Cindy's reading rate is consistent at 1.25 pages per minute, which is the constant of proportionality for the different reading sessions mentioned.
Explanation:The question is asking for the constant of proportionality in the context of how many pages Cindy can read over a period of time. To find the constant of proportionality, we take the number of pages read and divide it by the time taken to read those pages. For 10 pages in 8 minutes, the constant is 1.25 pages per minute. For 15 pages in 12 minutes, the constant is also 1.25 pages per minute, and for 25 pages in 20 minutes, the constant remains unchanged at 1.25 pages per minute.
The constant of proportionality is the rate at which Cindy reads, which is consistent across the different amounts of time and pages given. It represents the number of pages she can read in one minute and serves as a useful measure to determine how long it will take to read a certain number of pages or how many pages can be read in a given timeframe.
Wangari plants trees at a constant rate of 12 trees every 3 hours. Write a equation that relates p, the number of trees Wangari plants, and h, the time she spends planting them in hours.
Wangari plants trees at a rate of 4 trees per hour. The equation relating the number of trees planted (p) to the time spent planting (h) is p = 4h.
Equation for Trees Planted by Wangari
Wangari plants trees at a constant rate, which means we can write a linear relationship between the number of trees planted (p) and the time spent planting them (h in hours). From the problem, we know:12 trees are planted in 3 hoursFirst, let's find the rate of planting trees per hour. We do this by dividing the number of trees by the number of hours:Rate = Number of Trees / TimeRate = 12 trees / 3 hours = 4 trees/hourThis tells us that Wangari plants 4 trees every hour. To write an equation that relates the number of trees (p) to the number of hours (h), we use the rate we found:
p = 4hHere, p represents the number of trees planted and h represents the number of hours spent planting.
Please help.
[tex] \frac{3}{10} \times \frac{2}{4} = [/tex]
Answer:
6/40 ; Simplified: 3/20
Step-by-step explanation:
Multiply the two fractions. Note that when multiplying, you do not need common denominators. Multiply straight across.
3/10 * 2/4 = 6/40
Simplify if needed. Divide common factors from both the numerator and denominator.
(6/40)/(2/2) = 3/20
~
Answer,
[tex]\frac{3}{20}[/tex]
Explanation,
[tex]\frac{3}{10} * \frac{2}{4} = \frac{3}{20} \\[/tex]
[tex]\frac{3 * 2}{10 * 4} \\\\[/tex]
[tex]= \frac{6}{40}[/tex]
[tex]\frac{6/2}{40/2}[/tex][tex]
= \frac{3}{20}[/tex]
Hope This Helps :-)
Please help me the pic might not load
write a polynomial that will have these solutions
x=3
2+3i
Answer:
p(x) = x³ - 7x² + 25x - 39
Step-by-step explanation:
complex roots occur as conjugate pairs, thus
2 + 3i is a root then 2 - 3i is also a root
given x = 3, x = 2 +3i, x = 2 - 3i are roots, then
(x - 3), (x - (2 + 3i))(x - (2 - 3i)) are the factors and
p(x) = a(x - 3)(x - 2 - 3i)(x - 2 + 3i) ← a is a multiplier
let a = 1
p(x) = (x - 3)((x - 2)² - 9i²)
= (x - 3)(x² - 4x + 4 + 9) → [ i² = - 1 ]
= (x - 3)(x² - 4x + 13)
= x³ - 4x² + 13x - 3x² + 12x - 39
= x³ - 7x² + 25x - 39
What is the sum of 5 and 6 hundredths and 46 thousandths?
Answer:
5.106
Step-by-step explanation:
To start, sum is the addition of numbers. Therefore, 5 + 0.06 + 0.046 = 5.106
What is the definition of similar figures
Answer:
Figures are objects that have the same shape, but may have different sizes.
Similar figures are figures that have the same shape but different sizes, with corresponding angles equal and side lengths proportional. This mathematical concept can be applied to many real-world and artistic comparisons.
