Question 1.
The table shown below represents the results from a sample group of 50 students
surveyed about a preference for an additional sports team.
Sports Team
Gymnastics
Ice hockey
Lacrosse
Swimming
Number
10
11
23
6
If the school has 500 students, what can be inferred from the survey?
A. There would not be enough students to form a 20-person ice hockey
team.
B. About half of the students prefer lacrosse to the other sports.
C. Fewer than ten students in the school prefer swimming to the other
sports.
D. About 10% of the students prefer gymnastics.
TW

The time Jim takes alone to mow the lawn is 10 hours.

Jim and Craig, working together  can mow the lawn in 8 hours. Working alone, Craig take 4 times as long as Jim.

Therefore, the time it takes Jim to mow the lawn alone can be calculated as follows:

let

x = time use by Jim to mow the lawn

Therefore,

time Craig use to mow the lawn = 4x

Hence,

1 / 8 = 1 / 4x + 1 / x

1 / 8 =  1 + 4/ 4x

1 / 8 = 5 / 4x

cross multiply

4x = 40

x = 40 / 4

x = 10

Therefore,

time Jim takes alone to mow the lawn = 10 hours.

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If the expression be x² - 3x - 4 then the factorize term be (x - 4)(x + 1).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

If the expression, ax³ + bx² - 5x + 2a is exactly divisible by x² - 3x - 4, then it is also divisible by both x - 4 and x + 1

If f(x) = ax³ + bx² - 5x + 2a, then f(4) = f(-1) = 0 by the factor theorem.

Hence, a(4)³ + b(4)² - 5(4) + 2a = 0 and

a(-1)³ + b(-1)² - 5(-1) + 2a = 0

⇒ so, 66a + 16b = 20 and a + b = -5

33a + 8b = 10     ...(1)

a + b = -5           ...(2)

simplifying the above (1) and (2), we get

33a + 8(-5 - a) = 10

i.e. 25a - 40 = 10

so, a = 2 ⇒ b = -7

Therefore, the function be f(x) = 2x³ - 7x² - 5x + 4

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On solving the provided question, we can say that the equation will be  distance = distance 36t + 18 = 63t distance = 63t = 63(2/3) = 42 miles

A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the two sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.

the equatiοn will be

distance = distance

36t + 18 = 63t

27t = 18

t = 18/27 = 2/3 hr

distance = 63t = 63(2/3) = 42 miles

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The data in the table represents a linear function, as when x is increased by one, y is subtracted by a constant amount of 9.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

For this problem, the function is classified as linear, as the difference between consecutive terms is 9, while the ratios are different.

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On solving the provided question we can say that  the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 ,

A decagon in geometry is a decagon or not. A basic decagon has 144° of inner angles added up. A decagram is a self-intersecting regular decagon. A decagon is a polygon that has ten sides, ten internal angles, and ten vertices. A decagon or decagon is a shape that may be found in geometry. Furthermore, it has 10 horns and 10 horns. A 12-sided polygon is called a dodecagon. A regular polygon known as a regular dodecagon specifically has sides that are of the same length and angles that are uniformly spaced around a circle.

the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 ,

'a = side length of the decagon

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Answer:

75a%

or

3/4a

or

0.75a

Step-by-step explanation:

I answer for what I understand, a number a is reduced by 50% and the result increased by 50%

a - 50% = 50% or 1/2 or 0.5

    2. increase

50 + 50% = 75% or 3/4 or 0.75

Answer: ~ 7.72 square miles

Step-by-step explanation:

One square kilometer is equal to around 0.386 miles.

To get to 20 square kilometers, multiply 0.386 times 20.

hope this helps

MM

The length of segment YS within the square QRST is equal to 6.

Squares are quadrilaterals with four sides of equal length and two diagonals of equal length, in that order, diagonals QS and RT are the diagonals of square QRST. Besides, we have the following information:

VY = 13, RV = 19

The length of segment YS can be found by means of the following formula:

RV = VY + YS

YS = RV - VY

YS = 19 - 13

YS = 6

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The area of the polygon is 6x√3 / 3 units².

The polygon above is a triangle. The polygon has three sides. Therefore, the area of the polygon can be calculated as follows:

area of the polygon = 1 / 2 pa

where

Therefore, the perimeter of the polygon is the sum of the whole sides. The sides of the polygon is the same. Hence, the perimeter is 3x.

where

area of the polygon = 1 / 2 × 3x × 4√3 / 3

Hence,

area of the polygon =  3 / 2 x × 4√3 / 3

area of the polygon = 6x√3 / 3 units²

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The next number in this sequence is 63, which is the result of multiplying the previous number (39) by 2 and then adding 6.

