Answer & Step-by-step explanation:
To get the range of the function y = 2x + 1, we need to determine the set of all possible output values (y) that the function can produce for the given domain.
When x = -2, y = 2(-2) + 1 = -3.
When x = 4, y = 2(4) + 1 = 9.
When x = 6, y = 2(6) + 1 = 13.
So, the output values (y) for the given domain { -2, 4, 6 } are -3, 9, and 13.
Hope it helps! : )A company wants to have 5 digit phone extensions with the first digit not being zero. How many different phone extensions are possible?
90, 000 will be the total number of different phone extensions.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given, A company wants to have 5-digit phone extensions with the first digit not being zero.
This problem is an application of the Basic Counting Rule which was discussed above. We want to compute the number of different 5-digit phone extensions.
there are 10 different digits, which are 0,1,2,3,4,5,6,7,8,9. The first digit can't be 0.
There are 9 choices for the first digit. For each choice of the first digit, there are 10 choices for the second digit. For each choice of the first and second digits, there are 10 choices for the third digit, and so on.
According to the Basic Counting Rule, we know that the total number of phone extensions is the product of the number of ways to choose each digit (the product of the 6 above numbers).
the total number of different phone extensions is = 9 *10 *10 *10 *10
therefore, the total number of different phone extensions is = 90,000.
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How many solutions does this linear system have?
y = 2/3 x + 2 + 2
6x – 4y = –10
hey, I checked on desmos, which is a calculator for this type of stuff, and got 1.8,5.2. So I think that's one solution. Sorry if wrong.
Tanya decided to lease a car.
the lease includes a money factor of 0.00324.
What interest rate is shawna being charged in her lease? ( round to the nearest hundredth).
A. 0.78%
B. 7.78%
C. 1.35%
D. 13.5%
A correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
What is the interest rate?
Interest rate is the amount charged over and above the principal amount by the lender from the borrower. In terms of the receiver, a person who deposits money to any bank or financial institution also earns additional income considering the time value of money, termed as interest received by the depositor.
The interest rate in a lease can be calculated using the money factor, which is essentially a type of interest rate used in auto leasing.
To calculate the interest rate from the money factor, multiply the money factor by 2400.
In this case, the money factor is 0.00324, so the interest rate would be:
0.00324 * 2400 = 7.776%
Therefore, the correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
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A correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
Which interest rate is it?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
The money factor, which is essentially a sort of interest rate utilized in auto leasing, can be used to compute the interest rate in a lease.
By multiplying it by 2400, you can determine the interest rate from the money element.
Given that the money component in this situation is 0.00324, the interest rate would be:
The result of three consecutive conversions from an interest rate to a money factor is 2400 (1/2 × 1/12 × 1/100). 6/2400 = 0.0025 money factor, which can be multiplied by the entire amount borrowed to see how much the monthly interest would be roughly.
(1/2 × 1/12 × 1/100). 6/2400 = 0.0025
0.00324 × 2400 = 7.776%
Therefore, the correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.
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A, B, and C take turns flipping a coin. The first one to get a head wins. The sample space of this experiment can be defined by S= 1,01,001,0001, ..., 0000... (a) Interpret the sample space. (b) Define the following events in terms of S: (i) A wins = A. (ii) B wins = B. (iii) (A U B). Assume that A flips first, then B, then C, then A, and so on.
a) Strings of probability 0s and 1s, which reflect the results of the coin flips, make up the sample space, S.
In (b), I A wins equals (1, 01, 001, 0001), (ii) B wins equals (0, 10, 010, 0010), and (iii) (A U B) equals (1, 0, 01, 10, 001, 010, etc.).
(a) Strings of 0s and 1s, which reflect the results of the coin flips, make up the sample space, S. Each 0 denotes a tail, while each 1 denotes a head. Since there is no restriction on the number of coin flips that can take place, the sample space is unlimited. Due to the fact that every result can be expressed as a string of 0s and 1s, it is also a finite collection. (b) I A wins means that A flipped a head before B or C, and the results are 1, 01, 001, 0001, etc. (ii) B wins = 0 (zero), 10 (one), 010 (zero), 0010 (zero), etc., indicating that B flipped a head before A or C. (iii) (A U B) = 1, 0, 01, 10, 001, 010, etc., indicating that either A or B turned over a coin before C. Presumably, A flips first, followed by B, C, then A, and so on.