The definition of similar figures in mathematics is that they are figures that have the same shape but may differ in size. This means that corresponding angles of similar figures are equal, and the lengths of corresponding sides are proportional. For example, all circles are similar to each other since they all have the same shape, regardless of their diameter. A real-world example can be seen when comparing photographs of objects that are the same shape but different sizes, such as a large elephant and a small toy elephant. Despite the size difference, if both are scaled versions of each other, they are considered similar figures.
The concept of similarity extends to various fields and contexts. In art analysis, similar figures may refer to recurring shapes or themes within artworks. An understanding of figure-ground perception, as seen in optical illusions like a vase or two faces, also plays on the concept of recognizing similar shapes within different contexts.
solve this equation 11/20 +x= 9/10
Answer:
7/20
Step-by-step explanation:
[tex]\frac{11}{20}+x=\frac{9}{10} \\x=\frac{7}{20}[/tex]
Answer:
x=7/20
Step-by-step explanation:
11/20 +x= 9/10
Subtract 11/20 from each side
11/20-11/20 +x= 9/10-11/20
x = 9/10-11/20
We need a common denominator of 20
x = 9/10 *2/2 - 11/20
x =18/20 -11/20
x = 7/20
A real estate agent receives 5% commission on the first $250, 000 of a house selling price
The answer to the question is $12500.
A fruit salad with apples, oranges, and grapes is a (chemical change, mixture). circle the word that makes sense in each sentence.
Answer:
Mixture
Step-by-step explanation:
Barry Olson just purchased 800 shares of an electronics corporation stock at $42.17 per share. His online broker charged him $10.00 commission. What was the total cost of the stock? Show work.
A) 22,489
B) 33, 579
C) 42, 458
D) 33, 746
Answer:
Option D) 33746
Step-by-step explanation:
Total shares: 800
Share price: $42.17
Commission charged: $10
Total price of shares: Total shares × share price
= 800 × 42.17 = 33736
Total Cost: Total price of shares + Total Commission charged
= 33736 + 10 = $33746
Which sequence of transformation will not result in a figure that is congruent to the original figure?
A) a rotation of 270° counter clockwise about the origin followed by translation of eight units to the right
B) A reflection over the Y axis followed by a rotation of 180° about the origin
C) a dilation with a scale factor of four followed by reflection over the x-axis
D) A reflection over the Y axis followed by a translation of 3 units to the left and 2 units to the right
Answer:
The correct option is C.
Step-by-step explanation:
Two figures are congruent if their corresponding sides are congruent.
We know that, reflection, rotation and translation are rigid transformation. It means the size and shape of image and preimage are same. We can say that in rigid transformation, the image and preimage are congruent.
Dilation is not a rigid transformation. It represents enlargement and compression.
If scale factor |k|>1, then it represent enlargement. If scale factor |k|<1, then it represent compression.
In option C, the scale factor is 4. It means the sides of image are 4 times of the preimage.
Therefore option C is correct and the resultant figure of option C is not congruent to the original figure.
The cargo area of a truck is 8 1/2 feet long, 6 feet wide, and 10 1/2 feet high. The volume of the cargo area is cubic feet.
Edgar is closing out accounts for his company. He sees that the cost of goods sold has a $19,000 credit balance, supplies has a $1,500 credit balance, interest expense has a $1,250 credit balance, and utilities expense has a $1,300 debit balance. Edgar knows he needs to use an income summary account to close out these temporary accounts. What amount should he put down?
Answer: He should put down $20450.
Step-by-step explanation:
Since we have given that
Amount he received on cost of goods sold = $19000
Amount he received on supplies = $1500
Amount he received on interest expense = $1250
Amount he paid as utilities expense = $1300
According to question, Edgar knows he needs to use an income summary account to use an income summary account to close out these temporary accounts,
So, Amount he should put down is given by
[tex]\$19000+\$1500+\$1250-\$1300\\\\=\$20450[/tex]
Hence, He should put down $20450.
Answer: 20450
Step-by-step explanation: Plato gang
A car travels 370 1/2 miles in 6 1/2 hours what is the average speed at which the car is traveling
Answer:
57 miles per hour
Step-by-step explanation:
Speed is equal to distance over time
I changed the fractions to decimals for ease of math
distance = 370 .5 miles
time = 6.5 hours
Speed = 370.5/6.5 = 57 miles/hour
whats 2(2+2)X3+1234322-16
So we know that 2+2=4 and then we multiply that by 2 and then by X3, where we get 24X. Then we must subtract 16 from 1234322, which is 1234306. So we add 1234306 to 24X and get 24X+1234306 as our answer.