The number of containers needed is given as follows:

3 containers.

The number of containers needed is obtained applying the proportions in the context of this problem.

She has 2 cups, hence the number of fluid ounces that she has is given as follows:

16 fluid ounces.

Each container holds a total of 6 fluid ounces, hence the number of containers needed is given as follows:

16/6 = 3 containers.

(rounding up).

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Part A:

Look at photo

Part B:

After 5 minutes, the altitude of the airplane is 20,500 feet. This means that the airplane has been descending for 5 minutes and has lost an altitude of 10,250 feet.

After 30 minutes, the altitude of the airplane is -29,250 feet. This means that the airplane has been descending for 30 minutes and has lost an altitude of 60,000 feet. The negative value of the altitude indicates that the airplane has landed or is close to landing.

At both 5 minutes and 30 minutes, the airplane is descending. The rate of descent is constant, as represented by the slope of the equation, and is equal to -1025 feet per minute. At 5 minutes, the airplane is still at a high altitude, while at 30 minutes the airplane has landed or is close to landing, as indicated by the negative value of the altitude.

Answer:

Step-by-step explanation:

Part A:

x  |  y  |  Equation

0  | 30,750 | y = -1025*0 + 30,750

5  | 27,250 | y = -1025*5 + 30,750

8  | 23,750 | y = -1025*8 + 30,750

10 | 20,250 | y = -1025*10 + 30,750

30 | -20,250 | y = -1025*30 + 30,750

Part B:

After 5 minutes, the altitude is 27,250 feet. This means that the airplane has been descending steadily for 5 minutes and is now at a lower altitude than when it started.

After 30 minutes, the altitude is -20,250 feet. This means that the airplane has been descending steadily for 30 minutes and is now much lower than when it started. The airplane is close to the ground and about to land.

Answer:

Step-by-step explanation:

(-4 - 8)/(5 + 1)= -12/6 = -2

Option C

The product of a, b, and c would be, 9/8

What is Expression?

An expression, often known as a mathematical expression, is a finite combination of symbols that is well-formed according to context-dependent principles.

First, let's simplify the expression:

              [tex]\frac{6 x^y^{-1} }{\sqrt[{4} ]{(16x^5y^2)}}\\\\\ = \frac{(6x^2y^{-1} )}{4x^{\frac{5}{4} } y^{\frac{1}{2} } } \\\\[/tex]

We can simplify further by dividing both the numerator and denominator by x²:

                       [tex]\frac{6x^{2} y^{-1} }{4x^{\frac{5}{4} } y^{\frac{1}{2} }} \\\\= \frac{6y^{-1} }{4x\frac{3}{4} y^{\frac{1}{2} } } \\\\= \frac{\frac{6}{4} *x^{2} y^{-1} }{x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\=\frac{3}{2x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\[/tex]

So, a = 3, b = -3/4, and c = -1/2.

The product of a, b, and c is 3 * -3/4 * -1/2 = 9/8.

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(c) range, (d) variance, (e) standard deviation and (f) interquartile range measure variability.

Range, The range is the difference between the largest and smallest values in a dataset, indicating how spread out the data are.

Variance, The variance measures how far a set of numbers is spread out from their average. It provides a measure of how much the individual data points deviate from the mean.

Standard deviation, The standard deviation is the square root of the variance and is also a measure of how much the individual data points deviate from the mean. It is a widely used measure of variability, particularly in statistical analysis.

Interquartile range, The interquartile range (IQR) is the difference between the third and first quartiles of a dataset. It gives an idea of the spread of the middle 50% of the data and can help identify outliers.

The mean and median are measures of central tendency and do not directly measure variability.

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Step-by-step explanation:

[tex] \frac{ \tan( \alpha ) }{1 + \sec( \alpha ) } = - \cot( \alpha ) + \csc( \alpha ) [/tex]

Multiply by 1-sec(a)

[tex] \frac{ \tan( \alpha ) (1 - \sec( \alpha ) }{(1 + \sec( \alpha ) )(1 - \sec( \alpha ) )} [/tex]

[tex] \frac{ \tan( \alpha ) - \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]

[tex] \frac{ \tan( \alpha ) }{1 - \sec {}^{2} ( \\ \alpha ) } - \frac{ \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]

[tex] \frac{ \tan( \alpha ) }{ - \tan {}^{2} ( \alpha ) } + \frac{ \tan( \alpha ) \sec( \alpha ) }{ \tan {}^{2} ( \alpha ) } [/tex]

[tex] - \frac{1}{ \tan( \alpha ) } + \frac{ \sec( \alpha ) }{ \tan( \alpha ) } [/tex]

[tex] - \cot( \alpha ) + \frac{ \frac{1}{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } [/tex]

[tex] - \cot( \alpha ) + \frac{1}{ \sin( \alpha ) } [/tex]

[tex] - \cot( \alpha ) + \csc( \alpha ) [/tex]

The solution to the equation 16^{2x - 3} · 4^{-2x} = 4^2 include the following: C. x = 4.

