Writing and solving radical equations: Mastery Test
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The probability mass function of x  is P(0)= 1/8, P(1)= 3/8, P(2)= 3/8, P(3)= 1/8.

Here number of trials = 3

In tossing a coin for once, the outcomes of the trial are either head or tail.

The trials are independent.

probability of getting head(success)=p=1/2

probability of getting tail(failure)=1-p=1-(1/2)=1/2

Number of success=X

Since there are two mutually exclusive outcomes of independent trials, the probability mass function of Binomial = (nx)px(1−p)n−x(nx)px(1 − p)n−x {in this case n=3}

The probability distribution of X is -

= X=0, P(X=0)=1/8

= X=1, P(X=1)=3/8

= X=2, P(X=2)=3/8

= X=3, P(X=3)=1/8

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The required time it will take to fill the tank with gallons of water is 18 minutes.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,
From the figure, the equation of the trend line is given as,
y = 20.83x

Where y =  gallons of water and x is time in minutes

Now, put y = 375
375 = 20.83x
x = 18 min

Thus, the required time it will take to fill the tank with gallons of water is 18 minutes.

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Complete question,

Make Sense and Persevere The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend line, predict how long it will take to fill the tank with 375 gallons of water.

The domain of the function is not the set of all real numbers, that is why it is not from R to R

Here we want to see why the function f is not a function from R to R, where R is the set of the real numbers.

The function here is:

f(x) = 1/x

Notice that x is on the denominator, so we can't evaluate that function on x = 0.

So there is a real number that we can't use on that function, then the domain is not R, is R minus the element {0}

That is why f(x) is not a function from R to R, because the domain is not the set of the real numbers.

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Answer: The answer is 9

Step-by-step explanation: 3^3/3=9

The differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).

What is the differential equation?

A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)

a) To differentiate x² + xy + y² = 0 with respect to x, we can use the power rule and the chain rule.

The power rule states that the derivative of x^n is nx^(n-1)

The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx

x² + xy + y² = 0

dx/dx (x² + xy + y²) = dx/dx (0)

2x + y = 0

dy/dx = -x/y

b) To differentiate 1/x + 1/y = e^y with respect to x, we can use the chain rule and the reciprocal rule.

The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx

The reciprocal rule states that the derivative of 1/x is -1/x²

1/x + 1/y = e^y

dy/dx = dy/dx (e^y)

dx/dx (1/x + 1/y) = dx/dx (e^y)

-1/x² - 1/y² = e^y

dy/dx = e^y * (-1/x² + 1/y²)

Hence, the differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).

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The graph demonstrates that the function g's line goes through the locations (0,2) and (2,8). The slope of the line is 3, implying that its equation is g(x) = 3x + 2.

The steepness or inclination of a line, route, or surface is measured by slope. It is the vertical distance divided by the horizontal distance between two locations on a line, route, or surface.

According to the graph, the function g is a line with a slope of 3 and a y-intercept of 2. This suggests that the line's equation is g(x) = 3x + 2. According to this equation, increasing the y-coordinate by one increases the x-coordinate by three. The line connects the points (0, 2) and (2, 8), which means that when x = 0, y = 2 and when x = 2, y = 8. This may be demonstrated by plugging the x-values into the equation, which will produce the matching y-values.

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The TRUE statements about the inequality y ≤ 150x - 3100 are:

Inequality is a mathematical statement showing that two or more mathematical expressions are unequal or not equivalent.

Inequalities are represented by the following types and inequality symbols:

Check:

Ordered pairs (40, 2900)

y ≤ 150x - 3100

y ≤ 150(40) - 3100

y ≤ 6,000 - 3100

y ≤ 2900

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Answer:

The slope is [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

The slope formula would be: [tex]\frac{y2-y1}{x2-x1}[/tex]

So for (-2,9) and (-4,6), we can plug in the variables: (x1, y1) and (x2, y2)

Let's use the numbers in the equation provided above:

[tex]\frac{6-9}{-4-(-2)}[/tex]

= [tex]\frac{-3}{-2}[/tex]

= [tex]\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1} = \frac{6-9}{-4-(-2)} = \frac{-3}{-2} =\frac{3}{2}[/tex]

Answer: k=10

Step-by-step explanation:

Answer:4

Step-by-step explanation:

The mean of their ratings is 7.

Mean (also called the average) is used to describe the central tendency of a set of numerical data. It is calculated by summing up all the values in the data set and dividing by the number of values.

Since We have the ratings:

Destiny 9, Taylor 6, Jeremiah 5

Mean = (9 + 6 + 5)/3 = 20/3 = 7

Note: we divide by 3 because there are 3 people

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Answer: 100 inches

Step-by-step explanation:

Corresponding sides of similar figures have proportional side lengths, so:

[tex]\frac{10x}{24}=\frac{5x+5}{16} \\\\\frac{2x}{24}=\frac{x+1}{16}\\\\\frac{x}{12}=\frac{x+1}{16}\\\\16x=12x+12\\\\4x=12\\\\x=3\\\\[/tex]

So, the perimeter is [tex]5x+5+5x+5+10x+10x=100[/tex].

Note that if the family is to spend less than $60 dollars without further expenses, then they will have to spend nothing more than 6 hours. The inequality expression is given as: 36+4h < 60

First, the inequality expression is given as:

36+4h < 60

Where h is the number of hours they could spend.

We arrive at the above because we were given the following:

Cost of Movie = $36

Cost of parking Per Hour= $4

The maximum amount to be spent = $60

Thus, to find the number of hours the can spend without overshooting $60, we must find h. To do this, we must make h the subject of the formula by first removing 36 from both sides:

36+4h-36 < 60-36

4h < 24

h < 24/4

h < 6

What the above result show is that the number of hours that must be spent must be less than 6.

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Answer:

یه گل یک گل بام میی مه فیلم بام حس بام حس فمس یکم باشگاه هی یک گل یه حس سیم هی فکریه خشک پیل هر یک حس صب زی صب هم گچ نی بلن هر بر قل هم بی دو حس قیین

Step-by-step explanation:

سبک حس بام نی شیک حس

یا کمی سیم حس او

نی یک حس بکشم یک حس بام نی که خیلی تنیام که اما الا دیه انجام نمییم ای موضوع که دعوا خیلی تخفیف خیلی خوعه ای موضوع که اما الا دیمش خوش

۳ خشک هی یک هی بام نی با که اما ۷غ هه بام نی بلن کف بام نی بکر

به نمییم هی بام میی لاک حس بام

بلن هی یک

حالم ای زبونه فراموش که

فخ بیم فک

Answer:

d = 22

Step-by-step explanation:

you add 22 to a number in the sequence to get the next number

8 + 22 = 30

30 + 22 = 52 and so on...

The baker made a batch of chocolate chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is B. Likely.

Generally,  Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

A probability of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform decision-making in a wide range of fields, including statistics, finance, and engineering.

A probability of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.

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Answer:

D subtract 2 from both sides

Step-by-step explanation:

x + 2 - 2 = 5- 2

==>    x = 3

The solution of the equation is x = 3.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

An equation,

x + 2 = 5.

To solve the equation:

Subtract 2 from both sides,

x +2 -2 = 5 -2

x = 3

Therefore, the solution is x = 3.

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Answer:

6.94??????‽??????????????

Step-by-step explanation:

5÷4/5?????????

5×5?????????‽?/4

2.777777778/4

=69.4????????????????????

Based on the information provided, it can be concluded the student is not following the rule of allocating 50% to needs, 30% to wants, and 20% to savings.

Needs: 300 +10 + 50 +150 + 100 + 100=  $710

Now, let's calculate the percentage this represents:

710 x 100 / 1450 = 48%

Wants: 9.99 + 9.95 +9.99 + 19.99 + 25 + 500 + 65= $639.92

Now, let's calculate the percentage this represents:

639 x 100/ 1450 = 44%

Savings: 48 + 44 = 92 which means he can save 8%

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Answer:

Area = length x width (in feet)

Step-by-step explanation:

The area of a 2-dimensional shape can be found by multiplying its length by its width. The equation to find the area of a rectangle is:

Area = length x width

So if you know the length and width of a piece of glass in feet, you can use the above equation to find its area in square feet. For example, if the length of the glass is 10 feet and the width is 5 feet, the area would be:

Area = 10 feet x 5 feet = 50 square feet

So the equation to find the area of a piece of glass in square feet is:

Area = length x width (in feet)

It's worth noting that this equation applies to any 2-dimensional shape that has a length and a width, not just a rectangle.

Answer:

-----------------------

We observe on the graph:

The domain is:

Answer: D

Step-by-step explanation:

20 apples cost $17

100 apples = 100/20 * 17 = D

The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.

The solid has no negative x-values, meaning all x-values are positive. It has both positive and negative y-values, indicating that it is symmetrical around the x-axis. The solid has no negative z-values, meaning all z-values are positive. In the x y-plane, the solid has a straight side and a curved side. In the x z-plane, the solid has a curved side and in the y z-plane, the solid has a straight side.

The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.

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The area of a trapezoid is given by the formula A = 1/2(b1 + b2)h. In this case, b1 = 4, b2 = 3, and h = 8.

The area of a trapezoid can be determined using the formula A = 1/2h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the top and bottom bases of the trapezoid, respectively. To determine the area of a child's toy harp in square inches, we need to know the length of the top and bottom bases and the height of the trapezoid.

Therefore, the area of the harp is 1/2(4 + 3)8 = 20 square inches. To find the area of the harp, we first need to know the measurements of the base lengths, b1 and b2, as well as the height, h. Once we have these measurements, we can plug them into the formula for the area of a trapezoid and solve for A. In this case, the area of the harp is 20 square inches.

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Answer:

20 square inches

Correct Answer 100%. Pls, give me brainliest. Thank You.

The general solution to x squared dy over dx equals 3 plus 2y is given by 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant.

To calculate this, we begin by taking the derivative of both sides of the equation with respect to x. We then rearrange the equation to yield 2y + x^2 dy/dx = 3. We divide both sides by x^2 so that dy/dx is isolated on one side of the equation, yielding dy/dx = (3 - 2y) / x^2. We can then integrate both sides of the equation, with respect to x, to yield 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant. This equation is the general solution to x squared dy over dx equals 3 plus 2y.

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Answer:

For 3 books, costs are the same

$59

Step-by-step explanation:

x = number of books

$41 + ($6/book)(x) = $32 + ($9/book)(x)

41 - 32 = 9x - 6x

9 = 3x

x = 9/3 = 3

41 + 6(3) = 32 + 9(3) = $59

The correct statement regarding the dog’s movement at 5 seconds once the command was given is given as follows:

The dog was running towards the trainer.

The input and output variables for the function graphed are given as follows:

At a time of 5 seconds, the distance between the dog and the trainer is decreasing, meaning that the dog was moving towards the trainer, and thus the second option is the correct option.

The graph is given by the image presented at the end of the answer.

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Answer:

The dog was running towards the trainer.

The elevation of mountain mt.kenya is, x = 17,057.1 feet by substitution method from the elevation of mountain K2 given.

Given that,

K2 is 11,194.21 feet higher than mt.Kenya, write and solve an equation to find the elevation of mt.Kenya.

x = mt. Kenya ( since given that x represents the elevation of mt.kenya)

Let us consider/assume ,

y = K2 (say)

Therefore, the relation between x and y:

                   x = y - 11,194.21    ( or )

                   y = x + 11,194.21  

( since given that K2 is 11,194.21 more than mt.Kenya )

The elevation of K2 Mountain = 28251.31 feet

                                                  = y

substitute the value of y in x = y - 11,194.21

                                            x = 28251.31 - 11,194.21

                                       ∴ x = 17,057.1 feet.

Therefore the elevation of mt.kenya found to be, x = 17,057.1 feet by substitution method.

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The complete question is :

K2(Which is 28251.31) is 11,194.21 feet higher than Mt.Kenya Write and solve an equation to find the elevation of Mt.Kenya. use x to represent the elevation of mt. kenya.

The measure of all the angles are estimated.

For the stated question:

For ∠1

∠1 = 68 + 36 (sum of opposite interior angle equals exterior angle).

∠1 = 104

For ∠4.

∠4 = 180 - 70 - 65 (linear pair)

∠4 = 45

For ∠3.

∠3 = 65 (vertically opposite angle)

For ∠2.

∠2 = 180 - 65 - 36  (sum of angles of triangle are 180)

∠2 = 79

Thus, the measure of all the angles are estimated.

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The real number that represents the amount he owed on his home equity line of credit would be = $3,300

A real number is defined as the type of number that can be used to represent a one directional measurement which can be rational or irrational.

The first amount of money borrowed by a person from his home equity line of credit = $2100

The second amount of money borrowed by a person from his home equity line of credit = $1200

Therefore, the total amount that was borrowed= 2100+1200 = $3,300.

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