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mojhsa [17]
3 years ago
15

Find the coordinates of the midpoint of the line segment ab,where a and b have coordinates a(8.0),b(4.6)

Mathematics
1 answer:
umka2103 [35]3 years ago
4 0
\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 8}}\quad ,&{{ 0}})\quad 
%  (c,d)
&({{ 4}}\quad ,&{{ 6}})
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{4+8}{2}~~,~~\cfrac{6+0}{2} \right)\implies (6~~,~~3)
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Use the intermediate value theorem to determine whether the polynomial function has a real zeros between the given integers.
zavuch27 [327]
f(1)=-5\cdot1^4+8\cdot1^3+6\cdot1+1=-5+8+6+1=10\\
f(2)=-5\cdot2^4+8\cdot2^3+6\cdot2+1=-80+64+12+1=-3\\\\
f(1)>0\\
f(2)
It does.
3 0
3 years ago
9(4b-1)=2(b+3) Slove for b plz answer as quick as u can please
Jobisdone [24]

36b - 9 = 2b + 6 \\ 34b = 15 \\ b =  \frac{15}{34}
3 0
3 years ago
The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppos
xenn [34]

Answer:

(a) P(X > $57,000) = 0.0643

(b) P(X < $46,000) = 0.1423

(c) P(X > $40,000) = 0.0066

(d) P($45,000 < X < $54,000) = 0.6959

Step-by-step explanation:

We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.

Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.

<em>Let X = annual salaries in the metropolitan Boston area</em>

SO, X ~ Normal(\mu=$50,542,\sigma^{2} = $4,246^{2})

The z-score probability distribution for normal distribution is given by;

                      Z  =  \frac{X-\mu}{\sigma }  ~ N(0,1)

where, \mu = average annual salary in the Boston area = $50,542

            \sigma = standard deviation = $4,246

(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)

    P(X > $57,000) = P( \frac{X-\mu}{\sigma } > \frac{57,000-50,542}{4,246 } ) = P(Z > 1.52) = 1 - P(Z \leq 1.52)

                                                                     = 1 - 0.93574 = <u>0.0643</u>

<em>The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574</em>.

(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)

    P(X < $46,000) = P( \frac{X-\mu}{\sigma } < \frac{46,000-50,542}{4,246 } ) = P(Z < -1.07) = 1 - P(Z \leq 1.07)

                                                                     = 1 - 0.85769 = <u>0.1423</u>

<em>The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769</em>.

(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)

    P(X > $40,000) = P( \frac{X-\mu}{\sigma } > \frac{40,000-50,542}{4,246 } ) = P(Z > -2.48) = P(Z < 2.48)

                                                                     = 1 - 0.99343 = <u>0.0066</u>

<em>The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343</em>.

(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)

    P($45,000 < X < $54,000) = P(X < $54,000) - P(X \leq $45,000)

    P(X < $54,000) = P( \frac{X-\mu}{\sigma } < \frac{54,000-50,542}{4,246 } ) = P(Z < 0.81) = 0.79103

    P(X \leq $45,000) = P( \frac{X-\mu}{\sigma } \leq \frac{45,000-50,542}{4,246 } ) = P(Z \leq -1.31) = 1 - P(Z < 1.31)

                                                                      = 1 - 0.90490 = 0.0951

<em>The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively</em>.

Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = <u>0.6959</u>

3 0
2 years ago
The speed of sounds in water is 1.46 x 10^3 meters per second. The speed of sound in air is 3.31 x 10^2 meters per second. How m
dlinn [17]

Answer:

Hey there!

1.46x10^3-3.31x10^2

14.6x10^2-3.31x10^2

11.29x10^2

1.129x10^3

J is the correct answer.

Hope this helps :)

6 0
3 years ago
Simplify: StartRoot StartFraction 576 Over 64 EndFraction EndRoot The prime factorization of 576 is. The prime factorization of
riadik2000 [5.3K]

The prime factor of the 576 is 2^6 * 3^2 and the prime factor of the 64 is 2^6. And the expression \sqrt{\dfrac{576}{64}} is equal to 3.

<h3>What is simplification?</h3>

Simplification is to make something easier to do or understand and to make something less complicated.

Given

The expression is \sqrt{\dfrac{576}{64}}

The prime factor of the 576 will be

576 = 2^6 * 3^2

The prime factor of the 64 will be

64 = 2^6

Then the expression will be

\sqrt{\dfrac{576}{64}} = \sqrt{\dfrac{2^6 * 3^2}{2^6}}\\\\\sqrt{\dfrac{576}{64}} = \sqrt{3^2}\\\\\sqrt{\dfrac{576}{64}} = 3

More about the simplification link is given below.

brainly.com/question/12616840

5 0
2 years ago
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