Out of a sample of 650 high school students, 321 take the bus to school every day. construct a 99% confidence interval for the population mean of high school students that take the bus to school every day.

Answer:

Step-by-step explanation:

5 in.

a.

(6.257 25) in.

-

b. (6.25π – 12.5√2)in.²

d.

Find the value of x and y rounded to the nearest tenth.

C.

(6.25π- 12.5) in.2

Answer:  24

Step-by-step explanation:

You have 4 balloons to choose from.  

Once you have chosen a balloon, there are 3 remaining to choose from.  When you choose another balloon, there are only 2 remaining.

First pick   and    Second pick    and   Third pick

     4           x        3 remaining      x       2 remaining      =  24

The inequality can be rewritten into:

x > 4 or x < -4

And the graph can be seen in the image at the end.

We want to solve the inequality below and then graph it, the inequality is:

|x| + 3 > 7

moving the 3 to the right side we get:

|x| > 7 - 3

|x| > 4

Now we can break the absolute value part into two:

x > 4

x < -4

That is the solution:

x > 4 or x < -4

The graph is the one below.

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Answer:

2142 inches^2

Step-by-step explanation:

parallelogram's area: base * height

so, 34*63 = 2142

Answer: (3 , 7)

Step-by-step explanation: When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative. Since x and y are already negative, they become positive due to the double negative rule.

Answer:

320 toy cars and 25 toy trucks

Step-by-step explanation:

Answer:

m<ECB = 65°

Step-by-step explanation:

<ACB and <ACD are vertical angles. That means they are congruent and have equal measures.

m<ECB = 65°

Answer:

-5

2.45×10

2.45×103

2.45×107

Step-by-step explanation:

-5=5

2.45×10=24.5

2.45×103=252.35

2.45×107=262.15

Answer:

x = 6

Step-by-step explanation:

Add the numbers:

17x + 4 = 13x + 20

17x + 4 = 13x + 28

Subtract 4 from both sides of the equation:

17x + 4 = 13x + 28

17x + 4 - 4 = 13x + 28 -4

Simplify:

17x = 13x + 24

Subtract the numbers

Solution:

And you get

x = 6

Answer:

x=6

Step-by-step explanation:

17x+4=13x+8+20

17x-13x= 4x

4x=8+20-4

4x=24

x=24/4

x=6

Answer: answer for what?

Step-by-step explanation: oh I see it appeared iN wrong catogory I’m browsing History sorry

Answer:

Exact form : t=1/2 and Decimal: 0.5

Answer: 18%

Step-by-step explanation:

I gogled

Answer:

(1, eᵗ)

Step-by-step explanation:

r(t) = (t, eᵗ)

v(t) = dr/dt

v(t) = (1, eᵗ)

Answer:

a) r = 2

b)
GP a₆ = 384

AP a₆ = 32

Step-by-step explanation:

First term a₁ = 12 for both progressions

r = common ratio, d = common difference

nth term of geometric progression = a₁ x rⁿ⁻¹
nth term of arithmetic progression = a₁ + (n - 1)d

Second term of GP = Fourth term of AP

=> 12r¹ = 12 + 3d

==> 12r = 12+ 3d  (1)

Third term of GP = 10th term of AP

=> 12r² = 12 + 9d (2)

3 x (1) => 3(12r = 12 + 3d) => 36r  = 36 +  9d (3)

(2) - (3) gives12r² -36r = 12 - 36
12r² - 36r = 12 + 9d - (36 + 9d)

12r² -36r = -24

12r² -36r + 24 = 0

Dividing by 12 gives
r² - 3r + 2= 0

We can factor r² - 3r + 2 as (r - 1)(r-2)

r² - 3r + 2= 0
=>  (r - 1)(r-2) = 0

=> r = 1 or r = 2

r cannot be 1 since all terms of the GP will be equal with a common ratio of 1

Therefore r = 2  (Part a)

Using equation (1) we get:
12r = 12+ 3d
12 x 2 = 12 + 3d

24 = 12 + 3d

3d = 24 - 12 = 12

d = 12/3 = 4

So the common ratio, r,  is 2. Common difference d = 4

6th term of GP =12 x r⁵ =  12 x 2⁵ = 12 x 32 = 384

6th term of Ap = 12 + 5d = 12 + 5(4) = 12 + 20 = 32

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Answer:

y=  3x + 8

Step-by-step explanation:

y = mx + b

m = 3 inches of water added each day

x = 8 inches of water at start

y=  3x + 8 is the required equation.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Shannon's rain-catcher has 8 inches of water in it. Each day, 3 inches of water are added to the rain-catcher.

