What shape is this, why?

The percentage of middle school students that prefer each season and the percentage of high school students that prefer each season is 57.93% and 42.07% respectively.

The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.

Here,
Total number of students = 93 + 31 + 36 + 54 = 214

The percentage of students in middle school prefer spring,
= number of students in middle school prefer spring / total student × 100%
= 93/214 × 100%
= 43.45%

Similarly,
The percentage of students in middle school prefer winter,
= number of students in middle school who prefer winter/ total students × 100%
= 31/214 × 100%
= 14.48%

Thus, the percentage of middle school students that prefer each season and the percentage of high school students that prefer each season are 43.45 + 14.48 = 57.93% and 100-57.93% = 42.07%.

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The equation is simplified as a rational expression

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is a rational expression

Substituting the values in the equation , we get

And , A ratio of two polynomials is a rational expression. Two rational expressions with the same denominator can be added or subtracted by adding or subtracting the numerators, then writing the result over the shared denominator.

Firstly, we find the LCM of the denominator and then write each expression using the LCD. On simplifying the numerator by either adding or subtracting the values , we simplify the rational expressions

Hence , the rational equations are solved

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Answer:

360 degrees

2 pi radians, means you have 2 pi of something and they are radians. It is the same 360 degrees. A radius is the line from the side of the circle to the center.

Reason: pi radians is 180 degrees. Double each value to find that 2pi radians is 360 degrees. It's a full revolution of a circle. Use a unit circle if necessary.

Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.

Function can be defined in which it relates an input to output.

Given function ,

The function f(x) = x³ +9 is one-to-one.

To find the inverse function f1, we need to switch the roles of x and y in the equation for f(x). So, we have:

y = x³ + 9

Next, we need to solve for x in terms of y:

x³ + 9 = y

x³ = y - 9

x = (y - 9[tex])^{(1/3)}[/tex]

So, the inverse function is:

f1(y) = (y - 9[tex])^{(1/3)}[/tex]

To verify that f1 is the correct inverse function, we need to show that f(f1(y)) = y and f1(f(x)) = x:

f(f1(y)) = f((y - 9[tex])^{(1/3)}[/tex] = (y - 9[tex])^{(1/3)}^3[/tex] + 9 = y - 9 + 9 = y

And:

f1(f(x)) = f1(x³ + 9) = (x³ + 9 - 9[tex])^{(1/3)}[/tex] = [tex]\mathrm{ x^3^{(1/3)}}[/tex] = x

Therefore, Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.

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Answer:

the scale factor that Samir used in his drawing is 5/1.

Step-by-step explanation:

Here's a step by step explanation of how to find the scale factor of a drawing:

Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.

Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.

Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.

The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.

So, the scale factor that Samir used in his drawing is 5/1.

Answer: The equation "x + y = mb" represents a linear equation in two variables, x and y. In this equation, m is a constant and b is another constant or a known value. The equation states that the sum of x and y is equal to the product of m and b.

This equation can be used to model a variety of real-world situations where two quantities are related and their sum is equal to a constant value. For example, it could represent the amount of money saved by two people, where x and y are the savings of the two people and mb is the total amount of money saved.

To solve for x and y, we can use either substitution or elimination method, or any other method for solving systems of linear equations. The values of x and y that satisfy the equation "x + y = mb" are called the solutions of the equation.

Step-by-step explanation:

A. The value of the function at x = 8 will be 4. Then the correct option is B.

B. The average rate of change of the function in the interval of [2, 6]  will be 24. Then the correct option is D.

C. The total mass of 5,000 of these microorganisms will be 0.012 g. Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A. The function is f(x) = 8 / (x - 6), then the value of the function at x = 8 is given as,

f(8) = 8 / (8 - 6)

f(8) = 4

Then the correct option is B.

B.  The function is f(x) = 3x² - 5, then the average rate of change of the function in the interval of [2, 6] is given as,

Average rate = [3(6² - 4²)] / (6 - 2)

Average rate = 24

Thus, the correct option is D.

C.  The average mass of a certain type of microorganism is 2.4 × 10⁻⁶ grams. Then the total mass of 5,000 of these microorganisms is given as,

⇒ 2.4 × 10⁻⁶ × 5,000

⇒ 0.012 grams

Thus, the correct option is C.

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Answer:

Step-by-step explanation:

To factorise the expression, we can use the factor theorem which states that if a polynomial p(x) has a factor (x - r), then p(r) = 0.

We can use this theorem to find the factors of the polynomial expression:

(a - 2b)^3 + (2a - b)^3

We can write (a - 2b)^3 as (a - 2b)(a^2 - 4ab + 4b^2). Using the factor theorem, we see that:

(a - 2b)(a^2 - 4ab + 4b^2) = 0 when a = 2b

Similarly, we can write (2a - b)^3 as (2a - b)(4a^2 - 4ab + b^2). Using the factor theorem, we see that:

(2a - b)(4a^2 - 4ab + b^2) = 0 when a = b/2

Now we have two equations: a = 2b and a = b/2, which we can use to solve for a and b in terms of each other. We see that:

a = 2b = b/2

Multiplying both sides by 2, we get:

2a = b

We can substitute this back into the original expression:

(a - 2b)^3 + (2a - b)^3 = (a - 2(2a))^3 + (2a - (2a))^3 = (-3a)^3 + (0)^3 = -27a^3

So the factorised form of the expression is:

(a - 2b)^3 + (2a - b)^3 = -27a^3.

Work Shown:

Use the sum of cubes factoring rule

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

In this case,

So,

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

(a-2b)^3 + (2a-b)^3 = (a-2b+2a-b)((a-2b)^2 - (a-2b)(2a-b) + (2a-b)^2)

(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-ab-4ab+2b^2) + (4a^2-4ab+b^2))

(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-5ab+2b^2) + (4a^2-4ab+b^2))

(a-2b)^3 + (2a-b)^3 = (3a-3b)(a^2-4ab+4b^2 - 2a^2+5ab-2b^2 + 4a^2-4ab+b^2)

(a-2b)^3 + (2a-b)^3 = (3a-3b)(3a^2-3ab+3b^2)

(a-2b)^3 + (2a-b)^3 = 3*3(a-b)(a^2-ab+b^2)

(a-2b)^3 + (2a-b)^3 = 9(a-b)(a^2-ab+b^2)

The answer has been fully confirmed with WolframAlpha.

Note that the Polynomial Expression for to represent the total surface area of the two drums is: 4πrh + 4hr².

A polynomial expression is any expression that consists of variables, constants, and exponents and is combined using mathematical operators such as addition, subtraction, multiplication, and division.

According to the number of terms in the expression, polynomial expressions are classed as monomials, binomials, or trinomials.

Given that the total surface area of one cylinder is:

2πrh + 2πr²,

The total surface area of two drums will therefore be:

(2πrh + 2πr²) * 2

⇒ 4πrh + 4hr²

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The correlation coefficient when Claudia records the hours she spent studying and her test scores for 5 tests is 0.85. This is a strong positive correlation.

Any statistical association between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.

Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.

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Claudia records the hours she spent studying and her test scores for 5 tests.

What is the correlation coefficient?

-0.85-0.840.840.85

What is the strength of the model?

The composite function has its value to be g o h(x) = -20x^2 - 30x

from the question, we have the following parameters that can be used in our computation:

h(x) = 4x + 6

g(x) = -5x

Using the above as a guide, we have the following:

g o h(x) = g(x) * h(x)

substitute the known values in the above equation, so, we have the following representation

g o h(x) = (4x + 6) * -5x

Evaluate

g o h(x) = -20x^2 - 30x

Hence, the value is g o h(x) = -20x^2 - 30x

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Answer:

x=5 and LN= 30, MP= 40

Step-by-step explanation:

Add like terms to both sides of the equation and you will get your answer

For given ratio of orange juice and pineapple juice i.e. 5/6, proportion used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice will be 5 over 6 equals j over 21 i.e. 5/6=j/21.

What exactly is a ratio?

Fractions are commonly used to describe ratios and proportions. A ratio is demonstrated when a fraction is expressed as a:b, whereas a percentage indicates that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.

We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.

As a result, when b is larger than zero, the ratio, such as a:b, defines the relationship between two variables. For example, the 2:4 ratio is expressed as 2:4 = 1:2.

