Step-by-step explanation:
Give the slope between the points (-5,-2)(-2,-7)
slope = change in y / change in x
slope = (-2 - (-7)) / (-5 - (-2))
slope = ( -2 + 7) / ( -5 + 2)
slope = 5/-3
slope = -5/3 or -1.667
Suppose S is the set of integers that are multiples of 3, and T is the set of integers that are odd. Prove that |S| = |T| by constructing a bijection between S and T.
The bijection could be defined from the set of numbers and it is proved.
We can define a bijection f from S to T as follows: for any integer x in S, let f(x) = x + 1.
To show that f is a bijection, we need to prove that it is both injective and surjective.
To prove that f is injective, suppose f(x) = f(y) for some x, y in S. Then x + 1 = y + 1, which means x = y. Thus, f is injective.
To prove that f is surjective, let y be an arbitrary element of T. Since y is odd, we can write y = 2n + 1 for some integer n. Now consider the element x = 3n in S. We have f(x) = x + 1 = 3n + 1 = y, so f is surjective.
Therefore, f is a bijection from S to T, so |S| = |T|.
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suppose the exam instructions specify that at most one of questions 1 and 2 may be included among the nine. how many different choices of nine questions are there?
The number of different choices for nine questions is 384, when at most one of questions 1 and 2 may be included among the nine.
Given, the exam instructions specify that at most one of questions 1 and 2 may be included among the nine.
We have to find the number of different choices for nine questions.
Now, using the concept of Permutation and Combinations we get
There will be three cases,
Case 1 : we include question 1
Case 2 : we include question 2
Case 3 : we neither include question 1 nor question 2
Case 1 :
question 1 is included, so question 2 can not be included and remaining 7 questions have 2 choices.
Case 2 :
question 2 is included, so question 1 can not be included and remaining 7 questions have 2 choices.
Case 3 :
neither question 1 nor question 2 is included and also remaining 7 questions have 2 choices.
Total choices = 2^7 + 2^7 + 2^7
So, the number of different choices of nine questions are 384.
Hence, the number of different choices of nine questions are 384, when at most one of questions 1 and 2 may be included among the nine.
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In how many years will $ 1600 amount to $ 1852.20 at 5% per annum when compounded annually?
Answer:
3 years
Step-by-step explanation:
1600*[tex]1.05^{x}[/tex]=1852.20
1852.20/1600= [tex]1.05^{x}[/tex]
1.157625 = [tex]1.05^{x}[/tex]
[tex]log_{1.05} 1.157625= x[/tex]
x= 3
thus 3 years
Select the correct answer.
AC and BD are diagonals of quadrilateral ABCD is quadrilateral ABCD a parallelogram? Explain
D
с
OA. Yes, because the diagonals bisect each other
OB. Yes, because the sides are congruent.
OC. No, because the diagonals bisect each other.
OD. No, because the sides are congruent.
The given quadrilateral ABCD is a parallelogram because the diagonals bisect each other.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.
Given:
AC and BD are diagonals of quadrilateral ABCD.
From diagram we can see that the measure of AO and OC is same which is 4.
Also measure of BO and OD is same which is 6.
That is diagonals bisects each other.
Hence, the given quadrilateral ABCD is a parallelogram because the diagonals bisect each other.
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3) Find the value of FD. bited F 12 12 13x - 16 E 4x+11 D
The Length of FD = 26 cm
According to the given information
FE = FC = 12cm
As FE, FC both are radius of circle
The tangent segments to a circle from a external point are equal
Hence
CD = ED
13x - 16 = 4x + 11
13x - 4x = 11 + 16
9x = 27
x = 27/9
x = 3
CD = 13x - 16
= 13 × 3 - 16
= 23 cm
ED = 4x + 11
= 4 × 3 + 11
= 23 cm
In Triangle FED
FE is perpendicular to ED
According to Pythagoras Theorem
[tex]FD^{2}= FE^{2}+ED^{2}[/tex]
= [tex]12^{2}+ 23^{2}[/tex]
= 673
FD = 26 cm approx.
