Answer:
45/16 or 2 13/16, the maximum amount of sundaes that Anton can make with ice cream is 2.
Step-by-step explanation:
1 7/8=15/8
2/3x<=15/8
x<=(15/8)/(2/3)
x<=(15/8)(3/2)=45/16
On a certain hot summer's day, 643 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled
$1161.50. How many children and how many adults swam at the public pool that day?
249 children and 394 adults swam at the public pool.
Step-by-step explanation:
Number of people swam at pool = 643
Receipts = $1161.50
Cost for one child = $1.50
Cost for one adult = $2.00
Let,
x be the number of children
y be the number of adults
According to given statement;
x+y=643 Eqn 1
1.50x+2.00y = 1161.50 Eqn 2
Multiplying Eqn 1 by 2
[tex]2(x+y=643)\\2x+2y=1286\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](2x+2y)-(1.50x+2.00y)=1286-1161.50\\2x+2y-1.50x-2.00y=124.50\\0.5x=124.50[/tex]
Dividing both sides by 0.5
[tex]\frac{0.5x}{0.5}=\frac{124.50}{0.5}\\x=249[/tex]
Putting x=249 in Eqn 1
[tex]249+y=643\\y=643-249\\y=394[/tex]
249 children and 394 adults swam at the public pool.
Keywords: linear equation, subtraction
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A new car is listed at 27,000. A prospective buyer would incur initial expenses that consist of 4%. sales tax and a license fee of $36. what would the total amount in dollars of the incurred initial expenses be?
Answer:
$28,116
Step-by-step explanation:
27,000/100*104 = 28,080 + 36 = $28,116
Explain how you could convert 152 cups into gallons.
Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.
Step-by-step explanation:
[tex]5x - 15 + 130 = x - 2 [/tex]
Answer:
x=-117/4
Step-by-step explanation:
5x-15+130=x-2
5x-x+115=-2
4x+115=-2
4x=-2-115
4x=-117
x=-117/4
At one of the warehouse stores, paper towels cost $10.48 for a package of 8 rolls. What is the unit price?
Answer:
Unit price = $1.31/roll
Step-by-step explanation:
Divide total cost by number of units:
$10.48 / 8 rolls = $1.31/roll
The price of peaches at Al’s supermarket can be determined by the equation p=0.28n, where P is the price and n is the number of pounds of peaches what is the constant of proportionality
Answer:
k = 0.28
Step-by-step explanation:
The price of peaches at Al's supermarket can be determined by the equation P = 0.28n ........... (1)
where P is the price and n is the number of pounds of peaches.
Now, it is clear that the price of peaches is proportional to the number of pounds of peaches.
So, we can write,
P ∝ n
⇒ P = kn ............. (2) where k is the constant which we have to multiply to covert from proportionality to equation form.
Now, comparing equations (1) and (2) we get k = 0.28 which is the value of the constant of proportionality. (Answer)
Final answer:
The constant of proportionality in the equation p = 0.28n is 0.28, representing the price per pound of peaches at Al's supermarket.
Explanation:
The constant of proportionality in the equation p = 0.28n, where P is the price and n is the number of pounds of peaches, is 0.28. This constant represents the price per pound of peaches at Al's supermarket. When you want to compute the amount spent on peaches, you multiply the quantity (in pounds) by this constant of proportionality, which is the price per pound. As an example, if you have 10 pounds of peaches, the total cost would be calculated as 10 pounds × $0.28 per pound, resulting in a total of $2.80 for the peaches.
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.
What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?
Answer: C
Step-by-step explanation:
The answer is C because it says 360 and 300. If you do a problem solve for that one on a peace of paper I think it would be 16.7%
Answer:
Step-by-step explanation:
Change in number = number visited in 1st week - number visited in 2nd week
= 360-300 = 60
So percentage change in number= 60/360×100=16.67
Line 1 passes through the points -2,7 and 3,3. Line 2 passes through the points 5,1 and 9,1. Find the slope of each line. Which line has the greater slope?
Answer:
The slope of the given line 1 is -4/5.
The slope of the given line 2 is 0.
The line 2 has a greater slope then line 1.
Step-by-step explanation:
The slope of a line with points (x1,y1) and (x2,y2) is given as:
[tex]m = \frac{y_2- y_1}{x_2-x_1}[/tex]
Now, Here the, points of the line 1 are A (-2,7) and B (3,3)
So, here, the slope of line AB is [tex]m = \frac{3 -7}{3-(-2)} = \frac{-4}{3 +2} = \frac{-4}{5}[/tex]
Hence, the slope of the given line 1 is -4/5.