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A bus company is replacing all the old seats in its buses with new ones. The company owns 13 buses and each bus has 28 seats. It costs $89.40 to purchase
each new seat, as well as an additional $31.70 to install each new seat. What is the total cost the company will pay?
Answer:
$44.236.20
Step-by-step explanation:
First, we need to calculate the cost of purchasing new seats for all the buses. The company has 13 buses and each bus has 28 seats, so the total number of seats to be replaced is 13 * 28 = 364 seats. The cost of purchasing each seat is $89.40, so the total cost of purchasing new seats for all the buses is 364 * $89.40 = $32,610.40.
Next, we need to calculate the cost of installing new seats for all the buses. The cost of installing each seat is $31.70, so the total cost of installing new seats for all the buses is 364 * $31.70 = $11,625.80.
Finally, we need to add the cost of purchasing and installing new seats to get the total cost the company will pay. The total cost of purchasing new seats is $32,610.40 and the total cost of installing new seats is $11,625.80, so the total cost the company will pay is $32,610.40 + $11,625.80 = $44,236.20.
Question
If A = {2, 6, 7, 8, 10, 11}, B is the set of all even integers, and U is the set of all real numbers from 1 to 11 inclusively,
what is (A U B)?
Write your answer in set notation.
Provide your answer below:
(AUB) will be equal to {2,4,6,7,6,10,11, .....even numbers). The empty set, or 0, is one of the most significant sets in mathematics.
What is an example of a universal set?A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolized by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.
What set contains no members?A set with no elements is referred to as a null set or empty set. The null set is the intersection of two disjoint sets, or sets that have no elements in common.
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Ashely has $450 in her savings account. She plans to deposit $25 each week. Tanner has $200 in his savings account, and plans to deposit $40 each week. Complete the equation to find w, the number of weeks until Ashely and Tanner have the same amount in their savings accounts.
___ + 450 = ____ + 200
The completion of the equation to find w, the number of weeks until Ashely and Tanner have the same amount in their savings accounts is 25w + 450 = 40w + 200.
What is an equation?An equation is a mathematical statement claiming that two or more mathematical expressions are equivalent or equal.
Equations are depicted with the equation symbol (=) to show equality of the expressions.
Ashely Tanner
Savings $450 $200
Planned weekly deposits $25 $40
Let the number of weeks to save equal amounts = w
Equations:Ashely's total savings in w weeks = 25w + 450 ... Equation 1
Tanner's total savings in w weeks = 40w + 200 ... Equation 2
For the two friends to have an equal amount, Equation 1 must equal Equation 2:
25w + 450 = 40w + 200
-15w = -250
w = 16.67
Thus, for Ashely's and Tanner's savings to become equal in amount, it would take 16.67 weeks.
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Here is an equation: 4x-4=4x+____. Fill in the blanks to make the following statements true. Fill in the blanks to make the following statements true. True for one value of x.
It is not possible to make the statement true for one value of x, as the two linear functions have the same slope.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the initial amount.The number of solutions for a system of two linear functions is defined as follows:
Zero solutions: same slope and different intercept.One solution: different slopes.Infinite solutions: same slope and same intercept.The functions for this problem are defined as follows:
4x - 4.4x + b.As the two functions have the same slope, there are two possible number of solutions.
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Suppose you’re exchanging money from one form of currency to another, where $1.00 in currency A equals $1.70 in currency B.
The actual value of $10 in currency A would be of $1.7 in currency B.
$17.
How to obtain the actual value?The actual value is obtained applying the proportions in the context of this problem.
The exchange rate is given as follows:
$1 in currency A - $1.7 in currency B.
Hence the value in currency B of $10 in currency A is obtained as follows:
1.7 x 10 = $17.
Missing Information.The problem asks for the value in currency B of $10 in currency A.
