Final answer:
The man originally had $99. We determined this by setting up an equation based on the remaining amount after spending and misplacing portions of his money, then we solved for the original total.
Explanation:
To solve for the original amount of money the man had, let's call that amount x. First, he spent two-thirds of his money, which is (2/3)x. The remainder is x - (2/3)x = (1/3)x. He then misplaced one-third of this remainder which is (1/3) of (1/3)x = (1/9)x. So the portion he was left with is (1/3)x - (1/9)x = (2/9)x.
Since we know the final amount left is $22, we can express this as an equation:
(2/9)x = $22To find x, we will divide both sides of the equation by (2/9):
x = $22 / (2/9)When dividing by a fraction, we multiply by its reciprocal which is (9/2):
x = $22 * (9/2)x = $99Therefore, the man originally had $99.
The student government snack shop sold 32 items this week
The completed table would look like this:
Snack Type Number Sold Percentage
Fruit Cup 6 18.75%
Veggie Sticks 6 18.75%
Chips 14 43.75%
Water 4 12.5%
Veggie Sticks:
Look at the "number of items sold" column for veggie sticks. It shows 6.
Divide the number of veggie sticks sold by the total number of snacks sold (32) and multiply by 100% to find the percentage.
(Number of veggie sticks) / (Total number of snacks) * 100%
= 6 / 32 * 100%
= 0.1875 * 100%
= 18.75% (round to two decimal places)
Chips:
Look at the "number of items sold" column for chips. It shows 14.
Follow the same steps as for veggie sticks:
(Number of chips) / (Total number of snacks) * 100%
= 14 / 32 * 100%
= 0.4375 * 100%
= 43.75% (round to two decimal places)
Water:
Look at the "number of items sold" column for water. It shows 4.
Follow the same steps as for veggie sticks and chips:
(Number of water bottles) / (Total number of snacks) * 100%
= 4 / 32 * 100%
= 0.125 * 100%
= 12.5% (round to two decimal places)
Therefore, the completed table would look like this:
Snack Type Number Sold Percentage
Fruit Cup 6 18.75%
Veggie Sticks 6 18.75%
Chips 14 43.75%
Water 4 12.5%
For complete question refer to image:
Ham costs $3.40 a pound. How much is 1.2 pounds
Answer:$5.1
Step-by-step explanation: so since theres the 1 in 1.2 we know we have $3.40 right?, yeah so, half of $3.40 is 1.7 so jus add $1.7 to $3.40 wich is $5.1
I need help with question 15 parts a b and c
Answer:
(a)
let m represents renting movie and c represents the total cost of buying a rental card.
As per the given statement: A video store charges $10 for a rental card plus $2 per movie.
⇒ c(m) = 2m + 10 ......[1]
which implies that this equation represents the slope intercept form(i.e y = ax+b) where 2 is the slope and a y-intercepts of 10.
(b)
Graph of the given equation:
c(m) = 2m + 10
you can see in the figure given below.
(c)
now, to find the cost of buying a rental card and renting 6 movies.
⇒ m = 6 [ as m represents renting movie]
Substitute this m =6 in equation [1];
c(6) = 2(6) + 10
c(6) = 12 + 10
c(6) = 22.
Therefore, the total cost of buying a rental card and renting 6 movies is, $22.
The coach has 3 positions to fill on his basketball team. There are 9 students who are interested in being on the team. How many combinations of the three positions can he choose for the team?
A: 94
B:84
C:27
D:12
Answer: Option 'c' is correct.
Step-by-step explanation:
Since we have given that
Number of students who are interested in being on the team = 9
Number of positions to fill on his basket ball team = 3
So, the combinations of the three positions he can choose for the team is given by
[tex]3\times 9=27[/tex]
Hence, Option 'c' is correct.
The coach can choose 84 different combinations of the three positions from 9 interested students for the basketball team.
The coach needs to choose 3 out of 9 students to fill the positions on his basketball team. This is a combination problem, and the number of ways to choose [tex]\( r \)[/tex] items from [tex]\( n \)[/tex] items is given by the combination formula:
[tex]\[ C(n, r) = \frac{n!}{r!(n-r)!} \][/tex]
Here, [tex]\( n = 9 \) (number of students) and \( r = 3 \)[/tex] (number of positions to fill).
