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3 years ago

Which expression is equivalent to (44)2 . (47) 2? A. 1 46 1 1 B. 43 C. 411 D. 430

Mathematics

2 answers:

Alisiya [41]3 years ago

7 0

Answer:

Step-by-step explanation:

i dont know

Anit [1.1K]3 years ago

4 0

67 is the answer i think

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3. His teacher praised him.

balandron [24]

What’s the question

8 0

3 years ago

Examination of a large sample of people revealed a relationship between calcium intake and blood pressure. The relationship was

Vika [28.1K]

Answer:

a) The 95% confidence interval for the mean is (-1.171, 11.717).

b) No, there is not enough evidence to support the claim that increasing the amount of calcium in our diet reduce blood pressure (at a 5% significance level).

Step-by-step explanation:

The data for both groups are:

Group 1 (calcium): 7 -4 18 17 -3 -5 1 10 11 -2

Group 2 (placebo): -1 12 -1 -3 3 -5 5 2 -11 -1 -3

The mean and standard deviation for Group 1 is:

$M_1=\dfrac{1}{10}\sum_{i=1}^{10}(7+(-4)+18+17+(-3)+(-5)+1+10+11+(-2))\\\\\\ M_1=\dfrac{50}{10}=5$

$s_1=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{10}(x_i-M)^2}\\\\\\$

$s_1=\sqrt{\dfrac{1}{9}\cdot [(7-(5))^2+(-4-(5))^2+...+(-2-(5))^2]}\\\\\\$

$s_1=\sqrt{\dfrac{1}{9}\cdot [(4)+(81)+(169)+(144)+(64)+(100)+(16)+(25)+(36)+(49)]}\\\\\\s_1=\sqrt{\dfrac{688}{9}}=\sqrt{76.44}\\\\\\s_1=8.743$

The mean and standard deviation for Group 2 is:

$M_2=\dfrac{1}{11}\sum_{i=1}^{11}((-1)+12+(-1)+(-3)+3+(-5)+5+2+(-11)+(-1)+(-3))\\\\\\ M_2=\dfrac{-3}{11}=-0.273$

$s_2=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{11}(x_i-M)^2}\\\\\\$

$s_2=\sqrt{\dfrac{1}{10}\cdot [(-1-(-0.273))^2+(12-(-0.273))^2+...+(-3-(-0.273))^2]}\\\\\\$

$s_2=\sqrt{\dfrac{1}{10}\cdot [(0.53)+(150.62)+...+(115.07)+(0.53)+(7.44)]}\\\\\\s_2=\sqrt{\dfrac{348.182}{10}}=\sqrt{34.82}\\\\\\s_2=5.901$

a) We have to calculate a 95% confidence interval for the difference between means, with a T-model.

The Group 1, of size n1=10 has a mean of 5 and a standard deviation of 8.743.

The Group 2, of size n2=11 has a mean of -0.273 and a standard deviation of 5.901.

The difference between sample means is Md=5.273.

$M_d=M_1-M_2=5-(-0.273)=5.273$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{8.743^2}{10}+\dfrac{5.901^2}{11}}\\\\\\s_{M_d}=\sqrt{7.644+3.166}=\sqrt{10.81}=3.288$

The degrees of freedom for this test are:

$df=n_1+n_2-1=10+11-2=19$

The critical t-value for a 95% confidence interval and 19 degrees of freedom is t=1.96.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_{M_d}=1.96 \cdot 3.288=6.444$

Then, the lower and upper bounds of the confidence interval are:

$LL=M_d-t \cdot s_{M_d} = 5.273-6.444=-1.171\\\\UL=M_d+t \cdot s_{M_d} = 5.273+6.444=11.717$

The 95% confidence interval for the mean is (-1.171, 11.717).

b) This is a hypothesis test for the difference between populations means.

The claim is that increasing the amount of calcium in our diet reduce blood pressure.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0

The significance level is 0.05.

The sample 1, of size n1=10 has a mean of 5 and a standard deviation of 8.743.

The sample 1, of size n1=11 has a mean of -0.273 and a standard deviation of 5.901.

The difference between sample means is Md=5.273.

$M_d=M_1-M_2=5-(-0.273)=5.273$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{8.743^2}{10}+\dfrac{5.901^2}{11}}\\\\\\s_{M_d}=\sqrt{7.644+3.166}=\sqrt{10.81}=3.288$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{5.273-0}{3.288}=\dfrac{5.273}{3.288}=1.604$

The degrees of freedom for this test are:

$df=n_1+n_2-1=10+11-2=19$

This test is a right-tailed test, with 19 degrees of freedom and t=1.604, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t>1.604)=0.063$

As the P-value (0.063) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that increasing the amount of calcium in our diet reduce blood pressure.

4 0

3 years ago

The second group of trainee astronauts are all sitting around the table, waiting to start their first day of training.

nexus9112 [7]

Answer:

Seat 1: Peter
Seat 2: Lia
Seat 3: Kenny
Seat 4: Jennie
Seat 5: Harvey
Seat 6: Joyce
Seat 7: Rick
Seat 8: Mark

Step-by-step explanation:

From Rule 6: Jennie is at Seat 4 and next to Harvey; and by rule 1 (Harvey has a higher seat number than Jennie)

Seat 4: Jennie
Seat 5: Harvey

From Rule 2: Peter is across from Harvey.

Since Seat 5 is across from Seat 1

Seat 1: Peter

From Rule 7: Peter is next to Lia.

Therefore, Lia can either be in Seat 2 or Seat 8, but by Rule 3 (Neither Joyce nor Lia is in seat 8), therefore, Lia is in Seat 2.

Seat 2: Lia

By Rule 5: Lia is next to Kenny, therefore:

Seat 3: Kenny

From Rule 4: Rick is across from Kenny, and Rick is also next to Joyce.

Seat 7 is across from Seat 3, therefore:

Seat 7: Rick

Since Rick is also next to Joyce (and by Rule 3, Joyce cannot be on Seat 8)

Seat 6: Joyce

Therefore, we have:

Seat 1: Peter

Seat 2: Lia

Seat 3: Kenny

Seat 4: Jennie

Seat 5: Harvey

Seat 6: Joyce

Seat 7: Rick

Since Mark has the remaining seat, Mark is on Seat 8.

4 0

3 years ago

Rita wants to buy sweater that was originally priced at $25 today the sweater is on sale for 40% off the original price what is

gayaneshka [121]

15$, I just multiplied 25 by .4 the product is 10 then just subtract that

7 0

4 years ago

Read 2 more answers

PLEASE SOMEONE HELP ME WITH THESE MATH QUESTIONS!!! *VERY URGENT* *IF YOU ANSWER CORRECTLY, YOU'LL GET 10 POINTS!*

Tasya [4]

Answer:

Question 21: C.

Question 22: I.

Question 23: E.

Question 24: B.

Step-by-step explanation:

#21: The first statement is presented in the "Given" section.

#22: Since the reflexive property states that anything is equal to itself, BC ≅ BC.

#23: C being the midpoint of AD means that C is the same distance from both point A and point D. This then means that AC ≅ CD.

#24: AB ≅ DB due to the given, BC ≅ BC (since it's the same side), and we've proven that AC ≅ CD using a midpoint. We've proven <em>all three sides</em> on the two triangles to each other are congruent. This means that we've proven the triangles using SSS, which is B.

7 0

3 years ago

Which expression is equivalent to (44)2 . (47) 2? A. 1 46 1 1 B. 43 C. 411 D. 430 ​

Which expression is equivalent to (44)2 . (47) 2? A. 1 46 1 1 B. 43 C. 411 D. 430