Evaluate the algebraic expression for the given values of x = 3 and y = 4. 8x - y

Answer:

Quotient = 70

Remainder = 50

Step-by-step explanation:

The greatest number you can make is 9210, the smallest 3-digit number is = 129.

9210 / 129 = 71 with 50 left

so:

70 is the quotient and 50 is the remainder

Answer:

false 3.12 is in between 3 and 4  though

Step-by-step explanation:

Answer:

55% probability that a randomly selected depth is between 2.25 m and 5.00 m

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d is given by the following formula.

\(P(c \leq X \leq d) = \frac{d - c}{b - a}\)

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.

This means that \(a = 2, b = 7\)

What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?

\(P(2.25 \leq X \leq 5) = \frac{5 - 2.25}{7 - 2} = 0.55\)

55% probability that a randomly selected depth is between 2.25 m and 5.00 m

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remaining fraction:

1/5 of books are encyclopedia

Answer:

Let the total fraction of books be 1, then;

\(1 - ( \frac{1}{10} + \frac{2}{10} + \frac{1}{2} ) \\ 1 - ( \frac{(1 + 2 + 5)}{10} ) \\ (1 - \frac{8}{10}) = \frac{(10 - 8)}{10} \\ \frac{2}{10} = \boxed{ \frac{1}{5} }\)

Answer:

140 total interest

Step-by-step explanation:

Answer:

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Step-by-step explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.

Answer:

$ 4.86

Step-by-step explanation:

Subtract 7.19 and 2.33

7.19-2.33=4.86

Ok, so

We have the next system of equations:

The first equation is a line, and the second one is a parable.

If we graph, we would get the following:

Then, we notice that there's two intersection points between both graphs.

These points are located at ( -1 , -3 ), and ( 2 , -6)

Therefore, there are two solutions for this problem.

x = -1 and y = -3,

x = 2, and y = -6

Now, how to graph each equation?

First one, take the line y = -x-4

Notice that this equation tells us that the line given has its intersection with y-axis at ( 0 , -4 )

We also know that a line is formed with two points, so we could replace by any "x" number and see which value "y" takes.

For example:

If x = 1,

y = -1-4, which is y = -5

So we got other point: ( 1, -5).

Now, we just join both points and we get the line, like this:

And that's how you can graph the line.

Now, how could we graph the parable?

We know that we have to take three points to join to graph a parable. So, first, we would find its intersections with x - axis, if we equal the equation to zero.

x² – 2x - 6 = 0

If we solve this equation, we obtain that x could take two different values.

To solve it, we use the next equation:

x = 1 - √7 or

x = 1 + √7.

Then, we actually have two points.

Now, finally, we could find its vertex.

If we find the vertex of the parable, we notice that it is located in (1,-7)

Now, we just join these three points as this:

And if we put these graphs together, we obtain the first graph I drew, and notice that the solution for the system is the intersection between both functions.

Answer:

.5

Step-by-step explanation:

30 miles a hour divide by 60 so your going half a mile a minute

Your speed in feet per minute is 2640 ft/min.

A unit rate means a rate for one of something.

Given that, Your rate of speed is 30 miles for every 1 hour

We know, 1 mile = 5280 feet

Therefore, 30 miles = 30x5280 = 158400 feet

That means, you are travelling 158400 feet for every hour

In an hour, there are 60 minutes,

Therefore, you are travelling 158400 feet in every 60 minutes.

In 60 minutes = 158400 feet

In 1 minute = 158400/60 = 2640 feet

That means you are travelling 2640 feet in every 1 minute.

Hence, your speed in feet per minute is 2640 ft/min.

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If one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will be multiplied by a factor of 3.

Let's suppose we have two numbers, A and B, and we want to know how their product will change if one number is increased by a factor of 12 and the other is decreased by a factor of 4.

The initial product of the two numbers is:

A x B

If we increase A by a factor of 12, the new value of A will be 12A. If we decrease B by a factor of 4, the new value of B will be B/4. Therefore, the new product of the two numbers will be:

(12A) x (B/4) = (12/4) x A x B = 3AB

So the new product of the two numbers will be three times the initial product. In other words, if one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will increase by a factor of 3.

