If a normal distribution has a mean of 154 and a standard deviation of 15,
what is the value that has a z-score of 1.6?

9514 1404 393

Answer:

  C.  4/9

Step-by-step explanation:

There are a couple of ways you can do this.

  [tex]\log_3{4x}-2\log_3{x}=2\\\\\log_3{4}+\log_3{x}-2\log_3{x}=2\\\\\log_3{4}-2=\log_3{x}\\\\4\cdot3^{-2}=x\qquad\text{take antilogs}\\\\\boxed{x=\dfrac{4}{9}}\\\\\textsf{or}\\\\\dfrac{4x}{x^2}=3^2\qquad\text{take antilogs}\\\\\dfrac{4}{9}=x\qquad\text{cancel $x$, multiply by $\dfrac{x}{9}$}[/tex]

Answer:

x= -0.182 and +4

hope it helps

have a nice day

9514 1404 393

Answer:

  D

Step-by-step explanation:

The sine function is negative only for angles greater than 180°. This eliminates choice B.

The sine function is periodic with a period of 360°, eliminating choices A and C.

The only viable choice is D, which is the correct one.

Answer:

-2 and -2

Step-by-step explanation:

Answer:

9 (a) [tex]d = \frac{\sqrt{e}}{\sqrt{3}}[/tex]

9 (b) [tex]d = \frac{\sqrt{7k}}{\sqrt{2}}[/tex]

Step-by-step explanation:

Hope this helped!

Answer:

3, 5 and 15

Step-by-step explanation:

According to the triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. This means that you cannot draw a triangle with side lengths 3, 5 and 15, since 3 + 5 is less than 15.

Answer:

The answer is A

Step-by-step explanation:

Starting from -3 in the Y values of option A. If you subtract three from each value, you will get the next value to the right.

Answer:

Someone already answered it but I won't let 50 points go to waste. !!!!!

Step-by-step explanation:

Answer:

[tex] -\frac{9}{2} [/tex]

Step-by-step explanation:

Rate of change of x and y can be calculated using the following formula and using any two given pair of values from the table:

Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using (-12, 60) and (-6, 33).

Where,

[tex] (-12, 60) = (x_1, y_1) [/tex]

[tex] (-6, 33) = (x_2, y_2) [/tex]

Plug is the values

Rate of change = [tex] \frac{33 - 60}{-6 -(-12)} [/tex]

Rate of change = [tex] \frac{-27}{6} [/tex]

Simplify

Rate of change = [tex] \frac{-9}{2} [/tex]

Rate of change = [tex] -\frac{9}{2} [/tex]

Answer:

20

Step-by-step explanation:

your mom

Answer:

[tex]\frac{1}{(x+1)(x-2)}[/tex]

Step-by-step explanation:

[tex]\frac{x+2}{4x^2 + 5x + 1} \ \times \ \frac{4x+1}{x^2-4}\\\\=\frac{x+2}{4x^2 + 4x + x + 1} \ \times \ \frac{4x+1}{x^2-2^2}\\\\=\frac{x+2}{4x(x + 1) + 1( x + 1)} \ \times \ \frac{4x+1}{(x - 2)(x + 2)} \ \ \ \ \ \ \ \ [ \ (a^2 - b^2 = (a-b)(a+b) \ ]\\\\\\=\frac{x+2}{(4x + 1)(x+1)} \ \times \ \frac{4x+1}{(x-2)(x+2)}\\\\=\frac{1}{(x+1)} \ \times \ \frac{1}{(x-2)}\\\\= \frac{1}{(x+1)(x-2)}[/tex]

Answer:

D. 1/(x+1)(x-2)

Step-by-step explanation:

i looked it up on a simplifier :)

Answer:

x<8

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

X=-12/4

X=-3

hope it helps

Answer:

-3

Step-by-step explanation:

4x= -12

4x/4 = -12/4

x = -3

Step-by-step explanation:

Given:

[tex]\textbf{F} = (2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}[/tex]

This field will have a scalar potential [tex]\varphi[/tex] if it satisfies the condition [tex]\nabla \times \textbf{F}=0[/tex]. While the first x- and y- components of [tex]\nabla \times \textbf{F}[/tex] are satisfied, the z-component doesn't.

[tex](\nabla \times \textbf{F})_z = \left(\dfrac{\partial F_y}{\partial x} - \dfrac{\partial F_x}{\partial y} \right)[/tex]

[tex]\:\:\:\:\:\:\:\:\: = 3x^2 - 2x \ne 0[/tex]

Therefore the field is nonconservative so it has no scalar potential. We can still calculate the work done by defining the position vector [tex]\vec{\textbf{r}}[/tex] as

[tex]\vec{\textbf{r}} = x \hat{\textbf{i}} + y \hat{\textbf{j}} + z \hat{\textbf{k}}[/tex]

and its differential is

[tex]\textbf{d} \vec{\textbf{r}} = dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}}[/tex]

The work done then is given by

[tex]\displaystyle \oint_c \vec{\textbf{F}} • \textbf{d} \vec{\textbf{r}} = \int ((2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}) • (dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}})[/tex]

[tex]\displaystyle = (x^2y + xz^3) + x^3y + xz^3|_{(1, -2, 1)}^{(3, 1, 4)}[/tex]

[tex]= 422[/tex]

Step-by-step explanation:

first, determine the coordinates values like x =9 and y=-5

so x-6 =3

1

Step-by-step explanation:

[tex]\displaystyle \lim_{x \to 0}\dfrac{\sin x}{x}[/tex]

Let

[tex]f(x)= \sin x[/tex]

[tex]g(x)=x[/tex]

We are going to use L'Hopital's Rule here that states

[tex]\displaystyle \lim_{x \to c}\dfrac{f(x)}{g(x)}=\lim_{x \to c}\dfrac{f'(x)}{g'(x)}[/tex]

