Find the x- and y-intercepts of the graph of 4x - 9y = 20. State each answer as an
integer or an improper fraction in simplest form.

Yes, the two quantities have a proportional relationship because the variables x and y all have the same constant of proportionality.

Mathematically, a proportional relationship can be represented or modeled with the following mathematical expression:

y = kx

Where:

In order for the two quantities to have a proportional relationship, the variables x and y must remain in a constant ratio.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 2/3

When x = 90 and y = 60, we have:

Constant of proportionality (k) = 60/90

Constant of proportionality (k) = 2/3

When x = 120 and y = 80, we have:

Constant of proportionality (k) = 80/120

Constant of proportionality (k) = 2/3

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Answer:

x<3

Step-by-step explanation:

4x<5+7

4x < 12

4/4 x < 12/4

x < 3

There is a 0.33 percent chance that a woman is the owner of each of the firms identified. Therefore, there is a 0.036 percent chance that women own ALL three of the called businesses.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The probability that each of the firms called is owned by a woman is 0.33. Therefore, the probability that ALL three of the firms called are owned by women is:

percentage=0.33*0.33*0.33

percentage=0.035937

=0.036

There is a 0.33 percent chance that each of the businesses is run by a woman. As a result, there is a 0.036 percent chance that women own ALL three of the businesses mentioned.

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Answer:

Step-by-step explanation:

interior angles of polygons:

180(n-2)

1. =180(11-2)

=180(9)

=1620

2. 180(17-2)

=180(15)

=2700

The time taken for Wilson to paint the bookcase is 50 minutes.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Wilson paints 40% of a bookcase in 20 minutes. It should be noted that 40% = 0.4

Therefore, the time taken to paint the whole bookcase will be:

= Number of minutes / Percentage painted

= 20 / 0.4

= 50

He'll use 50 minutes.

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The distance between the points (5, 7) and (8,-5) is √13.

The length of the path joining two points determines their distance from one another. It's crucial to know how to calculate the distance between two points when working with graphs. This makes it possible for a learner to estimate how long the line is, which is useful in a variety of circumstances. Using the distance formula is the most typical method of determining the distance.

Points (5, 7) and (8,-5)

Formula:

AB² = (x₂ - x₁)² + (y₂ + y₁)²

AB² = (8 - 5)² + (-5+7)²

AB² = (3)² +(2)²

AB² = 9 + 4

AB² = 13

AB = √13

The distance between the points (5, 7) and (8,-5) is √13.

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Dennis spent 12 hours practicing.

1.5 hours = 90 mins
90 mins x 8
720 mins = 12 hours

81 of 270 pages in a book is a part of the situation.

A division is a process of splitting a specific amount into equal parts.

Given,

81 of 270 pages in a book.

Eighty one of two hundred seventy pages in a book.

In the given situation, A book has 270 pages in that we have taken 81 pages which are part of the book.

We have taken pat of the book,

In the given situation, book is whole and 81 is the part.

Hence  81 of 270 pages in a book is a part of the situation.

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The simplified form of the given inequality is w > -3.

What is inequality?

 When two values are compared, an inequality reveals whether one is bigger than, less than, or simply not equal to the other. The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to one another. The occurrence of an unfair distribution of opportunities and resources among individuals of a certain society is referred to as inequality. To different people and in various contexts, the term "inequality" may mean different things.

Here the given inequality is ,

=> -5w<15

=> -5 *w < 15

=> w>15/-5

=> w > -3.

Hence the correct simplified form of the inequality is w >-3.

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Answer:

[tex]y = |x - 3|+ 5[/tex]

y = |x| is the equation that forms the triangular shape. -3 and 5 reflect the shape to that position.

2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given that, Ariana purchased two drill set from a sale, each of them costs $25 less than its original price,

If f is the original price, then she must have purchased it at (f-25) and for two sets it's 2(f-25)

She paid $86 for her purchase, so,

2(f-25) =  $86

Hence, 2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.

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Dean halverson recently read that full-time college students study 20 hours each week. 0.000519 is the p -value.

Given :

Population mean, μ = 20

Sample mean, xbar = 22.4

Sample standard deviation, s = 3.7

Sample size, n = 31

The hypothesis :

H0 : μ = 20

H0 : μ > 20

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (22.4 - 20) ÷ (3.7/√(31))

T = 2.4*5.6 ÷ 3.7

Test statistic = 3.632

Using the Pvalue calculator :

df = n - 1 = 31 - 1 = 30

Pvalue(3.632, 30) = .000519.

The p-value is .000519.

The result is significant at p < .05

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The 99% confidence limit will be option B which is (45, 55)

90% confidence limits for the population mean are (46,54)

mean = 46+54 / 2 = 50.

the margin of error E = 54-46/2 = 4

For 90% Confidence Z- Critical value is = 1.645

But the margin of error

E = ZS/√n

4=(1.645)S/√n

S/√n = 4 / 1.645

= 2.4316

For 95% confidence Z-critical value is 1.96

A 95% confidence interval is = mean ± E

(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316

= 50+ 4.7660

= 45.2340, 54.7660

= (45, 55)

Hence the correct option is B which is (45, 55) as the 99% confidence limit.

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Answer:f(10) or the power generated by the wind turbine at the wind speed of 10 m/s is 190.26 kW

Answer:

Step-by-step explanation:

18x+15. Step-by-step explanation: 5(4x+3)-2x. Distribute the 5. 20x +15 - 2x. Combine like terms. 20x-2x +15.

The solution of x when solving x/2 + 1 = √3 is :

x is 2√3 - 2 .

