Answer:
Step-by-step explanation:
In the equation y=kx+1, k is the slope and 1 is the y-intercept.
To find the slope, use the formula k=y2-y1/x2-x1. To use this formula, you need two points. The first point, point M, is given to you. The second point can be the y-intercept, point (0, 1). Now, apply the formula to find the slope: k=3-1/1-0
k=2/1
k=2
We now have the equation y=2x+1.
The next step is to graph the line.
First, graph the y-intercept. Should look something like this: (star represents point. the point is on (0, 1).)
|
|
*
------------------------------
|
|
Then, use the slope to find your second point: (the point is on (1, 3)).
| *
|
*
------------------------------
|
|
Draw a line through those two points and you have your answer!
find the slope of the line passing through each of the following pairs
(10,4), (2,-5)
Answer:
m = 9/8
Step-by-step explanation:
Slope formula:
m = (y2-y1)/(x2-x1)
Given:
(10,4), (2,-5)
Work:
m = (y2-y1)/(x2-x1)
m = (-5 - 4)/(2 - 10)
m = (-9)/(-8)
m = 9/8
8. Write a paragraph proof.
Proof Given: In a plane, a is perpendicular to b, b id perpendicular to c, and c || d.
Prove: a || d
To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.
Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.
Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.
By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.
Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.
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The table below represents a frequency distribution for the age (in years) of employees at a particular company.
Age (in years) Frequency
23-29
25
30-36
41
37-43
37
Use the table to answer the following questions.
Your answers should be exact numerical values
The class width used for the frequency distribution is
The class midpoint for the class 23-29 is
The class midpoint for the class 30-36 is
The class midpoint for the class 37-43 is
Check
The class width used for the frequency distribution is 6.
The class midpoint for the class 23-29 is 26.
The class midpoint for the class 30-36 is 33.
The class midpoint for the class 37-43 is 40.
To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:
23-29
30-36
37-43
For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:
Class width = 29 - 23 = 6
So, the class width for the frequency distribution is 6.
To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.
For the class 23-29:
Class midpoint = (23 + 29) / 2 = 52 / 2 = 26
For the class 30-36:
Class midpoint = (30 + 36) / 2 = 66 / 2 = 33
For the class 37-43:
Class midpoint = (37 + 43) / 2 = 80 / 2 = 40
So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.
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The retail price of a television set is $4,500. If the buyer pays by cash, the price is 10% below the retail price. If the set is bought on higher purchase, the buyer pays a down payment of $675 and 24 monthly installments of $212.50. Calculate for the television the:
cash price to the buyer, if he pays by cash.
amount payable.
outstanding balance.
hire purchase price.
interest.
difference between the hire purchase and the cash price.
percentage interest charged.
Cash price to the buyer, if he pays by cash:
The cash price would be 10% less than the retail price of $4,500:
Cash price = $4,500 - (10% * $4,500)
Cash price = $4,500 - $450
Cash price = $4,050
Amount payable:
If the buyer chooses to purchase the TV on higher purchase, the amount payable would be the sum of the down payment and the total amount of monthly installments:
Amount payable = Down payment + (24 * Monthly installment)
Amount payable = $675 + (24 * $212.50)
Amount payable = $5,175
Outstanding balance:
The outstanding balance would be the difference between the amount payable and the down payment:
Outstanding balance = Amount payable - Down payment
Outstanding balance = $5,175 - $675
Outstanding balance = $4,500
Hire purchase price:
The hire purchase price would be the sum of the down payment and the outstanding balance:
Hire purchase price = Down payment + Outstanding balance
Hire purchase price = $675 + $4,500
Hire purchase price = $5,175
Interest:
The interest charged on the hire purchase would be the difference between the hire purchase price and the cash price:
Interest = Hire purchase price - Cash price
Interest = $5,175 - $4,050
Interest = $1,125
Difference between the hire purchase and the cash price:
The difference between the hire purchase price and the cash price would be the interest charged:
Difference = Interest
Difference = $1,125
Percentage interest charged:
To calculate the percentage interest charged, we can divide the interest by the hire purchase price and multiply by 100:
Percentage interest charged = (Interest / Hire purchase price) * 100
Percentage interest charged = ($1,125 / $5,175) * 100
Percentage interest charged = 21.74%
Therefore, the cash price to the buyer is $4,050, the amount payable is $5,175, the outstanding balance is $4,500, the hire purchase price is $5,175, the interest charged is $1,125, the difference between the hire purchase and the cash price is $1,125, and the percentage interest charged is 21.74%.
