SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 433 . Assume the population standard deviation is 115 .
(a) Construct a 99 % confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number.

Answer:

x=5i√2,−5i√2

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Step-by-step explanation:

math, way, . , com

Subtract the new value from original value to find the difference:

35 - 28 = 7

Divide the difference by the original amount and multiply by 100:

7/35 = 0.2 x 100 = 20%

The decrease was 20%

Answer:

20%

Step-by-step explanation:

First, subtract the new value from the original value to find the difference between the two.

35 - 28 = 7

Next, divide the difference by the original amount.

7 / 35 = 0.2

Then, multiply by 100.

.2 x 100 = 20%

We now know that the decrease was 20%

Answer:

(4x - 3)(x-2) = 0

Step-by-step explanation:

             4x² - 11x + 6 = 0

        To factorize this equation,

        -11

     4x6

These numbers are the key to the solution:

   find two numbers whose sum is -11 and the product is + 24 (4 x 6)

   So, the numbers are -3 and -8

    4x² - 8x - 3x + 6 = 0

   4x(x -2) - 3(x - 2) = 0

    (4x - 3)(x-2) = 0

Answer:

(4x - 3)(x - 2) = 0

That's your answer!!

Answer:

12.2 12.3 12.4 12.5

Step-by-step explanation:

Answer:

C. 36

because can not be expressed as a ratio

Answer:

45

Step-by-step explanation:

equate the two equations

2/5=18/x

Answer:

45grams

Step-by-step explanation:

Answer: The required length of each piece of wood is  or 9 inches.

Step-by-step explanation:  Given that a piece of lumber is  feet long is to be cut into 3 equal pieces.

We are to find the length of each piece of wood in feet and in inches.

We will be using the UNITARY method to solve the given problem.

The length of 3 pieces of wood is equal to  

Therefore, the length of each piece of wood will be

Thus, the required length of each piece of wood is  or 9 inches.

Answer: Yes it is right.

Step-by-step explanation: Have a blessed day!

Answer: Yes, it’s correct!

Step-by-step explanation: Have A Great Day Bro! :)

Answer:

There are 0 number of edges on a cylinder

Answer:

(f - g)(x) = -x - 6

(f + g)(x) = 3x - 4

(f*g)(4) = -9

Step-by-step explanation:

These are your equations:

f(x) = x - 5

g(x) = 2x + 1

To find (f - g)(x), subtract g(x) from f(x).

(f - g)(x) = x - 5 - (2x + 1)

(f - g)(x) = x - 5 - 2x - 1

(f - g)(x) = -x - 5 - 1

(f - g)(x) = -x - 6

To find (f + g)(x), add f(x) with g(x).

(f + g)(x) = x - 5 + 2x + 1

(f + g)(x) = 3x - 5 + 1

(f + g)(x) = 3x - 4

To find (f*g)(4), you need to first find (f*g)(4).  You can do this by multiplying f(x) wih g(x).

(f*g)(x) = (x - 5)(2x + 1)

(f*g)(x) = 2x² - 9x - 5

Now that you have (f*g)(x), solve with x as 4.

(f*g)(4) = 2(4)² - 9(4) - 5

(f*g)(4) = 2(16) - 9(4) - 5

(f*g)(4) = 32 - 36 - 5

(f*g)(4) = -9

The required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
f(x)=x-5
g(x) = 2x+1

According to the question,
[f + g ](x) = x - 5 + 2x + 1 = 3x - 4

[f + g ](x) =  3x - 4

[f - g ](x) =  x - 5 - 2x - 1
[f - g ](x) = -x - 6

(f.g)(x) = (x - 5)(2x + 1)
(f.g)(x) = 2x² -4x -5

(f.g)(4) = 2[4]² - 4[4] - 5
         = 32 - 16 - 5
         = 11
(f.g)(4) = 11

Thus, the required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.

Learn more about function here:

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Answer:

163

Step-by-step explanation:

Answer: its 3( 15+9 ) or 9( 5+3 ) go with your gut im srry if im wrong

Step-by-step explanation:

Daichi wo fumishimete

Kimi wa mezameteiku

Answer:

m [slope] = 5/2

Step-by-step explanation:

Find two points on the line where they are both integers(Whole numbers, positive or negative). (30,0) and (50,50).

There is a rise of 5 units for every run of 2 units.

(30,0) → (50,50) = (30 + 20, 0 + 50) : (x,y)

m = ∆y/∆x [Change in y over the change in x]

m = 50/20

m = 5/2

Answer:

it is c

Step-by-step explanation:

Answer:

C.) 0.5; Terminating

Step-by-step explanation:

Answer:

918=0.5

Showing the work

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 9 and 18 using

GCF(9,18) = 9

9÷918÷9=12

We know that

12

is the same as

1÷2

Then using

Long Division for 1 divided by 2

=0.5

Hope I helped

Brainliest plz

Answer:

the last 1

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2 × 2 = 4

Answer:

(x-14)^2+(y-3)^2=9

Step-by-step explanation:

equation of a circle is (x-h)^2+(y-h)^2=r^2

so center is (14,3) and is tangent externally means

(x-14)^2+(y-3)2=3^2

(x-14)^2+(y-3)^2=9 answer

The equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]

The standard formula for finding the equation of a circle is expressed as:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where

(a, b) is the centre

r is the radius

Given the center at (14, 3)

If the equation of a circle is externally tangent to the given circle and has a center at (14, 3), then the radius will be 3

Substitute the radius and the centre into the expression above to have:

[tex](x-14)^2 + (y-3)^2=3^2\\(x-14)^2 + (y-3)^2=9[/tex]

Hence the equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]

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Answer:

The ball lands on the ground at t=2.55 seconds

Step-by-step explanation:

Quadratic Equation

The following function models the height above the ground of a ball hit into the air at time t seconds:

[tex]h=25t-9.8t^2[/tex]

We need to find the value of t when the ball hits the ground.

