The norman h.s. math club has twice as many male members as female members twenty percent of the male members and 30 female members participated in a math contest. What fraction of those members participating in the math contest were female? express your answer as a common fraction

The list of equations is shown in the picture which equation has No Solution, One Solution, and Infinitely Many Solutions.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have given a linear equation in one variable.

\(\rm \dfrac{1}{2}y + 3.2y = 20\)

After solving:

y = 5.40   (one solution)

\(\rm \dfrac{15}{2}+ 2z -\dfrac{1}{4}=4z+\dfrac{29}{4} -2z\)

After solving:

\(\rm \dfrac{15}{2} -\dfrac{1}{4}=\dfrac{29}{4}\)

\(\rm \dfrac{29}{4}=\dfrac{29}{4}\) (Infinitely Many Solutions)

3z + 2.5 = 3.2 + 3z

2.5 = 3.2  (no solution)

Similarly, we can identify which equation has No Solution, One Solution, and Infinitely Many Solutions.

Thus, the list of equations is shown in the picture which equation has No Solution, One Solution, and Infinitely Many Solutions.

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What are functions ?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

What are asymptotes ?

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.

An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.

There are three types of asymptotes namely:

1) Vertical Asymptotes

2) Horizontal Asymptotes

3) Oblique Asymptotes

The point to note is that the distance between the curve and the asymptote tends to be zero as it moves to infinity or -infinity.

What are domain of a function ?

The domain of a function is the set of values that we are allowed to plug into our function.

This set is the x values in a function such as f(x).

What is range of a function ?

The range of a function is the set of values that the function assumes. This set is the values

that the function shoots out after we plug an x value in. They are the y values.

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Answer:

a. Possible outcomes for this chance experiment are:

(Here, D means a defective battery, and N means a nondefective battery.)

b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.

c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.

Answer:

3rd  option

Step-by-step explanation:

\(\frac{5}{7}\) y = 6

multiply both sides by \(\frac{7}{5}\) , the reciprocal of \(\frac{5}{7}\) )

\(\frac{7}{5}\) ( \(\frac{5}{7}\) y ) = \(\frac{7}{5}\) (6) , that is

y = \(\frac{42}{5}\)

Answer:

\(5^{15} * 5^{5}\)

= \(25^{20\\}\)

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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There are 20 possible routes that a man could take to go between cities and then take a different route back.

In mathematics, a permutation of a set is, broadly speaking, the rearranging of its elements if the set is already sorted, or the arrangement of its members into a sequence or linear order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context.

Let the number of roads between the cities A and B = 5.

The rules of permutation must be used in this situation.

A permutation is an arrangement of all or a portion of a collection of items that takes into account the arrangement's order.

The man uses five different routes to get from A to B because there are five different routes accessible.

He can get back by 4 (5 1) methods because he needs to take a different route.

Therefore, there are 20 possible routes that a man could take to go between cities and then take a different route back.

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The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30

Thus, for the given supplementary angles, the value of x is 30.

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**According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30 **

The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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Answer:

B. 0 is the correct answer.

Step-by-step explanation:

:)

To describe the center of the data, we can use either the mean or the median.

To describe the variation of the data, we can use either the range or the interquartile range (IQR).

Looking at the dot plot, it seems that the data is somewhat skewed to the right, with a few high-priced outliers. In this case, the median and the IQR may be more appropriate measures of the center and variation, respectively, as they are less sensitive to outliers.

To find the median and IQR:

Arrange the data in order from smallest to largest.

Find the median, which is the middle value. If there are an even number of values, take the average of the two middle values.

Find the first quartile, which is the median of the lower half of the data.

Find the third quartile, which is the median of the upper half of the data.

Calculate the IQR as the difference between the third quartile and the first quartile.

Here are the steps applied to the dot plot:

We can see that the smallest value is about 20 and the largest value is about 120, giving a range of 100 dollars.

The median is approximately 60 dollars, as it is the middle value between the 11th and 12th data points when the data is arranged in order.

The first quartile is approximately 40 dollars, as it isthe median of the lower half of the data points, which are found below the median.

The third quartile is approximately 80 dollars, as it is the median of the upper half of the data points, which are found above the median.

The IQR can be calculated as the difference between the third quartile and the first quartile, which is approximately 40 dollars.

Therefore, the most appropriate measures to describe the center and the variation for this data set are the median and the interquartile range (IQR), respectively. The median is approximately 60 dollars, and the IQR is approximately 40 dollars.

Answer: The description of that transformation is the triangle is rotated 90 degrees clockwise. Then, it's moved to the right TWICE. Finally, you go down 2 times.

