"5. Mr. Roberson created this frequency table to record the favorite color of each of his students. Which of the following statements are true based on the frequency table?
More students prefer red than green.
Twice as many students prefer green than purple.
More students prefer yellow than blue.
Two more students prefer blue than purple.
The same number of students prefer yellow or purple as the number who prefer blue."

The 85th percentile of a normal distribution is the score that is greater than or equal to 85% of the scores in the distribution. This means that the score at the 85th percentile is the same as the score that would be earned by the top 15% of individuals in the distribution.

To find the score at the 85th percentile, we can use the standard normal distribution table or use a calculator to find the z-score corresponding to the 85th percentile. The z-score is the number of standard deviations that a score is above or below the mean of the distribution.

Using a calculator or table, we find that the z-score corresponding to the 85th percentile is 1.04. Since the mean of the distribution is 100 and the standard deviation is 15, this means that the score at the 85th percentile is 100 + (1.04 * 15) = 120.4.

Therefore, the score of an individual who is at the 85th percentile on the Weshcler IQ test is 120.4.

When the level of confidence interval increases from 96% to 99% then the population mean will also become wider for a given fixed value of standard deviation and its fixed sample size, so the given statement is true.

As given in the question,

Let us consider 'σ' be the fixed standard deviation

And 'n' be the fixed sample size

Population mean = [tex]\bar{x}[/tex] ± z ( σ /√n )

Range of confidence interval increases from 96% to 99%

For a fixed standard deviation and sample size range of population mean become wider .

For fixed [tex]\bar{x}[/tex] , standard deviation 'σ' , and sample size 'n' the value of population mean get varied as per the change in confidence interval z-score.

Therefore, the given statement when level of confidence interval increases from 96% to 99% then population mean will get wider is a true statement.

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The nth term of the quadratic sequence is aₙ = n² + 2n

What is a quadratic sequence?

Finding the nth term rule of a quadratic sequence: The nth term rule of a quadratic sequence can always be written in the form an² + bn + c.

To find this rule, we need to find a, b and c

Given data ,

Let the expression be represented as = A

Now , the value of A is

A = 3 , 8 , 15 , 24 , 35 ..

Now , taking the difference of the second term and first term , we get

d₁ = 8 - 3 = 5

d₂ = 15 - 8 = 7

d₃ = 24 - 15 = 9

So , the difference of the numbers in the sequence is odd multiples

Therefore , the sequence goes in the multiples of ( n + 2 )

Now , when n = 1

a₁ = 3

when n = 2

a₂ = 8

So , a₂ = n ( n + 2 )

substituting the value for n = 2 , we get

a₂ = 2 ( 2 + 2 )

a₂ = 2 x 4

a₂ = 8

when n = 3

a₃ = 15

So , a₃ = n ( n + 2 )

substituting the value for n = 3 , we get

a₃ = 3 ( 3 + 2 )

a₃ = 3 x 5

a₃ = 15

Therefore , the nth term of the quadratic sequence will be

aₙ = n ( n + 2 )

aₙ = n² + 2n

Therefore , the sequence is aₙ = n² + 2n

Hence , The nth term of the quadratic sequence is aₙ = n² + 2n

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While constructing a confidence interval for the mean, when the population standard deviation is unknown, then we use normal distribution .

The error bound EBM and confidence interval are calculated using a standard normal distribution when the population standard deviation is unknown. We must determine the value of z that places an area in the centre of the standard normal distribution Z N that is equal to the confidence level (in decimal form) (0, 1).

We rarely know the population standard deviation in practise. When the sample size was huge is the , statisticians were not hindered by this. As an estimate for, they used the sample standard deviations, and they then carried out the same steps as before to compute a confidence range that produced near enough findings.

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Jenny has 6 marshmallows in her hot chocolate and Julie has 0 marshmallows in her hot chocolate

From the question, we are to determine the number of marshmallows Jenny and Julie each have in their hot chocolate

From the given information,

"Jenny put 6 more marshmallows in her cup than Julie"

Then, we can write that

x - y = 6  ---------- (1)

Also,

"Together Jenny and Julie had a total of 6 marshmallows"

That is,

x + y = 6 ---------- (2)

Add equations (1) and (2) together

   x - y = 6

+ [x + y = 6

--------------------

2x = 12

x = 12/2

x = 6

Substitute the value of x into equation (2)

x + y = 6

6 + y = 6

y = 6 - 6

y = 0

Hence, Jenny has 6 and Julie has 0

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The missing length in the given figure is 14.

A ratio in mathematics depicts the product of two numbers. For instance, the proportion of oranges to lemons in a serving of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8. (or 3:4). (or 4:7).

Any number of numbers, including counts of people or things, weights, lengths, and times, among other values, can be a component of a ratio. In settings, both numbers are often restricted to positive values.

A ratio's two constituent numbers can be specified as "a" and "b," or they can both be omitted.

From the given figure,

AC/BC=EC/DC

28+x/18=x/6

28+x=3x

2x=28

x=14

Therefore, the missing length in the given figure is 14.

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The value of the expression 2x+3 when x = 3 is 9.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given linear equation is

x + 2 - 6x = -13

Combine like terms:

(x - 6x) + 2 = -13

-5x + 2 = -13

The additive inverse of 2 is -2.

Add -2 on both sides:

-5x + 2 -2 = -13 -2

-5x = -15

Divide both sides by -5:

-5x/-5 = -15/-5

x = 3

Putting x = 3 in the expression 2x + 3

2x + 3 = (2×3) + 3

2x + 3 =6 + 3

2x + 3 = 9

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The length of segment QR is 8 units.

What is the mid-point segment of the triangle?

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

We have,

In ΔWUV

UV = 16 units

A line segment that connects two midpoints of the sides of a triangle is called a midsegment.

Mid-point segment of the triangle:

QR = 1/2(UV)         .............(1)

QR = 1/2(16)

QR = 8

Hence, the length of segment QR is 8 units.

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Answer:

(y - 5) = 1/4 (x - 8)

Step-by-step explanation:

Point-slope form is written in the form:

(y - y) = m (x - x)

Where the two y's and two x's are from the points, and m is the slope. To write the equation, you'd plug your points into the equation and solve for m, the slope.

(1 - 5) = m (-8 - 8)

-4 = m (-16)

m = 4/16 = 1/4

Plug m into the point-slope form equation as well as one of your points, and you have an equation.

The correct option for the errors made by Sabina are-

For the stated expression-

3x³ + x + 2 by when divided by (x + 2) by the long division method, the following is the quotient.

         _____________

x + 2 )    3x³ + x + 2      ( 3x² - 6x + 7

           -   3x³ - 6x²  

           __________

              - 6x²  + x + 2

             + 6x²  + 6x

           ____________

                       7x + 2

                     -7x   - 16

                  __________

                            - 14

                  ___________

Thus, the correct quotient for the polynomial is 3x² - 6x + 7.

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Choose the equation that represents this situation.

Use p to represent the price of a phone and t to represent the total cost. An online business adds a $6 shipping fee to the price of each phone it sells.

A. t = 6p

B. t = p + 6

C. p = t + 6

D. t + p = 6​

Answer:

12

Step-by-step explanation:

Pythag

Answer:

1/4

Step-by-step explanation:

The square root of 16 is 4, so its the same with fractions.

The partial fraction decomposition of the function is given as follows:

A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².

The function in this problem is defined as follows:

(x^4 + x² + 1)/(x²(5x² + 9)²)

Then the partial fraction decomposition is built considering the terms of denominator, as follows:

When a term is elevated to a power, the terms with the lower powers also have to be considered. For example, for the denominator x², x is also considered, hence the denominators are given as follows:

Then, considering the coefficients A, B, C and D, the partial fraction decomposition of the function is given as follows:

A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².

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Answer:

guy or girl

Step-by-step explanation:

The expression for the area that includes an exponent is 6² + (6 × 2) + 24

Area of the entire figure is 72 square inches

The dimension of the entire figure is 9 inches by 8 inches

From the question, we are to write an expression for the area of the entire figure

Area of the entire figure = Area of green shape + Area of white shape + Area of blue shape

Area of the entire figure = 6² + (6 × 2) + 24 square inches

The expression is 6² + (6 × 2) + 24

Thus,

Evaluating

Area of the entire figure = 6² + (6 × 2) + 24

Area of the entire figure = 36 + 12 + 24

Area of the entire figure = 72 square inches

b. The dimension of the entire figure

Width of the entire figure = Length of the green square + Width of the white rectangle

Width of the entire figure = 6 inches + 2 inches

Width of the entire figure = 8 inches

Then,

Length of the entire figure = Length of the white rectangle + Width of the blue rectangle

First, we will determine the width of the blue rectangle

Using the formula,

Area = l  × w

Where l is the length

and w is the width

24 = (2 + 6) × w

24 = 8 × w

w = 24/8

w = 3 inches

Therefore,

Length of the entire figure = 6 inches + 3 inches

Length of the entire figure = 9 inches

Hence, the dimension is 9 inches by 8 inches

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From the 2 column proof below, we have been able to prove the congruent triangles that ΔABC ≅ ΔCDA.

We will use a two column proof to prove that ΔABC ≅ ΔCDA.

Statement 1; AD ≅ BC

Reason 1; Given

Statement 2; AD ║ BC      

Reason 2; Given

Statement 3; AC ≅ AC  

Reason 3; Reflexive Property of congruence

Statement 4; ∠DAC ≅ ∠ACB

Reason 4; If 2 parallel lines are cut by a transversal, the alternate interior angles are congruent.

