a) The conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home is of: 0.5714 = 57.14%.
b) There is a negative association between not attending college and living on their own.
How to obtain a relative frequency?The relative frequency of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For the conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home, in item a, the outcomes are given as follows:
Desired outcomes: 20% that plans to live at home and not attend college.Total outcomes: 35% that plan to live at home.Hence the relative frequency is of:
p = 0.2/0.35 = 0.5714 = 57.14%.
Among people who plan to live on their own, the relative frequency of people who plan to attend college is of:
0.55/0.65 = 0.846 = 84.6%.
Hence there is a negative association between not attending college and living on their own, as people who live on their own are significantly more likely to attend college then people who do not live on their own.
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Find the measures of the numbered angles.
Answer: <1=104 degrees, <2=76 degrees, <4=104 degrees, <5=104 degrees, <6= 76 degrees, <7= 76 degrees, <8= 104 degrees
Step-by-step explanation:
<76 & < 2 are vertical angles, which means they are congruent. <1 & <2 are supplements, meaning when you add them up they equal 180 degrees (180-76=104 degrees). <1 & <4 are vertical angles. Using the Alternating Exterior Angles Theorem (AIA), <2 & <7 are congurent. Using the same theorem, <1 & < 8 are congruent. <7 & <5 are supplements, and so is <8 & <6.
The sum of 2 numbers is 27. One half of the first number plus one third of the
second number is 11. Find the numbers.
Answer:
x = 12, y = 15
Step-by-step explanation:
x + y = 27
1 / 2 x + 1 / 3 y = 11
y = 27 - x
1 / 2 x + (27 - x) / 3 = 11
1 / 2 x + 9 - 1 / 3 x = 11
1 / 6 x = 2
x = 12
12 + y = 27
y = 15
you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card. let x
The constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.
Given:
you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card.
x = the number of afternoon tickets and y = the number of evening tickets.
6x ≤ 60
10y ≤ 60.
so
6x + 10 y = 60.
Therefore the constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.
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A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=2. 5x+3 represents the cost y of bowling x games. Interpret the parameters of the function.
The number that represents the shoe rental charge is $3 and the price per game is $2.5.
Given:
The function y=2.5x+3 represents the cost y of bowling x games.
y = 2.5x+3
In the equation the 2.5 represents additional fee.
For 1 game = 2.5*1 = 2.5
For 2 games = 2.5 * 2
= 5
3 is the flat fee for renting the shoes.
Therefore the number that represents the shoe rental charge is $3 and the price per game is $2.5.
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What value of x is in the solution set of the inequality 4x - 12 ≤ 16 + 8x?
O-10
997
-9
-8
O-7
Answer:
-7
Step-by-step explanation:
Given inequality:
[tex]4x - 12 \leq 16 + 8x[/tex]
Subtract 4x from both sides:
[tex]\implies 4x - 12-4x \leq 16 + 8x -4x[/tex]
[tex]\implies -12\leq 16+4x[/tex]
Subtract 16 from both sides:
[tex]\implies -12-16\leq 16+4x-16[/tex]
[tex]\implies -28\leq 4x[/tex]
[tex]\implies 4x \geq -28[/tex]
Divide both sides by 4:
[tex]\implies 4x \div 4 \geq -28 \div 4[/tex]
[tex]\implies x \geq -7[/tex]
This means that x is equal to or greater than -7.
Therefore, the value of x that is in the solution set of the inequality is -7 as -10, -9 and -8 are all less than -7.
Answer:
x ≥ -7
Step-by-step explanation:
Given inequation,
→ 4x - 12 ≤ 16 + 8x
Then the value of x will be,
→ 4x - 12 ≤ 16 + 8x
→ 4x - 8x ≤ 16 + 12
→ -4x ≤ 28
→ x ≥ 28/-4
→ [ x ≥ -7 ]
Hence, the value of x is -7.
You go out to dinner and tip the waiter 21%. If your bill was $86.20, then what was your bill after
tipping 21%? Round to the nearest hundredth.
Answer:
The bill after tipping 21 percent would be $104.30.