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find the surface area
Answer: 1468.17
Step-by-step explanation:
A quadratic function is shown partially in the table below. The turning point of the function has the coordinates . Think about how outputs repeat in a quadratic function and answer the following.. (a) Fill in the missing output values from the table.. (b) What are the zeroes of the function? (c) What is this function’s y-intercept? (d) For the domain interval , what is the range of the function?
Can you help me to see what the length of the third side is ?
help wanted i kinda forgot some subjects
PLEASE PLEASE HELP Solve and explain the method you chose to use (distributive property, FOIL, multiplying special cases): (c+3)^2
After solving (c+3)², the procedure is an illustration of the distributive property of equations, and c = -3.
What is equations?Perhaps the most basic form has just been assumed to represent the fraction with the least process. How or when to decide mostly on fundamental form. Look for components that are present in both the denominator and the numerator. Sometimes it is possible to determine if a fractional integer is a power of two.
A algebraic theorem is a statement with two equal sides and an equal sign in the center. The degrees earned by each variable are stated in descending order, similar to an equation's general form. A linear equation has the formula x + b = 0. A three distinct linear function has the general form x + b y + c = 0. (or something similar). Mathematics can be categorized as identities or conditioned equations.
given:
[tex]( c+ 3 ) ^ 2[/tex]
= by using formulas of [tex]( a+ b ) ^2[/tex]
by distributive property
[tex]c^2 + 3^2 + 6c[/tex]
[tex]= c^2 + 9 + 6c[/tex]
[tex]c^2 + 3c + 3c + 9 = 0[/tex]
= (c + 3 )(c+ 3)
c = -3
After solving (c+3)², the procedure is an illustration of the distributive property of equations, and c = -3.
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Which relationship between x and y in the equation shows a proportional relationship?
1. y=5(x+3)
2. y = 5x + 3
3. y=x−2
4. y = 3x
Answer:
4. y = 3x
Step-by-step explanation:
A proportional relationship is one in which the ratio of two variables is always constant. This is also known as direct proportion.
Out of the given options, the equation that shows a proportional relationship is:
4. y = 3x
In this equation, the ratio of y to x (y/x) is always 3, so the relationship between y and x is proportional. As x increases, y also increases at a constant rate, and as x decreases, y decreases at a constant rate. This type of relationship is often represented by the equation y = kx, where k is the constant of proportionality.
11. Multiply (m² + 2m + 1) (m + 1). SHOW YOUR WORK
Answer:
[tex]m^3+3m^2+3m+1[/tex]
Step-by-step explanation:
[tex](m^2+2m+1)(m+1)=(m^2)(m)+(m^2)(1)+(2m)(m)+(2m)(1)+(1)(m)+(1)(1)=m^3+m^2+2m^2+2m+1m+1=m^3+3m^2+3m+1[/tex]
You could also use the binomial theorem because the expression is equivalent to [tex](m+1)^3[/tex] but either method works.
Find n if (n + 1)! = 16n! + 16(n-1)!
Step-by-step explanation:
(n+1)! = (n+1)n(n-1)(n-2)...×3×2
16n! = 16n(n-1)(n-2)...×3×2
16(n-1)! = 16(n-1)(n-2)...×3×2
we can now divide both sides by (n-1)! and get
(n+1)n = 16n + 16
n² + n = 16n + 16
n² - 15n - 16 = 0
1×n² - 15n - 16 = 0
we try to bring this into a form
(n + a)(n - b)
one factor has to contain "-", because we have "-16".
and because -15 = 1 - 16, we see that
a = 1
b = 16
n² - 15n - 16 = (n + 1)(n - 16)
and that is 0, when at least one of the factors is 0, because 0×... = 0.
so, the solutions are
n = -1
n = 16
n = -1 does not make any sense for n!
so, n = 16 is the solution.
A 14-inch-wide conveyor unloads 4000 bushels of wheat per hour. At this speed, how many bushels per hour will an 21-inch-wide conveyor unload?
An 21-inch-wide conveyor would unload
Answer:
6000 bushels per hour.