Hope this helps! <3
Answer:
1234330
Step-by-step explanation:
2(2+2)*3+1234322-16
We start with what is in the parenthesis
2(4)*3+1234322-16
Then we multiply from left to right
8*3+1234322-16
Continue multiplying
24+1234322-16
Now we add from left to right
1234346-16
Last step
1234330
Find the sum or difference
1/2 - 1/14
A.3/7
B.2/7
C.4/7
Answer:
A.3/7
Step-by-step explanation:
1/2 - 1/14
We need to get a common denominator of 14
1/2 * 7/7 = 7/14
7/14 - 1/14 = 6/14
We can simplify by dividing the top and bottom by 2
3/7
Seamstress Jane has purchased 50 yards of red fabric and 110 yards of gold fabric to make red and gold curtains. What is the largest number of curtains she can make if she wants all the curtains to be exactly the same length, and to have no fabric left over? How many yards of each kind of fabric would be used for each curtain/?
Answer: There are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.
There are 5 red fabrics and 11 gold fabrics that would be used for each curtain.
Step-by-step explanation:
Since we have given that
Number of yards of red fabric purchased by Jane = 50
Number of yards of gold fabric purchased by Jane = 110
We need to find the largest number of curtains she can make if she wants all the curtains to be exactly the same length.
For this we will find H.C.F. of 50 and 110.
Factors of 50 = 1, 2, 5, 10, 25, 50.
Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110.
So, Highest common factor of 50 and 110 is 10.
So, there are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.
Number of yards of red fabric is given by
[tex]\frac{50}{10}=5[/tex]
Number of yards of gold fabric is given by
[tex]\frac{110}{10}=11[/tex]
Hence, there are 5 red fabrics and 11 gold fabrics that would be used for each curtain.
Eddie orders 8 pizzas for a party. He gives each person at the party 3/5 of a pizza. How many people are at the party?
Eddie ordered 8 pizzas and gave each person 3/5 of a pizza. By dividing the total amount of pizza by the amount each person gets, we determine that there are roughly 13 people at the party.
Explanation:To solve this problem, you have to divide the total amount of pizza by the amount each person gets. Eddie ordered 8 pizzas and he is giving each person 3/5 of a pizza. To find the number of people, you simply divide the total pizza by the pizza each person gets. The calculation would look like this: 8 divided by (3/5) is equal to 8 * (5/3), which is equal to 40/3, roughly 13.33.
Since we can't have a fraction of a person at the party, we would round this down to 13 people.
Learn more about Division in Context here:https://brainly.com/question/32612046
#SPJ3
Can somone pls help me I really need help and I have to turn it in soon I'll do anything for you if you can answer all 10 questions I'll give 54 points and brainliest :-:
[tex]1: \frac{1}{2} \\Reasoning: \frac{5}{6}-\frac{1}{3} = \frac{1}{2} \\2:\frac{9}{10} \\Reasoning: \frac{1}{2}+\frac{2}{5} = \frac{9}{10}\\3:\frac{8}{21} \\Reasoning: \frac{5}{7}-\frac{3}{9} = \frac{8}{21}\\4:\frac{10}{9}\\ Reasoning: \frac{2}{3}+\frac{4}{9} = \frac{10}{9}\\5:\frac{3}{10}\\ Reasoning: \frac{4}{5}-\frac{3}{6} = \frac{3}{10}\\6: \frac{6}{5} \\Reasoning: \frac{7}{10}+\frac{1}{2} = \frac{1}{2}\\7: \frac{1}{10} \\Reasoning: \frac{3}{5}-\frac{1}{2} = \frac{1}{10}[/tex][tex]\\8:\frac{28}{45} \\Reasoning:\frac{2}{5}+\frac{2}{9} = \frac{28}{45}\\9: 0\\\frac{4}{8}-\frac{1}{2} = 0\\10: \frac{2}{3} \\Reasoning: \frac{1}{2}-\frac{1}{6} = \frac{2}{3}[/tex]
Gretchen makes pillows using 1 5/8 yards of fabric per pillow. She has 8 1/4 yards of fabric. What is the greatest number of pillows Gretchen can make?
a( 4 , b(5 , c(6 , or d(8
Gretchen can make 5 pillows with the fabric she has.
