Write the equation of the line in fully simplified slope-intercept form.

We need to find the function in slope-intercept form. We thus need the y-intercept and slope. We know there are 38000 gallons in the pool already, so the y-intercept is 38000. The pool drains 12 per minute, so the slope is -12.

y = mx + b
y = -12x + 38000

To find the time it takes to drain the pool, we need to find x where y = 0, so we set the equation to 0 and solve for x.

0 = -12x + 38000
-38000 = -12x
-38000/-12 = -12x/-12
3167 = x

Now, to fill it back up, the y-intercept is 0. We know the slope is 16, so the equation is:

y = 16x

Finally, we need to find 16x = 38000. This is simple enough.

y = 16x
38000 = 16x
38000/16 = 16x/16
2375 = x

The 96th term of the arithmetic sequence (1, -12, -25,.......) is 1234.

We are provided with the arithmetic sequence mentioned below;

1, -12, -25,...........

We know that, the rule to calculate the nth term in an arithmetic sequence is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + ( n - 1 ) d                             equation 1

Here, d is the difference between two consecutive terms in the arithmetic sequence , [tex]a_{1}[/tex] is the first term, n is the number of terms and [tex]a_{n}[/tex] is the nth term.

We have,

n = 96

[tex]a_{1}[/tex] = 1

d = -12 -1 = -13

Now, substitute these values in equation 1 i.e, formula of arithmetic sequence and on substituting we will get

[tex]a_{96}[/tex] = 1 + ( 96 - 1 ) ( -13 )

[tex]a_{96}[/tex] = 1 - (95) (13)

[tex]a_{96}[/tex] = 1 - 1235

[tex]a_{96}[/tex] = 1234

So, we can conclude that the 96th term of the arithmetic sequence  is 1234.

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Answer:

y = 2x+4

Step-by-step explanation:

2x - y = -4

We add y on both sides:

2x - y + y = -4 + y

so 2x = -4 + y

We now add 4 on both sides:

2x + 4 = -4 + 4 + y,

so 2x+4 = y,

so y = 2x+4

So intercept for y = 2x+4

Answer:

r=1

Step-by-step explanation:

1=2r-1

Add 1 on both sides

2=2r

Divide 2 on both sides

r=1

Answer:

probability is 1.

Step-by-step explanation:

In a lot of probability problems when asking for “at least two” is usually easier to see the opposite case, that is, the “none of them” case…

P(“at least one … X”) = 1 - P(“none of them … X”)

I will we exclude 29th of February, that is, considering none of the people was born on the leap day of a leap year.

First, let’s see what happens for 2 people. We can name one of those 2 people as “first” and the other as “second”. Whatever the birthday of the “first” one is, the other has 364 out of 365 days in the year to have a different birthday.

p(2) = 1–364/365 = 1/365

For 3 people, the “first” has a birthday, the “second” has a probability of 364/365 to have a different birthday and the third has a probability of 363/365.

p(3) = 1 - 364/365 * 363/365= (365^2 - 364*363)/365^2

For 4 people:

p(4) = 1 - 364/365 * 363/365 * 362/365

…

For n people, if n is less than 366:

p(n) = 1 - (364! / [365 - n]! )/365^(n-1)

p(n)=1−364!(365−n)!⋅365n−1

Obviously, if n is 366 or more, since we excluded the leap day there must be always 2 people with the same birthday (pigeonhole principle), and then in this cases the probability is 1.

No, Diego's estimation is not good because he overestimated the original value to nearly double the amount.

Overestimation is when we fix a value that is greater than the original value and underestimation when we fix a value that is less than the original value.

Given, Diego and his mom have been saving recycling items for months and today they traded them in they made 42 dollars on cans, 19 dollars on glass bottles, and 32 dollars on plastic bottles which are 83 dollars.

Diego estimates it to be 140 dollars which is nearly double the original amount and not a good estimate.

A good acceptable estimate can be of more or less than 5% of the original value.

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The measure of the angles 2 and 3 are 70°

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles also were generated when plane cross. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.

Given, angle 1 = 40°

and, angle 2 = angle 3 = x

In a triangle, sum of angles = 180°

or, m∠1 + m∠2 + m∠3 = 180°

or, 2x = 180-40

or, 2x = 140

or, x = 140/2 = 70°

Hence, the measure of the angles 2 and 3 are 70°

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1080 inches²  are the dimensions of the box with maximum volume .

What is rectangle?

rectangular box length = 24 inches

                       width = 45 inches

maximum volume = 24 * 45

                              = 1080 inches²

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The hypotenuse of the given right angle triangle is: 50 cm

What is hypotenuse?

In mathematics, the hypotenuse is the longest side of a right angle triangle. It is defined as the standard formula, which states that the square of the hypotenuse is equal to the square of their adjacent sides.

According to the question, to calculate the hypotenuse with the given parameters. First name all the three vertices.

AB = 30 cm; BC = 40 cm; AC = ?