What is the product of all the even integers from -6 to 8?
what is the distance between the tick marks on the number line?
A. 1/5
B. 1/4
C. 4
D. 5
Answer:
a 1/5
Step-by-step explanation:
Answer:
The answers A 1/5
Step-by-step explanation:
The FAA now figures the average checked bag to weigh 24 pounds. This is up from a previous figure of 10 pounds.
Find the amount of increase and the percent of increase, to the nearest whole percent.
Amount increase: — pounds
Percent of increase: — %
The amount increase is 14 pounds. Because if the previous is 10 pounds and the current is 24 pounds, all you have to do is subtract 10 from 24, which is 14.
The percent of increase is 140%. To find the percent of change, use this formula:
(new-old/2)(100)
So put in the numbers:
(24-10/10)(100)
(14/10)(100)
(1.4)(100)
140
Hope this helped!
Kyle and Linda are married with two children at home and a mortgage. Kyle's net pay per year is $32,000 and Linda's is $48,000. Their monthly expenses are $3,500.
Kyle and Linda each contribute 15% of their earnings to a retirement fund and they have $5,000 in savings. They also have a $100,000 life insurance policy on Kyle, but none on Linda.
As their financial advisor, what part of Kyle and Linda's financial plan would you encourage them to work on and why?
a.
Their plan for managing income.
Their net cash flow is negative.
b.
Their plan for managing their liquidity.
They are not prepared for emergencies.
c.
Their plan for retirement.
They don't contribute enough to meet their long term goals.
d.
Their plan for protecting their assets.
They should have life insurance on Linda.
Question: As their financial advisor, what part of Kyle and Linda's financial plan would you encourage them to work on and why?
ANSWER:
Their plan for protecting their assets.
They should have life insurance on Linda.
1000-(864%2+336%3+648%2)=
Answer:
959.72
Step-by-step explanation:
you have to simplify
Step-by-step explanation:
=1000-864%2-336%3-648%2
=1000-17.28-10.08-12.96
=-11123.36
The sum of the ages of two brothers Kofi and Kwaku is 35. Kofi age is 2/3 of Kwaku's age. find their ages.
2/3 of 35 is 23. Kofi is 23.
What is the simplified form of the following expression
What is the equation of the line that passes through the point (-6,8) and has a slope of -5/3? Please show step by step solution,
Answer:
The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We have the point (-6,8) and a slope of -5/3.
Step 1: Use the point-slope formula to find the equation of the line in point-slope form.
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point.
y - 8 = (-5/3)(x - (-6))
Simplify this equation:
y - 8 = (-5/3)(x + 6)
Step 2: Convert the equation to slope-intercept form.
Distribute (-5/3) to get:
y - 8 = (-5/3)x - 10
Add 8 to both sides:
y = (-5/3)x - 2
This is the equation of the line in slope-intercept form. Therefore, the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
There are 40 children watching a magic show. 24 of the children are boys, and 16 of the children are girls. The magician needs to select 4 children to help him with his show. What is the probability that all 4 helpers will be girls
Answer:
1.99%. (2% rounded)
Step-by-step explanation:
The total number of ways to select 4 children out of 40 is given by the combination formula:
C(40,4) = 40! / (4! * (40-4)!) = 91,390
The number of ways to select 4 girls out of 16 is given by the combination formula as well:
C(16,4) = 16! / (4! * (16-4)!) = 1,820
Therefore, the probability of selecting 4 girls out of the group of 40 children is:
P(4 girls) = C(16,4) / C(40,4) = 1,820 / 91,390 ≈ 0.0199 or 1.99%
So the probability that all 4 helpers will be girls is approximately 1.99%
Hope this helps!.
How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze?
Answer: 180 gallons needed
Step-by-step explanation:
Zykeith,
Assume x gallons of 50% antifreeze is needed
Final mixture is x + 60 gallons
Amount of antifreeze in mixture is 0.4*(x+60)
Amount of antifreeze added is .5x + .1*60 = .5x + 6
so .5x + 6 = .4(x + 60)
.5x -.4x = 24 -6
.1x = 18
x = 180
Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:
\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)
Simplifying the equation:
\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)
\(\qquad\quad\implies 0.1x = 21\)
\(\qquad\qquad\implies \bold{x = 210}\)
\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T′R′W′. Which ordered pair best represents the location of point R′?