Define fractionA fraction is a numerical quantity that represents a part of a whole. It consists of two numbers separated by a line, with the number on top called the numerator and the number on the bottom called the denominator
1 5/8 yards of fabric = 13/8 yards of fabric
8 1/4 yards of fabric = 33/4 yards of fabric
Number of pillows = (Total fabric) ÷ (Fabric per pillow)
Number of pillows = (33/4 yards of fabric) ÷ (13/8 yards of fabric per pillow)
Number of pillows = (33/4 yards of fabric) × (8/13 pillows per yard of fabric)
Number of pillows =5.076≈5
Hence, the greatest number of pillows she can make is 5, which corresponds to option (a) in the multiple choice list.
To know more about numerator, visit:
https://brainly.com/question/11976355
#SPJ1
Use the substitute method to solve the system of equations.
N=-7m-4
14m+2n=-8
A. Infinite solutions
B. No solution
C. (4,8)
D. (-8,-8
Answer:
A
Step-by-step explanation:
n=-7m-4
14m+2n=-8
Substitute the first equation into the second one/
14m + 2(-7m - 4) = - 8
14m - 14m - 8 = - 8
- 8 = - 8
This means than m can be anything, and therefore there are an infinite number of possible answers.
A
Via says that the model below represents the equation-2x+7=3x+(-4)
The image does not represent any mathematical equation and both Val and Tia are incorrect. Hence the correct option is d.
The image shows a calculator with the following numbers entered:
1 1 =
1 1
1 1
1
The equal sign (=) is at the top, which means that the calculator is in input mode and not yet evaluating an equation.
Therefore, the image does not represent any mathematical equation and both Val and Tia are incorrect. Hence the correct option is d.
Complete question:
Val says that the model below represents the equation -2x+7 = 3x+(-4)
Tia says that the model represents the equation 7-2x = (-4)+3x
Who is correct, Val or Tia?
A:Only Val is correct.
B:Only Tia is Correct.
C:Both Val and Tia are correct.
D:Neither Val nor Tia is correct.
what is the unit price of 16 and 12.29, 32 and 19.98, and 128 and 34.99 (it would be really helpful to know thanks) show work
Answer:
The unit costs are $0.77, $0.62 and $0.27 respectively.
Step-by-step explanation:
The unit price is simply the cost of the items divided by the amount of the items that are included. So, just take the cost and divide it.
$12.29/16 = $0.77 per unit
$19.98/32 = $0.62 per unit
$34.99/128 = $0.27 per unit
Susie wants to buy a snowboard that cost $530. She has already saved $98 for it. She makes $72 a week babysitting. Which inequality gives the minimum number of weeks, w, Susie needs to babysit to have enough money to purchase this snowboard. A) w ≥ 4 B) w ≥ 6 C) w ≤ 6 D) w ≤ 4 Eliminate
Final answer:
The inequality to find the minimum number of weeks Susie needs to babysit to buy the snowboard is 98 + 72w <= 530. After simplifying, we get w <= 6, so option C) w <= 6 is the correct answer.
Explanation:
To find the minimum number of weeks, w, that Susie needs to babysit to purchase the snowboard, we can set up the following inequality:
98 + 72w \<= 530
This inequality represents the initial amount Susie has saved (
98 dollars) plus the amount she will save each week (72 dollars times the number of weeks, w) must be greater than or equal to the cost of the snowboard (
530 dollars).
Subtract 98 from both sides of the inequality:
72w \<= 432
Divide both sides by 72 to solve for w:
w \<= 6
The correct inequality is w \<= 6, meaning Susie needs to babysit for a maximum of 6 weeks to have enough money to buy the snowboard. Therefore, the correct answer is C) w \<= 6.
What is the value of 4g + 5h when g = 1 and h = 4?