We know that

[tex]f'(x) = \cos x[/tex] and [tex]g'(x)=1[/tex]

so

[tex]\displaystyle \lim_{x \to 0}\dfrac{\sin x}{x}=\lim_{x \to 0}\dfrac{\cos x}{1}=1[/tex]

Answer:

The zeros are 1 and 2

Step-by-step explanation:

Given

[tex]y =x^2 - 3x + 2[/tex]

Required

The zeros

[tex]y =x^2 - 3x + 2[/tex]

Expand

[tex]y =x^2 - 2x-x + 2[/tex]

Factorize

[tex]y =x(x - 2)-1(x - 2)[/tex]

Factor out x - 2

[tex]y =(x - 1)(x - 2)[/tex]

Set to 0

[tex](x - 1)(x - 2)=0[/tex]

Solve for x

[tex]x - 1 = 0 \to x =1[/tex]

[tex]x - 2 = 0 \to x =2[/tex]

Hence, the zeros are 1 and 2

Answer:

The bottom one.

Step-by-step explanation:

Answer: 2617 centimeters cubed

Step-by-step explanation:

The formula for finding volume of a cylinder is [tex]V=\pi r^2h[/tex]

The radius is half of the diamerter which will be 7 for this figure.

The height is marked 17

[tex]\pi 7^2(17)\\\pi (49)(17)\\833\pi \\[/tex]

833π is about 2616.95

Rounded to the nearest whole number it is 2617

Answer:

1.3

Step-by-step explanation:

Raise/run = slope aka distance in this situation

8/6 = 1.3

Answer:

10 units

Step-by-step explanation:

use the distance formula as thought in school

Step-by-step explanation:

You can't expect to get exactly 2500 out of 5000 tosses more than a few times . You will come pretty close, but that's only good in horseshoes.

Of course I'm answering this on the basis of a computer language and not actually performinig this a million tmes, each part of a million consisting of 5000 tosses.

Simulations and not completely unbiased, but based on experience, 5000 is a very small number and getting 2500 more than a couple of times is unlikely

The probability of flipping a coin

coming up heads and tails is 1/2.

So, toss 5000 times 5000/2= 2500

heads: 2500

tails : 2500

Answer:

1=110 2=70 3=70 4=110 5=110 6=70 7=70 8 =110

Step-by-step explanation:

its the answer

Answer:

(3x-2)^2+8= 9x^2-12x+12

Answer:

Kerri

calculate z scores z= (x - xbar)/stdev

Kerri = 1.7

Cade = .7

Vincent = 1

Step-by-step explanation:

Answer:

Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.

Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.

Step 3: Write the answer using interval notation.

Answer:

Chad can divide his rope in 21 pieces. (Answer B)

Step-by-step explanation:

To solve we divide.

15 divided by 5/7 is what we need to know.

When dividing fractions it is the same thing as multiplying by the reciprocal (flipped version of the fraction).

[tex]15[/tex] ÷ [tex]\frac{5}{7}[/tex] = 15 × [tex]\frac{7}{5}[/tex]

[tex]\frac{15}{1}[/tex]  × [tex]\frac{7}{5}[/tex] = [tex]\frac{105}{5}[/tex]

[tex]\frac{105}{5}[/tex] = 21

Chad can divide his rope in 21 pieces.

Answer:

21 pieces

Step-by-step explanation:

Divide (5/7 yd / piece) into 15 yds:

   15 yds

----------------------- = 21 pieces

(5/7 yd / piece)

Answer: 11%

Step-by-step explanation:

Since the formula for interest is:

I = PRT

where.

P = 1200

I = 99

T = 0.75

I = PRT

R = I/PT

R = 99/(1200 × 0.75)

R = 99/900

R = 11%

Therefore, the rate is 11%

Answer:

Brainly's honor code doesn't allow quiz questions to be posted.

"Students are never allowed 2 post questions directly from tests, quizzes, and assessments, or copy answers found on Brainly during tests, quizzes, and assessments."

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Explanation:

To factor this, we need to find two numbers that

Through trial and error, you would find that the two numbers are -2 and -7

-2*(-7) = 14

-2 + (-7) = -9

So that's why the given trinomial factors to (y-2)(y-7)

You can use the FOIL rule to go from (y-2)(y-7) back to y^2-9y+14 again.

Answer:

The playable area has a width of 9 inches and a height of 6 inches.

Step-by-step explanation:

There are a number of ways you can get there.

1. Check the answers to see which have the right area and aspect ratio.

A: area = 24 in² — does not match 54 in²

B: area = 54 in², aspect ratio 6:9 = 2:3 — does not match 3:2 aspect ratio

C: area = 54 in², aspect ratio 9:6 = 3:2 — matches problem statement

D: area = 121.5 in² — does not match 54 in²

2. If the screen were 3:2 (inches), its area would be 6 in². The area of 54 in² is 9 times that value, so the actual screen dimensions are √9 = 3 times 3:2. That is, they are width:height = 9:6 inches — matches selection C.

3. You can write equations for width and height and solve.

w/h = 3/2

wh = 54

Substituting w=3/2·h into the second equation gives

... (3/2)h·h = 54

... h² = 36 . . . . . multiply by 2/3

... h = √36 = 6 . . . . square root, result in inches

Answer:

D. The playable area has a width of 9 inches and a height of 6 inches.

Step-by-step explanation:

if the playable area is 54 and that such ratio of dimensions is 3:2

Then we are basically being asked to find the factor of ratios below that also multiply to get 54

54 = 9 x 6 and this is also a ratio of 3:2

As 3(3 + 2) = 54

and as width was asked first when ratio was given 3:2

The width therefore is 9 and the height is 6

So answer is D