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3 years ago

Nia answered 80% of the 40 questions on a test correctly. How many correct answers did she have?

Mathematics

2 answers:

Vlad1618 [11]3 years ago

5 0

32 questions 40 * .80 = 32

Step2247 [10]3 years ago

3 0

Nia answered correct answers = 80% of the 40 questions

When we remove % sign from a number, we divide that number by 100

= $\frac{80}{100}$ of 40

= $\frac{80}{100} \times 40$

Cancelling the two zeroes from numerator and denominator,

= $8 \times 4$

= 32.

Total correct answers answered by Nia = 32

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Divide rate 456/12 divided 12/12= ?/1

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Answer:

Step-by-step explanation:

(456/12) / (12/2)

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38/6

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2 years ago

A marketing research manager analyzes the data collected through loyalty cards at a popular local coffee shop. She investigates

IRINA_888 [86]

Answer: See explanation

Step-by-step explanation:

Correlation is a term which simply measures the strength of the linear relationship that exist between two variables that are quantitative.

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3 years ago

Complete (assume $60,000 of overhead to be distributed): (Enter amount of overhead allocated as whole dollar amounts. Round your

Sedbober [7]

The completion of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:

Ratio Amount

Department A 0.25 $15,000

Department B 0.75 $45,000

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

The ratio is the proportion of the whole shared by two or more numbers.

Ratios are fractional values like proportions.

Ratios, depicted in fractions, decimals, and percentages, show how much a value or variable is contained in another.

Total distributable overhead = $60,000

Ratios = 10,000:30,000

= 1:3

Sum of Ratios = 4

= 0.25:0.75

Sum of Ratios = 1

<h3>Overhead Allocation:</h3>

Department Square Feet Ratio Amount of Overhead Allocated

Dept. A 10,000 A = 1 B = $15,000 ($60,000 x 0.25)

Dept. B 30,000 C = 3 D = $45,000 ($60,000 x 0.75)

Thus, based on the cost driver ratios, Department A bears <u>$15,000</u>, while Department B will be allocated <u>$45,000</u> of the distributable overheads.

Learn more about ratios at brainly.com/question/12024093

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1 year ago

Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yi

aalyn [17]

Answer:

a) $t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

$df=12+15-2=25$

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) $(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

Step-by-step explanation:

Notation and hypothesis

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}}+\frac{1}{n_2}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

Part a

The system of hypothesis on this case are:

Null hypothesis: $\mu_2 \leq \mu_1$

Alternative hypothesis: $\mu_2 > \mu_1$

Or equivalently:

Null hypothesis: $\mu_2 - \mu_1 \leq 0$

Alternative hypothesis: $\mu_2 -\mu_1 > 0$

Our notation on this case :

$n_1 =12$ represent the sample size for group 1

$n_2 =15$ represent the sample size for group 2

$\bar X_1 =85$ represent the sample mean for the group 1

$\bar X_2 =91$ represent the sample mean for the group 2

$s_1=3$ represent the sample standard deviation for group 1

$s_2=2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(12-1)(3)^2 +(15 -1)(2)^2}{12 +15 -2}=6.2$

And the deviation would be just the square root of the variance:

$S_p=2.490$

Calculate the statistic

And now we can calculate the statistic:

$t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

Now we can calculate the degrees of freedom given by:

$df=12+15-2=25$

Calculate the p value

And now we can calculate the p value using the altenative hypothesis:

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

Conclusion

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

Part b

For this case the confidence interval is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} S_p \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}$

For the 99% of confidence we have $\alpha=1-0.99 = 0.01$ and $\alpha/2 =0.005$ and the critical value with 25 degrees of freedom on the t distribution is $t_{\alpha/2}= 2.79$