All categories

3 years ago

Gary divides 48.026 by 6.49 using the work shown. Is Gary correct or incorrect? Explain your answer in full sentences.

Mathematics

1 answer:

Likurg_2 [28]3 years ago

3 0

Answer:

Here, we are required to judge judge Gary's calculation as portrayed in the question above.

Gary's calculation is correct according to the calculation.

Step-by-step explanation:

The question asks that 48.026 is divided by 6.49.

By first considering the whole numbers on the left hand side of the decimal point in each number,

We can conclude that 48 divided by 6 equals 8, i.e 48/6=8.

However, the calculation becomes much easier by shifting the decimal points in both numbers two spaces to the right as indicated in the diagram (i.e multiply both numbers by 100).

This leaves us with 4802.6 to be divided by 649.

Dividing 4802.6 by 649 yields 7 with a remainder of 259.6 (this is so because 7 × 649 = 4543).

259.6 can have it's decimal point shifted one space right to yield 2596.

And, 2596/649 = 4.

The condition above is hypothetical, and there's a need for the decimal point to be shifted one space back to the left, which leaves us with 0.4.

Ultimately, 48.026/6.49 = 7.4.

Therefore, Gary's calculation is correct using the work shown in the question above.

brainly.com/question/20915806&ved=2ahUKEwiRtIygpIbzAhUN8xQKHd9LACkQjjh6BAgnEAE&usg=AOvVaw2ymwQ-_WS0EVfUGoAy5WB_

You might be interested in

Step by step how to solve this equation by completing the square<br> x^2-16x+-60

anygoal [31]

Answer:

Step-by-step explanation:

x^2-16x+60

(x-6)(x-10) factor the equation

x-6=0

x=6

x-10=0

x=10

5 0

3 years ago

Which of the following are true statements?

MArishka [77]

Answer: Option A and Option B.

Step-by-step explanation:

You need to remember the logarithms properties:

$log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=b*log(a)$

You can observe in Option A:

$logM^p=p*logM$ (This is true)

You can observe in Option B:

$logM+logN=log(MN)$ (This is true)

You can observe in Option C:

$logM-logN=log(M-N)$ (This is not true)

You can observe in Option D:

$(logM)^p=p*logM$ (This is not true)

6 0

3 years ago

HELP ME PLEASE!! I NEED THIS!

Pani-rosa [81]

Answer:

min{5 x^2 - 20 x + 3} = -17 at x = 2

Step-by-step explanation: here's the graph

8 0

2 years ago

Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body b

sesenic [268]

Answer:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095$

-The sample is too small to make judgments about skewness or symmetry.

H0: $\mu_{1}=\mu_{2}$

H1: $\mu_{1} \neq \mu_{2}$

$t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013$

$p_v =2*P(t_{(14)}$

So the p value is a very high value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a we don't have a significant difference between the two means.

Step-by-step explanation:

First we need to find the difference defined as:

(Operator 1 minus Operator 2)

d1=1.326-1.323=0.003 d2=1.337-1.322=0.015

d3=1.079-1.073=0.006 d4=1.229-1.233=-0.004

d5=0.936-0.934=0.002 d6=1.009-1.019=-0.01

d7=1.179-1.184=-0.005 d8=1.289-1.304=-0.015

Now we can calculate the mean of differences given by:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001$

And for the sample deviation we can use the following formula:

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095$

Describe the distribution of these differences using words. (which one is correct)

We can plot the distribution of the differences with the folowing code in R

differences<-c(0.003,0.015,0.006,-0.004,0.002,-0.01,-0.005,-0.015)

hist(differences)

And we got the image attached. And we can see that the distribution is right skewed but we don't have anough info to provide a conclusion with just 8 differnences.

-The sample is too small to make judgments about skewness or symmetry.

Use a significance test to examine the null hypothesis that the two operators have the same mean. Give the test statistic. (Round your answer to three decimal places.)

$\bar X_{1}=1.173$ represent the mean for the operator 1

$\bar X_{2}=1.174$ represent the mean for the operator 2

$s_{1}=0.1506$ represent the sample standard deviation for the operator 1

$s_{2}=0.1495$ represent the sample standard deviation for the operator 2

$n_{1}=8$ sample size for the operator 1

$n_{2}=8$ sample size for the operator 2

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0: $\mu_{1}=\mu_{2}$

H1: $\mu_{1} \neq \mu_{2}$

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) like this:

$t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case: