write the following numbers in p by q form 2.015151515...​

Considering the given box plots, we have that:

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

Hence, for class A, we have that:

Then:

Hence, for class B, we have that:

Then:

Hence the correct options are given as follows:

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Using the median concept, it is found that:

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

Researching the problem on the internet, we have that there are 21 5th grade students. It is an odd number, hence the median is the 11th element, as (21 + 1)/2 = 11. Looking at the dot plot, the median is of 13.

There are 23 5th grade students. It is an odd number, hence the median is the 12th element, as (23 + 1)/2 = 12. Looking at the dot plot, the median is of 17.

The relationship is that 7th grade students have a higher median than 5th grade students.

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Solutions of the equation are 22.5°, 30°.

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)

=2cos4θsinθ  [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = 90/4

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = 1/2

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

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The algebraic solution to the situation is as follows:

x + y = 750

10x + 6y = 6860

The number of adult and student are 590 and 160 respectively.

One adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars.

One evening,750 people attended the play and the total receipts were 6860.

Therefore,

let

x = number of adult ticket

y = number of student tickets

Therefore,

x + y = 750

10x + 6y = 6860

10x + 10y = 7500

10x + 6y = 6860

4y = 640

y = 640 / 4

y = 160

Hence,

x  = 750 - y

x = 750 - 160

x = 590

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Answer:

0.1 cases

Step-by-step explanation:

100(1-0.90)^3

100(0.10)^3

100(0.001)

0.1

The percentage of increase in the size is 25%

According to the statement

We have to given that the

Size of the granola packages from 16 ounces to 20 ounces.

And we have to find the percentage of the size of the crunchee's granola packages.

So, For this purpose,

The formula to calculate the percentage of increase in the size is :

Percentage to increase the size = present size - past size / present size.

Now substitute the values in the given formula is

Percentage to increase the size = (20 - 16 / 16)*100

After solving it

Percentage to increase the size = (4/16) *100

Percentage to increase the size = 25%

So, The percentage of increase in the size is 25%

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The distance between the two schools on the map is (C) 4.2 inches.

To find the distance:

On the map,2 inches represents 5 miles.

Thus, we can write:

Since the actual distance between the two schools is 10.6 miles.

Multiplying both sides by 10.6 in equation (1).

Therefore, the distance between the two schools on the map is (C) 4.2 inches.

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The complete question is given below:
Kim is drawing a map of the different schools in her school district. she knows that her middle school is 10.6 miles away from the middle school that her best friend attends. if every 2 inches on the map represents 5 miles, how far apart will the two schools be on the map, to the nearest tenth of an inch?

(A) 0.2 inch

(B) 0.9 inch

(C) 4.2 inches

(D) 26.5 inches

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:

A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)

A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²

A = 276 cm²

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

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Answer:

6 1/10

Step-by-step explanation:

In order to add fractions, we have to make the denominators equal.  we can multiply 1/2 by 5/5 and get 5/10, and multiply 3/5 by 2/2 and get 6/10, to make the denominator equal. Now we add the fractions. 4 5/10 + 1 6/10 = 5 11/10 = 6 1/10

The percent is the new value of the house of the price they paid 20 years ago is 216.67%.

percent is the new value of the house = New price / Old price

= 520,000 / 240,000 × 100

= 2.16666666666666

= 216.666666666666%

Approximately,

percent is the new value of the house = 216.67%

Therefore, the percent is the new value of the house of the price they paid 20 years ago is 216.67%.

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The Laplace transformation of given equation is [tex]y=-\frac{9}{2}e^{3t}\sin \left(2t\right)[/tex].

According to the statement

we have given that the equation and we have to find the Laplace transformation of that equation.

So, For this purpose, we know that the

Laplace transformation is an integral transform that converts a function of a real variable to a function of a complex variables.

And the given equation is

y'' − 6y' + 13y = 0, y(0) = 0, y'(0) = −9

To convert into the Laplace transformation

firstly find the single derivative of given equation in the Laplace transformation and put y = -9 in this.

And now find second derivative of given equation in the Laplace transformation.

And and put y = 0 in the given equation.

After the Laplace transformation give value as a Laplace transformation is [tex]y=-\frac{9}{2}e^{3t}\sin \left(2t\right)[/tex].

So, The Laplace transformation of given equation is [tex]y=-\frac{9}{2}e^{3t}\sin \left(2t\right)[/tex].

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The value of x from the given set of values is 5

A rectangle is a 2 dimensional shape with 4 sides and angle. The formula for calculating the area and perimeter is given as:

Area = length * width

Perimeter = 2(length + width)

If the length of a rectangle is 2 inches more than its width and the perimeter of the rectangle is 24 inches, the resulting equation will be:

2x + 2(x + 2) = 24,

Expand and determine the value of "x"

2x+ 2x + 4 = 24

4x + 4 = 24

Subtract 4 from both sides

4x = 24 - 4

4x = 20

Divide both sides by 4

4x/4 = 20/4

x = 5

Hence the value of x from the given set of values is 5

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Complete question

The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation. The value of x from the set {1, 3, 5, 7} that holds true for the equation is . So, the width of the rectangle is inches and its length is inches.