Step-by-step explanation:
Let's assume that the rate at which the conveyor unloads wheat is proportional to its width.
If a 14-inch conveyor unloads 4000 bushels per hour, we can write this as:
Rate = 4000 bushels/hour * (Width of conveyor) / 14 inches
Now, if we want to find the rate at which an 21-inch conveyor would unload wheat, we can simply plug in the width into the equation:
Rate = 4000 bushels/hour * (21 inches) / 14 inches
Rate = 6000 bushels/hour
Therefore, an 21-inch-wide conveyor would unload 6000 bushels per hour.
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If a translation of T-3, -8(x, y) is applied to square
ABCD, what is the y-coordinate of B'?
O-12
O
8
O-6
O-2
If a translation is applied to square ABCD, the y-coordinate of B' = y_coordinate of B - 8 = -8.
What is the translation?
The translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. In a translation, every point of the object must be moved in the same direction and for the same distance.
When a translation of T-3, -8 is applied to square ABCD, it means that each point in the square is moved 3 units to the left and 8 units down.
The y-coordinate of B is found by moving 8 units down from the original y-coordinate of B.
Therefore, If a translation is applied to square ABCD, the y-coordinate of B' = y_coordinate of B - 8 = -8.
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wich expression represents a cube root of 1+i
The expression that represents the cube root of 1+i is ∛(1 + i)
How to determine the expressionFrom the question, we have the following parameters that can be used in our computation:
The cube root of 1+i
In mathematics and algebra, the cube root is represented as ∛
Using the above as a guide, we have the following:
The cube root of 1+i is ∛(1 + i)
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6. Which quadrant is the pre-image located in?
B
Quadrant III
Quadrant I
O Quadrant II
O Quadrant IV
9
A
Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.
What is data plotting?Graphing the correlation between two additional variables is the most common way to use a chart to present data. It is also permitted to use hand-drawn or digitally generated diagrams. Go three pieces up and 2 types to the right starting at the origin. Displaying the numbers for rows 2, 3, and 4 on the standard system is crucial. Make sure to be very clear in what you say.
Here,
Given :
A figure having pre image and post image ,
We have to find in which quadrant the pre image is located,
So,
In order to find that,
We see the image are in quadrant II and quadrant III
Since ,
After II quadrant III quadrant comes,
Thus , Pre image is located in II quadrant.
Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.
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A floor plan was drawn using the following scale:
1 inch: 2 1/2 feet
One wall of the house was represented by a line 6 1/2
inches long on the floor plan. Which proportion could be used to find the length of the actual wall, in feet? pls help me hurry than k u
Select one:
a. 2/5=13/2x
b. 2/5=13x/2
c. 5/2=13/2x
d. 5/2=13x/2
The proportion could be used to find the length of the actual wall, in feet is 2/5=13x/2, the correct option is B
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Given;
1 inch: 2 1/2 feet
One wall of the house was represented by a line 6 1/2 inches long on the floor plan.
Now,
6 1/2 inches= 13/2inch
1 inch: 2 1/2 feet=5/2feet
13/2inch=13/2 * 5/2
=65/4
b. 2/5=13x/2
Therefore, according to the given proportion the answer will be 2/5=13x/2.
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5. Which of the following expressions is the
factored form of 10x - 25 using the greatest
common factor?
A. 5(2x - 5)
B. 5(x - 5)
C. 10(x-2.5)
D. 5(2x-20)
Step-by-step explanation:
The expression that is the factored form of 10x - 25 using the greatest common factor is option A: 5(2x - 5).
To factor the expression, we need to find the greatest common factor of the terms, which in this case is 5. We then write the expression as a product of 5 and a second expression with the remaining terms:
10x - 25 = 5 * (2x - 5)
So, option A is the correct answer.
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
Dustin is doing laps around a track. Dustin can run 2 miles per hour faster than he can walk around the track. If Dustin walks around the track in 20 minutes and runs around the track in 15 minutes, at what rate is Dustin walking?