In Mathematics, laws of indices can be defined as the standard principles or rules that are used for simplifying an equation or expression that involves powers (exponents) of the same base.

By rewriting the mathematical expression and applying the multiplication law of indices, we have the following:

16^{2x - 3} · 4^{-2x} = 4^2

4^2{2x - 3} · 4^{-2x} = 4^2

2{2x - 3} + {-2x} = 2

4x - 6 - 2x = 2

2x = 2 + 6

2x = 8

x = 8/2

x = 4.

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The  fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.

One inch is equivalent to 25.4 millimeters internationally.

Expressing this relationship as a formula is as follows.

1 inch = 25.4mm

This official, standardized measurement has been used in international records since 1959.

Both inches and millimeters are units of measurement. Inches belong to the British system of units, and millimeters belong to the metric system of units.

Inches are used in the United States, but it is often necessary to convert this unit of measurement to a metric unit of measurement, such as "millimeters." for scientific purposes. Conversely, there are 0.0393700787402 inches in millimeters. 

Thus , the  fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.

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The area of the larger hexagon in discuss as required in the task content is; Choice B; b. 18√3 square units.

It follows from the task content that the area of the larger hexagon be determined.

Recall from the concept of similar shapes; if the ratio of side lengths of two similar shapes is; k, therefore the ratio of their perimeters is k and the ratio of their areas is; k².

On this note, since the larger hexagon is √2 times the side length of the smaller hexagon;

It follows that the area of the lager hexagon is (√2)² times the area of the smaller one.

Therefore, Area of larger hexagon = √2² × 9√3

= 18 √3.

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The kite is flying approximately 76.118 feet high.

What is ratio ?

Ratio can be defined as the given value divided by the total value.

We can use trigonometry to solve this problem.

Let's call the height of the kite h. Then, we have a right triangle, with one angle equal to 80 degrees and the adjacent side equal to 77 feet. We can use the sine function to find the height of the kite:

sin(80) = h/77

So, h = 77 * sin(80).

Using a scientific calculator or a trigonometry table, we can find the value of sin(80) to be approximately 0.98

Therefore, the height of the kite is:

h = 77 * 0.98 = 76.11

Hence, The kite is flying approximately 76.118 feet high.

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One thing that was not an impact of the Crusades was B. End of the Roman Empire.

The Crusades were a series of religious wars fought between Christians and Muslims in the 11th, 12th, and 13th centuries. The main objective of the Crusades was to recapture the Holy Land, which was considered the birthplace of Christianity, from Muslim rule.

The Crusades had a significant impact on the medieval world, but the end of the Roman Empire was not one of them. The Roman Empire ended several centuries before the start of the Crusades in the 11th century.

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The amount of protein in Peanut butter is 209.5g.

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the amount of protein in  838g of peanut butter.

Contents of peanut butter: 35%

Carbohydrates - 25%

Protein - 40% Fat

Now 25% of protein in 838g.

25/100×838

0.25×838

209.5 g of protein in peanut butter

Hence, 209.5 g of protein in peanut butter

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The total amount of the single payment will be $6,924.95.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The rate of interest is given as,

r = 0.0775 / 2

r = 0.03875

The amount for 2 years is given as,

A = $1,300 × (1 + 0.03875)⁴

A = $1513.52

The amount for 5 years is given as,

A = $3,700 × (1 + 0.03875)¹⁰

A = $5,411.43

The total amount of repayment is given as,

Total amount = $1513.52 + $5411.43

Total amount = $6,924.95

The total amount of the single payment will be $6,924.95.

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The value of x to the nearest integer is $294.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for the present value of an increasing annuity to solve this problem:

PV = x/(i-g) × (1 - (1+g)/(1+ i)ⁿ)

where PV is the present value,

x is the first payment,

i is the effective annual interest rate,

g is the annual increase rate of the payments, and

n is the total number of payments.