The Length of FD = 26 cm
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What is reciprocal of -4/1
Answer:
-1/4
Step-by-step explanation:
A reciprocal is simply defined as the inverse of a value or a number. So if we have a fraction of - 4/1 we can just flip the numerator and the denominator to get -1/4.
Find the area of a regular octagon with a side length of 17 meters and an apothem length of 21
meters. Round your answer to the nearest meter. Be sure to label the unit.
Answer:
Step-by-step explanation:
An octagon is a 2-dimensional shape with 8 sides and the area is the space within the 8 sides of the shape. To calculate the area of the octagon we can use the area of an isosceles triangle. We divide the area of the shape into eight equal isosceles triangles and calculate it accordingly. A regular octagon has the length of the sides equal and the angles between these sides are equal. The measure of each interior angle is 135° and the exterior angles measure 45° each.
Area of Octagon Formula
The formula used to calculate the area of an octagon is:
2s2(1+√2), where s is the length of the side of the octagon.
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
c(x) = 5.50 + 20.50x
c(x) = 5.50x + 20.50
c(x) = 5.50 + 21.60x
c(x) = 5.50x + 21.60
Answer:
c(x) = 5.50 + 21.60x
Step-by-step explanation:
To start, we are told that the service fee of 5.50 is added to the set price per ticket. So we can automatically eliminate B and D
Now, to find how much it costs per ticket, we have to divide 108.00 by 5 since we are told that it costs $108 to buy 5 tickets
108.00/5 = 21.60
This means that it costs $21.60 per baseball ticket
So the third answer choice is correct
How do you calculate modus?
Modus is a statistical measure that is used to identify the most frequently occurring number in a set of numbers.
To calculate modus, first arrange the numbers in numerical order. Then count the number of times each number occurs in the set. The number that occurs most often is the modus. To calculate modus, first list all the numbers in the set in numerical order. The number that appears most frequently is the modus. For example, if the set of numbers is [1, 2, 3, 3, 3, 4], the modus is 3 because it appears three times, which is more than any other number in the set.
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Amira just accepted a job at a new company where she will make an annual salary of $59000. Amira was told that for each year she stays with the company, she will be given a salary raise of $3500. How much would Amira make as a salary after 8 years working for the company? What would be her salary after t years?
Answer:
After 8 years working for the company, Amira would make a salary of $59000 + 8 * $3500 = $70500.
After t years working for the company, Amira would make a salary of $59000 + t * $3500.
Step-by-step explanation:
ovement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Solve for k, the constant of variation, in an inverse variation problem, where x = 3.3 and y = 24.
Ok = 79.2
Ok = .14
Ok=7.3
Ok = 20.7
Submit
Pass
The constant of proportionality in the inverse variation is 79.2
Constant of ProportionalityConstant of proportionality is defined as the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities:
Direct Variation Inverse Variation.This is often determined because of the formula used.
Given that the variation here is an inverse variation.
y ∝ 1/ x
y = k / x
k = y₁x₁ = y₂x₂ = y₃x₃
However, in this question, we can simply represent the constant of proportionality as
k = yx
Substituting the values given into the formula above;
k = 24 * 3.3
k = 79.2
The constant of proportionality is 79.2
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help please i need help
Simplify (−7b)(−16b).
112b
−112b
112b^2
−112b^2
Answer:
112b^2
Step-by-step explanation:
When you multiply two negative numbers, the outcome will always become positive.
7bx16b= 112b^2
Answer:
112b^2
Step-by-step explanation:
You are selling hats and mittens at a craft fair. You hope to have $240 in sales. Hats cost $10 and mittens cost $6. a) write an equation in standard form. b) Graph the equation using x- and y- incercepts. (Show your work)
a) The linear equation is given as follows: 10x + 6y = 240.
b) The graph of the linear function is given by the image shown at the end of the answer.
