Solve the system by substitution

2x + 10y = -32

x = -9y

90 middle school students prefer the Sci-Fi television genre.

What is Ratio?

Ratio is a comparison of two or more quantities of the same kind, often expressed as a fraction. Ratios are used to describe how much of one thing there is in relation to another thing.

The total percentage of the circle graph is 100%, and since the Sci-Fi section is 20%, we know that 20% of the 450 middle school students prefer the Sci-Fi television genre.

To find the number of middle school students who prefer the Sci-Fi genre, we can set up a proportion:

20/100 = x/450

where x is the number of middle school students who prefer the Sci-Fi genre.

Simplifying the proportion, we get:

0.2 = x/450

Multiplying both sides by 450, we get:

x = 0.2 * 450

x = 90

Therefore, 90 middle school students prefer the Sci-Fi television genre.

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The fraction of the entire class paired for the game is: 24/31

From the task content:

Hence, it follows that;

By substitution;

Hence;

Hence, the fraction of the entire that was paired is; 12/31 + 12/31 = 24/31.

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The fraction of the entire class is paired for the game is mathematically given as

Y=24/31

Question Parameters:

In a 3rd grade PE class, 3/4 of all of the boys are paired to 4/5 of all of the girls for a game on the playground.

Generally the equation for the statement  is mathematically given as

3/4 boys=4/5girls

Therefore

b/g=16/15

Hemece

Total class

T=16x+15x=31x

Paired student

Y=3/4=(16x)+4/5(15x)

The fraction paired for the game is

Y=24/31

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1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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Answer:

Longer side = 145ft

Shorter side = 135ft

Step-by-step explanation:

Here we have a rectangle.

Let's define L as the longest side (the one that is perpendicular to the wall of the house) and S as the shorter side.

We know that the perimeter of a rectangle is:

P = 2*L + 2*S

So if we wanted to fence this rectangle, we would need fencing equal to the perimeter.

But in this case, one of the shorter sides does not need to be fenced, so we only need:

2*L + S of fencing.

And we know that we will use 425ft of fencing, then:

2*L + S = 425 ft

We also know that The length of the fence opposite the house is 10 ft less than  either of the other two sides, then:

S = L - 10ft

Then we have two equations:

2*L + S = 425 ft

S = L - 10ft

Here we can just replace the second equation into the first one to get:

2*L + (L - 10ft) = 425 ft

Now we can solve this for L

2*L + L - 10ft = 425ft

3*L = 425ft + 10ft

3*L = 435ft

L = 435ft/3 = 145ft

This means that the longer side is 145ft long.

And by the equation:

S = L - 10ft

S = 145ft - 10ft = 135ft

S = 135ft

We know that the shorter side is 135ft long.

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Step-by-step explanation:

step 1. x intercepts are where y = 0

step 2. y = 0 when factors are equal to zero

step 3. the x intercepts are 0, sqr(3), -sqrt(3), -1/5

step 4. answer: 4.

ANSWER= the remaining piece of rope is 48 feet 9 inch long.

Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

Answer:

10 dollars

Step-by-step explanation:

5 + 5

Answer:

The correct answer is :

1. Line PQ (One line PQ).

Step-by-step explanation:

The first step to solve this question is to draw the plane A with the points P and Q lying on it.

We know that given two different points there is only one line that contains this two different points.

Let's analyze each option.

''2. Lines PQ and QP''

This option is wrong because there aren't two different lines. In fact it is only one line that can be named line PQ or line QP.

''3. The 2 lines PQ and QP plus another line that does not lie in plane A.''

This option is assuming that exist three lines that contain P and Q. This option is also wrong.

''1. Line PQ''

This option is correct. It will be clarify with the drawing I will attach.

''We can't name them all!''

This option is assuming that exist infinite lines that contain P and Q. This option is wrong.

In the drawing I call the line that contains P and Q as line L.

Given that P and Q lie in plane A necessarily the line L must lie on the plane A.

Only one line contains points P and Q

The given parameters are:

There are at least two points in a line

This means that, a line can contain points P and Q, and any other points

Hence, only one line contains points P and Q

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To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Concept

We can find the degree of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the leading term because it is usually written first. The coefficient of the leading term is called the leading coefficient.

From the function

Therefore,

The leading coefficient = 4

The degree = 3

Next, the end behavior of the function

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. So, the sign of the leading coefficient is sufficient to predict the end behavior of the function.