I assume that 0.53 with a bar means the decimal fraction in which 3 is repeating.

24/45, 8/15, and 48/90 all result in the same decimal value. Thus, we are simply looking for the one that is fully simplified.

The correct answer is 8/15.

Hope this helps!

Correct match for the quadratic equation are:

A. {-4, 4}

B.  {-5, 5}

C.  {-8, 8}

D.  {-11, 11}

E.  {3,-3}

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

2x² - 32 = 0

Adding thirty-two to both sides of the equation:

2x² = 32

Dividing between two on both sides of the equation:

x² = 322

x² = 16

Applying square root to eliminate the exponent:

x =  ±√16

x =  ±4

4x² - 100 = 0

Adding hundred to both sides of the equation:

4x² = 100

Dividing between four on both sides of the equation:

x² = 100/4

x² = 25

Applying square root to eliminate the exponent:

x = ±√25

x = ±5

x² - 55 = 9

Adding fifty-five to both sides of the equation:

x² = 9 + 55

x² = 64

Applying square root to eliminate the exponent:

x = ±√64

x =  ±8

x² - 140 = -19

Adding one- fourty to both sides of the equation:

x² = -19 + 140

x² = 121

Applying square root to eliminate the exponent:

x = ±√121

x = ±11

2x² - 18 = 0

Adding eighteen to both sides of the equation:

2x² = 18

Dividing between two on both sides of the equation:

x² = 182

x² = 9

Applying square root to eliminate the exponent:

x = ±√9

x = ±3

Correct match for the quadratic equation are: A. {-4, 4},B.  {-5, 5},

C. {-8, 8},D.  {-11, 11},E.  {3,-3}

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I understand that the question you are looking for is:

Match each quadratic equation with its solution set.

A. 2x2 - 32 = 0  {-8, 8}

B. 4x2 - 100 = 0  {-4, 4}

C. x2 - 55 = 9          {-5, 5}

D. x2 - 140 = -19         {-11, 11}

E. 2x2 - 18 = 0  {3,-3}

[tex]-16=r^3\implies \sqrt[3]{-16}=\sqrt[3]{r^3}\implies \sqrt[3]{-16}=r\implies \sqrt[3]{-2^4}=r \\\\\\ \sqrt[3]{(-2)^3\cdot 2^1}=r\implies -2\sqrt[3]{2^1}=r\implies -2\sqrt[3]{2}=r[/tex]

There are 7 ones on the left and only 2 on the right. The two sides need to be even, or balanced.

7 = 2 + r

r = 5

Hope this helps!

The value of x is $30.

From the question, it can be deduced that Jeremy's investment account earns a compound interest. Compound interest is when the amount invested and the interest that has already accrued increases in value anytime interest is paid.

The formula that can be used to determine the value of x is:

x = FV / (1+r)^t

X = 480 / (2^4) = $30

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The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

We are given;

Total number of objective questions = 5 questions

Number of choices of first 2 questions = 3 choices

Number of choices of last 3 questions = 4 choices

Number of ways of answering the first 2 questions = 3 * 3 = 9 ways

Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways

Total number of ways of answering the five questions = 9 * 64 = 576 ways

Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.

Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144

Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192

The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

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The trigonometric values we require :

[tex]\begin{tabular}{c | l}trigonometric value & numerical value \\\cline{1-2}tan 45^{o}& 1 \\cos 60^{o} & 0.5 \\sin 45^{o} & 1 \div \sqrt{2}\end{tabular}[/tex]

Now, let's solve for x.

tan 45° - cos 60° = x (sin 45°)

[tex]\mathrm {1 - \frac{1}{2} = x (\frac{1}{\sqrt{2}})}[/tex]

[tex]\mathrm {\frac{1}{2} = \frac{x}{\sqrt{2}}}[/tex]

[tex]\mathrm {x = \frac{\sqrt{2}}{2}}[/tex]

[tex]\mathrm {x = \frac{1}{\sqrt{2}}}[/tex]

The value of x is 1/√2.

I hope it helped you solve the problem

Good luck on your studies!

Nag basa nito walang jõwa

The value of a = 11

What is complex numbers ?

Let  a + i b = (a,b)

       c + i d = (c , d)

the distance between two points = [tex]\sqrt{( a - c)^{2} + (b -d )^{2} }[/tex]

put values in the formula -

[tex]\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }[/tex] = 29

square both sides

[tex]{(a + 9)^{2} + (21)^{2} } = 29^{2}[/tex]

(a + 9)² = 841 - 441 ⇒ 400

(a + 9) = √400 = + 20

a =  +20 -9

So,  a = -29  or 11

Therefore, the value of a = 11

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The answer is 0.