How to define the linear function?The first step is defining the linear function is identifying the variables, which are given as follows:
Variable x: number of hats purchased.Variable y: number of mittens purchased.You hope to have $240 in sales. Hats cost $10 and mittens cost $6, hence the equation is given as follows:
10x + 6y = 240.
The x-intercept is the point (x,0), hence:
10x = 240
x = 24.
The y-intercept is the point (0,y), hence:
6y = 240
y = 40.
Then the line is traced connecting the points (0,40) and (24,0), with only positive values, as they represent countable amounts.
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what is the solution to 12-3/4(8f-5/3+4f+2/3)?
Answer:
51/4 - 9f
Step-by-step explanation:
Answer:
12 3/4 -9f
Step-by-step explanation:
You want the simplified form of the expression 12-3/4(8f-5/3+4f+2/3).
SimplificationWe can simplify inside parentheses first. This consists of combining like terms.
= 12 -3/4((8+4)f +(-5/3+2/3)) = 12 -3/4(12f -1)
Then the distributive property is applied, and like terms are combined (again).
= 12 -9f +3/4
= 12 3/4 -9f
Solve the inequality and graph the solution. Just say the points (x, y).
1/2x < 6
No links or I will report. Please help.
The solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
The relationship between two values that are not equal is described by inequalities. Equal does not necessarily mean unequal. The "not equal symbol" is typically used to denote that two values are not equal.
Given:
1 / 2x < 6
x < 6 × 2
x < 12
Therefore, the solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.
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A contractor bought 7.6 to the power of 2 ft of sheet metal. she has used 2.3 to the power of 2 ft so far and has $159 worth of sheet metal remaining. The equation 7.6x-2.3x=159 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
what does the sheet metal cost per foot?
Answer:
Step-by-step explanation:
he bought 7.6 ft2 of sheet metal He used 2.3 ft2 7.6x−2.3x= $95.40 simplify 5.3x = $95.40 divide by 5.3 to get x by itself x = 18 so each sheet of metal costs $18.00 per square foot.
x-2/x-4+x-6/x-8=6 2/3
Answer:x=8.47
Step-by-step explanation:
HELP PLEASE
3. Julia makes apple juice for 3 people by adding 5 cans of water to 1 cans of frozen
concentrate. If Julia needs to make apple juice for 8 people, how many cans of frozen apple
juice concentrate does she need?
0 3
0 3 1/
04
041/
For making apple juice for 8 people she needs 2.67 cans of frozen concentration
What is Proportion?
A proportion is a component, share, or quantity compared to the total. A proportion is a comparison of two integers, each representing a piece of a larger whole.
Solution:
Since, Julia needs 1 can of frozen concentration for making apple juice for 3 people
We can say for 6 people she needs 2 cans
Similarly for 8 people she needs 8/3 cans = 2.67 cans
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() = 2^4 + 5^3 − 6^2 + 15 − 36
With All steps and work.
Please help me. I been working on this for 5 hours, and My brain can't even help me on one thing, and constant comments of WRONG WRONG WRONG just makes me feel so horrible doing this work.. Please help. any help will be appreciated. These two problems have me down to tears because I have no Idea what to do anymore. Please help.
Answer:
1. (2x-3)(x^2+3)(x+4)
2. (3x-1)(x+5)(4x^2+1)
Step-by-step explanation:
2x^4+5x^3-6x^2+15x-36
2x^4-3x^3+8x^3-12x^2+6x^2-6x+24-36
x^3(2x-3)+4x^2(2x-3)+3x(2x-3)+12(2x-3)
(2x-3)(x^3+4x^2+3x+12)
(2x-3)[x^2(x+4)+3(x+4)]
(2x-3)(x^2+3)(x+4)
12x^4+56x^3-17x^2+14-5
12x^4-4x^3+60x^3-20x^2+3x^2-x+15x-5
4x^3(3x-1)+20x^2(3x-1)+x(3x-1)+5(3x-1)
(3x-1)(4x^2+20x^2+x+5)
(3x-1)[4x^2(x+5)+x+5]
(3x-1)(x+5)(4x^2+1)
Number 15 is the question
The coordinate after reflection over y- axis is
A' ( 8 , 1),
B' (0 , -2)
C'( -3, 5)
What is Reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
Given:
A( -8, 1), B(0, -2) and C(3, 5).
