Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

Answer:

[tex]\dfrac{19}{840}[/tex]

Step-by-step explanation:

The given fraction is:

[tex]\dfrac{1}{168}+\dfrac{3}{180}[/tex]

We need to solve it.

The LCM of 168 and 180 is 2520.

So,

[tex]\dfrac{1}{168}+\dfrac{3}{180}=\dfrac{15+3\cdot14}{2520}\\\\=\dfrac{19}{840}[/tex]

So, the required answer is equal to [tex]\dfrac{19}{840}[/tex].

Given:

The diagram of triangle DEF and triangle D'E'F' on a coordinate plan.

To find:

The algebraic representation of the dilation.

Solution:

The vertices of triangle DEF are D(0,7), E(7,-7) and F(-7,-7).

The vertices of triangle D'E'F' are D'(0,2), E(2,-2) and F(-2,-2).

We know that, the dilation factor is:

[tex]k=\dfrac{x\text{ or }y\text{ coordinate of the dilated point}}{x\text{ or }y\text{ coordinate of the corresponding original point}}[/tex]

For point D' the y-coordinate is 7 and for point D the y-coordinate is 2. So,

[tex]k=\dfrac{2}{7}[/tex]

The rule of dilation is:

[tex](x,y)\to \left(kx,ky\right)[/tex]

[tex](x,y)\to \left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)[/tex]

The algebraic representation of the dilation is [tex]\left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)[/tex].

Therefore, the correct option is b.

Answer:

0.4970

Step-by-step explanation:

I might be wrong

The probability that an injection-site reaction occurs for the first time on the 6th patient of the day will be 0.4970. Then the correct option is D.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%.

The probability that an injection-site reaction occurs for the first time on the 6th patient of the day is given as,

P = (1 - 0.11)⁶

P = (0.89)⁶

P = 0.4970

The probability that an injection-site reaction occurs for the first time on the 6th patient of the day will be 0.4970. Then the correct option is D.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ2

Answer:

-14

Explanation:

Elasticity of demand is the degree of change in demand after a change I'm price, basically demand's sensitivity to price change.

Formula for calculating price elasticity is: change in price/change in quantity =dq/dp

Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:

2p+2+dq/dp=0

dq/dp=-2p-2

Given p =6, we substitute:

dq/dp=-2×6-2

dq/dp=-12-2

dq/dp=-14

With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.

Answer:

i got Profit = $125,129,007.1

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

5x2= 10

7x8= 56

10+56= 66

Answer:

106

Step-by-step explanation:

split the shape, so you have 2 rectangles.

Multiply 8 and 7 = 56

add 2 and 8 =10, then multiply 10 by 5. =50

add 50 and 56

therefore your answer is 106.

Answer:

z2=-3-3i

Step-by-step explanation:

3z1+0z2=6+18i

z1+z2=5+9i (×3)

3z1+3z2=15+27i

3z1+0z2=6+18i (-) =

-3z2=9+9i

z2=-3÷(9+9i)

z2=-3-3i

Answer:

$17.750 ; 15.979 ; 72

Step-by-step explanation:

Given that :

Cummulative sales, S(t) is represented by the equation :

S(t) = 72/(1 + 9e^-0.36t)

Cummulative sales after 3 weeks :

Put t = 3 in the equation, as t = time after launch

S(3) = 72/(1 + 9e^-0.36(3))

S(3) = 72 / (1 + 9e^-1.08)

S(3) = 72 / (1 +3.0563597)

S(3) = 72 / 4.0563597

S(3) = 17.749905 = $17.750 thousands

Amount of time required for sales to reach 70000

S(t) = 72/(1 + 9e^-0.36t)

S(t) = 70

70 = 72/(1 + 9e^-0.36t)

70 * (1 + 9e^-0.36t) = 72

(1 + 9e^-0.36t) = 72 / 70

1 + 9e^-0.36t = 1.0285714

9e^-0.36t = 1.0285714 - 1

9e^-0.36t = 0.0285714

e^-0.36t = 0.0285714 / 9

e^-0.36t = 0.0031746

Take the In of both sides ;

In(e^-0.36t) = In(0.0031746)

-0.36t = - 5.752573

t = - 5.752573 / - 0.36

t = 15.979

About 16 weeks

The limiting value in sales :

Take the limit as t - - > ∞

S(t - - > ∞) = 72/(1 + 9e^-0.36t)

Put t = 0

S(0) - - > 72 / (1 + 0)

72 / 1

= 72

Answer:

The slope of the line is [tex]-\frac{1}{5}[/tex]  in fraction form or -0.2 in decimal form.

Step-by-step explanation:

To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

For finding the slope of this line with the points (-2,-1) and (8,-3), start by writing down the information given from the question.

[tex]y_{2}= -3[/tex]

[tex]y_{1}=-1[/tex]

[tex]x_{2}=8[/tex]

[tex]x_{1}= -2[/tex]

Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(-1)}{8-(-2)}[/tex]. Then, simplify the equation, which will look like [tex]\frac{-2}{10}= -\frac{1}{5}[/tex]. The final answer will be [tex]-\frac{1}{5}[/tex]  in fraction form or -0.2 in decimal form.