Now,

Given that In recipe ratio of  orange juice / pineapple juice =5/6

then to make a recipe with 21 L of pineapple juice, the orange juice (j)

needed will be

5/6=j/21

j=17.5 L

hence,

           proportion used to find the amount of orange juice, j will be 5 over 6 equals j over 21 i.e. 5/6=j/21.

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Answer: its D

Step-by-step explanation:

pls i belieive most of yall are npcs

The probability that at least 1 of the 4 cards drawn is a face card is 0.6.

A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.

Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.

A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:

P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).

The likelihood that none of the four draws will produce a face card is:

P(no face cards are present) = (10/13)4 = 0.432

As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:

P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568

The chance, rounded to one decimal place, is roughly 0.6.

Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.

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Answer: The answer is A. (-∞0, +00)

The amount of money which would be in the account after 14 years is; $18,123.77.

The number of years it'd take for the money to double is; 13.86 years.

Since the given model of the account is;

A (t) = 9000e^0.05t

After 14 years, it follows that; t = 14.

Therefore;

A (14) = 9000e^0.05(14)

A (14) = 9000 × 2.013752707

A (14) = $18,123.77.

Also, the doubling time implies that; A (t) = 18,000

Therefore, 18000 = 9000e^0.05t

2 = e^0.05t

0.05t = ln (2)

t = ln (2) / 0.05

t = 13.86 years.

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(a) Randomized experiment, (b) There are three criteria for a randomized experiment

a) This is a randomized experiment.

b) The three criteria for a randomized experiment are:

Random assignment, the children were randomly assigned to the xylitol or placebo group.

Control group, a placebo group was used as a control.

Manipulation, the children were given different forms and doses of xylitol or placebo.

c) The explanatory variable is the form and dose of xylitol or placebo given to the children. The response variable is the incidence of ear infections.

d) Diagram of the randomized comparative experiment:

Population of healthy children in daycare centers

↓

Random assignment to xylitol or placebo group

↓

Intervention group: given xylitol in syrup, gum or lozenge form

Control group: given a placebo in gum, syrup or lozenge form

↓

Comparison of incidence of ear infections in intervention and control groups

↓

Analysis of results to determine the effectiveness of xylitol in reducing ear infections.

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Answer:

3ab2+1 = -23

3a^2b-1 =-25

Step-by-step explanation:

Following are the values of the functions -

1) f(a) = 8a - 4

2) f(a+h) = 8a+ 8h - 4

3)[tex]\frac{f (a+h)-(a) }{h}= 8[/tex]

An expression or relationship with one or more variables is called a function. Both its inputs and outputs are numerous. There is just one output per input. The function explains how the inputs and outputs are related.

To evaluate f(a), we simply substitute the value of "a" into the function:

1) f(a) = 8a - 4

To evaluate f(a+h), we substitute the value of "a+h" into the function:

2) f(a+h) = 8(a+h) - 4

f(a+h) = 8a+ 8h-4

To find the expression for [tex]\frac{f (a+h)-(a) }{h}[/tex], we divide the result by h: L(a+h)-f(a) h we can subtract f(a) from f(a+h) and then

3) [tex]\frac{f (a+h)-(a) }{h}[/tex]

[tex]= \frac{ (8a+8h-4-(8a-4)}{h} \\= \frac{8h}{h}= 8[/tex]

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Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

Given :

percent distribution : 40% , 35% , 15% , 7% , 3%

Vehicles : 420

First, add the percentage of cars containing 3 people, 4 people, and 5 or more people:

15% + 7% + 3% = 25%

Thus, 25% of the cars contained at least 3 people, so use that to calculate the number of cars:

420 × 0.25 = 105 cars.

Hence , Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

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Complete question:

A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning.

How many of the 420 vehicles contained at least 3 people?

A. 42

B. 63

C. 105

D. 315

a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have P(x) = 12x + 300√x - 2500.

b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x) is dP/dx = 12 + 300/2√x.

c. The marginal average profit function is the derivative of the profit function divided by the number of units sold is dP/dx ÷ x = (12 + 300/2√x) ÷ x.

d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201 is $16.62.

What do you mean by  profit function?

A profit function is a mathematical model that represents the profit made from selling a certain product or service as a function of the number of units sold. The profit function is calculated as the difference between the total revenue and the total cost of producing and selling the product.