[tex]\[ C(9, 3) = \frac{9!}{3!(9-3)!} \][/tex]
[tex]\[ C(9, 3) = \frac{9!}{3!6!} \][/tex]
[tex]\[ C(9, 3) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \][/tex]
[tex]\[ C(9, 3) = \frac{504}{6} \][/tex]
[tex]\[ C(9, 3) = 84 \][/tex]
So, the coach can choose from 84 different combinations for the team positions.
The correct answer is:
B: 84
You are planning a trip to the United States. The exchange rate is $1 = 78p Approximately how many dollars will you get if you change 160 pounds for dollars?
Answer: If the rate of change is $1 = 78p, then if you have 160p, how much dollars you will get?
(if p are penys)
100p = 1 pound
if $1 = 78p = 0.78 pound
→ 1 pound = $1/0.78 = $1.28
→ 160*1 pound = $160/0.78 = $205.13
So if you change 160 pounds, you will get 205 dollars and 13 cents.
The number of dollars when 160 pounds is exchanged will be 205.13.
You may multiply the pounds by the exchange rate to get how many dollars you will receive for 160 pounds if the exchange rate is $1 = 78p.
160 pounds multiplied by the 78p to the dollar conversion rate results in:
160 pounds multiplied by 100 pence equals 16,000 pence.
Since there are 100 pence in a pound, we divide the amount in pence by 100 to get dollars:
16,000 p divided by 78p is $205.13
Consequently, if you convert 160 pounds to dollars at the current exchange rate of $1 = 78p, you will get around 124.80 dollars in return.
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The rectangle below has an area of 15x^3y^415x 3 y 4 square meters and a length of 3x^2y3x 2 y meters.What is the width of the rectangle?
Answer:
The width of the rectangle is [tex]5xy^3[/tex].
Step-by-step explanation:
The area of a rectangle is the product of length and width of the rectangle.
[tex]A=length\times width[/tex]
It is given that the area of the rectangle is [tex]15x^3y^4[/tex] square meters and the length of the rectangle is [tex]3x^2y[/tex].
[tex]15x^3y^4=3x^2y\times width[/tex]
[tex]width=\frac{15x^3y^4}{3x^2y}[/tex]
[tex]width=\frac{3\times 5\times x^2\times xy^3\times y}{3x^2y}[/tex]
Cancel out common factors 3x²y.
[tex]width=5xy^3[/tex]
Therefore the width of the rectangle is [tex]5xy^3[/tex].
PLEASE HELP ME!!!
I will give brainlest answer!!!
URGENT.
Answer:
PLEASE GIVE BRAINLIEST
Step-by-step explanation:
30% + 25% =55%
55/100 = 11/20
Rates/ratio $1.00 for 5 apples
20 cents per apple
1/5=.20
On a map, 1 inch equals 7.2 miles. Two houses are 1.5 inches apart on the map. What is the actual distance between the houses
Answer:
10.8
Step-by-step explanation:
7.2 X 1.5 = 10.8
Assuming two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.
Actual distanceLet x represent the actual distance
Given:
1 inch = 7.2 miles
1.5 inch =? miles
Hence:
1/ 7.2 = 1.5/ x
x= 7.2×1.5
x=10.8 miles
Inconclusion assuming two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.
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Joan picks a random counter out of a bag 10 times, and she got a yellow counter 7 times. What is the experimental probability of picking a yellow?
Answer:
she has a 70 percent chance of getting a yellow one
Step-by-step explanation:
Answer:
7/10 is your answer.
Simplify the expression using the laws of exponents. (x^2/3y^1/3)^3
Answer:
X^2 y
Step-by-step explanation:
So now you can make this x^2 y because the ^3 cancels it out
Answer:
x^6/27y
Step-by-step explanation:
(x^2/3y^1/3)^3
x^2 ^3/ (3^3 y^1/3 ^3)
Using the power of power rule, when a power is raised to a power, we multiply the powers.
x^ (2*3)/ (3^3 y^(1/3*3))
x^6/(27 y^1)
x^6/27y
Estimate then record their products 3 × 46
Answer:
Estimate is 150 and actual product is 138.
Step-by-step explanation:
To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.
Given are the numbers 3 and 46.
We can round 46 ≈ 50.
So Estimation would be 3 x 46 ≈ 3 x 50
3 times 5 is 15 and we can add zeros after it.
So estimation is 3 x 46 ≈ 150.
Now actual product would be...
3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.
3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.
