As a town gets smaller the population of its high school decreases by 4% each year the senior class has 160 students now. In how many years will it have about 100 students? write an equation. then solve the equation without graphing.

d = 4

b = -3. c = 1

a = 3 and d = 1

What are three polynomials factorized below?

To get the missing values in the table, we will factorize the given expression and compare the factored expression with the expression containing the missing constants.

1) For the expression x²+2x-8, on factorizing we have;

x²+2x-8

= (x²+4x)-(2x-8)

Factoring out the common terms from both parenthesis;

= x(x+4)-2(x+4)

= (1x+4)(1x-2)

=  (1x-2)(1x+4)

Comparing the resulting expression with (ax+b)(cx+d)

a = 1, b = -2, c = 1 and d = 4

2) For the expression 2x³+2x²-24x

Factoring out the common term we will have;

= 2x(x²+x-12)

= 2x(x²-3x+4x-12)

= 2x{x(x-3)+4(x-3)}

= 2x{(x+4)(x-3)}

=  2x(1x-3)(1x+4)

Comparing the resulting expression with 2x(ax+b)(cx+d)

a = 1, b = -3. c = 1 and d = 4

3) For the expression 6x²-15x-9 we will have;

On simplifying,

= 6x²+3x-18x-9

= 3x(2x+1)-9(2x+1)

= (3x-9)(2x+1)

Comparing the resulting expression with (ax+b)(cx+d)

a = 3, b = -9, c = 2 and d = 1

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According to the information, the coach will buy 9 ice cream sandwches and 6 frozen juice pops.

To calculate how many sandwiches and frozen juices the coach bought we have to perform the following mathematical operation:

First we have to built a equation incluiding all the values of the problem.

Now, we have to include the price of each product

$2 * I + 2.50 * J = 33.00

Then we have to solve the equation.

According to the above the number of sanwiches is 9, and the number of juices is 6.

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There are 16128 ways to form the committee when 2 of the men refuse to serve together, 23040 ways to form the committee when 2 of the women refuse to serve together, and 5040 ways to form the committee when 1 man and 1 woman refuse to serve together.

(a) When two of the men refuse to serve together, there are 6 men to choose from for the first 3 positions, 4 for the next, and 2 for the last. So there are 6 × 4 × 2 = 48 ways to choose the 3 men.

There are 8 women to choose from for the first 3 positions, so there are 8 × 7 × 6 = 336 ways to choose the 3 women. Thus there are 48 × 336 = 16128 ways to form the committee when 2 of the men refuse to serve together.

(b) When two of the women refuse to serve together, there are 8 women to choose from for the first position, 6 for the next, and 4 for the last. So there are 8 × 6 × 4 = 192 ways to choose the 3 women.

There are 6 men to choose from for the first 3 positions, so there are 6 × 5 × 4 = 120 ways to choose the 3 men. Thus there are 192 × 120 = 23040 ways to form the committee when 2 of the women refuse to serve together.

(c) When 1 man and 1 woman refuse to serve together, there are 7 women to choose from for the first 3 positions and 6 men to choose from for the last 3 positions.

So there are 7 × 6 × 5 × 4 × 3 = 5040 ways to form the committee when 1 man and 1 woman refuse to serve together.

The answer to each of the questions is the number of different committees that can be formed under the given conditions.

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--The given question is incomplete; the complete question is

"From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together? (b) 2 of the women refuse to serve together? (c) 1 man and 1 woman refuse to serve together?"--

The answers for the given units are 1 g = 0.001 kg; 1 m = 1000 mm; 1 cm = 10 mm; 1 dL = 100 mL; 1 kg = 1000 g; 1 pg = 1 × 10⁻¹² g; 1 g = 1 × 10¹² pg; and 1 mL = 1 cc.

A unit is a name given to a known quantity that is used to measure something. A gram is one-thousandth of a kilogram used to measure weight. This is written as 1 g = 0.001 kg or 10⁻³ kg and kg to g is written as 1 kg = 1000 g. In terms of their relationship, 1 m and 0.001 mm are equivalent. This is written as 1 m = 1000 mm or 10³ mm. The relationship between millimeters and centimeters is written as 1 cm = 10 mm.

