SAT scores were originally scaled so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Use the empirical rule to estimate the probability that a randomly-selected student gets a section score between 400 and 700.
a. 68%
b. 95%
c. 81.5%
d. 13.5%

Answer:

x <2

Step-by-step explanation:

3(x+1)<9

Divide by 3

3/3(x+1)<9/3

x+1 < 3

Subtract 1 from each side

x+1-1 < 3-1

x <2

Answer:

x < 2

Step-by-step explanation:

Distribute the 3 to (x + 1):

3(x + 1)

3x + 3

→3x + 3 < 9

Subtract 3 from both sides:

→3x < 6

Divide both sides by 3:

→x < 2

Answer:

Step-by-step explanation:

Let x be the random variable representing the number of miles that each person walked each day for 6 months. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

For Rueben,

µ = 5

σ = 1.1

the probability that Rueben walked more than 6.1 miles is expressed as

P(x > 6.1) = 1 - P( x ≤ 6.1)

For x = 6.1,

z = (4 - 6.1)/1.1 = - 1.91

Looking at the normal distribution table, the probability corresponding to the z score is 0.02807

P(x > 6.1) = 1 - 0.02807 = 0.97193

P(x > 6.1) = 0.97 × 100 = 97%

For Victor,

µ = 4.4

σ = 1.4

the probability that Victor walked less than 5.8 miless is expressed as

P(x < 5.8)

For x = 5.8,

z = (5.8 - 4.4)/1.4 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x < 5.8) = 0.84 = 84%

Answer:

There would be no change in the standard deviation if each one of the numbers in the set was decreased by 4.

Step-by-step explanation:

We are given that the standard deviation of a set of numbers is 22.2.

And we have to check that what would be the standard deviation, if each one of the numbers in the set was decreased by 4.

For concluding this, we will take a simple example;

Suppose that there are three set of numbers : 6, 8 and 10

Firstly, we will calculate the standard deviation for these numbers;

           X                        [tex]X - \bar X[/tex]                        [tex](X-\bar X)^{2}[/tex]

           6                      6 - 8 = -2                           4

           8                      8 - 8 = 0                            0

          10                     10 - 8 = 2                           4    

                                                                             8    

Here, the Mean of the three numbers is given by;

        Mean, [tex]\bar X[/tex]  =  [tex]\frac{6+8+10}{3}[/tex]  = 8

Now, standard deviation formula is given by;

      Standard deviation, s  =  [tex]\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }[/tex]  

                                            =  [tex]\sqrt{\frac{8 }{3-1} }[/tex]  = 2

Now, we will decrease each of the three numbers by 4, we get ;

              X                        [tex]X - \bar X[/tex]                        [tex](X-\bar X)^{2}[/tex]

              2                      2 - 4 = -2                           4

              4                      4 - 4 = 0                            0

              6                      6 - 4 = 2                           4    

                                                                                8    

Here, the Mean of the three numbers is given by;

        Mean, [tex]\bar X[/tex]  =  [tex]\frac{2+4+6}{3}[/tex]  = 4

Now, standard deviation formula is given by;

      Standard deviation, s  =  [tex]\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }[/tex]  

                                            =  [tex]\sqrt{\frac{8 }{3-1} }[/tex]  = 2

From this, we observe that even after decreasing each number by 4, the standard deviation remains same.

SO, we can conclude that if each one of the numbers in the set was decreased by 4 , the standard deviation of a set of numbers will be 22.2 only.

The additive property of equality states that if the same amount is added to both sides of an equation, then the equality is still true.

Answer:

75.36 cm

Step-by-step explanation:

Radius for circle is half of diameter

given diameter is 24

therefore radius = half of 24 = 24/2 = 12

circumference of circle is given by [tex]2\pi r[/tex]

where r is the radius

therefore ,circumference of circle

[tex]circumference = 2\pi r = 2*3.14*12\\\\circumference = 75.36[/tex]

Thus, circumference of circle is 75.36 cm

Answer:

4x^2 -25

Step-by-step explanation:

(2x + 5)(2x - 5)

FOIL

first: 2x*2x = 4x^2

outer : 2x*-5 = -10x

inner : 5*2x = 10x

last: -5*5 = -25

Add them together

4x^2 -10x +10x -25

Combine terms

4x^2 -25

Answer:

4x²- 25

Step-by-step explanation:

Let's use the FOIL (First, Outer, Inner, Last) method to solve:

(2x + 5)(2x - 5)

FOIL

First:

(2x + 5)(2x - 5)

2x(2x)

= 4x²

FOIL

Outer:

(2x + 5)(2x - 5)

2x(-5)

= -10x

FOIL

Inner:

(2x + 5)(2x - 5)

5(2x)

= 10x

FOIL

Last:

(2x + 5)(2x - 5)

(5)(-5)

= -25

Let's put it all together:

4x² - 10x + 10x - 25

Combine like terms:

4x² - 10x + 10x - 25

4x²- 25

Therefore, the product is 4x²- 25.

Answer:

(a) (i) x + y ≤ 24

(ii) y ≥ 4 + x

(b) draw a graph with the coordinate given below:

* note that you must draw 2 lines in your graph as there are 2 linear inequalities

(i) (0,24) and (24,0)

(ii) (0,4) and (-4,0)

*when the sign is ≤ , shade below the drawen line on the graph.

*when the sign is ≥, shade above the drawen line on the graph.

(c) x=8

8 + y ≤ 24

y ≤ 16 ( maximum )

y ≥ 4+8

y ≥ 12 (minimum)

Answer:

Probability = 0.500

Step-by-step explanation:

If it is given that the reader is a teen, we have a total of 80 readers, where 40 of those readers have Rowling as their favorite.

So the probability that the reader's favorite is Rowling given that the reader is a teen is the number of teen readers that have Rowling as favorite (40) over the total number of teen readers (80)

Probability = 40 / 80 = 0.500

Answer:

Step-by-step explanation:

-2.5b + 15.2 = -3.5b

-2.5b + 2.5b + 15.2 = -3.5b + 2.5b

15.2 = -1b

15.2/-1 = -1b/-1

-15.2 = b

b = -15.2

Step-by-step explanation:

a)

total no. of pupils is not more than 24

therefore first equation is

(x+y) ≤ 24. ....(1)

No. of girls exceeding the no. of boys by atleast 4

(y-x) ≥ 4. .....(2)

b) Now Liza chooses 8 boys

Maximum no. of girls = ?

Using first inequality

y+8= 24 ( maximum value of less than or equal to function is equal to itself)

Therefore,

y= 24-8

=16

Minimum no. of girls = ?

Using second inequality

y-8 =4 (minimum value of greater than or equal to function is equal to itself)

Therefore,

y= 4+8

y=12

Answer:

a) 2linear inequalities

(x+y) ≤ 24

(y-x) ≥ 4

b) Max no. of girls = 16

Min no. of girls = 12

Hope it helps...

Answer:

B, 1 right angle

Step-by-step explanation:

Triangles don't have the same length of there sides. The sides are uneven which makes the triangle unique. Also, right triangles only have 1 right angle

Hope this helps

Mark brainliest pls

Answer:

B

Step-by-step explanation:

Another way you can think about it is by thinking about the total possible angle sum. The angles in a triangle must sum to 180, so if there are 2 or more right angles, then you either cant have a 3rd angle because thats already at or over 180 degrees. That is why it must be 1.

Answer:

D) 0.0004

Step-by-step explanation:

(0.02)^2=0.02*0.02=0.0004

Answer:

6th degree trinomial

Step-by-step explanation:

Because the highest exponent is 6, and there are 3(tri) numbers.

Answer:

6th degree trinomial.

Answer:

A) 5

Step-by-step explanation:

Distance between two points is calculated as:

Step 1: locate the coordinate points:

Point 1- (x₁ , y₂) = (-5, -2)

Point 2-(x₁ , y₂)= (-9, -5)

Formula to find distance between two points = √(x₂−x₁)² + (y₂−y₁)²

Step 2: input the values

√(−9− −5)² + (−5− −2)²

= √(−4)² + (−3)²

=√16 + 9

= √25 ........ square root of 25

= 5

Distance between points (-5, -2) and (-9, -5) is 5

work by Tolaosunrinde

Answer:

DA

Step-by-step explanation:

Answer:

Diana will be able to maek 12

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Since the interior angles of a triangle will always add up to 180 degrees, angle B must equal 180-67-40=73 degrees, meaning that angle B corresponds to angle E in the other triangle. A corresponds to D, and F maps to C. Since no rotation is necessary, all you need to do is align two of the vertices to their corresponding vertice on the other triangle. The only answer choice here that does this is choice D, meaning that it is the correct answer. Hope this helps!