Mathematically, if R(x) represents the total revenue from selling x units of a product and C(x) represents the total cost of producing and selling x units of the product, then the profit function can be represented as P(x) = R(x) - C(x).

a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have:

P(x) = 14x - (2x - 300√x + 2500)

P(x) = 12x + 300√x - 2500

b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x):

dP/dx = 12 + 300/2√x

c. The marginal average profit function is the derivative of the profit function divided by the number of units sold.

dP/dx ÷ x = (12 + 300/2√x) ÷ x

d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201:

P(201) = 12 * 201 + 300 * √201 - 2500 = $3347.09

Since we want the profit from the sale of one unit, we divide the profit by 201:

P(201) ÷ 201 = $16.62

So, the estimated profit from the sale of the 201st doll is $16.62.

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Answer:

1,3 or 4,2

Step-by-step explanation:

The value of sin B rounded to the nearest hundredth is 0.80.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

The right triangle represented in the question is given below.

We know that sine of an angle in a right angled triangle is the ratio of it's opposite side to hypotenuse.

In the triangle ABC, AB is the hypotenuse and AC is the opposite side of B.

Sin B = AC / AB

Sin B = b / c

Sin B = 20 / 25

Sin B = 0.8

Hence the value of sine of B is 0.8.

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Find the total distance that Ramesh ran is 23km. His average running speed for the whole journey is 3 5/6 km/h.

To find the average speed,

We find the total distance and divide it by the total time.

During the first part of the run, she ran 3 hours at a speed of 7 km/h.  

To find the the distance she ran, multiply the speed times the time:  3 x 7 = 21 km.

From the second part of the run, she ran 2km.

So the total distance he ran is 21 + 2 = 23km.

The total time was 6 hours.

To find the the average speed;  

Divide 23 by 6 to get the average speed, which comes to 3 5/6 km/h.

hence, the average speed is 3 5/6 km/h.

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An equation to show the sequence is -25n.

When all the terms of the geometric sequence are added, than that expression is known as geometric series.

The sum of terms of a geometric sequence;

Now, lets suppose its initial term is   , multiplication factor will be r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

We are given that;

The first term of sequence=-25

D= -50-(-25)

=-25

Now,

an = a + (n-1)d

=-25+(n-1)-25

=-25-25n+25

=-25n

Therefore, the answer of the sequence will be -25n.

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Answer:

Step-by-step explanation:

m=3-1/2-7= -2/5

c⇒ -2

y=mx+c

y=-2/5x-2

Answer: 994 beads

Step-by-step explanation:

Red Beads = 275

Blue Beads = 825 (275 x 3)

825 + 275 = 1100 beads (total)

1100 - 156 = 994 beads

The simplified form of the expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex] is  [tex]6\frac{1}{8}[/tex].

Given the expression in the question:

[tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex]

To simplify the given expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex], first, rewrite the expression using the negative exponent rule:

[tex]( \frac{1}{2^{\frac{1}{2} }} * 7^{\frac{1}{3} )^6[/tex]

Next, combine the fractions:

[tex]( \frac{7^{\frac{1}{3} }}{2^{\frac{1}{2} }} )^6[/tex]

Simplify the numnerator:

[tex]\frac{49}{(2^{\frac{1}{2} })^6}[/tex]

Simplify the denpminator:

[tex]\frac{49}{8}\\ \\6\frac{1}{8}[/tex]

Therefore, the simplified form is [tex]6\frac{1}{8}[/tex]

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Answer:

Step-by-step explanation:

To determine which option is faster, we need to determine the total number of nights required for each option.

First, let's find the number of pages Nora still needs to read by subtracting the number of pages she's already read from the total number of pages: 280 pages * 30% = 84 pages

So, Nora still needs to read 280 pages - 84 pages = 196 pages.

For Option 1, Nora would read 25% of the remaining pages each night, so the number of pages she reads each night would be: 196 pages * 25% = 49 pages

The total number of nights required would be 196 pages / 49 pages/night = 4 nights.

For Option 2, Nora would read 28 pages each night, so the total number of nights required would be 196 pages / 28 pages/night = 7 nights.

Since 4 nights is less than 7 nights, Nora should choose Option 1 to finish reading the book in the least amount of time.