estimate 0.047512968 to the nearest hundredth express your answer as a single digit times a power of 10

Complete Question

The SAT are scored so as to yield a mean of 500 and a standard deviation of 100. These scores are close to being normally distributed. An exclusive club wishes to invite those scoring in the top 5% on the College Boards to join. a. Find percentages of scores that is between 480 and 590. b. What score is required to be invited to join the club? c. What score separates the top 60% of the population from the bottom 40%? What do we call this value? (hint: the score that separates the top 20% of the population from the bottom 80% is called the 80th percentile)

Answer:

a

 [tex]P(480 < X  <  590) =  0.3952[/tex]  

b  

  [tex]x =  664.5 [/tex]

c

 [tex]x_1 =  474.67[/tex]

The value is called the [tex]40^{th}[/tex] percentile

Step-by-step explanation:

From the question we are told that

The mean is [tex]\mu = 500[/tex]

The standard deviation is [tex]\sigma = 100[/tex]

Generally the percentage of the score that are between 480 and 590 is mathematically represented as

[tex]P(480 < X < 590) = P(\frac{ 480 - 500}{ 100} < \frac{ X - \mu }{ \sigma } < \frac{ 590 - 500}{ 100} )[/tex]

Here [tex]\frac{ X -\mu}{\sigma } = Z[/tex]

=> [tex]P(480 < X < 590) = P(\frac{ 480 - 500}{ 100} < Z < \frac{ 590 - 500}{ 100} )[/tex]

=> [tex]P(480 < X < 590) = P(-0.2< Z < 0.9 )[/tex]

=> [tex]P(480 < X < 590) = P(Z < 0.9 ) - P(Z<-0.2) [/tex]

From the z table (reference calculator dot net )

[tex] P(Z < 0.9 )= 0.81594 [/tex]

And

[tex] P(Z < -0.2 )= 0.42074 [/tex]

=> [tex]P(480 < X < 590) = 0.81594 - 0.42074 [/tex]

=> [tex]P(480 < X < 590) = 0.3952[/tex]

Converting to percent

[tex]P(480 < X < 590) = 0.3952 * 100[/tex]

[tex]P(480 < X < 590) = 39.52\% [/tex]

The percentage invited to join the club is the top 5% , this can be mathematically represented as

[tex]P(X > x ) = 0.05[/tex]

Here x is the score that is within the top 5%

=> [tex]P(X > x) = P( \frac{X - \mu }{\sigma } > \frac{ x - 500}{100} )= 0.05[/tex]

Generally the critical value of 0.05 from the normal distribution table is

[tex]Z_{0.05} = 1.645[/tex]

So

[tex]\frac{ x - 500}{100} = 1.645[/tex]

=> [tex]x - 500 = 164.5[/tex]

=> [tex]x = 664.5 [/tex]

Generally the probability of having a score that separates the top 60% of the population from the bottom 40%

[tex]P(X > x_1 ) = 0.60[/tex]

=> [tex]P(X > x_1) = P(\frac{ X - \mu }{\sigma } > \frac{x - 500}{100} ) = 0.60[/tex]

The critical value of 0.60 from the normal distribution table is

[tex]Z_{0.60} = - 0. 2533[/tex]

So

[tex]\frac{x_1 - 500}{100} = -0.2533[/tex]

=> [tex]x_1 = 474.67[/tex]

From the hint given we can see that this value is called the [tex]40^{th}[/tex] percentile

Answer:

a) H1: µ < 7.5

Step-by-step explanation:

From the given information:

mean = 7.5

sample size = 50

sample mean = 9.3

The main task we are to carry out is to identify the correct alternative hypothesis:

Now to do that, let's state the null and the alternative hypothesis from the given study.

The null hypothesis can be computed as:

[tex]\mathbf{H_o: \mu \geq 7.5}[/tex]

The alternative hypothesis can be computed as:

[tex]\mathbf{H_1: \mu < 7.5}[/tex]

Thus, this test hypothesis is a one-tailed test (left tailed).

Answer: it’s =

i just got the test results

Answer:

0.83 but draw a repeating bar over the 3

Step-by-step explanation:

gOoGlE

Answer:

7.6

Step-by-step explanation:

(4−(−3))2+(−2−1)2

=7^2+(−2−1)2

=49+(−2−1)2

=49+(−3)^2

=49+9

=58

=7.6

Answer:

2

Step-by-step explanation:

9x2=18

5x2=10

10/18=5/9

10/18 divided by 2 5/18

so its 2

Answer:

B A C C

Step-by-step explanation:

Answer:

-2^5

Step-by-step explanation:

Answer:

24^3-52x^2+34x+18

Answer:

There are NO solutions

Step-by-step explanation:

On the left hand side, we have an absolute value;

which means that the left hand side will always be greater than or equal to 0

On the right hand side, we have a negative value;

Since the LHS can NEVER be negative, it will never be less than a negative number

Hence, No value of y can make this equation true

Answer:

5

Step-by-step explanation:

2/4=y/10

=> 2x10=yx4

=> 20=yx4

=>y=5

Answer:

T,F,T,F,T

Step-by-step explanation:

1. It crosses it there becuase 4(0)-15=-15 for y

2: both top and middle answers are -23, so continuous

3: it increases over that period because the exponent keeps getting bigger

4: No, its not decreasing because -12 plugged in is far less than -23 when -2 is plugged in, meaning its increasing

5: There is no number that would cause an imaginary number or make you divide by zero, meaning all real numbers are fine.