It means the actual product is 3 x 48 = 138.
which of the following is a valid exclusion for the algebraic fraction 8ab^2x/4a^2b-8ab^2
Answer:
a ≠ 2b
Step-by-step explanation:
The given expression is
[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}}[/tex]
[tex]=\frac{8ab^{2}x}{4ab(a-2b)}[/tex]
Simplifying it, we have
[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}} = \frac{bx}{a-2b}[/tex]
For the above fraction to exist, the denominator must not be equal to zero.
i.e, a-2b ≠ 0
=> a≠2b
∴ The algebraic fraction exists when a≠2b.
Answer:
A valid exclusion for the algebraic fraction is when a=2b
Step-by-step explanation:
You have:
[tex]8ab^2x/4a^2b-8ab^2[/tex]
First you must to simplify:
Taking out common factor 4ab
[tex]4ab(2bx)/4ab(a-2b)[/tex]
[tex]2bx/a-2b[/tex]
The fraction can be written only if the denominator is different to zero, then
a-2b[tex]\neq[/tex]0
the excluded values are where
a-2b=0
this expression is equal to 0 when a=2b
which equation describes the graph a) y=-2|x|-1 b) y=2|x|+1 c) y=-2|x|+1 d) y=2|x|-1
Answer:
D: y=2|x|-1
Step-by-step explanation:
We need to find the equation which describes the graph
The general form of equation for this graph is y=|x|
The graph opens upwards so its positive
We cannot choose option (a) and option (d) because it has -2
Lets check with option b and d
In the graph, the y values starts at -1. (0,-1) is the vertex.
Lets plug in (0,-1) and check with option b
y=2|x|+1
-1= 2|0|+1
-1=+1, its false.
Lets check with option (d)
y=2|x|-1
-1= 2|0|-1
-1=-1, its true
Option D is the answer
The circumference of a circle can be found using the formula C = 2pi r. Which is an equivalent equation solved for r?
Answer:
[tex]\frac{C}{2\pi } =r[/tex]
Step-by-step explanation:
Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. Since we need r, we will use the second formula for circumference.
We start by solving for r in the Circumference formula. using inverse operations. We divide both sides (as the inverse of multiply) by 2pi.
[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex].
Answer: C
Step-by-step explanation:
[tex]e = \frac{o + 4m + p}{6} [/tex]
find in terms of p
[tex]\dfrac{o+4m+p}{6}=e\qquad\text{multiply both sides by 6}\\\\o+4m+p=6e\qquad\text{subtract o and 4m from both sides}\\\\\boxed{p=6e-o-4m}[/tex]
at a concession stand 9 slices of pizza and 5 soft pretzels cost $33.25. If 4 slices of pizza and 6 soft pretzels cost $19.50. What is the cost of a soft pretzel?
Answer:
The cost of soft pretzel is $1.25
Step-by-step explanation:
Let $x be the price of one slice of pizza and $y be the price of one soft pretzel.
1. 9 slices of pizza cost $9x and 5 soft pretzels cost $5y. Together they cost $33.25, then
9x+5y=33.25.
2. 4 slices of pizza cost $4x and 6 soft pretzels cost $6y. Together they cost $19.50, then
4x+6y=19.50.
3. Solve the system of two equations:
[tex]\left\{\begin{array}{l}9x+5y=33.25\\4x+6y=19.50\end{array}\right..[/tex]
Multiplythe first equation by 4, the second equation by 9 and subtract them:
[tex]4(9x+5y)-9(4x+6y)=4\cdot 33.25-9\cdot 19.50,\\ \\36x+20y-35x-54y=133-175.5,\\ \\-34y=-42.5,\\ \\y=\$1.25.[/tex]
Then
[tex]4x+6\cdot 1.25=19.50,\\ \\4x=19.50-7.50,\\ \\4x=12,\\ \\x=\$3.[/tex]
Answer: Each soft pretzel cost $1.25
Step-by-step explanation:
Hi, we have to write an equation for each case:
9 x + 5 y = 33.25
4x +6 y = 19.50
Where x is the price of 1 slice of pizza, and y is the price of each soft pretzel.