Over a milliliter, a deciliter is greater. This is written as 1 dL = 100 mL. The relationship between picogram and gram is written as 1 pg = 1 × 10⁻¹² g

and 1 g = 1 × 10¹² pg. The relationship between a milliliter and a cubic centimeter is written as 1 mL = 1 cc.

The required answers are

1 g = 0.001 kg

1 m = 1000 mm

1 cm = 10 mm

1 dL = 100 mL

1 kg = 1000 g

1 pg = 1 × 10⁻¹² g

1 g = 1 × 10¹² pg

1 mL = 1 cc

The complete question is -

Select the correct prefix to complete the equality. Drag the appropriate labels to their respective targets. Note: not all labels will be used.

1 g = -----kg

1 m = -----mm

1 cm = ----- mm

1 dL = ----- mL

1 kg = ----- g

1 pg = ----- g

1 g = ----- pg

1 mL = ----- cc

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The symbol for sample deviation or standard deviation is "σ"(sigma).

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. The standard deviation shows a "typical" variation from the mean. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Because it is the square root of the means of the squared deviations from the arithmetic mean, the standard deviation is often referred to as root-mean-square deviation or sample deviation, sample standard deviation.

the standard deviation of sample deviation is denoted by σ(sigma).

Hence the symbol is "σ"(sigma).

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The interpretation of the confidence interval is that "we can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214".

Given :

A random sample of 1,175 people in a certain country was asked whether they thought climate change was a problem.

The sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as (0.146, 0.214).

95% confidence interval means a person is 95% confident that true population lies in it.

95% confidence interval is given by (0.146,0.214).

So, the interpretation of the confidence interval is that "we can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214".

Therefore, the correct option is C) We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.

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Each one of the given ratios should be expressed in its simplest form as follows:

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this exercise, you are required to express each of the given ratios in its simplest form. Therefore, we would divide both sides of the ratio by highest common factor (HCF) as follows;

50:150 = 50/150 = 1/5 = 1:5. (divide both sides by 50).

25:40 = 25/40 = 5:8. (divide both sides by 5).

33:99 = 1:3. (divide both sides by 33).

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Complete Question:

Express each one of the following ratios in its simplest form.

(i) 50: 150

(ii) 25:40

(iii) 33 : 99​

The exact value of cot A is .20/21

The denominator means moving the radical term square root or cube root to the numerator such that a denominator is a whole number.

We have been given that sin( A ) = 21/29 and angle A is in quadrant 1. We are asked to find the exact value of  cot (A) in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

Since = opposite

            hypotenuse

This means that opposite side is 21 units and hypotenuse is 29 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

Cot = Adjacent

         opposite

Now we will find adjacent side using Pythagoras theorem as:

Adjacet² = hypotenuse² - opposite²

Adjacent² = 29² - 21²

Adjacent² = 841 - 441

Adjacent² =400

Let us take positive square root on both sides:

√Adjacent² = √400

 Adjacent = 20

Therefore, adjacent side of angle A is 20 units.

Cot (A) = 20/21

The exact value of cot A is .20/21

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A function that represents the amount of air that is f(r)=4/3π[3r²+3r+1]

Since a function is a rule that applies a specific output to a specific input, we can define a function in a variety of ways. This could involve a change in variables, for example, or defining a function that represents a rate of change.

The amount or volume of air required to inflate the spherical balloon from a radius of r inches to a radius of r+1 inches.

The formula for the volume of a sphere is V = 4/3 πr³

where V = volume and r = radius.

V= 4/3π[(r+1)³−r³]

V=4/3π[r³+3r²+3r+1−r³]

V =4/3π[3r²+3r+1]

 For r in inches and V(r) in inches cubed,

 f(r)=4/3π[3r²+3r+1].

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The area of the major sector in the given diagram is 115.5 sq.unit.

The region having a greater area is known as Major Sector while the one which has a smaller area is the minor sector.

A sector with a central angle greater than 180° is called a major sector and the formula is given below:

/360° ₓ r²

The radius is 7m and is 270°

Therefore 270/360 × 3.142 × 7² =  115.5sq.unit.

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Answer:I think it is 6

Step-by-step explanation:

Answer:

h(2) = 6

Step-by-step explanation:

This function is called h.

In function notation, it is h(x).

h(2) means the value of the y-coordinate of the point whose x-coordinate is 2.