We have,

m = 3 inches of water added each day

x = 8 inches of water at start

Converting in y = mx + b, we get,

y = 3x+8

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Step-by-step explanation:

So here are the two solutions...

A.-10

B.6

Hope it helps you

Answer:

(x+2)(2x+2) = 130

x=6.58m

Step-by-step explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

(2+2x)(2+x)= 130

(x+2)(2x+2) = 130

Expand the bracket:

\(2x^2+2x+4x+4=130\\2x^2+6x+4=130\\\)

Divide through by 2

\(x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63\)

Complete the square by adding the square of the half of the coefficient of x to both sides:

\((x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2\)

\((x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25\)

Take the square root of both sides

\(\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m\)

Hence the value of x is 6.58m

Answer:

We can begin by simplifying each equation:

A. 52 = 8n + 4 can be rewritten as 48 = 8n or 6 = n

B. 4(2n + 1) = 52 can be simplified to 8n + 4 = 52 or 8n = 48 or 6 = n

C. 4=52-8n can be rewritten as 8n = 48 or 6 = n

D. 4n = 48 can be simplified to n = 12

Therefore, equations A, B, and C are equivalent, and equation D is not equivalent to the others.

So, the correct answers are A, B, and C.

Answer:

Step-by-step explanation:first you have to multiply then divide then add then subtract and then substitute and then you will get the answer.

Answer:

5560

Step-by-step explanation:

5894 rounded to the nearest tenth would be 5890.

Rounding 331 to the nearest tenth would be 330.

So 5890-330= 5560.

The amount of interest earned after 15 years at rate of 5% on $3,500 amount is $6125.

Simple interest is a method to calculate the amount of interest which is applied on the principal amount, rate for a given time intereval.

SI = P × R × T/100

The principal amount is given as $3,500, rate is 5% and time period is 15 years.

SI = P × R × T/100

SI = $3,500 × 5 × 15  /100

SI = $2625

Since, the total value of the amount of interest = $2625 + $3,500

                                                                              = $6125

Therefore, the amount of interest earned after 15 years at rate of 5% on $3,500 amount is $6125.

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Answer:

$2,625

Step-by-step explanation:

I=prt

3,500(.05)(15)

2,625+3,500=Account balance ($6,125).

Answer:

7 6 8 9

The value of 6 is in the hunderth place and represents 600

Hope this helps!! <3

the light is 17 feet from the wall

angular speed is found with

w = change in rotation / change in time

2pi / 4

pi / 2

y = 17 tan(θ)

derivative

y = 17 sec^2 (θ)

y = 17 * pi/2 * sec^2(θ)

y = 17 * pi/2 * sec^2(15)

y = 28.62 ft per second

Answer:

\(-x^{15}y^{21}\)

Step-by-step explanation:

To simplify the given expression, use exponent rules.

Given expression:

\(\left(-2x^5y^7\right)^3+7x^{15}y^{21}\)

\(\textsf{Apply the exponent rule:} \quad (a^b)^c=a^{bc}\)

\(\implies (-2)^3x^{(5 \cdot 3)}y^{(7\cdot3)}+7x^{15}y^{21}\)

Simplify:

\(\implies -8x^{15}y^{21}+7x^{15}y^{21}\)

Factor out the common term x¹⁵y²¹:

\(\implies \left(-8+7\right)x^{15}y^{21}\)

Simplify:

\(\implies \left(-1\right)x^{15}y^{21}\)

\(\implies -x^{15}y^{21}\)

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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The area of the teacher workroom is 64 feet squared