Select the correct answer.

Using the normal distribution, it is found that 15.87% of the students received a score below 64.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given by, respectively: [tex]\mu = 70, \sigma = 6[/tex].

The proportion of students who received a score below 64 is the p-value of Z when X = 64, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{64 - 70}{6}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

Hence, 15.87% of the students received a score below 64.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Answer:

I think the answer is B

Step-by-step explanation:

The error which is made by Mel in drawing square in the circle is that thefour chords that ob , chord wx must be a diameter

A square is a 2 dimensional figure having four sides and four angles which are equal to 90°. All sides of square are always equals to each other.

First draw a circle in which we want to draw such square.

Next draw a chord in the circle.

From one end, draw a straight line connecting a point on the circle and end point of the chord in such a way that the line and chord are perpendicular to each other.

Next draw another line also from the end of line formed in second step.

Lastly draw a line from the other end of chord and join it with the line we have drawn lastly.

In this way we will get square in circle.

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The expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].

Given trigonometric expression is:

[tex]Cos(\frac{\pi }{2}+r )[/tex]

The value of [tex]Cos(\frac{\pi }{2}+\theta )[/tex] is [tex]-Sin\theta[/tex] because [tex]\frac{\pi }{2} +\theta[/tex] lies in the second quadrant and the cosine function is negative in the second quadrant.

So, [tex]Cos(\frac{\pi }{2}+r )= -Sin r[/tex]

The range of sine and cosine functions is the same i.e. [-1,1].

Both the functions are periodic functions with periods 2π.

Hence, the expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].

To get more about trigonometric functions visit:

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Answer:

268

Step-by-step explanation:

Derivative Rule

On deriving,

Substitute x = 3

Solution:

268

=============================

[tex]\sf \bold{ \rightarrow } \ y = 9x^3 + 4x^2 + x + 3[/tex]

[tex]\sf \bold{ \rightarrow } \ \dfrac{dy}{dx} = \dfrac{d}{dx} ( \ 9x^3 + 4x^2 + x + 3 \ )[/tex]

[tex]| | \ \mathrm{ If \ y = x^n , \ then \ \frac{dy}{dx} = nx^{n-1}} \ | |[/tex]

[tex]\sf derivative \ of \ constant \ is \ always \ 0 \ || \ \sf\dfrac{d}{dx}\left(a\right)=0 \ ||[/tex]

solving step wise

[tex]\sf \bold{ \rightarrow } \ \dfrac{d}{dx} ( 9x^3) + \dfrac{d}{dx}(4x^2) + \dfrac{d}{dx}(x )+ \dfrac{d}{dx}(3 )[/tex]

[tex]\sf \bold{ \rightarrow } \ \sf ( 3(9x^{3-1}) +2(4x^{2-1}) + (1)(x^{1-1} )+ 0[/tex]

[tex]\sf \rightarrow 27x^2+8x+1+0[/tex]

[tex]\sf \rightarrow 27x^2+8x+1[/tex]

when x = 3

[tex]\sf \hookrightarrow 27(3)^2+8(3)+1[/tex]

[tex]\sf \hookrightarrow 243+24+1[/tex]

[tex]\sf \hookrightarrow 268[/tex]

Step-by-step explanation:

Ans of 8

x + 3x + 2x = 180 (sum of all angle of triangle is 180)

6x = 180

x = 60

Ans of 9

(2x-2)+(x+5)+90 = 180

3x+3+90 = 180

3x + 93 = 180

3x = 180-93

x = 87/3

x = 29

Answer:

Step-by-step explanation:

The height of the building is: 26.585 m.

The angle formed by the line of sight and the horizontal plane for an object below the horizontal.

Given:

angle of depression= 28 degree,

distance between car and building= 50m

using trigonometry,

tan 28= P/B

0.5317= P/50

P= 26.585 m

Hence, the height of the building is 26.585 m.

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8x + 11 - 11 = 35 - 11

8x = 24

x = 24/8

x = 3

check

8 * 3 + 11 = 24 + 11 = 35

Answer/Step-by-step explanation:

Quotient is simply the ratio of the first numerator to the second numerator:

Let's [tex]\frac{x_1}{y}\;and\;\frac{x_2}{y}[/tex] are two fractions in same terms.