Look up 2 on the y axis.

Now go up until you get to the blue line of the function.

What y value does that correspond to? Go left horizontally until you get to the y-axis. You intersect the y-axis at 6. That means that

h(2) = 6

The word problem "8 times the sum of 2 and a number" is equal to 8(2 + n).

In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

Assuming the variable n represents the unknown numerical value (number), we would translate the word problem into an algebraic expression as follows;

Algebraic expression = 8 × (2 + n)

Algebraic expression = 8(2 + n).

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+4.533 is the percent error for the company's estimate

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Bay City Balloons studied the demand in Bay City before opening a hot air balloon company. The owners expected to book 375 hot air balloon rides in their first ninety days of business. Instead, they booked 392 rides in that period.

Since percentage error:

Percent error is the difference between the estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

Thus in our case

Percentage error = ((392 - 375)/ 375) * 100

Percentage error = 4.533

therefore, the percent error for the company's estimate is +4.533.

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we conduct a one-sided test on the statistic one tail of a critical area of distribution.

The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.

What is a critical value?

A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.

Test of significance of linear regression between x and y.

Null hypothesis: There is no significant linear relationship between x and y.

Alternative hypothesis: There is a significant linear relationship between x and y.

Test statistic:

F0 = Mean square due to regression/  mean squared error ~ F(1, n-2)

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If f(-8) = 1, then the point (-8, 1) is on the graph of f.

The numeric value of the function at x = -8 is given as follows:

f(-8) = 1.

The format of each point on the coordinate plane is given as follows:

(x,y).

In which y is the numeric value of the function at x, meaning that the point can also be written as follows:

(x, f(x)).

Considering that when x = -8, f(x) = 1, the point is given as follows:

(-8,1).

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Using the arithmetic operation of multiplication, two cities having a distance of 2.5 inches on map have an actual distance of 50 miles.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The value of 1 inch on scale = 20 miles.

The distance between two cities on map = 2.5 inches

To find the distance between two cities in actual use the arithmetic operation of multiplication.

Let the original distance value in miles be x.

The equation for distance will be -

x = 2.5 × 20

Solve the equation -

x = 2.5 × 20

x = 50

Therefore, the actual distance in miles is 50 miles.

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The distance of the line segment joining the two points is [tex]2\sqrt{2}[/tex].

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

Given;

The two points;

(2,0) (0,-2)

Now,

D=[tex]\sqrt{(0-2)^2+(-2-0)^2}[/tex]

=2[tex]\sqrt{2}[/tex]

Therefore, the distance between two points will be 2[tex]\sqrt{2}[/tex]

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The number of weeks, it will take before it is up to 45 minutes of walking per day is, 9 weeks.

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

Given that,

The therapist suggests walking for 5 minutes each day for the first week

Increasing that time by 5 minutes per day each week

Number of weeks will it be before you are up to 45 minutes of walking per day = ?

At the end of first week, he will walk for 5 minute

in the beginning of second he started increasing time 5 minutes per day

So, before he reach up to 45 minutes weeks passed,

Before up to 45 minutes,

number of weeks =   ?

45 =  5 + 5n

n  =  8

Total number of weeks of walking = 1 + 8

                                                         =  9

Hence, the number of weeks is 9

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Answer:

Step-by-step explanation:

Answer:

24 workers

Step-by-step explanation:

solution

A wall can be built in 48 hrs by = 15 workers

A wall can be built in 1 hr by = 15× 48 workers

A wall can be built in 30 hrs by= 15 × 48/ 30 workers

= 24 workers

The solution to the equation is x = 7.

What is the linear equation in one variable?

A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.

The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.

Hence, the solution to the equation is x = 7.

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Answer:

9 234

Step-by-step explanation:

base area multiplied by height is volume

Exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.

Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty.

Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that exactly two of the students are guilty.

Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty. Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that only one of the three is not guilty and it is not A or B. Therefore, exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.

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Answer:

see below

Step-by-step explanation:

S+L = 22

L=2+3S

so S+2+3S =22

4S=22-2 = 20

S =5

L =17

Answer:

Step-by-step explanation:

Option (d) is the correct answer i.e. that hyperbola has both vertices in the same quadrant.