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Answer:

Sample space = 216 elements

a) P = 25/72

b) P = 91/216

Step-by-step explanation:

If each die has six possible values, the number of possible outcomes for three dice is 6^3 = 216 possible outcomes

a)

If we want exactly one die to be red, we have that one die is red (probability of 1/6) and the other two are not red (probability of 5/6), and the red die can be any of the three dice (combination of 3 choose 1), so the probability is:

P = C(3,1) * (1/6) * (5/6) * (5/6) = 3 * 25/216 = 75/216 = 25/72

b)

To find the probability of at least one die is red, we can find the probability of all dice not being red, and then find the complement of this probability (1 - P).

The probability of one die not being red is 5/6, so we have:

probability of all dice not being red = (5/6)^3 = 125/216

probability of at least one die being red = 1 - 125/216 = 91/216

Answer:

i). 14/75 or 19%

ii). 2/25 or 8%

Step-by-step explanation:

i). Using the combinations formula if repetition is allowed

If n choose r,

(r+n-1)!/r!(n-1)!

Where n is the things we have to pick from and r is the objects we want. We want 2 objects and we have 24 objects to pick from.

So our equation will be

(2+24-1)!/2!(24-1)!

(25)!/2!(23)!,

This gives us 300. So there is 300 possible combinations.

Since we have two independent events, we can multiply two events and divide it by 300 to find the probability.

i) There is 14 good defects and 4 major defects so

\( \frac{14 \times 4}{300} = \frac{56}{300} = \frac{14}{75} \)

So the probability is 14/75 or 19%

ii) We can do the same thing in question 1

There is 6 minor defects and 4 major so

\( \frac{6 \times 4}{300} = \frac{24}{300} = \frac{8}{100} = \frac{2}{25} \)

So this means the probability is 8% or 2/25

Answer:

See below

Step-by-step explanation:

\(\csc\theta=1.2711\\\\\frac{1}{\csc\theta}=\frac{1}{1.2711}\\ \\\sin\theta=\frac{1}{1.2711}\\ \\\theta=\sin^{-1}(\frac{1}{1.2711})\\\\\theta\approx51.88^\circ\approx52^\circ\)

Remember the identity \(\csc\theta=\frac{1}{\sin\theta}\), so \(\sin\theta=\frac{1}{\csc\theta}\) and it makes the problem easier. Just remember to take the inverse sine (let me know if you are not sure what that means).

The value of the θ in csc θ = 1.2711 is 51.88°.

A trigonometric ratio is a ratio of the length of sides of a right-angle triangle. It relates the ratio of sides to the respective angle. The most common trigonometric ratios are sine, cosine, and tangent.

Given csc θ = 1.2711, we need to find the value of θ,

So, csc θ = 1.2711

θ = csc⁻¹(1.2711)

θ = 51.88°

Hence, the value of the θ in csc θ = 1.2711 is 51.88°.

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Answer:

4p = 8

Step-by-step explanation:

2 × 4 = 8

4p = 8

Since E is the midpoint of DF, DE and EF are two halves of DF. First, let's write down what we know.

DE = 3x + 4

EF = 5x - 2

DE = EF

DE + EF = DF

Now, let's plug our values for DE and EF into our first expression.

3x + 4 = 5x -2

Add 2 to both sides and subtract 3x from both sides.

6 = 2x

Divide both sides by 2

3 = x

Let's plug 3 in for x into DE.

DE = 3x + 4 = 3(3) + 4 = 9 + 4 = 13

DE = EF = 13

We can plug 13 in for DE and EF to get DF

DF = DE + EF = 13 + 13 = 26

Answer:

25/33

Step-by-step explanation:

Answer:

\(\frac{25}{33}\)

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

let x = 0.7575..... (1) ← multiply both sides by 100

100x = 75.7575... (2)

subtract (1) from (2) thus eliminating the repeating digits

99x = 75 ( divide both sides by 99 )

x = \(\frac{75}{99}\) = \(\frac{25}{33}\) ← in simplest form

Answer:

Step-by-step explanation:

It is the point where the graph passes through the y-axis.