Multiplying the first equation by 4, and the second equation by 9
36x +20y =133
36x +54y =175.5
And subtracting the first equation to the second equation
36x +54y =175.5
-
36x +20y =133
____________
34 y = 42.5
Solving for y
y =42.5/34
y = $1.25
Each soft pretzel cost $1.25
I need help on number 12,13,24
Answer:
12.=0.06
13. =-5.12
14. =0.5
Step-by-step explanation:
12. .1 + .2 -.3 x.4/.5
.1+.2 -.12/.5
.1+.2-.24
.3-.24=.06
13. 3.2^2
10.24-15.36=-5.12
14. 4.2 x5/6 /10 +3/20
3.5 / 10 + 3/20
0.35+3/20
7/20+3/20=10/20
0.5
Find the distance between points (3, 5) and (4, 6) to the nearest tenth.
A) 3.2
B) 2
C) 2.8
D) 1.4
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (3, 5) and (4, 6). Substitute:
[tex]d=\sqrt{(4-3)^2+(6-5)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt2\approx1.4[/tex]
Answer: D) 1.4The distance between the two points is 1.4.
Option D is the correct answer.
What is the distance between two points of a line?The distance between two points of a line is given as:
Distance = √(c - a)² + (d - b)²
We have,
To find the distance between the two points (3, 5) and (4, 6)
We can use the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given values, we get:
d = √((4 - 3)² + (6 - 5)²)
d = √(1² + 1²)
d = √2
To the nearest tenth, the distance is approximately 1.4.
Therefore,
The distance between the two points is 1.4.
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Simplify 3(2+q) + 15
Answer: 3(7+q)
Step-by-step explanation:
Answer:
The simplified form of [tex]3(2+q) + 15[/tex] is 3(7+q)
Step-by-step explanation:
Given: 3(2+q) + 15
Step 1: Multiply bracket with 3
[tex]=3\times (2+q)+15[/tex]
Step 2: Now combine like terms
[tex]=6+15+3q[/tex]
Step 3: Add the combined terms
[tex]=21+3q[/tex]
Step 4: taking 3 common :
[tex]=3(7+q)[/tex]
The simplified form of [tex]3(2+q) + 15[/tex] is 3(7+q)
Which expression represents “y less than 6”?
Answer:
6-y
Step-by-step explanation:
Six less than y means you take away y from six.
Hope this helps
Part A: What is Leslie’s number and why. Part B: what is the least number that can be made using each digit exactly once and explain why the value of the 4 is greater than the value of 6
Answer:
976 421; 124 679
Step-by-step explanation:
Part A. Largest number
Leslie's number was 976 421.
This is because the largest numbers are in the positions of largest value.
For example, 9 in the hundred thousands place, the next largest number in the ten thousands place, and so on.
===============
Part B. Smallest number
The smallest possible number is 124 679.
The value of the 4 is greater than the value of the 6 because the 4 is in the thousands place and the 6 is only in the hundreds place.
4000 > 600.
Ice is placed around a bowl of water to lower the temperature. The equation D=-7/5+ 22, shows the time, t , measured in minutes and temperature, D, measured in degrees Celsius. Which statement is correct?
Answer:
Before cooling begins, the temperature of the water is 22°C.
Step-by-step explanation:
I think this is right
Answer:
Before cooling begins, the temperature of the water is 22°
22
°
C
.
Step-by-step explanation:
According to the table listing average daily expenses for a tourist by country based on high and medium categories, Brazil has a range from $12.25 to $18.33, and Greece has a range from $9.48 to $16.55. Which of the two countries has the larger difference between categories?
Answer:
Greece had a larger difference ($7.07)
Step-by-step explanation:
Brazil -
18.33 - 12.25 = 6.08
Greece-
16.55 - 9.48 = 7.07
Answer:
Greece has the larger difference between categories
Step-by-step explanation:
Difference in categories of Brazil
[tex]= 18.33 - 12.25\\= 6.08\\[/tex]
Difference in categories of Greece
[tex]= 16.55 - 9.48\\= 7.07\\[/tex]
Thus, Greece has the larger difference between categories
How do I find the slope if a line when y=4x+5
Answer:
slope =4
Step-by-step explanation:
The slope intercept equation of a line is written in the form
y= mx+b
where m is the slope and b is the y intercept.
Since y =4x+5 is written is this form, we can see that 4 is the slope and 5 is the y intercept
Given: 1/3 x + y = 15. Which if the following are ordered pairs of this equation?
{(-3, 14), (0, 15), (3, 16)}
{(-3, 16), (0, 15), (3, 14)}
{(16, -3), (15, 0), (14, 3)}
Answer:
Option B - {(-3, 16), (0, 15), (3, 14)}
Step-by-step explanation:
Given : Equation [tex]\frac{1}{3}x+y=15[/tex].