A hyperbola is a conic section in analytical geometry that is formed when a plane intersects a double right circular cone at an angle that spans both cone halves.

Let's see each option one by one:

(a) We've a = 11 and b = 10

   This hyperbola is centered at (-10,3) and has vertices as (1,3) and (-21,3).

So, both vertices are not in the same quadrant.

(b) We've a = 9 and b = 12

   This hyperbola is centered at (-6,8) and has vertices as (-6,17) and (-6,-1).

So, both vertices are not in the same quadrant.

(c) We've a = 12 and b = 8

   This hyperbola is centered at (1,11) and has vertices as (13,11) and (-11,11).

So, both vertices are not in the same quadrant.

(d) We've a = 9 and b = 11

   This hyperbola is centered at (-1,10) and has vertices as (-1,19) and (-1,1).

So, both vertices in the same quadrant.

Hence, option (d) is the correct answer.

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a. The frequency which she hears is 440Hz.

b. The person in the car would hear a frequency of 391.98 Hz when the ferry leaves the dock and heads directly away from the driver.

(a) The frequency that the person in the car hears is affected by the motion of the car and the sound source (the ferry). The effect is called the Doppler effect, which causes the perceived frequency of sound to change depending on the observer and the relative motion of the source.

If the car is moving toward the ferry, the frequency will be higher than the actual frequency of the sound. The perceived frequency is given by the formula:

f' = f (v + v_s) / (v + v_s)

where

f = the actual frequency of the sound (400 Hz)

v = the velocity of sound (approximately 340 m/s)

[tex]v_s[/tex] = the velocity of the car (60 km/h = 16.67 m/s)

So,

f' = 400(340 + 16.67) / (340 - 16.67) = 400(356.67) / 323.33 = 440 Hz

Hence, the frequency which she hears is 440Hz.

(b) The perceived frequency when the ferry leaves the dock and heads directly away from the driver is also affected by the Doppler effect.

f' = f (v - v_s) / (v - v_s)

where

f = the actual frequency of the sound (400 Hz)

v = the velocity of sound (approximately 340 m/s)

v_s = the velocity of the ferry (15 km/h = 4.17 m/s)

So,

f' = 400(340 - 4.17) / (340 + 4.17) = 400(335.83) / 344.17 = 391.98 Hz

The person in the car would hear a frequency of 391.98 Hz when the ferry leaves the dock and heads directly away from the driver.

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Answer:

Step-by-step explanation:

B. $342.95 is your answer

The sequence of transformation which includes a reflection and a translation that maps triangle ΔABC to ΔA'B'C' are;

A reflection transformation is one in which the mirror image of the figure is produced, on the other side of a line known as the line of reflection.

The vertices of the triangle ΔABC are A(-1, 2), B(-2, 5), C(-5, 1), the vertices of triangle ΔA'B'C' are A'(3, -2), B'(4, -5), C'(7, -1)

A reflection of the triangle ΔABC across the y-axis, we get;

A''(1, 2), B''(2, 5), C''(5, 1)

A reflection of the triangle ΔA'B'C', across the x-axis produces;

A'''(3, 2), B'''(4, 5), C'''(7, 1)

The rule that maps the coordinates of the vertices of ΔA''B''C'' to the coordinates of the vertices of ΔA'''B'''C''' is a translation of triangle 2 units to the right,

Therefore, the sequence of transformation that maps ΔABC to ΔA'B'C' are;

A reflection across the y-axis, followed by ⇒A translation of two units to the right, then ⇒ A reflection across the x-axis.

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Answer: Because instead it equals 0.005

Step-by-step explanation:

The reason 5/100 is not equal to 0.5 is that they are written in different forms.

5/100 is written in the form of a fraction, where the numerator (5) represents the number of parts out of a whole, and the denominator (100) represents the total number of parts in the whole. So, 5/100 represents 5 parts out of 100 parts, which is equal to 0.05.

On the other hand, 0.5 is written in decimal form. It represents the number of parts out of 1, where the digits to the right of the decimal point represent the number of tenths, hundredths, thousandths and so on. So, 0.5 represents 5 tenths, or 5 parts out of 10 parts.

In conclusion, while they represent the same value, they are written in different forms and it's important to know how to read and convert them correctly.