Step-by-step explanation:

Hope this helps :)

triangle B is in dofferent orientation from triangle B so we know it was either mirrored or rotated. Triangle B isnt in the exact opposite orientation as A so we know it wasnt mirrored. So we now know that it was rotated and know we have to find the point of rotation. we can tell that the rotation was 270 degrees anti clockwise since it cant be clockwise because no points of rotation match. since we know triangle A was rotated 270 degrees anti clockwise to get triangle B we cant find the point of rotation by seeing which point works and if we test the points we will see that (0;-1) is the point of rotation. So triangle A was rotated 270 degrees anti clockwise on the point (0;-1) to make triangle B

The value of the z-test statistic = 1.16667

When told the question that a random number of samples is tested

z test statistic formula = x - x bar(x with bar above it) /Standard error

From the question

x = raw score = 46 pounds

x bar (x with bar above it)= sample mean = 45.5 pounds

Standard Error = σ/√n

Standard deviation = σ = 3

n = random number of samples = 49

z = 46 - 45.5/3/√49

z = 0.5/ 3/7

z =0.5/ 0.4285714286

z = 1.16667

Therefore, the value of the z-test statistic = 1.16667

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Answer:

Step-by-step explanation:

I'm assuming that the barrel is in the shape of a cylinder..

Givens

r = 7

pi = 3.14

V = 2041.11

Formula

V = pi * r^2 * h

h = V / (pi * r^2)

Solution

h = 2041.11/(3.14 * 7^2)

H = 2014.11 / 153.86

H = 13.09

Answer:

I believe the answer is 6+5x³ over 2x

Step-by-step explanation:

The amount of pounds that an 11-foot beam can support is 496.

Variation is a topic majorly in mathematics which expresses the relations between dependent and independent variables in form of equation. Some types of variation are: direct variation, inverse variation, constant variation etc.

In the given question, let the strength of a beam be represented by S and its length by l.

Thus;

S \(\alpha\) 1/ l^2

S = k/ l^2

where k is the constant of proportionality.

when l = 10 ft, S = 600 pounds, then;

600 = k/(10)^2

600 = k/100

k = 600*100

  = 60000

k = 60000

So that;

S = 60000/ l^2

Now, when l = 11 ft, then;

S = 60000/ 11^2

  = 60000/ 121

  = 495.88

S = 496 pounds

The amount of pounds that 11 ft beam can support is 496.

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The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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x=6

hopefully im not wrong^^

Answer:

Answer of this question is 10

Answer:

K = 3/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

k−9=5(k−3)

k+−9=(5)(k)+(5)(−3)(Distribute)

k+−9=5k+−15

k−9=5k−15

Step 2: Subtract 5k from both sides.

k−9−5k=5k−15−5k

−4k−9=−15

Step 3: Add 9 to both sides.

−4k−9+9=−15+9

−4k=−6

Step 4: Divide both sides by -4.

-4k/-4 = -6/-4

K = 3/2

Answer: It's 11.5

Explanation ( took so long)

\(C = \sqrt{a^{2} + b^{2} }\\14 = \sqrt{8^{2} + b^{2} }\\14 = \sqrt{64 + b^{2} }\\14^{2} = 64 + b^{2} \\196 = 64 + b^{2} \\64 +b^{2} = 196\\b^{2} = 196 - 64\\b^{2} =132\\b = \sqrt{132} \\b = 11.48\)

Answer:

26

Step-by-step explanation:

206÷ 8= 25.75 (remainder was 6)

that means 25 classes will be needed but since the are 6 students remaining 1 more class can be added makes 26 classes

Answer:

\(x\geq 2\)

Step-by-step explanation:

Write out the problem

\(\frac{x}{-5+6} \geq 2\)

Simplifiy -5 + 6 = 1

\(\frac{x}{1} \geq 2\)

Remember that any fraction with a denominator of 1 is equilvalent to the numerator, so

\(\frac{x}{1} =x\)

\(x\geq 2\)

Answer:

3)7/12

4)2*14/25

5)25

hope my effort will help you in some way

Answer:

Step-by-step explanation:

3)   \(1\frac{3}{4}\) ÷ 3 = \(\frac{7}{4}\) ÷ 3

                \(= \frac{7}{4} * \frac{1}{3}\\\\= \frac{7*1}{4*3}\\\\= \frac{7}{12}\)

4) \(1\frac{3}{5}\) ÷ \(\frac{5}{8}\) = \(\frac{8}{5}\) ÷ \(\frac{5}{8}\)

             \(= \frac{8}{5} * \frac{8}{5}\\\\= \frac{64}{25}\\\\= 2\frac{14}{25}\)

5) 10 ÷ \(\frac{2}{5} = 10 * \frac{5}{2}\)

              = 5 * 5

              = 25

Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.

Minutes | Distance Traveled (in miles)

50 | 20

20 | f

40 | 60

100 | a

125 | 80

100 | 100

To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:

Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.

Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.

Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.

Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.

Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.

Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:

Slope = Distance Change / Time Change

= 20 miles / 25 minutes

= 0.8 miles per minute

So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

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