A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is:_______
a. 0.9545.
b. 0.9332.
c. 0.0668.
d. 0.4332.

(1) D

[tex]L_s\left\{t\right\} = \displaystyle\int_0^\infty te^{-st}\,\mathrm dt[/tex]

Integrate by parts, taking

[tex]u = t \implies \mathrm du=\mathrm dt[/tex]

[tex]\mathrm dv = e^{-st}\,\mathrm dt \implies v=-\dfrac1se^{-st}[/tex]

Then

[tex]L_s\left\{t\right\} = \displaystyle \left[-\frac1ste^{-st}\right]\bigg|_{t=0}^{t\to\infty}+\frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle -\frac1{s^2}e^{-st}\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \boxed{\frac1{s^2}}[/tex]

(2) A

[tex]L_s\left\{1\right\} = \displaystyle\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\left[-\frac1se^{-st}\right]\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\boxed{\frac1s}[/tex]

Answer:

13

Step-by-step explanation:

If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

25+144= c^2

169 = c^2

Take the square root of each side

sqrt(169) = sqrt(c^2)

13= c

Answer:

The length of the hypotenuse is 13.

Step-by-step explanation:

[tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex]

[tex]a^2 = 12^2 + 5^2[/tex]

[tex]a^2 = 144 + 25[/tex]

[tex]a^2 = 169[/tex]

a=[tex]\sqrt{169}[/tex]

a= 13

Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which  [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.

HOPE THIS HELPED

9514 1404 393

Answer:

Step-by-step explanation:

The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.

__

No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.

Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.

Answer:

Step-by-step explanation:

If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:

[tex]11=-5t^2+30t+1[/tex] and

[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get

t = .35 seconds and t = 5.6 seconds

Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.

9514 1404 393

Answer:

  1/63

Step-by-step explanation:

There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:

  4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63

The larger fraction is 1/63 unit larger than the smaller fraction.

Answer:

A. 50º

Step-by-step explanation:

we are given the exterior angles 140º and 90º

exterior angles + corresponding interior angles = 180º

that means the two other angles of the triangle are:

180 - 140 = 40º

and

180 - 90 = 90º

the sum of interior angles in a triangle = 180

p = 180 - (40 + 90)

p = 180 - 130

p = 50º

Answer:

total = m/n * c

m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid

Answer:

(x-7) and (x+12) are the factors and the rest are non factors...

Answer:

54ft

Step-by-step explanation:

if 3foot is 4ft tall

then a shadow of 72 ft will be how tall?= x

4x =3ft by 72ft

4x= 216ft

x= 216/4

×=54

Answer:

$4,966.25

Step-by-step explanation:

3 x 15 = 45

After 15 years, Naomi would have earned a total of 45% interest rate.

3,425 x 1.45 = 4,966.25

Don't use .45 as the multiplier

3,425 x .45 = 1,541.25 <- incorrect

Answer:

YWX = DFE

Step-by-step explanation:

AAS means angle angle side. so, we need 2 angles and 1 side.

we have 1 side and one angle confirmed.

so, we need one of the other two angles (W or Y vs. F or D) confirmed.

they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.

Answer: Distance: 2250

Step-by-step explanation:

Find GCF of 450 and 250

Answer:

2y^3-7y^2+7y

Step-by-step explanation:

7y - 2y^3 + 5y^2 - (  12y^2 – 4y^3)

Distribute the minus sign

7y - 2y^3 + 5y^2 - 12y^2 + 4y^3

Combine like terms

2y^3-7y^2+7y

Answer:

Step-by-step explanation:

CD/6.5 = 2.6/4.9    This is the result of the angle bisector theorem.

The theorem basically says that the side opposite the angle being bisected is divided  the ratio of the sides enclosing the angle.

Multiply both sides of the proportion by 6.5

CD = 2.6 * 6.5 / 4.9

CD = 3.4489

CD = 3.4 rounded.

Notice that

6 + 7 = 13

13 + 7 = 20

so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is

a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1

The last term in the series is 111, which means the series consists of 16 terms, since

7k - 1 = 111   ==>   7k = 112   ==>   k = 16

Then in summation notation, we have

[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]

Answer:

A

Step-by-step explanation:

(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)

[tex]g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1[/tex]

Answer:

-7

Step-by-step explanation:

x = y - 6

2x = 5y - 9

Use the internet for full steps

x = -7

y = -1

Answer:

153/50

Step-by-step explanation:

3.06

Rewriting as

There are two numbers after the decimal so we put the number over 100

306/100

Divide top and bottom by 2

153/50

To write 3.06 as a fraction you have to write 3.06 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

3.06 = 3.06/1 = 30.6/10 = 306/100

And finally we have:

3.06 as a fraction equals 306/100

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

3x - 5 = 37

Step 2: Solve for x

Answer:

1. 8+(30/(2+4)) = 8+(30/6) = 8+5 = 13

2. ((8+30)/2)+4 = (38/2)+4 = 19+4 = 23

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

23:

(8 + 30) ÷ 2 + 4

13:

8 + 30 ÷ (2 + 4)

please give me the brainliest if u can

Answer:

x=30°

hopefully this answer can help you to answer the next question

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]

Answer:

y=-2/3x+3

Step-by-step explanation:

the equation of line J is y=3/2x-5

perpendicular slope would be -2/3

you want it at point (6, -1) so sub the points into y=-2/3x+b

-1=-2/3(6)+b

-1=-4+b

3=b

y=-2/3x+3

Answer:

D. Find the cost of 1 week of guitar lessons for each store and compare.

Step-by-step explanation:

Find the cost for 1 week of guitar lessons by finding the slope of the data.

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\ A.)\frac{132-66}{6-3}=\frac{66}{3}=22\\\\ B.)\frac{168-84}{8-4}=\frac{84}{4}=21[/tex]

Therefore, Store B would be the best choice.

Answer:

16 days

Step-by-step explanation:

Here,

By the question,

4 men takes 4 days working each day 4 hours to complete 4 units of work..

then..

if 1 man works 1 hour each day then i would take ( 4×4×4 ) days

= 64days

then..

if 2 men work for 2 hours per day then.

it would take

4×4×4 / 2×2 days

= 16 days

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

Answer:

The value 138 means that this height (138cm) is less than the average height of a 4th grader.

Answer: No credit wanted

Step-by-step explanation:

The other guy is completely right.

Answer:

[tex]a + 2b -3 c + - 3a + b + 2c + 2a - 3b + c \\ = a - 3a + 2a + 2b + b - 3b - 3c + 2c + c \\ 0a + 0b + 0c \\ thank \: you[/tex]

a+2b-3c+(-3a+b+2c) +(2a-3b+c)

=a+2b-3c-3a+b+2c+2a-3b+c

=a-3a+2b+2b+b-3b-3c++2b+c

=0a+0b+0c

=0

Therefore, the addition of the expressions, a+2b-3c+(-3a+b+2c) +(2a-3b+c) is zero or 0.

To know more about algebraic expressions

https://brainly.com/question/28307605

Answer:

0.0286 = 2.86% probability that today is Monday.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]

What is the probability that today is Monday?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]

0.0286 = 2.86% probability that today is Monday.