Substituting the given values, we have:

7229.50 = x/(0.07-0.04) (1 - (1+0.04)/(1+0.07)²⁰)

Simplifying and solving for x, we get:

x = 7229.50×0.03 × (1 - 1/1.07^20) / (1.04 × (1 - 1/1.07²⁰))

x= $294

Therefore, the value of x to the nearest integer is $294.

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a. The possible range of values in this row is from 210 to 219, inclusive.

To see why, note that the stem value is 21, so each leaf represents a number that should be added to 21. The smallest possible value is when the leaf is 0, which gives 21 + 0 = 210. The largest possible value is when the leaf is 9, which gives 21 + 9 = 219.

b. There are 6 data values in this row.

c. The actual values in this row are 210, 211, 213, 215, 217, 219.

In statistics, a leaf is the last digit or digits of a data point in a stem-and-leaf plot. A stem-and-leaf plot is a graphical display of data that shows the distribution of values by separating each value into two parts: a stem, which consists of the leading digits of the value, and a leaf, which consists of the final digit or digits of the value. The stem values are listed in a vertical column, and the leaves are listed in a row next to the corresponding stem. This type of plot allows us to see the shape of the data and the distribution of values within it.

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The graph of the quadratic function y = x² - 5 is given by the image presented at the end of the answer.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function is given as follows:

y = x².

Which is concave up with vertex at the origin.

The translated function is given as follows:

y = x² - 5.

Meaning that the function was translated 5 units down, hence the vertex is at (0,-5) and the roots are plus/minus square root of 5.

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We can see here that simplifying, we have:

a. h²

b. h³

c. 1/(1 + h)

d. 3h

e. 3h/(64 + 4h)

f. h/(4h + 2h²)

Simplification is the process of reducing something to its most basic form or removing any unnecessary complexity.

In mathematics, simplification is often used to make equations or expressions easier to work with, solve, or understand. This can involve combining like terms, cancelling out common factors, or using rules of exponents and logarithms to simplify an expression.

We see here that the below gives us the workings:

a. (5 + h)³ - 125/ h = h³ +  5³ - 125/h = h²

b. [tex]\frac{(3 + h)^{4} - 81 }{h} =\frac{ 3^{4} + h^{4} - 81}{h} = \frac{ h^{4} + 81 - 81}{h} = h^{3}[/tex]

c. (1/1+h) - 1/h = 1/1+h - 1 ÷ h = 1/1+h

d. 3(1 + h)² -3/h = 3h² + 3 - 3/h = 3h²/h = 3h

e. [(3/4+h) - 3/4]/4 = (3/4+h - 3/4) ÷ 4 = 3h/64+4h

f. (-1 + 2 + h) + 1/2 ÷ h = h/4 + 2h × 1/h = h/4h + 2h²

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Answer:

Step-by-step explanation:

To find the number of solutions for a system of linear equations, we can use the method of substitution or elimination. Here, we'll use the method of substitution.

We'll start by solving for x in one of the equations and then substitute that expression into the other equation. If the resulting equation has a unique solution, then the system has a unique solution. If the resulting equation has no solution, then the system has no solution. If the resulting equation has infinitely many solutions, then the system has infinitely many solutions.

Let's start by solving the first equation for x:

y = -7/2 x + 11

To solve for x, we'll isolate x by subtracting 11 from both sides of the equation:

y - 11 = -7/2 x + 11 - 11

y - 11 = -7/2 x

Next, we'll multiply both sides of the equation by -2/7 to cancel out the fraction on the right side:

-2/7 (y - 11) = -2/7 (-7/2 x)

-2/7 y + 22/7 = 7/2 x

Now, we have an expression for x in terms of y. We can substitute this expression into the second equation:

7x + 2y = 20

7 (-2/7 y + 22/7) + 2y = 20

Substituting -2/7 y + 22/7 for x, we get:

7 (-2/7 y + 22/7) + 2y = 20

Expanding the left side of the equation, we get:

-2y + 22 + 2y = 20

0y = -2

Since 0y is never equal to -2, this equation has no solution.

Therefore, the system of equations has no solution, and there are no values of x and y that satisfy both equations simultaneously.

So, the system of equations y = -7/2 x + 11 and 7x + 2y = 20 has no solutions.

Answer: C) triangles ABC is not similar to  the triangle DEF because angles B and D re not congruent.

Step-by-step explanation:

...as it say...

7/12 can be written as a mixed number as follows:

7/12 = 7 ÷ 12/12 = 0 and 7/12.

So 7/12 can be expressed as "zero and seven twelfths" or simply "seven twelfths."