Dustin walk at the rate of 6 miles per hour.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Dustin can run 2 miles per hour faster than he can walk around the track. If Dustin walks around the track in 20 minutes and runs around the track in 15 minutes.
Let the speed of Dustin walking = x
We know that;
Speed = Distance / Time
For walking;
Speed = Distance / Time
x = Distance / (20/60)
x × 20/60 = Distance
Distance = x/3 miles
For run;
Speed = Distance / Time
⇒ x + 2 = (x/3) / (15/60)
⇒ 3 (x + 2) = 4x
⇒ 3x + 6 = 4x
⇒ 4x - 3x = 6
⇒ x = 6
Thus, Dustin walk at the rate of 6 miles per hour.
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Show that if f is analytic in a domain D and |f(z)|| is constant in D, then the function f(z) is constant in D
Because f is analytic variable in D, it is differentiable, and every place in D has a zero derivative. Therefore, f in D must be constant.
A function f must be differentiable in the domain D if it is analytic there. The derivative of f must therefore exist and be continuous in D. The derivative of f must be zero everywhere in D if the absolute value of f, |f(z)|, is constant in D since the derivative of an absolute value of a function is always zero. As a result, f must be constant in D since the derivative of f is zero everywhere in D. Due to the fact that the derivative of |f(z)| is always zero, this holds true regardless of the value of |f(z)|. As a result, the function f(z) is constant in the domain D if f is analytical in D and |f(z)| is constant in D.
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Find the equation of the line with z-intercept (-1,0) and y-intercept (0, -3).
y =
The line's equation is y = 3x - 3 with the z-intercept (-1, 0) and the y-intercept (0, -3).
What does "intercept" signify in mathematics?What do intercepts mean? The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.
Put x = 0 and work out y to determine the y-intercept. The purpose will be (0, y). Set y = 0 and solve for x to determine the x-intercept. The purpose will be (x, 0).
What does intercept form mean exactly?It gives both a slope and an intercept, hence the name "slope intercept form." Thus, this is your slope. You can move by keeping in mind that slope is rise over run.
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Jeff created the following shape to fill with skittles. He also wants to decorate the outside with Skittle wrappers. Find the surface area to determine the number of skittle wrappers he would need to save and volume to determine how the amount of Skittles he could fill it with
The Surface area of Figure is 496 ft².
The Volume of Figure is 608 ft³.
What is Surface area?A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.
Given:
Surface Area of Pyramid
= Base area + 1/2 x P x l
= 64 + 1/2 x 32 x 3
= 64 + 16 x 3
= 112 ft²
and, Volume of Pyramid
= 1/2 x 64 x 3
= 96 ft³
So, total Surface Area
= 112 + 384
= 496 ft²
and, The total volume
= 96 + 512
= 608 ft³
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Which of the following is the amount of revenue reported on the income statement of a retail company?
The cash collected from customers during the current period.
Both cash and credit sales for the period.
Cash sales for the period and collections from customers.
Cash sales and stockholders' investments.
Both cash and credit sales for the period are reported on the income statement of a retail company. So the correct statement is option (b) Both cash and credit sales for the period.
What is income statement?An income statement shows the income, expenses, and profitability of a company for a specified period. It is also sometimes referred to as the Income Statement (P&L) or Income Statement. it shows you:
Revenue from sales of products or services.
What does income statement tell you?An income statement shows how much revenue a company has generated, what expenses it has spent, and what income it has allocated over a period of time. You can use it to understand your company's business model and understand how your company is competitive within your industry.
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for a sample of categorical data, the____for a given category is the number of sample items in that category divided by the sample size.
The relative frequency or proportion of a given category is the number of sample items in that category divided by the total sample size.
The relative frequency or proportion of a given category is a measure of how often that category appears in a sample of categorical data. It is calculated by dividing the number of sample items in that category by the total sample size. For example, if a sample contains 10 items and three of them are in category A, then the relative frequency for category A is 3/10 or 0.3. This indicates that 30% of the sample items are in category A. Relative frequencies are used to compare categories within a sample, as well as to compare samples of different sizes. This allows us to draw conclusions about the frequency of occurrence of different categories within a population.
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