At ground level, h is zero, thus:

[tex]25t-9.8t^2=0[/tex]

This is an incomplete quadratic equation that can be easily solved by factoring:

[tex]t(25-9.8t)=0[/tex]

There are two solutions:

t=0

t=25/9.8=2.55 s

The first solution corresponds to the moment when the ball is hit, and the second is when it returns to the ground, thus:

The ball lands on the ground at t=2.55 seconds

Hope this help you!!! :))

Answer:

58

Step-by-step explanation:

Answer:

270 degree rotation about point 0 composition .translations of negative 2 units

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Took the test

Answer:

Step-by-step explanation:

Hello,

c= -4 * 2 = -8 as

[tex]x^2+bx+c=(x+4)(x-2)=x^2+2x-8[/tex]

with the quadratic formula

[tex]x_1=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

And

[tex]x_1x_2=\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{c}{a}[/tex]

thanks

Answer:

t=8

Step-by-step explanation:

400 divided by 50 hopefully that helps with your question

Answer:

p = -2

Step-by-step explanation:

24 divided by -12

p= -2

Answer:

A. 31 cm

Step-by-step explanation:

Hopefully its right :)

Answer:

The probability is   [tex]P(X  >300 ) = 0.97219 [/tex]

Step-by-step explanation:

From the question we are told that

 The capacity of  an Airliner  is  k =  300 passengers

 The sample size n =  320 passengers

  The probability the a randomly selected passenger shows up on to the airport

    [tex]p = 0.96[/tex]

Generally the mean is mathematically represented as

    [tex]\mu  =  n*  p[/tex]

  => [tex]\mu  =  320 *  0.96[/tex]

    => [tex]\mu  = 307.2[/tex]

Generally the standard deviation is  

    [tex]\sigma =  \sqrt{n *  p *  (1 -p ) }[/tex]

=>  [tex]\sigma =  \sqrt{320  *  0.96 *  (1 -0.96 ) }[/tex]

=> [tex]\sigma =3.50 [/tex]

Applying Normal approximation of binomial distribution

Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

  [tex]P(X  > k ) =  P( \frac{ X -\mu }{\sigma }  >  \frac{k - \mu}{\sigma } )[/tex]

Here [tex]\frac{ X -\mu }{\sigma }  =Z (The \ standardized \  value \  of  \ X )[/tex]

=>[tex]P(X  >300 ) =  P(Z >  \frac{300 - 307.2}{3.50} )[/tex]

Now applying  continuity correction we have

    [tex]P(X  >300 ) =  P(Z >  \frac{[300+0.5] - 307.2}{3.50} )[/tex]    

=>    [tex]P(X  >300 ) =  P(Z >  \frac{[300.5] - 307.2}{3.50} )[/tex]

=>    [tex]P(X  >300 ) =  P(Z >  -1.914 )[/tex]

From the z-table  

    [tex]P(Z >  -1.914 ) =  0.97219[/tex]

So

    [tex]P(X  >300 ) = 0.97219 [/tex]

Answer:

a. The sum of an odd and an even integer is odd: 3 + 2 = 5

b. The sum of two odd integers is an even integer: 3 + 5 = 8

c. The square of an odd integer is an odd integer: 3² = 9

d. . The product of two odd integers is an odd integer.: 3 x 5 = 15

Step-by-step explanation:

Proving the following statements using a direct proof;

a. The sum of an odd and an even integer is odd:

let the odd integer = 3

let the even integer = 2

3 + 2 = 5

5 is an odd integer, proved

b. The sum of two odd integers is an even integer.

let the first odd integer = 3

let the second odd integer = 5

3 + 5 = 8

8 is an even integer, proved

c. The square of an odd integer is an odd integer. .

let the odd integer = 3

3² = 9

9 is an odd integer, proved

d. The product of two odd integers is an odd integer.

let the first odd integer = 3

let the second odd integer = 5

3 x 5 = 15

15 is an odd integer, proved

Answer:

a. The sum of an odd and an even integer is odd: 3 + 2 = 5

b. The sum of two odd integers is an even integer: 3 + 5 = 8

c. The square of an odd integer is an odd integer: 3² = 9

d. . The product of two odd integers is an odd integer.: 3 x 5 = 15

Step-by-step explanation:

Proving the following statements using a direct proof;

a. The sum of an odd and an even integer is odd:

let the odd integer = 3

let the even integer = 2

3 + 2 = 5

5 is an odd integer, proved

b. The sum of two odd integers is an even integer.

let the first odd integer = 3

let the second odd integer = 5

3 + 5 = 8

8 is an even integer, proved

c. The square of an odd integer is an odd integer. .

let the odd integer = 3

3² = 9

9 is an odd integer, proved

d. The product of two odd integers is an odd integer.

let the first odd integer = 3

let the second odd integer = 5

3 x 5 = 15

15 is an odd integer, proved