Interpretations:

As x tends to positive infinity, f(x) tend to positive infinity

As x tends to negative infinity, f(x) tend to positive infinity

Answer:

b

Step-by-step explanation:

The row with the most sucktastic runtime is the one with\(2^n\), as it takes exponentially longer to run than the other runtimes.

No, we do not have any non-integer answers.

Second: 72

Minute: 1000

Hour: \(2^(17)\)

Day: \(2^25\)

Month: \(2^30\)

Year: \(2^35\)

Second: f(n) = 72 => n = 72

Minute: f(n) = 1000 => n = 1000

\(Hour: f(n) = 2^n = > n = 17Day: f(n) = 2^n = > n = 25 Month: f(n) = 2^n = > n = 30Year: f(n) = 2^n = > n = 35\)

Seconds: The runtime for an input of size n is 72 microseconds, so the largest input that can be calculated in a second is 72.

Minutes: The runtime for an input of size n is 1000 microseconds, so the largest input that can be calculated in a minute is 1000.

Hours: The runtime for an input of size n is\(2^n\) microseconds, so the largest input that can be calculated in an hour is \(2^17.\)

Days: The runtime for an input of size n is \(2^n\) microseconds, so the largest input that can be calculated in a day is \(2^25\)

Months: The runtime for an input of size n is \(2^n\) microseconds, so the largest input that can be calculated in a month is \(2^30.\)

Years: The runtime for an input of size n is \(2^n\) microseconds, so the largest input that can be calculated in a year is \(2^35.\)

The row with the most sucktastic runtime is the one with \(2^n\), as it takes exponentially longer to run than the other runtimes. Therefore, the longer the time period, the larger the input size that can be calculated. No, we do not have any non-integer answers as the runtimes of the inputs are in microseconds and the input size is given as an integer.

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The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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Answer:

The question doesn't make any sense

Step-by-step explanation:

Answer: It would be 9/5

Step-by-step explanation: Hope this helps ! This was a bit hard for me . Lol

Thus, the measure of the  angle TRS for the given arc on the circle is found as: ∠TRS = (2x - 80) in terms of x.

An angle is said to be inscribed if its vertex is on a circle and both of its sides are chords of that circle.

An inscribed angle will always be one-half the size of either the central angle or just the intercepted arc that shares the ends of the inscribed angle's sides, according to the Inscribed Angle Theorem.

From the Inscribed Angle Theorem

Inscribed Angle = 1/2 (Inscribed arc)

From the question:

∠TRS = 1/2 (arc ST)

∠TRS = 1/2 *(4x-160)

∠TRS = 2x - 80

Thus, the measure of the  angle TRS for the given arc on the circle is found as: ∠TRS = (2x - 80) in terms of x.

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Complete question:

Chords RS and RT are drawn on a circle such that the measure of arc RS is (3x) the measure of arc ST is (4x-160) and the measure of arc TR is (x+120) as shown below what is the measure of angle TRS in terms of 'x'.

Answer:

10

Step-by-step explanation:

AB²=8²+6²

=64+36

=100

AB=10

Answer:

10 units

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

6² + 8² = c²

c = √100

10 units

Answer:

3^12

Step-by-step explanation:

(3^3/4(2) - 3/8) ^4/9

(3^6/8-3/8)^4/9

(3^3/8)^4/9

3^3/8(4/9)

3^27/72(32/72)

3^864/72

3^12

Sorry if it's hard to read...

Answer: 165 miles

Step-by-step explanation: In order to figure out the answer, you must do 55 x 3 because he drove for 3 hours at 55 mph so you could break it up and go 50 x 3 to equal 150 and 5 x 3 to equal 15 and add those to get 165.

Answer:

The answer is 165miles

Step-by-step explanation:

\(distance = speed \times time\)

d=55×3

d=165 miles

a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

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Answer: 20 sq. units .

Step-by-step explanation:

Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.

First we plot these points on coordinate plane, we get parallelogram ABCD.

By comparing the y-coordinate of B and C with A and D , we get

height = 2+2 = 4 units

Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units  

Area of parallelogram = Base x height

= 5 x 4 = 20 sq. units

Hence, the area of a parallelogram ABCD is 20 sq. units .

Answer:

7 schools have fewer than 50 classrooms.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

\(y=\frac{3}{4}x -0.25\)

Hope This Helps! :)

Answer:

eye eye eye eye eye eye eye eye eye eye eye

Answer:

each of four equal groups into which a population can be divided according to the distribution of values of a particular variable.

how many cookies? for 2 cups

Step-by-step explanation:

2