Answer:

The line of symmetry for function f is x = 2 and the line of symmetry for function g is x = 1.

The y-intercept of function f is greater than the y-intercept of function g.

Over the interval [2, 4], the average rate of change of function f is greater than the average rate of change of function g.

Answer:

The histogram for the data is attached below.

Step-by-step explanation:

The data for the number of houses Gregg the garbage man visited each day last week is as follows:

S = {12, 28, 33, 37, 23, 14, 9​}

In this case we need to create a histogram for the provided data.

According to the graph provided we know that the class intervals are:

CI = 0 - 10, 10 - 20, 20 - 30, 30 - 40

The frequency distribution table is as follows:

Class Interval     Frequency

    0 - 10                    1

   10 - 20                  2

  20 - 30                  2

  30 - 40                  2

The histogram for the data is attached below.

Answer:

This is from Khan Academy.

There are 1 squares in 0-10

There are 2 squares in 10-20

There are 2 squares in 20-30

There are 2 squares in 30-40

Answer:

The price per serving is $0.315, therefore, it's less than $0.5

Step-by-step explanation:

In order to calculate the price per serving, we can first calculate the price per cup, this is done by dividing the total value of the box by the number of cups it can serve:

[tex]price_{cup} = \frac{3.8}{9} = 0.42[/tex]

Since each serving is [tex]\frac{3}{4}[/tex] of a cup, then it's price has the same proportion and is given by:

[tex]price_{serving} = \frac{3}{4}*0.42 = 0.315[/tex]

The price per serving is $0.315, therefore, it's less than $0.5

Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A(4, 7) and (x₂, y₂ ) = B(2,3)

m = [tex]\frac{3-7}{2-4}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2 , thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 3), then

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = 2x - 1 ← equation of line

Answer:[tex]\frac{x}{6}[/tex] + 5

Step-by-step explanation:

Answer:

x/6 + 5.

Step-by-step explanation:

The quotient of x and 5 is x/6.

Adding 5 we get:

x/6 + 5.

Answer:

Not sure what the answer choices are, but choose the choice that says the new image is either stretched or shrunk. In a dilation, the shape/corresponding sides of the pre-image are preserved in the new image, but the size of the new image is altered.

Step-by-step explanation:

hope this helps!

Answer:

the answer would be 2/3. I hope this helps.

Step-by-step explanation:

The weight of this cereal is bran is 3/4 fraction.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

A different breakfast cereal is made using only fruit and bran.

The ratio of the weight of fruit to the weight of bran is 1 : 3.

That means,

the total amount = 3x + x = 4x.

Then fraction of the weight of this cereal is bran,

3x/4x

= 3/4

Therefore, 3/4 is the required fraction.

To learn more about the fractions;

https://brainly.com/question/10354322

#SPJ2

Answer:

Step-by-step explanation:

Adam plans to choose a video game from a section of the store where everything is 75% off.

The expression written by him for this situation is d - 0.75d.

Here, the part d represents the sale price before discount and the part 0.75d is the discount amount.

The expression written by Rena is 0.25d.

Here, the part 0.25d is the price after discount. Since 75% is the discount, the rate after disount is 25% and 25% of d is 0.25d.

Answer:

$6.8

Step-by-step explanation:

5+10+2+7+10=34

34/5=6.8

Answer:

$40 will be the total cost of the ribbon.

Step-by-step explanation:

To find the cost of ribbon to be put on the edges of rectangular banner, we need to:

1. Find the perimeter of the rectangle.

2. Multiply the perimeter with the per foot cost to find the total cost.

Let us find the perimeter first:

Perimeter of a rectangle is given as:

[tex]P = 2 \times \text{(length+width)}[/tex]

Here, the dimensions of rectangle are 4ft by 6ft.

So, perimeter = [tex]2 \times (4+6) \Rightarrow 20\ ft[/tex]

It is given that per foot cost is $2.

Total cost of the ribbon = [tex]2 \times 20 \Rightarrow $40[/tex]

$40 will be the total cost of the ribbon.