Now, Here the, points of the line 2 are P (5,1) and Q (9,1)
So, here, the slope of line PQ is [tex]m = \frac{1-1}{9-5} = \frac{0}{4} = 0[/tex]
Hence, the slope of the given line 2 is 0.
Now, as we can see 0 > ( -4 / 5)
So, the line 2 has a greater slope then line 1.
8 1/3 s for s = 4 1/2
Answer:
75/2 (or 37 1/2)
Step-by-step explanation:
Here we're multiplying 4 1/2 by 8 1/3.
Converting both numbers to improper fractions:
9/2 times 25/3, or
9 25
---- * ------
2 3
Reducing the fractions, we get:
3 25
---- * ------ = 75/2 (answer)
2 1
The value of the given expression is 36.
Use the concept of fraction defined as:
A fraction is part of a whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that,
[tex]s = 4\dfrac{1}{2}[/tex]
We have to calculate [tex]8\dfrac{1}{3} \test{s}[/tex]
Now convert both fractions into improper fractions,
[tex]4\dfrac{1}2} = \dfrac{8 + 1}{2}\\\\4\dfrac{1}{2} = \dfrac{9}{2}\\\\[/tex]
And [tex]8\dfrac{1}{3} = \dfrac{24}{3}[/tex]
Now we have,
s = 9/2
Therefore,
[tex]8\dfrac{1}{3}s = \dfrac{24}{3}s\\\\8\dfrac{1}{3}s = \dfrac{24}{3}\times\dfrac{9}{2}\\\\[/tex]
Simplifying we get,
[tex]8\dfrac{1}{3}s = 12 \times 3\\\\ 8\dfrac{1}{3}s = 36[/tex]
Hence the value of the expression is 36.
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Which of the following is the perimeter of a triangle with side lengths of 7 inches, 8 inches, and 13 inches?
15 inches
13 inches
28 inches
27 inches
Answer: 28 inches
Step-by-step explanation:
Side1 + side 2 + side 3 =
7 inches + 8 inches + 13 inches =
28 inches
what is slope of a line that passes through (1,4) (-2,6) awarding more points
Answer:
-2/3
Step-by-step explanation:
m=(6-4)/(-2-1)=2/-3=-2/3
Answer:
[tex]\large\boxed{m=-\dfrac{2}{3}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, 4) and (-2, 6).
Substitute:
[tex]m=\dfrac{6-4}{-2-1}=\dfrac{2}{-3}=-\dfrac{2}{3}}[/tex]
What is the constant of proportionality in the equation y=0.41x
Answer:
0.41
Step-by-step explanation:
formula; y = kx (where k is the constant variation)
the standard equation representing direct variation
y = 0.41 x is the equation to find the constant of proportionality
so, K = 0.41
Factor 3x2 - 18x + 27 completely.
Answer:
3(x - 3)²
Step-by-step explanation:
Given
3x² - 18x + 27 ← factor out 3 from each term
= 3(x² - 6x + 9)
= 3(x - 3)² ← in factored form
State under which condition the original and the simplified expressions are equivalent.
The expressions are equivalent if...
a) a≠0
b) a≠x
c) a≠-x
[tex]\frac{a^2}{ax-x^2} +\frac{x}{x-a}[/tex]
Answer:
a doesn't equal 0
Step-by-step explanation:
State under which condition the original and the simplified expressions are equivalent
Which choice is a factor of 62?
A.13
B.20
C.62
D.3
Answer:
C, the answer is 62.
Step-by-step explanation:
Well, 1 x 62 is 62 so that's the only factor of 62 out of all of them.
Write the decimal as a fraction or a mixed number in simplest form.
5.76
Answer:
Step-by-step explanation:
it is 145/25 which is reduced to 29/5
Answer:
5 19/25
Step-by-step explanation:
Prove that using: X ∩ (Y ∪ Z ) =(X∩Y) ∪ (Y ∩ Z )
Listing Method; or
Membership Table.
Given
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
X = {2, 5, 8, 9}
Y = {1, 4, 6, 7, 8}
Z = {5, 7, 9}
There should be a typo in the question: the correct formula would be
[tex]X\cap(Y\cup Z)=(X\cap Y)\cup (X\cap Z)[/tex]
Let's compute [tex]X\cap (Y\cup Z)[/tex] first. We have
[tex](Y\cup Z)=\{1, 4, 5, 6, 7, 8, 9\}[/tex]
If we intersect this set with X, we have
[tex]X\cap (Y\cup Z) = \{5, 8, 9\}[/tex]
So, that would be the left hand side. For the right hand side, we have
[tex]X\cap Y = \{8\},\quad X\cap Z = \{5,9\}[/tex]
And their union is again [tex]\{5,8,9\}[/tex]
Final answer:
The intersection of two sets can be proven using a membership table for the given sets X, Y, and Z.
