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VMariaS [17]
3 years ago
15

Question 2 of 10

Mathematics
1 answer:
agasfer [191]3 years ago
4 0

A

Step-by-step explanation:

two of the triangles' corresponding angles are the same even if the side lebgths are not, making these two similar

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g In a one-tail hypothesis test where you reject H0 only in the lower tail, what is the p-value if Z STAT
zepelin [54]

Answer:

The P-value is 0.0166.

Step-by-step explanation:

<u>The complete question is:</u> In a​ one-tail hypothesis test where you reject H0 only in the lower ​tail, what is the p-value  if ZSTAT = -2.13.

We are given that the z-statistics value is -2.13 and we have to find the p-value.

Now, the p-value of the test statistics is given by the following condition;

                    P-value = P(Z < -2.13) = 1 - P(Z \leq 2.13)

                                  = 1 - 0.9834 = <u>0.0166</u>

Assuming that the level of significance is 0.10 or 10%.

The decision rule for rejecting the null hypothesis based on p-value is given by;

  • If the P-value of the test statistics is less than the level of significance, then we have sufficient evidence to reject the null hypothesis.
  • If the P-value of the test statistics is more than the level of significance, then we have insufficient evidence to reject the null hypothesis.

Here, the P-value is more than the level of significance as 0.0166 > 0.10, so we have insufficient evidence to reject the null hypothesis, so we fail to reject the null hypothesis.

3 0
3 years ago
"m divided by 3" is the same as
KonstantinChe [14]
M/3
OR
the quotient of a number, m, and 3

hope this helps :)
6 0
3 years ago
Read 2 more answers
Solve for y -2(x + 3 y) =18
LUCKY_DIMON [66]

Answer:

y= -3y - 1/3x

Step-by-step explanation:

-2(x + 3y) = 18 Distribute the -2 to the x + 3y

-2x - 6y = 18

+2x          +2x    Add the 2x to both sides

-6y = 18 + 2x   Divide both sides by -6

y= -3y - 1/3x

3 0
3 years ago
For each of the following numbers, write 4 decimals that would round to this whole number when rounde to the nearest whole numbe
Natalka [10]
Round to the nearest whole number:

a) 14 ⇒ 13.5 ; 13.9 ; 14.1 ; 14.4
b) 28 ⇒ 27.5 ; 27.9 ; 28.1 ; 28.4
c) 32 ⇒ 31.5 ; 31.9 ; 32.1 ; 32.4
d) 50 ⇒ 49.5 ; 49.9 ; 50.1 ; 50.4
e) 67 ⇒ 66.5 ; 66.9 ; 67.1 ; 67.4
f) 71 ⇒ 70.5; 70.9 ; 71.1 ; 71.4
g) 88 ⇒ 87.5; 87.9 ; 88.1 ; 88.4
h) 95 ⇒ 94.5; 94.9 ; 95.1 ; 95.4

If the following number is within the range of 1 to 4 then round down.
<span>If the following number is within the range of 5 to 9 then round up.</span>
8 0
3 years ago
Find the directional derivative of the function at the given point in the direction of the vector v. G(r, s) = tan−1(rs), (1, 3)
alexandr1967 [171]

The <em>directional</em> derivative of f at the given point in the direction indicated is \frac{5}{2}.

<h3>How to calculate the directional derivative of a multivariate function</h3>

The <em>directional</em> derivative is represented by the following formula:

\nabla_{\vec v} f = \nabla f (r_{o}, s_{o})\cdot \vec v   (1)

Where:

  • \nabla f (r_{o}, s_{o}) - Gradient evaluated at the point (r_{o}, s_{o}).
  • \vec v - Directional vector.

The gradient of f is calculated below:

\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial r}(r_{o},s_{o})  \\\frac{\partial f}{\partial s}(r_{o},s_{o}) \end{array}\right]   (2)

Where \frac{\partial f}{\partial r} and \frac{\partial f}{\partial s} are the <em>partial</em> derivatives with respect to r and s, respectively.

If we know that (r_{o}, s_{o}) = (1, 3), then the gradient is:

\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right]

\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right]

\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right]

If we know that \vec v = 5\,\hat{i} + 10\,\hat{j}, then the directional derivative is:

\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right]

\nabla _{\vec v} f (r_{o}, s_{o}) = \frac{5}{2}

The <em>directional</em> derivative of f at the given point in the direction indicated is \frac{5}{2}. \blacksquare

To learn more on directional derivative, we kindly invite to check this verified question: brainly.com/question/9964491

3 0
2 years ago
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