [17.3948 , 20.6052]

4 0

2 years ago

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents,

RoseWind [281]

Answer:

The statement that "the margin of error was given as $\pm5$ percentage points" means that the population proportion is estimated to be with a certain level of confidence, within the interval $\hat{p} \pm 0.05$ ; where $\hat{p}[tex] is the sample's proportion. The correct answer is C. The statement indicates that the interval [tex]0.14\pm0.05$ is likely to contain the true population percentage of people that prefer chocolate pie.

Step-by-step explanation:

The margin of error for proportions is given by the following formula:

$z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}$

Where:

$z_{\alpha /2}$ is the critical value that corresponds to the confidence level; the confidence level being $1-\alpha$ ,

$\hat{p}$ is the sample's proportion of successes,

$n$ is the size of the sample.

In this exercise we have that $\hat{p}=0.14$ and that the margin of error is 0.05.

Therefore if we replace in the formula to calculate the confidence interval we get:

$\hat{p}\pm 0.05=0.14\pm0.05=(0.09, 0.19)$

Which means that the true population proportion is estimated to be, with a certain confidence level, within the interval (0.09, 0.19).

7 0

2 years ago

Tripp and Rico are two dogs. Tripp weighs exactly 35 pounds more than Rico. Together, they weigh exactly 49 pounds. How much doe

babymother [125]

Call the weights of the two dogs $t$ and $r$ .

We know that Tripp weights 35lbs more than Rico, or:
$t=r+35$

We also know that the total weight of both dogs is 49lbs.:
$t+r=49$

Now, by substitution:
$(r+35)+r=49$
$2r+35=49$
$2r+35-35=49-35$
$2r=14$
$r=\frac{14}{2}$
$r=7$
Rico weighs 7lbs.

Then:
$t=r+35$
$t=7+35$
$t=42$
Tripp weighs 42lbs.

To check our work:
$t+r=49$
$42+7=49$
$49=49$ CHECK!

5 0

2 years ago

How do you simplify 15/40​

How do you simplify 15/40