As, The rule for a reflection over the y -axis is (x,y)→(−x,y) .
So, the coordinate after reflection is
A' ( 8 , 1),
B' (0 , -2)
C'( -3, 5)
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dr. holmes reported inferential statistics in the results section of her study to show the probability of future outcomes. in this study inferential statistics help psychologists obtain the goal of
This study inferential statistics help psychologists obtain the goal of Prediction.
What is prediction in statistics?
Predictions are frequently made using measurements. For instance, they can assist in making predictions about a 4-year-future old's height, which pupils are more likely to thrive in a certain academic programme, or which job candidates have the best chances of success.a prediction of what you believe the future will hold: Please don't expect me to predict anything about the meeting tomorrow.Rain is expected this afternoon, according to every local weather forecaster. She says she has the ability to foretell the future. The outcome of the election is difficult to foresee. Although it was widely believed that the store would fail, it has done extremely well. The forecast for sales is the same as last year.To know more about predictions check the below link:
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1. If you decide whether or not you want to see a new movie or television program on the basis of the "coming attractions" or television commercial previews, are you using a sampling technique? A scientific sampling technique?
2. Name some possible sampling frames for the following:
a. Electric contractors
b. Tennis players
c. Dog owners
d. Foreign-car owners
e. Wig and hair goods retailers
f. Minority-owned businesses
g. Men over six feet tall
Yes. The decision of watching a movie on television is a technique of sampling.
Given,
If you decide whether or not you want to see a new movie or television program on the basis of the "coming attractions" or television commercial previews.
We have to find that whether it is using a sampling technique here;
Here,
Yes, this is a sampling technique. This kind of sampling, meanwhile, is typically not of a scientific nature. Instead of being representative of those movies, the parts that are shown are typically the most entertaining. Although a subset of all potential television shows or movie scenes have been observed, they are not chosen at random to make up the sample.
That is,
Yes. The choice to watch a movie on television is a sampling technique.
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What is true about the angles in the diagram shown below? Triangle E F G is shown. Segment H K goes from side E F to side E G and forms triangle E H K. Angle E K H and angle E G F have right angle labels. Angle E is labeled x degrees. Angle F is labeled two x degrees. Enter the correct answers in the boxes.
Correct option is C and the angle D and F are complementary angles.
∠D+∠E+∠F=180⁰
....Angle sum property
∵∠E=90⁰
⇒∠D+∠F=180⁰
−90 ⁰
⇒∠D+∠F=90⁰
What is complementary angles?Complementary angles are defined with respect to the addition of two angles. If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.When two line segments or lines meet at a common point (called a vertex), at the point of intersection an angle is formed. When a ray is rotated about its endpoint, then the measure of its rotation in an anti-clockwise direction is the angle formed between its initial and final position.To learn more about supplementary angles refer to:
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total cost of
Task 2:
P3 Solve a practical engineering problem involving a geometric progression..
2) Car production in the first week of a new model was 150 cars. If production continues with
an increase of 1.75% per week find:
a) How many complete cars are produced in the 25th week
b) How many complete cars are produced in the first 6 months of production.
c) How many complete cars are produced in the next 6 months.