So if it passes through the point where y = 2,  the y-intercept is (0, 2) - note the x coordinate is 0 at this point.

If we are asked to find the y-intercept of the graph of the equation y = 3x - 4

we put  x = 0 and work out y as follows:

y = 3(0) - 4 = 0 - 4

y = -4

so the y-intercept is (0, -4).

Answer:

E=10.75h-6.5

Step-by-step explanation:

10.75h for every hour she work

-6.5 for the bus fare

The request dimensions of the rectangle for maximum area are,

Length of perimeter is, \(l = 41 m . ,\)

Width of perimeter is, \(w = 41m\)

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.

Let \(l\) and \(w\) denote the length and width of the Rectangle.

Its Perimeter is \(2(l+w)\), which is given to be, 164.

\(l+w\) = 164/2

\(l+w\) =82                         (Equation-1)

Now, Area \(A\) of the Rectangle, is, given by,

\(A = lw\)

We can substitute equation-1,

\(A = l(82-l)\)

\(A = 82l-l^{2}\)

which is a function of \(l\),

So let us,

Write it as,

\(A(l) = 82l-l^{2}\)                 (Equation-2)

We are request to maximize \(A\).

We know that, for \(A_{max}\), \(A^{|}l\) = 0 , and \(A^{||} l\) < 0

We can equation-2,

\(A^{|}l\) = 0 ⇒ \(82-2l = 0\)

\(l = \frac{82}{2}\)

\(l = 41\)

Further,

\(A(l) = -2\) < 0, ∀\(l\) , and  in particular, for \(l = 41\) , too.

Thus, \(l = 41\) gives \(A_{max}\)

Hence, the request dimensions of the rectangle for maximum area are,

\(l = 41 m . ,\) and \(w = 82 -l = 41m\)

Therefore,

The request dimensions of the rectangle for maximum area are,

Length of perimeter is, \(l = 41 m . ,\)

Width of perimeter is, \(w = 41m\)

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9514 1404 393

Answer:

  90°

Step-by-step explanation:

The ratio of the largest angle to the total is ...

  10/(3+7+10) = 10/20 = 1/2

The largest angle is half the total of all angles:

  1/2×180° = 90° . . . . measure of the largest angle

The expression that  is equivalent to 0 is eight less than ten minus two because it will give the zero expression when expressed mathematically.

The mathematical expression  can be described as the finite combination of the mathematical items which can be symbols which is been  according to rules and this can be based on the particular expressions items that is been given.

In this case we can come into conclusion that, eight less than ten minus two will gives us zero which implies that out of the given option, option A is correct.

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9514 1404 393

Answer:

  4 in 3492 is 100 times 4 in 704

Step-by-step explanation:

To find the value of a particular digit, set the other digits to zero.

  4 in 3492 = 400

  4 in 704 = 4

The first 4 is 100 times the value of the second 4.

Answer:

Step-by-step explanation:

6. Which of the following equations represents the data in the table?

Х

-4

0

4

8

y

5

2

-1

-4

O A. y = x + 2

O B. y = -x + 2

oc. y = x + 8

OD. y = -

3 + 8

M

help plzzzzzzzzzzzzzzzzzzzzz

Answer: m∠ATC = 54°

Step-by-step explanation:

Ok, we know that:

m∠ATB = 20° and  m∠BTD = 72°

then we must have that the angle between A and D, is equal to the sum of the angles between A and B, and B and D, or:

m∠ATD = m∠ATB + m∠BTD = 20° + 72° = 92°

Now, we also know that m∠CTD = 38°

And the angle:

m∠ATC  will be equal to the angle between A and D, minus the angle between C and D, or:

m∠ATC = m∠ATD - m∠CTD = 92° - 38° = 54°