Step-by-step explanation:
$86.20 x 0.21 = $18.102
$86.20 + $18.102 = $104.302
$104.302 ≈ 104.30
Hope my answer helped! Have a great afternoon.
9/g +2h +5 when g=3 and h=6
Answer:answer is 20
Step-by-step explanation:9/3=3 then add that to 2 times 6 which is 12+3=15 then 15+5+20
1. Use substitution to solve each system of equations
y = -2
y = 3x - 20
Answer:
[tex]x=6, y=-2[/tex]
Step-by-step explanation:
[tex]-2=3x-20 \\ \\ 3x=18 \\ \\ x=6 \\ \\ \therefore x=6, y=-2[/tex]
Answer:
The answer is x = 6. If you want to solve the equation by inputting the x and y value, then take the x value and input it into the equation as well as the y value.
Step-by-step explanation:
To solve this equation, plug in the value equal to y and solve for x. The first thing you have to do is make the equation -2 = 4x - 20, since we already have the value for y which is given in the question. Then add 20 to both sides of the equation. We now have 18 = 3x, divide both sides by 3 and you have your answer.
Hence, X = 6.
What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3? m
The y-coordinate of the point that divides the directed line segment from J to K into a ratio of is 5.
The coordinates of point that divides the line segment into m:n ratio can be obtained as follows,
Coordinates of point = [tex](\frac{mx_{2}+ nx_{1} }{m+n} \frac{my_{2}+ ny_{1}}{m+n} )[/tex]
The coordinate of point J is (-3,1)
The coordinate of point K is (-8,11)
Consider the point that divides the line segment into 2:3 ratio as P(x,y).
The coordinates of point that divides the line segment into 2:3 ratio can be calculated as follows,
[tex]Coordinates of P = (\frac{3(-3)+2(-8)}{2+3}, \frac{3(1)+2(11)}{2+3} )[/tex]
[tex]= (\frac{-9-16}{5}, \frac{3+22}{5} )\\\\= (\frac{-25}{5} \frac{25}{5} )[/tex]
= (-5,5)
Hence the answer is The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.
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PLEASE HELP ME!!
A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18
jerseys for a total of (18x-36) dollars. What can you conclude about the discount?
If the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.
According to the question,
We have the following information:
A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x-36) dollars.
Now, the original price of 18 jerseys will be 18x.
Now, when 36 is subtracted from 18x to find the total cost then it means that this is the discount from the original price.
Hence, if the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.
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answer the question in the screenshot please?
The value of x and y in the vector matrix are 2 and 5
What is a vector Matrix?If a matrix has only one row or only one column it is called a vector.
A matrix having only one row is called a row vector.
A matrix having only one column is called a column vector.
The matrix for two equations
3 - x/4 = 5/2 ---------------------1
8 - 12/4 = y ----------------------2
From equation 1,
collect like terms
x/4 = 3-5/2
x/4 = 1/2
cross multiply
2x = 4
x = 4/2
x = 2
From equation 2,
8 - 3 = y
y = 5
In conclusion, the value of x = 2 and the value of y = 5
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Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60\%60%60, percent of their plants are flowers and 40\%40%40, percent are vegetables. They have 505050 plants growing in the garden.
How many vegetable plants do they have?
If Emily's family loves to work together in the garden . The number of vegetable plants they have is :20.
How to determine the number of vegetable plants?Using this formula to determine the number of vegetable plants
Number of vegetable plants = Percentage of vegetable plants × Number of plants
Let plug in the formula
Number of vegetable plants = 40% × 50
Number of vegetable plants = 20
Therefore we can conclude that the number of vegetable plants is 20.
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The correct question is :
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60 percent of their plants are flowers and 40 percent are vegetables. They have 50 plants growing in the garden.
How many vegetable plants do they have?
Find the slope of the line shown of the graph to the right
The slope will be 1, for the right.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
m = (4-3)/(4-3)
m = 1
Hence the slope of the line is shown in the graph is 1.
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Project: Chef for a DayImagine you are the pastry chef at your favorite restaurant. The manager has just told you that you have a large crowd coming in for lunch tomorrow and you need to prepare. This project includes a recipe for chocolate chip cookies. You are expecting 60 people, but the recipe does not serve that many people, so you will need to adjust the ingredients so there will be enough.
Chocolate Chip Cookies (makes 12 servings)
1 ¼ cups all-purpose flour
½ teaspoon baking soda
¼ teaspoon salt
¾ cup sugar
1 egg
2 tablespoons milk
1 ¾ cup chocolate chips
Read each question below carefully and provide complete answers.
1. This recipe serves 12 people, but you need to serve 60 people. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?
2. Show the steps involved in finding out how much flour you will need to make 60 servings of chocolate chip cookies, as if you were teaching someone how to multiply with fractions. Please do not use decimals in your work or in your final answer.
3. Show the steps involved in finding out how much baking soda you will need to make 60 servings of chocolate chip cookies, as if you were teaching someone how to multiply with fractions. Please do not use decimals in your work or in your final answer.
4. Rewrite the rest of the chocolate chip cookie recipe for 60 servings. Be sure to show your work for each ingredient and express each amount as a fraction.
_____teaspoons salt
_____cups sugar
_____eggs
tablespoons milk
_____ cups chocolate chips
5. How many more eggs do you need for 60 servings than you need for 12 servings? How did you obtain this number?
6. If you wanted to make exactly 78 servings of chocolate chip cookies, what number would you need to multiply the original amount of each ingredient by to adjust the recipe? How did you determine this number?
7. Consider you make a mistake with the salt and multiply wrong which adds more salt then needed. Your cupcakes might not taste the greatest. Another mistake might be you incorrectly find the wrong amount to make. You make too little or not enough. What we do after the mistake is the important part. These mistakes are really not a big deal but in some instance in life we make bigger mistakes that weigh heavy on us. God is a loving and forgiving God. Isaiah 41:10 Fear not, for I am with you; be not dismayed, for I am your God; I will strengthen you, I will help you, I will uphold you with my righteous right hand.
Reflect on a time when you made a mistake. It can be a big mistake, a small mistake, or somewhere in between. Please don’t go into specifics but talk about how you handled the situation with God’s help and how you felt after. Please write a paragraph of at least 5 sentences.
NEED HELP FAST ITS A PROJECT!
The number needed to multiply the amount of each ingredient by to adjust the recipe is 5. It's determined by dividing the number of people that needs to be served by the number of people the provided ingredients will serve.
The steps involved in finding out how much all-purpose flour needed to make 60 servings of chocolate chip cookies is multiplying Quantity of flour provided by number needed to multiply each ingredients with.The steps involved in finding out how much baking soda needed to make 60 servings of chocolate chip cookies is multiplying Quantity of baking soda provided by number needed to multiply each ingredients with.Quantity of other ingredients needed expressed as a fraction:1 ¼ teaspoons salt
3 ¾ cups sugar
5 eggs
10 tablespoons milk
10 ½ cups chocolate chips
The number of eggs needed for 60 servings than 12 servings is 4 eggs. This is obtained by subtracting eggs needed for 12 servings from eggs needed for 60 servingsThe number needed to multiply the amount of each ingredient by to adjust the recipe to 78 servimgs is 6 ½. It's determined by dividing the number of people that needs to be served by the number of people the provided ingredients will serve.How to adjust given ingredients to the required number of servingsThe ingredients provided serves = 12 peopleNumber of people that needs to be served = 60 people1. Number needed to multiply the amount of each ingredient by to adjust the recipe = Number of people that needs to be served ÷ The ingredients provided serves
= 60/12
= 5
2. Steps involved in finding out how much flour you will need to make 60 servings of chocolate chip cookies.
Quantity of flour provided = 1 ¼ cups
Flour needed for 60 servings = Quantity of flour provided × number needed to multiply each ingredients with
= 1 ¼ × 5
= 5/4 × 5
= 25/4
= 6 ¼
3. Steps involved in finding out how much baking soda you will need to make 60 servings of chocolate chip cookies
baking soda needed for 60 servings = Quantity of baking soda provided × number needed to multiply each ingredients with
= ½ × 5
= 5/2
= 2 ½
4. Teaspoons salt = ¼ × 5 = 5/4 = 1 ¼
Cups sugar = ¾ × 5 = 15/4 = 3 ¾
Eggs = 1 × 5 = 5
tablespoons milk = 2 × 5 = 10
Cups chocolate chips = 1 ¾ × 6 = 7/4 × 6 = 42/4 = 10 ½
5. The number of eggs needed for 60 servings than 12 servings = eggs needed for 60 servings - ieggs needed for 60 servings
= 5 - 1
= 4
6. Number needed to multiply the amount of each ingredient by to adjust the recipe to 78 servings = Number of people that needs to be served ÷ The ingredients provided serves
= 78/12
= 6 ½
7. One time I made a mistake of keeping bad company, it really affected my studies because I lost concentration in school. My parents were disappointed in me but they helped me get back on the right track.
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[tex]\frac{2\sqrt{3 }-1 }{3\sqrt{3}+4 }[/tex]
A biologist uses a box-shaped fish trap that measures 1/4 meter by 2/3 meter by 3/5 meter. What is the volume of the trap in cubic meters?
Answer:
1/10 or 0.1 m^3
Step-by-step explanation:
V = 1/4 * 2/3 * 3/5 = 6/60 = 1/10 m^3 = 0.1 m^3
8: fatuma's frower Garden is a Squase. If the enlarge it by increasing the Width by 1 m the length by 3m the area will be 19 square meters morethan the Present area.
A,find the length of the side of original garden B,What is the width of the new garden?
C,what is the length of the new garden?
D,find the area of the new garden?
A. The length of the side of original garden is 4 m
B. The width of the new garden is 5m
C. The length of the new garden is 7m
D. The area of the new garden is 35 m²
Let the side of the garden = x m.
area = x² m²
From the question, we have
The new length is (x+3) m and the new width is (x+1) m.
Then the new area = (x+3)(x+1) m².
(x+3)(x+1)=x²+19
⇒ x²+3x+x+3=x²+19
⇒ 4x+3=19
⇒ 4x=19-3
⇒ 4x=16
⇒ x = 4 m
The length of the side of original garden is 4 m
new length = (x+3) m = (4+3)m = 7 m
new width = (x+1) = (4+1) = 5 m
new area = (x+3)(x+1) m² = 7*5 = 35 m²
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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I need to write an equation the Aline’s with the stars so that the purple ball will fall on to the line and hit all the stars
Answer:
y = - [tex]\frac{3}{4}[/tex] x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 12, 4 ) and (x₂, y₂ ) = (0, - 5 ) ← coordinates of 2 end stars
m = [tex]\frac{-5-4}{0-(-12)}[/tex] = [tex]\frac{-9}{0+12}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex]
the lowest star is on the y- axis at (0, - 5 ) ⇒ c = - 5
y = - [tex]\frac{3}{4}[/tex] x - 5
1. The floor of a building is 120 feet long
and 80 feet wide. A scale model of the
building has a length of 24 inches. What
is the width of the model?
Step-by-step explanation:
120 ft relate to 24 inches.
120/80 must be the same ratio as 24/model width.
120/80 = 3/2
so,
24/width = 3/2
48/width = 3
48 = 3width
width = 48/3 = 16 inches
Answer please with proofs and statements
Proved that ΔABC ≅ ΔDEC
SAS rule of congruent states that if two sides and one angle of the triangle is equal to the two sides and one angle of the another triangle, then the both triangles are congruent
The line BE and AD intersect at point C
The measure of the angle BCA = The measure of the angle ECD
The length of the side BC = The length of the side EC
The length of the side AC = The length of the side DC
Consider the triangle ABC and triangle DEC
Two sides and one angle of the triangle ABC is equal to the two sides and one angle of the triangle DEC, according to SAS rule of congruent the triangle ABC and triangle DEC are congruent
Hence, proved that ΔABC ≅ ΔDEC
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Convert 7/10 into a decimal
Please help me please
Answer:
x = 2
Step-by-step explanation:
The image shows a large rectangle with a similar, smaller triangle inside of it. The small leg on the small rectangle is 4, and the small leg on the large rectangle is 12. This tells me that the scale factor is 3.