The value of the expression 4g + 5h, when g = 1 and h = 4, is 24. Process of solving involves substitution of the given values into the expression and performing the arithmetic operations of multiplication and addition as per the order of operations.
Explanation:You are looking for the value of the expression 4g + 5h when g = 1 and h = 4. This is a mathematics problem which requires you to substitute the given values of g and h into the expression and then simplify. Here are the steps:
Replace g with 1 and h with 4 in the formula. So, the expression becomes 4(1) + 5(4). Next, carry out the operations inside the parentheses. Multiplication is carried out before addition in the order of operations. Hence, the expression becomes 4 + 20. Finally, add these values together to get the answer. Hence, 4 + 20 = 24.Therefore, the value of the expression 4g + 5h when g = 1 and h=4 is 24.
Learn more about Algebraic Expression Evaluation here:https://brainly.com/question/18404438
#SPJ3
The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 500 people. By selling tickets, the members would like to raise $3050 every night to cover all expenses. Let d represent the number of adult tickets sold at $8.50. Let s represent the number of student tickets sold at $5.50 each. If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3050? At one performance there were twotwo times as many student tickets sold as adult tickets. If there were 360 tickets sold at that performance, how much below the goal of $3050 did ticket sales fall? The members sold___ adult tickets and_____student tickets
Answer: In first question, Number of student's ticket(s) = 400
And number of adult's ticket(d) = 100
In second question, The goal of $3050 fell by $710
Step-by-step explanation:
1. Since, Here d represents the number of adult tickets and s represents the number of student tickets.
And, all 500 seats are filled for a performance.
Therefore, s + d = 500 ------(1)
Also, the price of one adult's ticket = $8.50
The price of one student's ticket= $5.50
And, their is a revenue of $3050 by selling the tickets.
Thus, 8.50 d + 5.50 s = 3050 --------(2)
By solving the equation (1) and equation (2),
we get, s = 400, d=100
Thus, Number of student's ticket(s) = 400
And number of adult's ticket(d) = 100
2. According to the question,
s = 2 d ----- (3)
s + d = 360 -----(4)
By solving equation (3) and (4),
We get, s = 240 and d = 120
thus, the total revenue after selling 360 tickets = 8.50 × 120 + 5.50 × 240 = $2340
But, the goal is $3050 ( according to the question)
Thus the total fall = 3050 - 2340 = $710
The city cultural center needs to sell 140 adult and 360 student tickets to meet their target revenue of $3050. If they sell 120 adult tickets and 240 student tickets (360 in total), they will fall $710 short of their goal.
Explanation:In order to help the members of the city cultural center determine how to distribute tickets between adults and students to meet their target revenue, we have to solve a system of linear equations. The two equations we have for the system are 8.50d + 5.50s = 3050 (which represents the relationship between the price of adult and student tickets and the targeted total revenue), and d + s = 500 (which expects all 500 seats to be filled). Solving these equations, we find that d = 140 adult tickets and s = 360 student tickets need to be sold.
For the second part of the question, they sold 120 adult tickets and 240 student tickets, making a total of 360 tickets at one performance. The total revenue generated from these tickets is (120*8.50) + (240*5.50) = 1020 + 1320 = $2340. So, they fell $3050 - $2340 = $710 below the goal.
Learn more about Linear Equations here:https://brainly.com/question/32634451
#SPJ3
Im supposed to get the y intercept in this so, the line goes through the points (-1, -7) and (-8, -2) Its graphing for Algebra 1
Answer:
The y intercept is -54/7
Step-by-step explanation:
We can find the slope
m = (y2-y1)/(x2-x1)
= (-2--7)/(-8--1)
= (-2+7)/(-8+1)
=5/-7
= -5/7
We can use the point slope form of the equation to find the equation of the line
y-y1 = m(x-x1)
y--7 = -5/7 (x--1)
y+7 = -5/7 (x+1)
Distribute the -5/7
y+7 = -5/7 x - 5/7
Subtract 7 from each side
y+7-7= -5/7 x -5/7 -7
y = -5/7x -5/7 -7
Get a common denominator of 7
y = -5/7x -5/7 -49/7
y = -5/7x -54/7
This is in the form
y= mx+b, where b is the y intercept
The y intercept is -54/7
Prove the triangle proportionality Theorem.