An ordered pair which best represents the location of point R′ include the following: B. (−3n, −5n).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage (Triangle TRW) by using a scale factor of n centered at the origin as follows:
Ordered pair T (-3, 5) → Ordered pair T' (-3 × n, 5 × n) = Ordered pair T' (-3n, 5n).
Ordered pair R (-3, -5) → Ordered pair R' (-3 × n, -5 × n) = Ordered pair R' (-3n, -5n).
Ordered pair W (4, -5) → Ordered pair W' (4 × n, -5 × n) = Ordered pair W' (4n, -5n).
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Complete Question:
Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair best represents the location of point R′?
answer choices
(-3/n, -5/n)
(−3n, −5n)
(−3+n,−5+n)
(−3−n,−5−n)
Triangle EFG has coordinates E (0, 0), F (0, 2), and G (3, 0). If ΔEFG ≅ ΔXYZ, what is the measure of XY? 1.5 units 2 units 3 units 3.5 units
Answer:
2 units
Step-by-step explanation:
Since EFG and XYZ are congruent, we can write it like this:
E = X
F = Y
G = Z
Due to E and F being two units apart on the coordinate plane, we can conclude X and Y are also at a measurement of 2 units! Hope this helps!
Armando and Mikayla have a new grandson. How much money should they invest now so that he
will have $80,000 for his college education in 18 years? The money is invested at 8% compounded
annually
9514 1404 393
Answer:
$20,020
Step-by-step explanation:
The future value formula is helpful.
FV = P(1 +r)^t
$80,000 = P(1.08^18) = 3.9960195P
P = $80,000/3.9960195 = $20,019.92
They should invest about $20,020 now.
Choose the expression which represents the phrase, “the sum of 12 and a number H”
Answer:
the correct answer is option C
Answer:
Hello There!!
Step-by-step explanation:
The answer is c. 12+h as sum means adding 12 and then with h.
hope this helps,have a great day!!
~Pinky~
When families play “fill and dump” activities and explore large and small objects with the children, they extend learning in the
Number and Quantity strand.
Measurement and Comparison strand.
Geometry and Spatial Thinking strand.
Mathematical Reasoning strand.
Submit
The correct option is the Measurement and Comparison strand.
When families play "fill and dump" activities and explore large and small objects with children, they are likely extending learning in the Measurement and Comparison strand of the mathematics curriculum. This strand involves understanding and using concepts of size, weight, capacity, and length to compare, measure, and describe objects and events. Activities like filling and dumping containers of different sizes and comparing the quantities of objects can help children develop their understanding of these concepts and their ability to compare and measure objects.
The Number and Quantity strand involves understanding and using numbers and number concepts to count, compare, and describe quantities. The Geometry and Spatial Thinking strand involves understanding and using geometric concepts and spatial reasoning to describe, analyze, and compare shapes and spatial relationships. The Mathematical Reasoning strand involves using logical thinking and problem-solving skills to make sense of mathematical ideas and solve problems. All of these strands are important for children's overall mathematical development and can be supported through a variety of activities and experiences.
THE PROBLEM IS ON THE PHOTO
Answer:
its 24.2
Step-by-step explanation:
If the left-hand limit of is equal to the right-hand limit of as x approaches 10, the limit of as x approaches 10 is and the value of k is .
The limit of f(x) as x approaches 10 is 315 and The value of k is 250.
The function f(x) is a piecewise function, so we need to evaluate it separately for x < 10 and x >= 10.
\(f(x)= { \frac{(0.1x(2)+20x+15,x < 10)}{(0.25x(3)+k,x > 10)}\)
For x < 10, the function is equal to 0.1x^2 + 20x + 15. So the left-hand limit of f(x) as x approaches 10 is equal to 0.1(10)^2 + 20(10) + 15 = 315.
For x >= 10, the function is equal to 0.25x^3 + k. So the right-hand limit of f(x) as x approaches 10 is equal to 0.25(10)^3 + k = 250 + k.
Since the left-hand limit and the right-hand limit are equal, the limit of f(x) as x approaches 10 is also equal to 315, and the value of k is equal to 250.
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Angles A and B are supplementary angles. Angle A measures 72° and angle B measures (3x + 6)°.
Find x.
22
34
72
108
pls help
Answer: 180 degrees
Step-by-step explanation:
Quadrilateral ABCD is a square and the length of BD¯¯¯¯¯ is 10 cm.