Explanation:
The intersection of two sets, written as AnB, is a set consisting of all elements that are both in A and B. We can use a membership table to prove the following equation: X ∩ (Y ∪ Z) = (X ∩ Y) ∪ (Y ∩ Z).
Rachel has 8/12 of a fun of frosting. If she used 1/4 of it, how much was left?
Answer:
6/12
Step-by-step explanation:
A fourth of 8 is 2, so there would be 6/12 of the tub of frosting left.
Answer:
5/12
Step-by-step explanation:
8/12=2/3
2/3-1/4=8/12-3/12=5/12
Priya and Han are biking in the same direction on the same path.
Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after hours.
Priya started riding a half hour before Han. If Han has been riding for hours, how long has Priya been riding?
Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for hours.
Use your expressions to find when Han and Priya meet.
I copy the complete questions again to make them clearer:
Priya and Han are biking in the same direction on the same path.
a. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after [tex]t[/tex] hours.
b. Priya started riding a half hour before Han. If Han has been riding for [tex]t[/tex] hours, how long has Priya been riding?
c. Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for [tex]t[/tex] hours.
d. Use your expressions to find when Han and Priya meet.
Answer:
a) [tex]H=16t[/tex]b) [tex]t+0.5[/tex]c) [tex]P=12(t+0.5)[/tex]d) Han and Priya meet 1.5 hours after Han started riding.Explanation:
a. Since Han is riding at a constant speed of 16 miles per hour, the number of miles that he has gone is proportional to the number of hours, t, that he has been riding, the constant of variation is 16, and the expression for the number of miles he has gone is:
[tex]H=16\times t=16t[/tex]Where, H is the number of miles Han has gone, and t is the number of hours.
b. Since Priya started riding a half hour before Han, you have to add 1/2 or 0.5 to the time of Han, which is t, to express how long Priya has been riding:
[tex]t+0.5[/tex]c. Since, Priya is riding at a constant speed of 12 miles per hour, the number of miles that she has gone is proportional to the number of hours, t + 0.5, that she has been riding, the constant of variation is 12, and the expression for the number of miles she has gone is:
[tex]P=12\times (t+0.5)=12(t+0.5)[/tex]Where P is the number of miles Priya has gone, and t is the number of hours since Han is riding.
d. To find when Han and Priya meet, you just need to solve the sytem of equations, making H = P, which means that the number of miles that both Han and Priya rides is equal:
[tex]H=P\\ \\ 16t=12(t+0.5)\\ \\ 16t=12t+6\\ \\ 4t=6\\ \\ t=6/4=3/2=1.5[/tex]
Which means that they meet when it has passed 1.5 hours since Han started riding.
a store in Rogers's neighborhood sells boxes of pencils that have 6 pencils in each box. roger bought several boxes of pencils at the store. which could be the number of pencils he bought?
Answer:
Step-by-step explanation:
It could be 42 pencils
f the chance of rain for tomorrow is 30%, what is the chance that it will NOT rain?
A. 70%
B. 0%
C. 50%
D. 30%
Select EACH correct answer!
If there is a 30% chance of it raining, then that means there is a 70% chance of it not raining.
100%-30%=70%
Answer: 70%
Step-by-step explanation: In terms of probability, 100% is the maximum which means something is certain. There are some occasions where it can be higher than 100% like dealing with percent increase or decrease, but in this case, we're talking about 100%.
In this problem, we're given that the probability of rain for tomorrow is 30% and we're asked to find the probability that it will not rain.
Since 100% will be the maximum when dealing with probability, we will subtract the chance it will rain tomorrow which is 30% from 100%.
100% - 30% = 70%.
Therefore, the probability/chance it will not rain is 70% which means it's likely it will not rain.
A cookie recipe calls for 6 cups of flour
and 2 cups of sugar. What is the ratio of
the amount of sugar to the amount of
flour?
Answer:
1:3
Step-by-step explanation:
Sugar : Flour
2 : 6 (substitute the numbers of cups)
1 : 3 (simplify by reducing. divide both sides by 2)
The ratio is 1:3.
Answer:
1:3
Step-by-step explanation:
2:6[sugar is to flour]
1:3[to simplify divide both sides by two]
abraham lincoln declared thanksgiving a holiday in 1863 what is the prime factorization of 1863
3 x 3 x 3 x 3 x 23 = 1,863. It can also be written in exponential form as 3 to the power of four times 23.
Answer:
1863 = 3 · 3 · 3 · 3 · 23Step-by-step explanation:
[tex]\begin{array}{c|cc}1863&3\\621&3\\207&3\\69&3\\23&23\\1\end{array}[/tex]
What is the length of the side opposite angle B?