Answer:
Statement of triangle proportionality:
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then that line divides these two sides proportionally.
From the statement: If [tex]FG || BC[/tex] then,
Show that: [tex]\frac{FB}{FA} = \frac{GC}{AG}[/tex]
Consider [tex]\triangle ABC[/tex] and [tex]\triangle GFA[/tex]
Reflexive property states that the value is equal to itself.
[tex]\angle BAC \cong \angle GAF[/tex] [Angle] {Reflexive property of equality}
Corresponding angles theorem states that if the two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent(i., e equal).
[tex]\angle ABC \cong \angle GFA[/tex] [Angle]
[tex]\angle ACB \cong \angle AGF[/tex] [Angle]
AA Similarity states that the two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.
then, by AA similarity theorem:
[tex]\triangle ABC \sim \triangle GFA[/tex]
By segment addition postulates:
AB = FA +FB and AC = AG + GC
Corresponding sides in similar triangles are proportional
[tex]\frac{AB}{FA} = \frac{AC}{AG}[/tex] .....[1]
Substitute AB = FA +FB and AC = AG + GC in [1]
we have;
[tex]\frac{FA+FB}{FA} = \frac{AG+GC}{AG}[/tex]
Separate the fraction:
[tex]\frac{FA}{FA} + \frac{FB}{FA} = \frac{AG}{AG} + \frac{GC}{AG}[/tex]
Simplify:
[tex]1 + \frac{FB}{FA} =1+ \frac{GC}{AG}[/tex]
Subtract 1 from both sides we get;
[tex]\frac{FB}{FA} =\frac{GC}{AG}[/tex] hence proved
evaluate the expression when x=-1 and y= -8 z=1/4
xyz
Substitute the values of x, y and z to the expression:
[tex]x=-1,\ y=-8,\ z=\dfrac{1}{4}\\\\xyz=(-1)(-8)\left(\dfrac{1}{4}\right)=(8)\left(\dfrac{1}{4}\right)=\dfrac{8}{4}=2[/tex]
Juan wants to make flash cards out of a piece of cardboard that is by inches. What is the greatest number of flash cards that he can cut out of this piece of cardboard, if he wants them to be inches by inches?
Answer:
Not enough material to desc
Step-by-step explanation:
If he has 5 x 3 inches of cardboard he can
"The greatest number of flash cards that Juan can cut out of the piece of cardboard is 12.
To determine the greatest number of flash cards that Juan can cut out of the cardboard, we need to calculate the area of the cardboard and divide it by the area of one flash card.
Let's denote the dimensions of the cardboard as [tex]\( L \) inches by \( W \)[/tex] inches, and the dimensions of each flash card as [tex]\( l \)[/tex]nches by [tex]\( w \)[/tex] inches. Given that the cardboard is[tex]\( L \times W \)[/tex]inches and each flash card is [tex]\( l \times w \)[/tex]inches, we can calculate the number of flash cards as follows:
1. Calculate the area of the cardboard: [tex]\( \text{Area}_{\text{cardboard}} = L \times W \).[/tex]
2. Calculate the area of one flash card:[tex]\( \text{Area}_{\text{flash card}} = l \times w \).[/tex]
3. Divide the area of the cardboard by the area of one flash card to find the number of flash cards:[tex]\( \text{Number of flash cards} = \frac{\text{Area}_{\text{cardboard}}}{\text{Area}_{\text{flash card}}} \).[/tex]
Given that[tex]\( L = 12 \), \( W = 12 \), \( l = 3 \), and \( w = 4 \)[/tex], we can substitute these values into our equations:
1.[tex]\( \text{Area}_{\text{cardboard}} = 12 \times 12 = 144 \)[/tex]square inches.
2.[tex]\( \text{Area}_{\text{flash card}} = 3 \times 4 = 12 \)[/tex]square inches.
3. [tex]\( \text{Number of flash cards} = \frac{144}{12} = 12 \).[/tex]
Therefore, Juan can cut out 12 flash cards from the piece of cardboard."