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3 years ago

Three less than a number is halved to give six

Mathematics

1 answer:

pentagon [3]3 years ago

6 0

Answer: x-3/2=6

Step-by-step explanation: The terms "less than" means to subtract, and to flip the terms provided. This gives you x-3. Halved suggest to divided by 2. Now you have x-3/2=6.

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Which number belongs in the integers area on the Venn diagram?

Whitepunk [10]

Answer:

-19 - Integer

-5 - Integer

12 - Whole Number

14.25 - Rational Numbers

Step-by-step explanation:

Whole numbers = {0, 1 , 2, 3, . . . }

They are the the natural numbers and zero.

Integers: {. . . , -3, -2, -1, 0 , 1, 2, 3, . . . }

Rational Numbers: These are the numbers that can be written in the form of $\frac{p}{q}$ where $q \ne 0$ .

Note that All Whole numbers are integers.

All Integers are in turn Rational Numbers. (When q = 1, we get all the integers.).

In the given problem, we have: -19 Negative number. It should be an Integer.

Similarly -5 is also an integer.

12 is a whole number. Note that it is also an integer. Consequently, a rational number.

And 14.25 = $\frac{1425}{100}$ is in the form of $\frac{p}{q}$ . So it is a rational number.

7 0

3 years ago

Researchers obtained a sample of n = 10 children who attended daycare before starting school. The children are given a standardi

attashe74 [19]

Answer:

$t=\frac{55.5-50}{\frac{4.249}{\sqrt{10}}}=4.093$

$p_v =2*P(t_{9}>4.093)=0.00084$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

We can say that at 5% of significance the true mean is significantly different from 50.

Step-by-step explanation:

Data given and notation

53, 57, 61, 49, 52, 56, 58, 62, 51, 56

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X))^2}{n-1}}$

And we got:

$\bar X=55.5$ represent the sample mean

$s=4.249$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =50/tex] represent the value that we want to test [tex]\alpha=0.05$ represent the significance level for the hypothesis test (ASSUMED).

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is equal or not to 50 :

Null hypothesis: $\mu = 50$

Alternative hypothesis: $\mu \neq 50$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{55.5-50}{\frac{4.249}{\sqrt{10}}}=4.093$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=10-1=9$

Since is a two-sided tailed test the p value would given by:

$p_v =2*P(t_{9}>4.093)=0.00084$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

We can say that at 5% of significance the true mean is significantly different from 50.

6 0

4 years ago

1 point

DedPeter [7]

Answer:

160000m³

Step-by-step explanation:

Volume of a rectangular prism= A x h

V= l x b x h

V= 80x 50 x 40

V= 160000m³