Here in the question given equation ,

x/2 + 1 = √3

To find solution,

we have to subtract 1 from LHS and RHS of equation,

⇒ x/2 + 1 - 1 = √3 - 1

⇒ x/2 = √3 - 1

Next multiply both sides  by 2

2( x/2) = 2(√3 -1)

By simplifying both sides we get,

x = 2√3 - 2

So the value of x = 2√3 -2.

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Answer:

1/23

Step-by-step explanation:

Answer:

Step-by-step explanation:

The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!

0.1717 is Probability that none has ever been married from selected 5 young women in age category at random.

In the question we have,

the number of females age 20 to 24 has never been married = 70.3%

the number of young women in this age category (20 to 24) at random = 5

We shall find out the probability that none has been maaried from selected group of 5 females.

Probability of female age 20 to 24 has never been married = 0.703

So, the probability that none has been married from selected group of 5 females ( p)= 0.703×0.703×0.703×0.73×0.73

= 0.1717

Therefore, The probability that none has ever been married is 0.1717.

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The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1

Arithmetic sequence can be represented with the formula as follows:

aₙ = a + (n - 1)d

where

Therefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..

a = 4

d = 7 - 4 = 3

Therefore,

aₙ = 4 + (n - 1)3

aₙ = 4 + 3n - 3

aₙ = 3n + 4 - 3

aₙ = 3n + 1

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Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.

In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the   system of experimentation.

Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.

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The number written on the board is 2 2/5

A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0. where, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. where, x and y are variables, A and B are coefficients and C is a constant.

represent the number on the board by x, the result of the second student by y , therefore the result of the first student is 2y

solving for the first student, 12+x= 2y

for the second student , 3x= y

substituting 3x for y in first equation

12+ x= 2(3x)

12+x= 6x

collecting like terms

5x= 12

divide both side by5

x= 12/5= 2 2/5.

Therefore the number on the board is 2 2/5

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Answer:

[tex]y_{min}=-17[/tex]

[tex]y_{max}=15[/tex]

Step-by-step explanation:

Given function:

[tex]y=2x^2-12x+1[/tex]

The critical points are those values of x which make the derivative of the function zero.  

Differentiate the function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2 \cdot 2x^{2-1}-12x^{1-0}+0[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=4x-12[/tex]

Set the derivative to zero and solve for x:

[tex]\implies 4x-12=0[/tex]

[tex]\implies 4x=12[/tex]

[tex]\implies x=3[/tex]

To find the y-value of the critical point, substitute the found value of x into the function:

[tex]\implies 2(3)^2-12(3)+1[/tex]

[tex]\implies 2(9)-12(3)+1[/tex]

[tex]\implies 18-36+1[/tex]

[tex]\implies -18+1[/tex]

[tex]\implies -17[/tex]

Therefore, the critical point is (3, -17).

To find the endpoints of the function in the interval [0, 7], substitute x = 0 and x = 7 into the function:

[tex]\begin{aligned} x=0 \implies 2(0)^2-12(0)+1&=0-0+1\\&=1\end{aligned}[/tex]

[tex]\begin{aligned} x=7 \implies 2(7)^2-12(7)+1&=2(49)-12(7)+1\\&=98-84+1\\&=14+1\\&=15\end{aligned}[/tex]

Therefore:

Therefore the minimum y-value is -17 and the maximum y-value is 15 in the given interval [0, 7]

The minimum and maximum y value of the function is -17 and 15 respectively.

This is a basic problem in calculus.

Given function: [tex]y=2x^{2} -12x+1[/tex]

Step 1: First, let's find the derivative of the function

[tex]\frac{dy}{dx} = 2.2x^{2-1} -12x^{1-0} +0\\\frac{dy}{dx} = 4x-12[/tex]

Step 2: Equate the derivative with zero

4x-12=0

x=3

Therefore, x=3 is the critical value for x

Step 3: Find the critical value for y

[tex]y=2x^{2} -12x+1[/tex]

[tex]y=2\times3^{2} -12\times3+1\\y=-17[/tex]

Thus, the critical points for the function [tex]y=2x^{2} -12x+1[/tex] are (3,-17)

Step 4: Find endpoints using the given interval [0,7]

This can be done by substituting x1=0 and x2=7 simultaneously in the given function and finding y1 and y2.

For x1=0,

[tex]y1=2\times0^{2} -12\times0+1\\y1=0+0+1\\y1=1[/tex]

For x2=7,

[tex]y2=2\times7^{2} -12\times7+1\\y2=98-84+1\\y2=15[/tex]

Now, we have both critical points and endpoints.

Therefore, The minimum and maximum y value of the function is -17 and 15 respectively.

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The slope of the linear equation is 0, and the solution of the second equation is x = 10.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

So if the line passes through (-12, 6) and (4, 6), the slope is:

slope = (6 - 6)/(4 + 12) = 0

The slope is 0.

2) How to solve the equation for x?

Here we have the equation:

2/8 = 3/(x + 2)

If we move the denominators we get:

2*(x + 2) = 3*8

2x + 4 = 24

2x = 24 - 4

2x = 20

x = 20/2 = 10

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The other leg has its length to be 11.49 units

To calculate the length of the other leg distance, we make use of the Pythagoras theorem

Mathematically, this theorem is represented by:

w² = y² + z²

Such that x = hypotenuse, y = leg and  z = other leg

From the question, we have the following parameters

w = 14, y = 8 and z = the other leg

Substituting these values in w² = y² + z²

14² = 8² + y²

Evaluate the exponents

196 = 64 + y²

Evaluate the like terms

y² = 132

Take the square roots of both sides

y = 11.49

Hence, the length of the other leg is 11.49 units

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Answer: 11 units

Step-by-step explanation: i took the test and got it right

Answer:

A

Step-by-step explanation:

∠ A = ∠ P

∠ C = ∠ R

AC = PR

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

The included side is the side between the vertices of the 2 angles.

Then the triangles are congruent by the ASA postulate