If the scale factor is 3, then
[tex]6*3=6+6x[/tex]
Simplify
[tex]18=6+6x\\12=6x\\x=2\\[/tex]
The selling price of an item is $600. It is marked down by 10% , but this sale price is still marked up from the cost of $450. Find the markup from
cost to sale price.
$135 is markup price when cost is $450.
What is the cost price and an example?
Cost price, for instance, equals selling price plus profit ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ) Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)selling price of item = $600
cost = $450
10%×$650=$585
$585-$450=$135
$135 is markup price .
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What is the value of q in the solution to this system of equations?
2m - 5q = 8
4m + 2q = 64
Answer:
q = 4
Step-by-step explanation:
Step 1: Set up the equation
The system of equations can be solved algebraically by substitution or elimination.For substitution, solve one of the equations for m and plug it into the other equation in order to solve for q.For elimination, cancel the m terms in order to solve for q.Step 2: Solve for q
Substitution:2m - 5q = 84m + 2q = 644m = 64 - 2qm = [tex]\frac{64-2q}{2}[/tex]m = 16 - [tex]\frac{1}{2}[/tex]q2(16 - [tex]\frac{1}{2}[/tex]q) - 5q = 832 - q - 5q = 8-6q = -24q = 4Elimination:2m - 5q = 8 (multiply whole equation by -2 in order cancel m terms)4m + 2q = 64-2(2m - 5q = 8)-4m + 10q = -164m + 2q = 6412q = 48q = 4The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A.
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A it is true.
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A. A determinant of an n×n matrix can be defined as a sum of multiples of determinants of (n−1)×(n−1) sub matrices.
This is done by deleting the row and column which the elements belong and then finding the determinant by considering the remaining elements. Then find the co factor of the elements. It is done by multiplying the minor of the element with -1i+j. If Mij is the minor, then co factor, [tex]c_{ij}[/tex] [tex]= -1^{i+j}[/tex] + [tex]m_{ij}[/tex].
Each element in a square matrix has its own minor. The minor is the value of the determinant of the matrix that results from crossing out the row and column of the element .
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A television can be purchased cash for $1800 or on hire purchase for a deposit of 20% and 18 monthly payments of $90. If taken on hire purchase calculate:
A) the deposit
B) the hire purchase price
C) Hence, the amount saved if the television is bought for cash.
(a) 11³ x 11=11
11³
||³ + x = || 2
Step-by-step explanation:
I suspect you mean
11³ × 11 = ?
11³ ÷ 11 = ?
11³ × 11 = 11⁴
11³ ÷ 11 = 11²
why ?
11³ = 11×11×11
11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴
11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²
Find x and y please
10 points
The value of x is 15 and the value of y is 4 for the given triangle.
According to the question,
We have the following information:
We have a figure of triangle and a line parallel to the base is drawn. Some measurements of the sides are given.
Now, to find the values of x and y, we will use Basic Proportionality theorem which states that the ratio of the corresponding sides are equal.
For the larger triangle, we have:
12/y = 18/6
Using the cross multiplication method:
y = 12*6/18
y = 4
Now, using the same theorem for the smaller triangle:
12/y = x/5
12/4 = x/5
Using the cross multiplication method:
x = 15
Hence, the value of x is 15 and the value of y is 4 for the given triangle.
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Simplify the expression.
the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity
negative 48 over 28 times r minus 1
negative 3 over 14 times r plus negative 17
negative 3 over 14 times r minus 1
9 over 28 times r plus negative 17
The value of the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity is B. negative 3 over 14 times r plus negative 17
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Based on the information given, the expression will be:
= (-1/4r - 8 - 5/7r) - (-3/4r + 9)
Collect like terms
-1/4r - 5/7r + 3/4r - 8 - 9.
= - 3/14r - 17
In conclusion, the correct option is B.
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Answer:
Step-by-step explanation:
b
You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why ?
I will have to reject the offer of the rival company since it's lesser than $40560.
How to calculate the amountFrom the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:
= 40 × 19.50 × 52
= $40560
The rival company offers you an annual salary is $36000.
I'll reject the rival company's offer since it's lower.
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