All categories

2 years ago

Given one of the roots of the quadratic equation x2 + kx + 12 = 0 is three times the other root. Find the values of k.

Mathematics

1 answer:

gtnhenbr [62]2 years ago

5 0

$\huge\bold{\purple{\bold{⚡Kaboom!⚡}}}$

You might be interested in

Is 8/10 greater than 1/2

Kay [80]

Yes because 8/10 as a decimal is 0.8 while 1/2 is 0.5

5 0

3 years ago

Read 2 more answers

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

Is how many student passed the math test a statistical question

Soloha48 [4]

Answer:

No it is not statistical

Step-by-step explanation:

It would be statistical if the answers varied which in this case they don't because there is a certain amount of people that passed and the answers do not vary. However, asking what was your score is statistical because answers will vary.

4 0

3 years ago

Help Me! what is 6 1/3 - 4 1/9?<br> A. 2 7/9<br> B. 2 5/9<br> C. 2 4/9<br> D. 2 2/9

GalinKa [24]

The answer is D. 2 2/9

7 0

3 years ago

Please help me find the perimeter of the figure.

Fiesta28 [93]

Just add all of the sides together
10+3+33+15+33+3 = 97

Perimeter is the distance around the edge of a shape.

7 0

3 years ago

Read 2 more answers