Thus, [tex]\frac{x_1}{y}\div\frac{x_2}{y}[/tex] {Divided by a fraction is equal to multiplied by its reciprocal}

=[tex]\frac{x_1}{y}\times\frac{y}{x_2}[/tex]

Quotient is simply the quotient of their numerators.

Example could be:

[tex]\frac{2}{7}\div\frac{3}{7}[/tex]

[tex]\frac{2}{7}\times\frac{7}3}[/tex]

[tex]\frac{2}{3}[/tex]

2 is first numerator and 3 is the second numerator.

~lenvy~

Answer:

y = - 4

Step-by-step explanation:

x = - 2

3x - 2y = 2

substitute x = - 2 into 3x - 2y = 2

3(- 2) - 2y = 2 ← step 1

- 6 - 2y = 2 ( add 6 to both sides ) ← step 2

- 2y = 8 ( divide both sides by - 2 )

y = - 4

Answer:

1440 ounces

Step-by-step explanation:

there are 16 ounces in a pound so multiply 90 by 16 and you get 1440 hope this helps!

Answer:

C. Odd

Step-by-step explanation:

If you reflect this function across the y-axis it is not symmetrical, therefore it is not an even function

But, if you rotate this function by 180 degrees, it is unchanged, therefore it is and odd function

Answer:

Formula for volume of square pyramid:-

V = 1/3 x a^2 x h

Where 'a' is the length of one side of the base, and 'h' is the height.

Plug in our values, given that:

16.6m = side length of base.

9.1m = height of pyramid.

V = 1/3 x a^2 x h

V = 1/3 x 16.6^2 x 9.1

V = 1/3 x 275.56 x 9.1

V = 1/3 x 2507.596

V = 2507.596/3

V = 835.865, which rounds to 835.9 cubic meters.

Answer:Its A, Tiffani's prediction is valid. The probability of the next customer ordering a white bib is about 30%.

Step-by-step explanation:Did the K12 quiz

Answer:

Her solution is incorrect. The correct solution for the equation is x=7

Step-by-step explanation:

Sasha solved the equation incorrectly.

The correct way to solve this equation would be:

8x = 56

Divide both sides by 8.

[tex]\frac{8x}{8}= \frac{56}{8}[/tex]

You would get x=7.

This equation has 1 solution.

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

Stay Brainy!

−Kallmekrish

[tex]\\ \rm\rightarrowtail x^2-21x+108[/tex]

[tex]\\ \rm\rightarrowtail x^2-12x-9x+108[/tex]

[tex]\\ \rm\rightarrowtail x(x-12)-9(x-12)[/tex]

[tex]\\ \rm\rightarrowtail (x-9)(x-12)[/tex]

Done!

Answer:

32h=d

Step-by-step explanation:

yea, this is big brain time lol

also edge lol

Answer: 60% increase

Step-by-step explanation:

First, find how many more people attended this year: 1,520 - 950 = 570.

Now, find what percent of 950 570 is: 950 * x = 570 → x = .6 * 100 = 60% :)

Answer: 12 miles

Step-by-step explanation:

Answer:

C the number of toothbrushes :)

Step-by-step explanation:

You can show how many were given away each month on a dot plot :)

The others would not make sense with the dot plot :)

Haeva great day!

Please rate and mark brainliest!

Answer:

[tex]x=7 + \sqrt{3}[/tex]

[tex]x=7 - \sqrt{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]5x^2-70x=-230[/tex]

Divide both sides by 5:

[tex]x^2-14x=-46[/tex]

Square half of the coefficient of [tex]x[/tex]:  [tex](-14 \div 2)^2=49[/tex]
and add this to both sides:

[tex]x^2-14x+49=-46+49[/tex]

Factor the left side and simplify the right side:

[tex](x-7)^2=3[/tex]

Square root both sides:

[tex]x-7=\pm\sqrt{3}[/tex]

Add 7 to both sides:

[tex]x=7 \pm \sqrt{3}[/tex]

[tex]\sf x=\pm \sqrt{3}+7[/tex]

solving step wise:

[tex]\sf 5x^2-70x=-230[/tex]

divide the following by 5

[tex]\sf x^2-14x=-46[/tex]

completing square

[tex]\sf (x-\dfrac{14}{2})^2-(\dfrac{14}{2})^2 =-46[/tex]

should look like this

[tex]\sf (x-7)^2-49=-46[/tex]

simplify by changing sides

[tex]\sf x-7=\pm \sqrt{3}[/tex]

final answer:

[tex]\sf x=\pm \sqrt{3}+7[/tex]

Answer:

V = πr²h

Step-by-step explanation:

Answer:

V = Bh or what the guy above/below me said

Step-by-step explanation:

Answer:

  36.24 cm²

Step-by-step explanation:

The shaded region is the inscribed circle in the isosceles triangle. In order to find its area, we need to know the radius of the circle.

__

One way to find the radius of the circle is to make use of the Angle Bisector theorem. It tells us an angle bisector divides the sides of a triangle proportionately. In the attached figure, that means angle bisector CD divides segment AE in proportion to sides CA and CE.

To make use of this theorem, we need to know the length of side CA. That is the hypotenuse of right triangle AEC, so can be found using the Pythagorean theorem. Isosceles triangle ABC is given as having height AE=10 and base BC = 12.

  CA² = CE² +AE²

  CA² = 6² +10² = 136 . . . . . . . CE is half the base length: 12/2 = 6

  CA = √136 = 2√34

__

Now we can write the proportion using the angle bisector theorem.

  DE/CE = DA/CA

  r/6 = (10 -r)/(2√34)

  r√34 = 3(10 -r) . . . . . . . multiply by 6√34

  r(3 +√34) = 30

  r = 30/(3 +√34)

__

From this, we can find the area of the shaded circle to be ...

  A = πr² = (3.14)(30/(3 +√34))²

  = 3.14·900/(43 +6√34) ≈ 36.2374 . . . cm²

The area of the shaded region is about 36.24 cm².

_____

Additional comment

Using area considerations, the formula for the radius of the inscribed circle in an isosceles triangle with base 'b' and sides 'a' can be found to be ...

  [tex]r=\dfrac{b}{2}\sqrt{\dfrac{2a-b}{2a+b}}[/tex]

For a=√136 and b=12, this becomes ...

  [tex]r=\dfrac{12}{2}\sqrt{\dfrac{2\sqrt{136}-12}{2\sqrt{136}+12}}=6\sqrt{\dfrac{(\sqrt{34}-3)^2}{34-9}}=1.2(\sqrt{34}-3)\approx3.39714[/tex]

This is the same value we found above.

Answer:

4.295cm

Step-by-step explanation:

Here,

Circumference = 27cm

We know,

C=2πr

or, 27 = 2×22×r

7

or, 44×r = 27

7

27

or, r = 44

7

or, r = 27×7

44

Therefore, r = 4.295cm

Answer:

energy

Step-by-step explanation:

Answer:

energy

Step-by-step explanation:

Answer:

-35/91 is the required answer

Hope it helps

make me brainlist

Answer:

answer is the butt world

Step-by-step explanation:

in a function every valid values of x has exactly one assigned y value.

in an ordered pair the first number is x, the second number is y.

the y in (k, 0) is therefore 0.

and this y is different to all other y values in the relation.

therefore, k must be different to all other defined x values (otherwise it would give an x value a second y value, which would make this a not-function).

so, k must be an integer not out of {-9, 0, 2}

Answer:  3 out of 19  

Step-by-step explanation:

Answer:

P(caramel) = 3/10

P(raspberry) = 1/3

Step-by-step explanation:

Given:

⇒ Total chocolates = 3 + 3 + 4 = 10

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(picking \ caramel \ chocolate) = \dfrac{3}{10}[/tex]

If the picked caramel chocolate is NOT replaced then:

[tex]\sf \implies P(picking \ raspberry \ chocolate) = \dfrac39=\dfrac13[/tex]

Answer:

42.67π ft³

Step-by-step explanation:

Given

Formula

Solving

Based on the relative frequency and the number of times the experiment is to be performed, the number of times Event A should occur is 10 times.

The relative frequency in this regard is 1/3.

The number of times it will occur can be found as:

= Relative frequency x Number of times event was performed

Solving gives:

= 1/ 3 x 30

= 10 times

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