Answer:

51+(4x+7)=90

4x+58=90

-58      -58

4x=32

4x/4=32/4

x=8

Step-by-step explanation:

Answer:

otation of a point through 180°, about the origin when a point M (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, it takes the new position M' (-h, -k). Find the co-ordinates of the points obtained on rotating the points given below through 180° about the origin.(i) A (3, 5)            

(ii) B (-2, 7)          

(iii) C (-5, -8)      

(iv) D (9, -4)

Solution:

When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.

(i) The new position of the point A (3, 5) will be A' (-3, -5) ii) The new position of the point B (-2, 7) will be B' (2, -7) (iii) The new position of the point C (-5, -8) will be C' (5, 8)

(iv) The new position of the point D (9, -4) will be D' (-9, 4)

2. Plot the point M (-1, 4) on the graph paper and rotate it through 180° in the anticlockwise direction about the origin O. Find the new position of M.

Solution:

180 Degree Rotation

0Save

When rotated through 180° in the anticlockwise direction about the origin O, then M (-1, 4) → M'' (1, -4).

3. Draw a line segment joining the point P (-3, 1) and Q (2, 3) on the graph paper and rotate it through 180° about the origin in anticlockwise direction.

Solution:

180 Degree Rotation about the Origin

0Save

On plotting the points P (-3, 1) and Q (2, 3) on the graph paper to get the line segment PQ.

Now rotate PQ through 180° about the origin O in anticlockwise direction, the new position of points P and Q is:

P (-3, 1) → P' (3, -1)

Q (2, 3) → Q' (-2, -3)

Thus, the new position of line segment PQ is P'Q'.

Step-by-step explanation:

Answer: 4. No, the graph is NOT a function because using the vertical line test, it intersects at two points at a time.

5. Yes, it is a relation, and it is also a function because once those points are plotted if given the vertical line test, there would not be two points crossed at once. So, yes, it is a function.

6. Yes, it is a relation. No, it does NOT make up a function because a vertical line would intersect all the points given.

Answer:

$105

Step-by-step explanation:

5.5+8.5=14

14 * 7.5=105

Answer:

y = 1/3x + 2

Step-by-step explanation:

Rise over run + y intercept

Answer:

117

Step-by-step explanation:

The average of all 7 people is the total weight of the original 6 people, plus the weight of the 7th person, all divided by 7.

For problems like this involving an average of numbers that are "close" together, here is a different strategy for solving the problem that you might like to try.

The original 6 people have an average weight of 173, which is 8 pounds more than the average of all 7 people. So all together, the weight of those 6 people is 6*8=48 pounds over the 165 average. That means the 7th person's weight must be 48 pounds below the 165 average.

So the weight of the 7th person is 165-48 = 117 pounds.

Answer:

The 7th person weighted 117

Step-by-step explanation:

Average Value

The mean or average of a number n of measurements is defined as the sum of all values divided by n.

[tex]\displaystyle \bar x=\frac{\sum x_i}{n}\\[/tex]

The question gives us some input data. The average weight of n=6 people is [tex]\bar x=173[/tex]. With this information, we can set this relationship:

[tex]\displaystyle 173=\frac{\sum x_i}{6}[/tex]

From the above equation, we know the sum of the first 6 persons:

[tex]\sum x_i=6*173=1,038[/tex]

When a 7th person gets on, the new average gets down to 165 and n=7. The equation for the new average is:

[tex]\displaystyle 165=\frac{\sum x_i+X}{7}[/tex]

Note we have a new summand to the numerator. It's the weight of the 7th person. Let's solve for X:

[tex]\displaystyle 165=\frac{1,038+X}{7}[/tex]

Multiply by 7:

[tex]7*165=1,038+X[/tex]

Operate and swap sides:

[tex]1,038 +X=1,155[/tex]

[tex]X=1,155-1,038=117[/tex]

The 7th person weighted 117

Answer: In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power. For example, 8xyz² and −5xyz² are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all constant terms are like terms.

I HOPE THIS HELPED ! :) mark me brainlist pls

Answer:

by combining them like the ordinary like ordinary integers.

Step-by-step explanation:

For example we have

8x + 4y = 3x - 6

you will bring 3x to the left so it will become -3x

8x - 3x + 4y = -6

then combine like terms

there you have

5x + 4y = -6

The given:

8x + 4y = 3x - 6

8x - 3x + 4y = -6

5x + 4y = -6

answer for the example: 5x + 4y = -6

Answer:

a^m-n

Step-by-step explanation:

If we have the expression m^a / m^n, we can use exponent rules to simplify this.

Exponent rules say that x^a / x^b = x^a-b. In this case, x is a, a is m and b is n, so the same rule applied here.

So a^m / a^m  will be equal to a^m-n

Hope this helped!

The correct answer is 12.

I hope this helps you!!

Answer:

12

Step-by-step explanation:

so here, the ratio of apples to oranges is 1:3. this can also be represented as the fraction 1/3. now, we are trying to find the number of oranges when there are 4 apples using this ratio. this means 1/3=4/x, where x is the number of oranges. we can multiply 1 by 4 (the numerator) to get 4, so we can multiply the denominator of the first fraction by 4 as well 3*4=12, so there are 12 oranges for every 4 apples. (4/12 can also be written as 4:12.)

Answer:

12

Step-by-step explanation:

nos of oranges for 4 apples = 4x 3

                                               = 12

therefore, the ratio is 4:12 i.e. 1:3

pls mark as brainliest!

Answer:

The product is 8.6

Step-by-step explanation:

you move two decimal places to your right

Answer:

4. 180

5. PQ

Step-by-step explanation:

Answer:0.4

Step-by-step explanation:

4 is bigger than one so it would be like 400>127

Answer:

0.4 would be the greater number

Answer:

28 action movies

Step-by-step explanation:

I hope this helps!