Rename 200 tens into hundreds

3. Jason uncle buys a 1.5 pound bag of pencils for the beginning of the year. He puts 1/2 of the pencils in a box. If Jason gets

Tems11 [23]

The quantity of pounds of pencils that Jason gets, based on his sharing ratio, is <u>0.15 pounds</u>.

<h3>What is the sharing ratio?</h3>

The sharing ratio is the percentage or ratio that is held by a person out of the total value of the thing being shared.

Jason's share of the pencil can be determined by multiplying the total pencils in the box (1.5 x ¹/₂) by Jason's sharing ratio (¹/₅).

<h3>Data and Calculations:</h3>

Quantity of pencils bought = 1.5 pounds

Half of the pencils in a box = 0.75 pounds (1.5 x ¹/₂)

The pounds got by Jason from the box = <u>0.15 </u>(0.75 x ¹/₅)

Thus, the quantity of pounds of pencils that Jason gets is <u>0.15 pounds</u>.

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4 0

2 years ago

(0.020) (0.030) / (0.10)x = 2.3 × 10-4

Naya [18.7K]

The value of x in the equation is 26. 087

<h3>What are algebraic expressions?</h3>

Algebraic expressions are defined as expressions made up of terms, constants, coefficients, factors and variables.

They may also include certain mathematical or arithmetic operations which includes;

Bracket
Division
Addition
Subtraction
Parentheses
Multiplication and so on

Given the equation;

(0.020) (0.030) / (0.10)x = 2.3 × 10-4

We can simply the equation following the steps;

expand the brackets, we have;

6× 10^-4/ 0.10x = 2.3 × 10^-4

Now, cross multiply

0.10x × 2.3 × 10^-4 = 6× 10^-4

Divide both sides by 2.3 × 10^-4

0. 10x = 6× 10^-4/2.3 × 10^-4

Find the quotient

0. 10x = 2. 608

Let's make the variable 'x' by dividing both sides by it's coefficient

0. 10x/0.10 = 2. 608/0. 10

x = 26. 087

Hence, the value is 26. 087

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4 0

1 year ago

Simplify expression X^2+x-2/x^3-x^2+2x-2

professor190 [17]

Answer:

$=\frac {x+2}{x^2+2}$ is the simplest form of given expression.

Step-by-step explanation:

The given question is $\frac{x^2+x-2}{x^3-x^2+2x-2}$

To solve the problem we have to group or split middle term and then factorise

$\frac{x^2+(2x-x)-2}{(x^3-x^2)+(2x-2)}$

Taking $x^2$ common from first two terms of denominator and 2 from next two terms

$= \frac{x^2+2x-x-2}{x^2(x-1)+2(x-1)}$

Now,taking x common from first two terms of numerator and -1 from next two terms and in denominator taking(x-1) common from both terms

$= \frac{ x(x+2)-1(x+2)}{(x-1)(x^2+2)}$

$=\frac{(x+2)(x-1)}{(x-1)(x^2+2)}$

Now cancel out x-1 from both numerator and denominator we get

$=\frac {x+2}{x^2+2}$ is the required simplest form.

7 0

3 years ago

The expression 3(x-9) is equivalent to (Look at picture for answer choices)

Vaselesa [24]

Answer:

The last one

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found

irakobra [83]

Answer:

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

A manufacturer of nails claims that only 4% of its nails are defective.

At the null hypothesis, we test if the proportion is of 4%, that is:

$H_0: p = 0.04$

At the alternative hypothesis, we test if the proportion is more than 4%, that is:

$H_a: p > 0.04$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

4% is tested at the null hypothesis

This means that $\mu = 0.04, \sigma = \sqrt{0.04*0.96}$

A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.

This means that $n = 20, X = 0.1$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}$

$z = 1.37$

P-value of the test and decision:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

7 0

3 years ago

Read 2 more answers