Considering the car production in Geometric progression (a) about 25th term is 7.00*10¹⁹ cars can be produced in the first 25th week. (b) in the first 6 months, there will be 7.1*10¹⁸ cars. ( c) production in the next 6 months would be 7.1*10¹⁸ cars too
How to determine total production?Geometric progression is the type of sequnce in which consecutive terms are gotten by the multiplication of a constant term known as the constant ratio.
the given parameyers are
a=150 cars
r=1.75%
r=1.75/100*150
r= 6.6
Nth term of GP is given as
Nth = [tex]ar^{n-1}[/tex]
a. The 25th term is given as
25th= [tex]150*6.6^{24}[/tex]
25th term is 7.00*10¹⁹
b. In a month, there are 4 weeks
in 6 months there are 4*6 = 24 weeks
524th term is 150*6.6²³
7.1*10¹⁸
c. In a month, there are 4 weeks
in 6 months there are 4*6 = 24 weeks
524th term is 150*6.6²³
7.1*10¹⁸
In conclusion there will be 7.00*10¹⁹ cars , 7.1*10¹⁸ cars and 7.1*10¹⁸ cars for options a, b, and c respectively
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Graph triangle ABC with vertices A(6,-2), B(8, -6), and C(4,-8) and its image after the following transformations. Give the coordinates of the final image.
A’(___,___)
B’(___,___)
C’(___,___)
Answer:
Step-by-step explanation:
When you rotate 270 degrees counterclockwise, (a,b) turns to (b,-a)
So,
A'(-2,-6)
B'(-6,-8)
C'(-8,-4)
:]
2. Latrina is planning to serve hors d'oeuvres at her wedding. She plans on offering
8 hors d'oeuvres for every 3 people. If she has 240 people RSVP to the wedding, how many hors
d'oeuvres will she serve? Set up a proportion to solve.
I KNOW:
PLAN AND WORK:
I NEED TO KNOW:
SOLUTION:
She will serve 640 hors d'oeuvres to 240 people.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total number of people = 240
Number of hors d'oeuvres per 3 people = 8
Number of hors d'oeuvres to serve 240 people.
= 8 x 240 ÷ 3
= 8 x 240/3
= 8 x 80
= 640
Thus,
The number of hors d'oeuvres to serve is 640
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an urn contains 5 green balls and 3 red balls . what is the probability that when two balls are selected at random with no replacement , both are green ? ( round to three decimal places)
By using probability, it can be calculated that
Probability that when two balls are selected at random with no replacement , both are green = 0.357
What is probability?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Number of green balls = 5
Number of red balls = 3
Total number of balls = 5 + 3 = 8
Probability that when two balls are selected at random with no replacement , both are green = [tex]\frac{5}{8} \times \frac{4}{7} = \frac{5}{14} = 0.357[/tex]
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identify the statistical test in which the mean difference between two groups are compared to a distribution of differences between means.
The statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups is independent-sample t test.
Given that,
We have to find the statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups.
We know that,
The independent Samples t take a look at analyzes the manner of two separate organizations to see if there's statistical guide that the populace imply values are statistically extensively distinctive. A parametric take a look at is the unbiased Samples t take a look at.
since, the two agencies are independent and we're checking if difference is good sized is independent-samples t test.
consequently, the statistical test that compares the distribution of imply differences between two companies to the imply difference among corporations is unbiased-pattern t check.
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A cylinder has height of 17 centimeters it volume 1921.68 cubic centimeters what is the radius cylinder
The radius of the cylinder is found to be 6 cm.
What is a right circular cylinder?A right circular cylinder is a three dimensional figure having its base and top as a circle and the height is perpendicular to circular base. The volume is given as V = πr²h.
Given that,
The height of the cylinder is 17 cm.
And, the volume is 1921.68 cm³.
Suppose the radius be r cm.
Substitute the corresponding values in the expression of volume V = πr²h as follows,
V = πr²h
=> 1921.68 = π × r² × 17
=> π × r² = 1921.68/17
=> r² = 1921.68/17π
=> r = 6
Hence, the radius of the cylinder is obtained as 6 cm.
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