Using standard hypotenuse formula, which states:

AB² + BC² = AC²

⇒ 30² + 40² = AC²

⇒ AC² = 900 + 1600 = 2500

⇒ AC = 50 cm

Hence, the hypotenuse of the given right angle triangle is: 50 cm

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The probability that the nurse will find the two patients is P =  0.49.

We know that the probability that the nurse finds the client on a particular day is 0.7

So, each time that the nurse goes that a home, that probability is the same and is independent of what happened before.

So if the nurse goes to two houses, the probability that she will find the client on the first home is 0.7

And the probability that she will find the client on the second home is 0.7

Then the joint probability (the product of the two individual ones) is:

P = 0.7*0.7 = 0.49

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Answer:

Step-by-step explanation:

The wood is (8/9) foot long. If cut into 4 pieces, each piece would be (8/9)/4 foot long.

(8/9)/4

((8/9)(1/4)= 8/36 or 2/9 foot long for each piece.

If he sells all 4 pieces for a total of $10, he will charge $10/4) = $2.50 each.

Answer:

Step-by-step explanation:

15

The number of miles for which the cost of Uber and Lyft is the same is 30.

How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.

Let the number of miles covered be = x
Given, the cost of travel = Pickup Fee + Cost per mile
Given, the pickup fee for Uber = $ 0
The cost per mile for Uber = $ 0.25
Again, the pickup fee for Lyft = $ 3
The cost per mile for Lyft = $ 0.15
Thus, the cost of travel for Uber = 0 + 0.25x -- (i)
Also, the cost of travel for Lyft = 3 + 0.15x -- (ii)
As per question, (i) and (ii) are equal.
Thus, 0 + 0.25x = 3 + 0.15 x ⇒ (0.25 - 0.15)x = 3 ⇒ 0.10x = 3
⇒ x = 3/0.10 ⇒ x = 30
Thus, for 30 miles  the cost of Uber and Lyft is the same.

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The union of set A = {1, 5, 8, 12, 17} and B = {5, 17} is

AUB= {1, 5, 8, 12, 17}

This is further explained below.

Generally, The set that contains all of the elements that are part of both sets A and B, or all of the elements that are part of both sets combined, is referred to as the union of the two sets A and B. The symbol is used to represent the union of all the elements in the set.

In conclusion, The union of these sets sees the value of both sets represented

A = {1, 5, 8, 12, 17} and B = {5, 17}

AUB= {1, 5, 8, 12, 17}

Option A

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Answer:

Step-by-step explanation:

just like when you have 5+(17-8) you don't have to do all the work you can just do this 17-8 is 9 and that is  when you add 5+9 is 14

The percentage of yield after cleaning and trimming the celery is 75%.

Given, a bunch of celery is bought which weighs 16 ounces.

After cleaning and trimming the celery, you are left with 12 ounces.

let the x be the percentage yield.

Based on the conditions, formulate:

16 × x = 12

⇒ 16x = 12

⇒ x = 12/16

minimize the terms.

⇒ x = 3/4

to convert it into percentage, multiply by 100

⇒ x = 3/4 × 100

⇒ x = 75%

Hence the percentage of yield is 75%.

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There are 60 boys to make up the boys' teams and 40 girls to make up the girls' teams.

We are also told that the teams should be the same size.

This means that irrespective of the number of teams, each team should contain the same number of players.

Thus, the largest number of people that can be placed on a team is;

The highest common factor ;

The HCF is 10 x 2 = 20, therefore;

The largest number of people that can be placed on a team is 20.



The mean of all exam scores in the class is found = 71

Normally distribution

A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

While data points are referred to as x in a normal distribution, they are called z or z-scores in the z-distribution. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies: A positive z-score means that your x-value is greater than the mean.

The z-score is found by;

z = (x - μ)/σ

x =  sample mean

μ =  mean score

σ =  standard deviation

Now, from this,

x = zσ + μ

For p = 80th percentile= 0.8, see z value from z score table.

z = 0.85

x = 85 points

85 = 0.85σ +  μ  .....eq 1

For p = 30% = 0.3, see the z value from the z score table.

z = -0.3802

x = 65

65 = -0.3802σ +  μ  .....eq 2

Solving eq 1 and 2.

σ = 16.25

Put in eq 1

μ = 71.19

μ = 71

Thus, the mean of all exam scores in the class is found = 71

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Answer:

x = 45, y = 85

Step-by-step explanation:

In this figure we can see a Z-angle, which tells us that x = 45

In a triangle, the sum of the angles is 180 degrees,

so the unknown angle in the triangle is 180 - 45 - 85 = 50

For a straight line, the total angle is 180 degrees,

, so y + x + unknown angle of triangle = 180

since x = 45, and unknown angle of triangle = 50,

y = 180 - 45 - 50 = 85

This can also be seen when you realise that the two parallel lines give an F-angle, which tells us that Y = 85

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

28 students in total.

6 are female.

so, we have 28-6 = 22 male students.

7 of the 28 students have an A.

17 male students do not have an A.

that means 22-17 = 5 male students have an A.

and that means 7-5 = 2 of the female students have an A.