What is the length of AE¯¯¯¯¯ ?
Enter your answer in the box.
the length of AE¯¯¯¯¯ =
cm
The length of AE¯¯¯¯¯ is 5√2 cm.
Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.
Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.
Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.
In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal (the hypotenuse) is the same as the side length, s.
Applying the Pythagorean theorem:
s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2
10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2
100 = 2 * AE¯¯¯¯¯^2
AE¯¯¯¯¯^2 = 50
Taking the square root of both sides:
AE¯¯¯¯¯ = √50
Simplifying the square root:
AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm
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Which of the following best describes the graph shown below?
-4
+3
-2
+1
5
-4
-3
-2
-V
1
2
3
4
+-1
-2
+-3
+-4
Answer:
2 & 4Step-by-step explanation:
ODYSSEY
Can someone please just help me with 1-3 I’ll mark brainliest it’s urgent?
Answer:
In the instruction above, it gives us some helpful information.
2 days with no professional sports game.
3 forms of ratio --> a to b, a : b, a / b
1) Remember there are 365 days in a year.
Days without games to Days in a year --> 2 to 365
Days without games : Days in a year --> 2 : 365
Days without games / Days in a year --> 2 / 365
2) Now there is a plot twist. It ask days with games. To find that we need to subtract 365 - 2 = 363 days with games.
Days with games to Days in a year --> 363 to 365
Days with games : Days in a year --> 363 : 365
Days with games / Days in a year --> 363 / 365
3) Days with games to Days without games --> 363 to 2
Days with games : Days without games --> 363 : 2
Days with games / Days without games --> 363 / 2
Hope this helps and sorry for not answering you. For some reason I was not getting any notification, but it is fixed now. Thank you :) !!
how many miles is 2 hours
Answer:
if you go 70 miles in one hour you will go 140 miles in 2 hours
Step-by-step explanation:
Answer:
You need to be traveling at a certain speed to determine how many miles you travel in 2 hours. For example, if you go 70 miles in 1 hour, then you'll go 140 miles in 2 hours, as long as your speed is constantly 70 mph.
Question 1
Kapoor Corporation uses the following activity rates from its activity-based costing to assign overhead costs to products.
Activity Cost Pools Activity Rate
Setting up batches $86.50 per batch
Assembling products $4.63 per assembly hour
Processing customer orders $52.16 per customer order
Data concerning two products appear below:
Product J00A Product S06U
Number of batches 34 43
Number of assembly hours 105 812
Number of customer orders 17 32
Required:
a. How much overhead cost would be assigned to Product J00A using the company's activity-based costing system?
b. How much overhead cost would be assigned to Product S06U using the company's activity-based costing system?
Overhead Cost:
There are some expenses incurred at the time of manufacturing of products and services that are not directly attributable to the finished products. These expenses are known as manufacturing overheads or indirect expenses.
The overhead cost would be assigned to Product J00A using the company's activity-based costing system is $4313.87.
How to calculate the cost?The overhead cost that would be assigned to Product J00A using the company's activity-based costing system will be:
= ($86.50 × 34) + ($4.63 × 105) + ($52.16 × 17)
= $2941 + $486.15 + $886.72
= $4313.87
The overhead cost would be assigned to Product S06U using the company's activity-based costing system will be:
= ($86.50 × 43) + ($4.63 × 812) + ($52.16 × 32)
= $3719.50 + $3759.56 + $1669.12
= $9148.18
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A math book cost $22.85 less than a physics book. The math book cost $83.75. How much did physics book cost?
Answer:
$106.60
Step-by-step explanation:
You have to add the cost of the math book which was $83.75 with $22.85 to get $106.06
3x+12y=-8 show ur work
Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.
17. You probably know the Fibonacci numbers 1,1,2,3,5,8,⋯ , where f n+2 =f n+1 +f n and we number as f 1 =1,f 2 =1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers? As a function or formula of n , how long does it take?
Applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers is GCD of that numbers .
Given :
You probably know the Fibonacci numbers 1 , 1 , 2 , 3 , 5 , 8 , ⋯ , where f n+2 = f n+1 + f n and we number as f 1 = 1,f 2 = 1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers .
Euclidean algorithm :
The Euclidean Algorithm is a technique for quickly finding the GCD of two integers .
GCD ( 1 , 2 )
2 = 1 * 2 + 0
GCD ( 1 , 0 )
hence GCD ( 1 , 2 ) is 1 .
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