3 units
4 units
5 units
6 units
Answer:
B
Step-by-step explanation:
4 units is the answer. i got an 100% on the quiz
The triangle missing from the question has attached and the opposite side of angle B is 4 units.
What is a traingle?A triangle is a three sides lines geometry in which the sum of all angles is 180°.
Given that a triangle ABC and has sides as
AB = 4
BC = 3
AB = 5
It's clearly visible that the opposite side of angle B is AC which has length as 4 units.
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11. The distance from Mac's house to school
is 575 yards. Mac's goal is to walk to
school in 5 minutes. How many yards
does Mac need to walk each minute to
meet his goal?
Answer:
115 yards per minute
Step-by-step explanation:
575/5= 115
Answer:
115 yds per minute
The drawing will help
25 + 11/12b =47 please answer
Answer:
The answer is b = 1/24.
Step-by-step explanation:
Given:
25+11/12b=47.
Now, to solve the equation to get the value of b:
[tex]25+\frac{11}{12b}=47[/tex]
Subtracting both sides with 25 we get:
[tex]\frac{11}{12b}=22[/tex]
Multiplying both sides by 12b we get:
[tex]11=264b[/tex]
Dividing both sides by 264 we get:
[tex]\frac{1}{24}=b[/tex]
Therefore, the answer is b = 1/24.
A basketball arena can hold approximately 7,000 people. Fans bought 5,134 tickets before the game. About how many more seats are left to fill before the game.
To determine the number of seats left in the basketball arena, the number of tickets sold (5,134) is subtracted from the total arena capacity (7,000), resulting in 1,866 seats remaining available.
A basketball arena can hold approximately 7,000 people.
Fans bought 5,134 tickets before the game.
The number of seats left to fill before the game can be calculated by subtracting the tickets bought from the total arena capacity: 7,000 - 5,134 = 1,866 seats left to fill.
what is 3.1n - 1.1n =
There are 482 studemts in the school and there are two Grade 4 classes: Ms.Ashley's and Mr.Ben's classes. Mrs. Aheley's class had 15 boays and 6 girls. Mr Ben's class ahd 14 girls and 10 boys. In Ms. Ashley's class, 2/3 of the students wear glasses.
In Mr. Ben's class, 1/4 of the kids have others siblings in the school.
1. What fraction of the students in the school are in grade 4?
2. What fraction of the grade 4 students are boys?
3. What fraction of the grade 4 students are in Ms. Ashley's class?
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
Answer:
1. 45/482 of the students are in grade 4.
2. 5/9 of the students of the grade 4 are boys.
3. 7/15 of the grade 4 students are in Ms. Ashley's class
4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.
5. There are 14 students with glasses and 7 without glasses.
Step-by-step explanation:
1. Let's review the information given to us for solving the questions:
Number of students in the school = 482
Ms. Ashley's Grade 4 class = 21 students
Ms. Ashley's Grade 4 class boys = 15 students
Ms. Ashley's Grade 4 class girls = 6 students
Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students
Mr. Ben's Grade 4 class = 24 students
Mr. Ben's Grade 4 class boys = 10 students
Mr. Ben's Grade 4 class girls = 14 students
Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students
2. Let's answer all the questions:
1. What fraction of the students in the school are in grade 4?
(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school
21 + 24 / 482 = 45/482
2. What fraction of the grade 4 students are boys?
(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
15 + 10 / 21 + 24
25 / 45 = 5/9
3. What fraction of the grade 4 students are in Ms. Ashley's class?
Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
21 / 21 + 24
21 / 45 = 7/15
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class
24 - 6 / 24
18 / 24 = 3/4
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
There are 14 students with glasses and 7 without glasses.
33. Sarah has $200 in her bank account now. If she
deposits $10 weekly, which of the following formulas
will show her deposits (D) at the end of h weeks?
(1) D=200+ 10
in
(2) D = (200)(10n)
(3) D = 200 + 10
(4) D = 200 + 10
(5) D = 200n + 10
Answer:2
Step-by-step explanation:if she deposits 10 dollars every week she would be adding 10 dollars which means we have to multiply 10 by however many weeks she saves
Sarah's weekly deposits after h weeks can be calculated using the linear equation D = 200 + 10h. This equation includes her starting balance of $200 and adds $10 for each week.
Explanation:The subject of this question is Mathematics, specifically focusing on the concept of linear equations.
The correct formula to show Sarah's deposits at the end of h weeks would be (3) D = 200 + 10h. This formula works by establishing 200 as her starting amount (her current bank balance), and adding $10 for each week (h).
For instance, if h was 5 weeks, Sarah would have D = 200 + 10 * 5 = 200 + 50 = $250 in her bank account. This demonstrates how the formula allows you to calculate her weekly deposits effectively.
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