"given that they have an A".

that reduces our totally possible cases to 7.

the probability that an A-student is male is therefore

5/7 = 0.714285714...

and FYI

the probability that an A student is female is

2/7 = 0.285714286...

The probability that a student is male given that they have an A is approximately 0.538.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

We can use Bayes' theorem.

P(male | A) = P(A | male) x P(male) / P(A)

We are given:

P(A | male) = 7/17

(7 students are male and have an A, out of 17 male students)

P(male) = 17/28

(17 students are male, out of 28 total students)

P(A) = (6+7) / 28

(13 students have an A, out of 28 total students)

Plugging in these values.

P(male | A) = (7/17) x (17/28) / (13/28) = 0.538

Therefore,

The probability that a student is male given that they have an A is approximately 0.538.

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Answer:

Point Form:

(

−

13

4

,

−

7

4

,

1

)

Equation Form:

x

=

−

13

4

,

y

=

−

7

4

,

z

=

1

Step-by-step explanation:

When we want to find the slope of a line, we divide its increase on the [tex]y[/tex]-axis by its increase on the [tex]x[/tex]-axis. In other words, we look at its [tex]tan(a)[/tex]. As you can see in the photo, I chose two points that exactly intersect the axes and connected them in a right triangle. I then divided the increase in the [tex]y[/tex]-axis ([tex]3[/tex]) by the increase in the [tex]x[/tex]-axis ([tex]4[/tex]). Since the line slopes to the right, its sign will be positive. Also, this line intersects the [tex]y[/tex]-axis [tex](x=0)[/tex] at [tex]1[/tex].

The equation of the circle in standard form is (x + 5)² + (y)² = 9/4.

The general representation of the equation is:

(x-h)² + (y-k)²= r²

Where (h,k) is the coordinates of the center of the circle and r is the radius.  And x and y are the corresponding x and y values of the point the circle passes through

Since we have the coordinate of the center as (-5,0)  and the circle passes through (-5, 3/2). Therefore:

h = -5, k = 0, x = -5 and y = 3/2

Let's put these values in the formula.

(x-h)² + (y-k)²= r²

(-5 - (-5) )² + (3/2 - 0)² =  r²  

(-5 + 5)² + (3/2)²= r²

(0)² + (3/2)²= r²

(3/2)² = r²

r = 3/2

Putting radius, r = 3/2,   h = -5 and k = 0 back into the formula wiil give:

(x + 5)² + (y - 0)²= (3/2)²

(x + 5)² + (y)² = 9/4

Therefore,the standard form of the equation of the circle is (x + 5)² + (y)² = 9/4.

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The equation which show the cost of windows:-

C = $75.75 * W

where W = no of windows

What is equation ?

A mathematical equation can be defined in a variety of ways.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

$227.25 ÷ 3 =  $75.75

The equation which show the cost of windows:-

C = $75.75 * W

where W = no of windows

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0.578 can be expressed as a percent if we can multiply the decimal by 100%

Step 1: Multiply 0.578 by 100

To multiply by 100, we simply have to shift the decimal point by the number of zeros (twice)

0.578 x 100 = 57.8%

Answer = 57.8%

The domain of the function would be a positive integer.

So option 1) positive integer is correct.

Domain of a function is the set of values accepted by the function.

So in this question the value is always a integer.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function if it successfully allows the production of a single value y using another value for x.

And the model is made to determine the amount of money spend to complete the project.

We can't define money in negative term.

So it must be a positive integer.

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Answer:

tan θ = 4.5

Step-by-step explanation:

tan = opposite/adjacent

The opposite of θ is 45 cm long

The adjacent of θ is 10 cm long

tan θ = 45 / 10 = 4.5

The solution is: the value of tan is : tan θ = 4.5.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

Here, we have,

we know,

tan = opposite/adjacent

from the given diagram, we get,

given that,

The opposite of θ is 45 cm long

The adjacent of θ is 10 cm long

so, we get,

tan θ = 45 / 10

        = 4.5

Hence, The solution is: the value of tan is : tan θ = 4.5.

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Answer:

they're similar

Step-by-step explanation:

hello again ;)

Consider the formula,

The expression is given as,

Solve the expression as,

Thus, the given expression is evaluated as,

[tex]6(y) + 6( -5 ) = 18 - 2y \\ 6y - 30 = 18 - 2y \\ 6y + 2y = 18 + 30 \\ 8y = 48 \\ \frac{8y}{8} = \frac{48}{8} \\ y = 6[/tex]

ATTACHED IS THE SOLUTION

The functions whose graphs consist only of lines are-

A function is a relationship between a set of inputs (referred to as the domain) and a set of permissible outputs (referred to as the codomain), in which each input is connected to exactly one output. A function on one variable is frequently denoted by f.

Linear functions: A straight line just on coordinate plane is represented by a linear function. For instance, y = 3x - 2 symbolizes a straight line on the a coordinate plane and thus a linear function.

Constant functions: A constant function is employed to portray a quantity that remains constant over time and is considered the simplest type of real-valued function.

Linear absolute value functions: The Absolute Value Function is a two-linear function piecewise defined function.

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