Answer:

x = 13

Jack is 13 years old and Jill is 11 years old.

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

Explanation:

x = Jack's age

x-2 = Jill's age, since she is 2 years younger than Jack

Add up the ages and set the sum equal to 24 to solve for x

x+(x-2) = 24

2x-2 = 24

2x = 24+2

2x = 26

x = 26/2

x = 13

Jack is 13 years old and his sister is x-2 = 13-2 = 11 years old

Check: 13+11 = 24, so the answer is confirmed.

Answer:

Step-by-step explanation:

(2×4-6)/(3-2)=2

Answer:

[tex]{ \tt{f(x) = x - 2}} \\ { \bf{f(3) = 3 - 2 = 1}} \\ \\ { \tt{g(x) = 2x - 6}} \\ { \bf{g(4) = 2(4) - 6 = 2}} \\ \\ { \boxed{ \tt{ \frac{g(4)}{f(3)} = \frac{2}{1} = 2}}}[/tex]

Step-by-step explanation:

5x 3 1/2 = 3 x 5 1/2 is false

Answer:

0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.

Step-by-step explanation:

I am going to treat these events as Venn probabilities, considering that:

Event A: Lying to the teacher.

Event B: Male

48% of high school students would admit to lying at least once to a teacher during the past year and that 25% of students are male and would admit to lying at least once to a teacher during the past year

This means that [tex]P(A) = 0.48, P(A \cap B) = 0.25[/tex]

Assume that 50% of the students are male.

This means that [tex]P(B) = 0.5[/tex]

What is the probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year?

This is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Considering the values we were given:

[tex]P(A \cup B) = 0.48 + 0.5 - 0.25 = 0.73[/tex]

0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.

Answer:

24

Step-by-step explanation:

y=8(3)= twenty four

you just fill in the x

Answer:

[tex]y=\frac{4}{3}x-4[/tex]

Step-by-step explanation:

----------------------------------------

The slope-intercept form formula is: [tex]y=mx+b[/tex]

The [tex]m[/tex] stands for the slope and the [tex]b[/tex] stands for the y-intercept.

By looking at the graph, I can figure out that the y-intercept is -4 because y-intercept is where the lines cross the y-axis and in this graph, the line crosses the y-axis at (0,-4).

The slope is [tex]\frac{4}{3}[/tex] because to get to the ordered pair (3,0), from (0,-4), you would have to go up 4 and over 3 to the right so it's [tex]\frac{4}{3}[/tex]

So now, if we insert the values in the formula, it would be [tex]y=\frac{4}{3}x-4[/tex]

----------------------------------------

Hope this is helpful.

Answer:

y = 4/3x -4

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

    = ( 0 -  -4)/( 3 - 0)

   = (0+4)/( 3-0)

   = 4/3

The y intercept is -4

The slope intercept form of the equation is

y = mx+b  where m is the slope and b is the y intercept

y = 4/3x -4

Answer:

in a triangle, the angle with the smallest measure is always opposite the shortest side.

Step-by-step explanation:

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

Explanation:

The recursive rule

f(n+1)=f(n)-3

can be rearranged to

f(n) = f(n+1)+3

after adding 3 to both sides

----------------

Now let's say we plug in n = 3

f(n) = f(n+1)+3

f(3) = f(3+1)+3

f(3) = f(4)+3

f(3) = 22+3

f(3) = 25

Repeat for n = 2

f(n) = f(n+1)+3

f(2) = f(2+1)+3

f(2) = f(3)+3

f(2) = 25+3

f(2) = 28

Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).

Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.

Answer:

[tex]\cos(2\, x) = 1 - 2\, (\sin(x))^2[/tex].

Step-by-step explanation:

Angle sum identity for cosine: [tex]\cos(a + b) = \cos(a) \, \cos(b) - \sin(a) \, \sin(b)[/tex].

Pythagorean identity: [tex](\cos(a))^{2} + (\sin(a))^{2} = 1[/tex] for all real [tex]a[/tex].

Subtract [tex](\cos(x))^{2}[/tex] from both sides of the Pythagorean identity to obtain: [tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex].

Apply angle sum identity to rewrite [tex]\cos(2\, x)[/tex].

[tex]\begin{aligned}&\cos(2\, x)\\ &= \cos(x + x) \\ &= \cos(x) \, \cos(x) - \sin(x)\, \sin(x) \\ &= (\cos(x))^{2} + (\sin(x))^{2}\end{aligned}[/tex].

[tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex] follows from the Pythagorean identity. Hence, it would be possible to replace the [tex](\cos(x))^{2}[/tex] in the previous expression with [tex](1 - (\sin(x))^{2})[/tex].

[tex]\begin{aligned}&(\cos(x))^{2} - (\sin(x))^{2}\\ &= \left[1 - (\sin(x))^{2}\right] - (\sin(x))^{2} \\ &= 1 - 2\, (\sin(x))^{2} \end{aligned}[/tex].