Statement 5; ΔABC ≅ ΔCDA                    

Reason 5; Side Angle Side(SAS) Congruence  Postulate

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Answer:

(-4,5)

Step-by-step explanation:

Answer: y=2

Step-by-step explanation:

6y-8=3y-2

3y=6

y=2

Length of diagonal WY is 13.03 units

What is Distance Formula?

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

According to the given question:

WXYZ is a rectangle and diagonals of a rectangle are equal in length

Coordinates of W = (-4,5) and Y = (3,-6)

To find the length of diagonal WY, we need to find distance between points W and Y.

Using distance formula to find WY

= √((3 – (-4))² + (-6 – 5)²)

= √170

= 13.03 units

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Answer:

ijsjsjdjdjjejjeks she e nsjksid the Earth travels in around the sun 6.2 Seasonal changes 6.3 Plants and animals are

Step-by-step explanation:

www2 and I 3333333 uth the sun is a bit better now and the Sun 6.2 is better off the moon

The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in the m:n ratio, finding the mid-point of the line, etc.

Let the coordinate of the point D be (x, y).

Point E has a similar y-coordinate as point D. Then the ordinate of the points will be the same.

And the x-direction of point E is something contrary to the x-direction of point D. Then the coordinate of point E will be (-x, y).

The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

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Answer:

16.7

Step-by-step explanation:

YX is similar to AX

XZ is similar to XB

so the triangle AXB is similar to YXZ thus AB is YC

The same goes for the rest of the triangles  (YAC and CBZ)

See image attached.

In 11.71 years the amount will double to the principal amount

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal amount and Compounded interest. This is the major distinction between compound and simple interest is this.

The formula  used for

where P = Principal amount

r = Rate of interest in decimal

n = Number of compounds per year  

t = Time period  

Here from the given data,

Principal amount, p = $ 2500

Rate of interest, r = 6% = 6/100 = 0.06

Number of compounds, n = 2    [ ∵ 12/6 = 2 ]

Here we need to find the time period

Let's assume that after 'n' years the amount will be doubled i.e $ 5000

From the given problem,

Amount, A = 2500(1+0.06/2)²ⁿ        

= 2500(1+0.06/2)²ⁿ  

= 2500(1 + 0.03)²ⁿ  

= 2500 (1.03)²ⁿ    

As we assumed after 'n' years the amount is $ 5000

=>  2500 (1.03)²ⁿ   = 5000

=> (1.03)²ⁿ   = 2  

Apply to log on both sides

=> log (1.3)²ⁿ  = log 2

=> 2t log (1.3) = log 2

=> 2t = log 2/ log(1.03)

=> 2t = 0.301029996/(0.0128372247)

[ use calculator for log (1.03) and log 2]

=> 2t = 23.4497722

=> t = 11.7248861  

=> t = 11.71 ≅ 11 years

Therefore,

In 11.71 years the amount will double to the principal amount

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The required probability for purchasing more than one costume is 0.03.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The given problem can be solved as follows,

The number of visitors purchasing no costume, exactly one and more than one costumes are given as 81, 6 and 3 respectively.

Then, the total number is 81 + 6 + 3 = 90

Now, the probability of purchasing more than one costume is given as,

P(More than one costume) = 3/90

                                            =  1/30

                                            = 0.03

Hence, probability that the next person will purchase more than one costume is 0.03.

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The circle's radius is the same as the radius of the circle whose equation is x2 + y2 = 9.

A circle's standard equation is written as:

x² + y² + 2gx + 2fy + C = 0

The radius of the center is (-g, -f) and radius = √g² + √f² - C

Given a circle with the equation,

x² + y² - 2x - 8 = 0

Find the circle's center.

2gx = -2x

2g = -2

g = -1

Likewise, 2fy = 0.

f = 0

(-(-1), 0) = Centre (1, 0)

This demonstrates that the circle's center is on the x-axis.

r = radius

= √g² + √f² - C

By substituting,

radius = √1² + 0² - (-8)

          =√9  

          = 3 units radius

The circle's radius is three units.

The radius of the circle x² + y² = 9 is written as:

r² = 9

radius = 3 units

As a result, the radius of this circle equals the radius of the circle whose equation is x² + y² = 9.

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The value of x for which the equation satisfies  is -10/3 .

What is an equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main Body:

According to the question:

y = 2

and ,

y = 3/5 x+4

to solve the equation , we need to substitute the value of y in other equation.

2 = 3/5 x +4

now take like terms to one side for solving,

2 - 4 = 3/5 x

   -2 = 3/5 x

multiplying by 5 on both sides,

-2 *5 = (3/5)*5x

  -10 = 3 x

     x = -10/3

Hence the value of x is -10/3.

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The range for the given function, with x=1 is 10.

The given function is f(x)=10x.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

Here, put x=1 in the function y=10x, we get

y=10(1)

y=10

So, the range for the given x=1 is y=10.

Therefore, the range for the given function, with x=1 is 10.

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