The expression in algebraic form is :

We know subtracting a term from its equivalent term will be 0.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

“[tex]\textsf{x minus x}[/tex]”

[tex]\huge\textbf{Simplifying it: }[/tex]

[tex]\textsf{x minus x}[/tex]

[tex]\mathsf{= x - x}[/tex]

[tex]\mathsf{= 1x - 1x}[/tex]

[tex]\mathsf{= 0x}[/tex]

[tex]\mathsf{= 0}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak 0}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A).

The equation of the line is represented by a polynomial of the form y = m · x + b, where m is the slope of the line and b is the intercept of the line. The slope is equal to the change in the dependent variable (Δy) and in the independent variable (Δx) and the intercept is the vertical distance of the line with the origin when x = 0.

In accordance with the picture, we notice that the scatter plot indice that Δy < 0 and Δx > 0 and therefore, m < 0. Besides, the intercept of the equation of the line must be greater than zero. Thus, the equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A)

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She has 38 nickels

N as the number of nickels, D as the number of dimes, and Q as the number of quarters.

She has 140 coins in total, so we can writen:

N + D + Q  = 140.

And the total value is $19.00

Then we have:

N*0.05 + D*0.10 + Q*0.25 = 19

And "The difference in the number of dimes and the number of quarters is 10."

D - Q = 10.

So we have a system of 3 equations and 3 variables:

N + D + Q  = 140

N*0.05 + D*0.10 + Q*0.25 = 19

D - Q = 10.

First, let's isolate one of the variables in the third equation, i will isolate D.

D = 10 + Q.

Now we can replace this in the other two equations:

N + (10 + Q) + Q = 140

N*0.05 + (10 + Q)*0.10 + Q*0.25 = 19.

Now we can isolate Q in the first equation:

N + 10 + 2*Q = 140

2*Q = 140 - 10 - N

Q = 130/2 - N/2. = 65 - N/2

Now we can replace this in the other equation:

N*0.05 + 10*0.10 + Q*(0.10 + 0.25) = 19

N*0.05 + 10*0.10 + (65 - N/2)*( 0.35) = 19

Now we can find the number of nickels.

N*0.05 + 1 + 22.75 - N*0.175 = 19

23.75 - N*(0.175 - 0.05)  = 19

23.75 - 19 = N*0.125

4.75/0.125 = N

38 = N

She has 38 nickels

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5x² + 9x - 1 is  the expression that represents a quadratic expression.

What is  quadratic expression?

A quadratic expression is of the form

ax² + bx +c = 0                    where a ≠ 0

The give options are-

9x - 2

5x² + 9x - 1

-2x³ + 8x² - 7x +1

[tex]x^{4} - 12 x^{3} + 8x^{2} - 7x +1[/tex]

From the given options, the only expression which is quadratic is

5x² + 9x - 1

wChoose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 −here a =5, b=9 and c=-1

Therefore, 5x² + 9x - 1 is  the expression that represents a quadratic expression.

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Answer: [tex]\Large\boxed{\angle DAB=62^\circ}[/tex]

Concept:

Here, we need to know about the idea of a cyclic quadrilateral.

In a cyclic quadrilateral, the sum of either pair of opposite angles is supplementary, which means they add up to 180°.

Please refer to the attachment below for a graphical explanation

Solve:

Given information

∠DAB = 2x + 4

∠ABC = 4y + 4

∠BCD = 4x + 2

∠CDA = 3y + 8

Derived formula from the concept

∠DAB + ∠BCD = 180°

∠ABC + ∠CDA = 180° (Not Important)

Substitute values into the formula that includes ∠DAB

∠DAB + ∠BCD = 180°

(2x + 4) + (4x + 2) = 180

Combine like terms

2x + 4 + 4x + 2 = 180

2x + 4x + 4 + 2 = 180

6x + 6 = 180

Subtract 6 on both sides

6x + 6 - 6 = 180 - 6

6x = 174

Divide 6 on both sides

6x / 6 = 174 / 6

x = 29

Substitute values into the angle expression of ∠DAB

∠DAB = 2x + 4

∠DAB = 2 (29) + 4

∠DAB = 58 + 4

[tex]\Large\boxed{\angle DAB=62^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

2.5 feet

Step-by-step explanation:

Since circumference is just pi(we're using 3.14 in this case) * diameter, which is our answer, we need to divide the circumference(which is 7.58) BY 3.14, which is pi. This leaves us with the diameter, which is 2.5. The unit is already feet, so we needn't do anything about that.

A cell's expected frequency can be defined as the number of people in its row divided by the total number of people, multiplied by the number in its column and is therefore denoted as option C.

This is defined as the number of occurrences of a repeating which takes place per unit time.It also helps to measure how frequent something occurs when counted or observed and is also used in the calculation of the  different types of statistical data present or given.

This type of frequency is theoretical and are values which will most likely be in an experiment. it is calculated by multiplying the number in its column by the number of people in the row and dividing by the total number of people in this context.

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