Conclusion:

[tex]\begin{aligned}&\cos(2\, x) \\ &= (\cos(x))^{2} + (\sin(x))^{2} \\ &=1 - 2\, (\sin(x))^{2}\end{aligned}[/tex]

Answer:

[tex]n^{2} -3=39.2=78\\n^2=78+3=81\\n=\sqrt{81} \\n=9[/tex]

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplifying the radicals in the expression

[tex]\sqrt{52}[/tex]

= [tex]\sqrt{4(13)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{13}[/tex]

= 2[tex]\sqrt{13}[/tex]

------------------

[tex]\sqrt{117}[/tex]

= [tex]\sqrt{9(13)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]

= 3[tex]\sqrt{13}[/tex]

Then

[tex]\sqrt{52}[/tex] + [tex]\sqrt{117}[/tex]

= 2[tex]\sqrt{13}[/tex] + 3[tex]\sqrt{13}[/tex]

= 5[tex]\sqrt{13}[/tex] → G

[tex]{\small\sf{The\:expression \sqrt{52} + \sqrt{117} \:is \: equivalent \: to}}[/tex]

[tex]\small\bf{F.} \: \sf{13} [/tex]

[tex]\small\bf{G.}\sf \:5 \sqrt{13} [/tex]

[tex]\small\bf{H.}\sf\:6 \sqrt{13} [/tex]

[tex]\small\bf{J.}\sf\:13 \sqrt{13} [/tex]

[tex]\small\sqrt{52}+\sqrt{117}\sqrt{4•13} +\sqrt{9•13}\tiny\sf\purple{(Product\:Property)}[/tex]

[tex]\small{ \: \:\: \: \: \: \: \:=\sqrt{2²•13}+\sqrt{3²•13}\tiny\sf\purple{(Prime\:Factorization)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=\sqrt{2²}\sqrt{13}+\sqrt{3²}\sqrt{13}\tiny\sf\purple{(Product\:Property)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=2\sqrt{13}+3\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=5\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]

So, the correct option is D.

#Hope it helps!

(ノ^_^)ノ

Answer:

ok so its a triangle with one side being

11

on side being

2

and one side is x

so we just use the formula

11^2+2^2=c^2

11^2+2^2=125

125 squared is 25

so

3 times the square root of 13 is 10.8166538264

so no

5 times the square root of 5 is 11.1803398875

so the answer i guess might be a?

Hope This Helps!!!

Answer:

D. x=36

Step-by-step explanation:

3x-5=103

3x=103+5

3x=108

x=36

Câu trả lời:

0,0584

Giải thích từng bước:

Câu hỏi đưa ra đáp ứng điều kiện cần thiết cho phân phối xác suất nhị thức:

Số câu hỏi, số lần thử, n = 10

Xác suất, p = 1 / số lựa chọn = 1/4 = 0,25

q = 1 - p = 1 - 0,25 = 0,75

Tính xác suất để sinh viên đó được 5 điểm, x = 5;

Gợi lại:

P (x = x) = nCx * p ^ x * q ^ (n-x)

P (x = 5) = 10C5 * 0,25 ^ 5 * 0,75 ^ 5

P (x = 5) = 252 * 0,25 ^ 5 * 0,75 ^ 5

P (x = 5) = 0,0584

Answer:

It is D.

Step-by-step explanation:

x ≤ 3 or x ≥ –1

Answer:

D) X <_ 3 or X _> -1

Whole Unit Test Review Answers:

1) D

2)D

3)B

4)C

5)D

6)A

7)B

8)C

9)A

10)B

11)D

12)D

13)B

14)B

15)D

(I got a 100%, and these were my answers, hope they help!)

(The pic below is a screenshot of the 100%, for reassurance)

Answer:

a. 8 cm

Step-by-step explanation:

Given:

EH = 6 cm

FG = 4.00 cm

Based on the mid-segment theorem of a trapezoid, we have:

EH = ½(FG + DI)

Plug in the values

6 = ½(4 + DI)

Multiply both sides by 2

6*2 = 4 + DI

12 = 4 + DI

12 - 4 = 4 + DI - 4

8 = DI

DI = 8 cm

Answer:

She will be 17

Step-by-step explanation:

My sister is like that but she's graduating in 22'

It sort of depends where Sarah lives -.-  

But if she starts high school when she's 15 (in 2021) and she graduates in 2024 it means high school is three years.

So 15 plus 3.

Sarah will be 18 when she graduates high school.

Answer:

Step-by-step explanation:

hope it's helpful :-)

Answer:

The Probability would be 2.78%

Step-by-step explanation: Hope this helps :)

1

is the correct answer lol ez stuff

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: y = \frac{17 - 11x}{7} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]\\11x + 7y = 17[/tex]

[tex] \\➺ \: 7y = 17 - 11x[/tex]

[tex]\\➺ \: y = \frac{17 - 11x}{7} [/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]