Consider vectors u and v, where u=(1,-1) and v=(1,1). What is the measure of the angle between the vectors? 0° 60° 90° 180°

gavmur [86]

Answer:

angle y = 49°

Step-by-step explanation:

If AB = AD and BC = DC, then the two triangles are isosceles triangles. The altitude from the top to the base divides the top angle into two equal angles, with 90° angles at the base. If angle C is divided into two equal angles (41°) and at the base is a 90° angle, that makes angle CBD 49°. On an isosceles triangle, the two angles opposite to the equal sides are identical. So angle y is identical to angle CBD.

6 0

3 years ago

Read 2 more answers

Write an equation of a function that is not linear

arlik [135]

Y=X^2+3 I hope this help you

6 0

3 years ago

The monthly salary of a married civil servant is RS 25700 and 10% of his salary is deducted as his provident fund .How much inco

OverLord2011 [107]

Step-by-step explanation:

you deduct the 10 percent provident funds first .

Then u calculate for the 1 percent of d deduction .

ur answer should be 27756

7 0

3 years ago

A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilog

Zanzabum

Answer:

Step-by-step explanation:

Hello!

*Full text*

A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is

weight = b + width * m

This model was fit to the data using the method of the least squares. The following results were obtained from statistical software.

(See attachment for output)

R2 = 0.423

A.) What is the regression equation for this example?

The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963

In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:

^Y= 2.3013 + 0.7963Xi

B.) What is the explanatory, or predictor, variable in this study?

The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:

X: Width of a horseshoe crab (cm)

C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.

To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.

The hypotheses are:

H₀: β=0

H₁: β≠0

α: 0.05

$t= \frac{m-\beta }{S_m} ~t_{n-2}$

$t_{H_0}= \frac{0.7963-0}{0.0939}= 8.48$

The value of the statistic under the null hypothesis is t= 8.48

D.) What can we say about the p-value?

This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:

P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001

E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?

As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:

Critical values ± $t_{n-2;1-\alpha /2}$ = ± $t_{98; 0.975}$ = ± 1.984

This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-

F.) Find the confidence interval for the slope.

Using a 95% confidence level, the interval for the slope is:

[m ± $t_{n-2;1-\alpha /2}$ Sm]

[0.7963 ± 1.984 * 0.0939]

[0.61; 0.98]

G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.

Yes, there is a significant relationship between the width and weight of the horseshoe crabs.

Using the critical value approach:

The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.

I hope this helps!

6 0

3 years ago

Drag the system of equation to the point that represents the solution to the system.

PIT_PIT [208]

Solving of the system equation: 2x-y=-13 ⇒(1)   and    y=x+9 ⇒(2)
by substituting from (2) at (1)
2x-(x+9)=-13
2x-x-9=-13
x=-4 ⇒ substituting at (2) ∴ y = -4+9 = 5
The point that represents the solution to the system = (-4,5)
========================================================

solving of the system equation: 3x+2y=10 ⇒(1) and 6x-y=10 ⇒(2)
by multiplying equation (2) ⇒    12x-2y=20 ⇒(3)
adding (1) and (3)
                            15 x = 30 ⇒   x=2
from equation (2) 6x-y =10 ⇒⇒⇒ y = 6x-10 =12-10=2
The point that represents the solution to the system = (2,2)
=======================================================

solving of the system equation: 4x-3y=5 ⇒(1) and 3x+2y=-9 ⇒(2)
solve for x, y
we find   x=-1 and y=-3

The point that represents the solution to the system = (-1,-3)
=======================================================

solving of the system equation: x+y=7 ⇒(1)   and    x-y=-1 ⇒(2)
adding (1) and (2)
                           2x=6 ⇒⇒⇒ x = 3
substitute at (1)
                         y =7-x=7-3=4
The point that represents the solution to the system = (3,4)
=======================================================

solving of the system equation: y=3x-7 ⇒(1) and y=2x-5 ⇒(2)
equating (1) and (2)
solve for x and y
we find x=2 ⇒⇒⇒ y = -1
The point that represents the solution to the system = (2,-1)
=======================================================

The system equation : y = 6    and x =-5
The point that represents the solution to the system = (-5,6)
=======================================================
The attached figure represent a conclusion for the answer

5 0

3 years ago