To find : Which if the following are ordered pairs of this equation?
Solution :
Re-write the equation in linear equation format,
[tex]y=-\frac{1}{3}x+15[/tex]
Taking point, (-3,16)
We substitute x=-3,
[tex]y=-\frac{1}{3}(-3)+15[/tex]
[tex]y=1+15[/tex]
[tex]y=16[/tex]
It is true.
Taking point, (0,15)
We substitute x=0,
[tex]y=-\frac{1}{3}(0)+15[/tex]
[tex]y=0+15[/tex]
[tex]y=15[/tex]
It is true.
Taking point, (3,14)
We substitute x=3,
[tex]y=-\frac{1}{3}(3)+15[/tex]
[tex]y=-1+15[/tex]
[tex]y=14[/tex]
It is true.
Therefore, the ordered pairs are {(-3, 16), (0, 15), (3, 14)}.
So, option B is correct.
which values of a and b make the expression true (2xy)^4/4xy = 4x^a y^b
A. a=0,b = 0
B. a=3,b =3
C. a=4,b =4
D. a=5,b =5
Answer: (B) a=3, b=3
Step-by-step explanation:
[tex]\dfrac{(2xy)^4}{4xy}[/tex]
[tex]=\dfrac{2^4x^4y^4}{4xy}[/tex]
[tex]=\dfrac{16x^4y^4}{4xy}[/tex]
[tex]=4x^{4-1}y^{4-1}[/tex]
[tex]=4x^3y^3[/tex]
Answer:
b
Step-by-step explanation:
15. Aroon has 180 cat toys to pack in boxes. He packs 30 toys in each box. How many boxes does he need? Write an equation using the letter n to stand for the unknown factor. Explain how to find the unknown factor??
Answer:
n=6
Step-by-step explanation:
n= the amount of boxes he needs
so if he puts 30 toys in each box out of 180 you divide 180 by 30 and you get your answer.
so the amount of boxes he needs = 6
Final answer:
To find the number of boxes needed to pack 180 cat toys with 30 toys in each box, divide the total number of toys by the number of toys per box to get the answer of 6 boxes.
Explanation:
The number of boxes Aroon needs can be calculated by dividing the total number of cat toys by the number of toys packed in each box.
Let n represent the unknown factor, which is the number of boxes he needs.
The equation representing this situation is n = 180 ÷ 30.
Solving n = 6, Aroon needs 6 boxes to pack all 180 cat toys.
A store sells tiles in the shape of a parallelogram. The perimeter of each tile is 33 inches. One side of each tile is 2.5 inches longer than another side. What are the side lengths of the tile?
Answer: Two sides are 7in, and the two other sides are 9.5 in.
Step-by-step explanation:
Since there are two sides that will be longer than the other two, 2.5 will be subtracted twice:
33in -2.5in -2.5in = 28in
Since there are 4 sides, 28in is divided by 4:
28in/4 = 7in
To find the 2 larger sides, add 2.5 back to the side length:
7in +2.5in = 9.5in
Parallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. The length of the parallelogram tile of the shorter side is 7 in and the length of the longer side is 9.5 in.
Given Information-A store sells tiles in the shape of a parallelogram.
The perimeter of each tile is 33 inches.
One side of each tile is 2.5 inches longer than another side.
Perimeter of the ParallelogramParallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. As the opposite sides are equal in parallelogram thus the perimeter of the parallelogram is twice the sum of the two different sides.
Let l be the length of the shorter side. Thus longer side will be (2.5+l ).
Now the perimeter [tex]P[/tex] of the parallelogram tile can be given as,
[tex]P=2[l+(2.5+l)}[/tex]
[tex]33=4l+5[/tex]
[tex]4l=33-5[/tex]
[tex]l=\dfrac{28}{4}[/tex]
[tex]l=7[/tex]
Thus the length of the parallelogram tile of the shorter side is 7 in and the length of the longer side is 9.5 in.
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A rectangular coffee table has an area measure of 10x² + 13x - 3 square units. which of the following could represent the perimeter of the rectangle in terms of x?
To find the perimeter of a rectangle in terms of x, add up the length and width and multiply by 2.
Explanation:The perimeter of a rectangle can be found by adding up all four sides. In this case, the length and width of the rectangle are represented by the factors of the area measure:
10x² + 13x - 3 = (2x - 1)(5x + 3)
So the length is (2x - 1) and the width is (5x + 3). The perimeter can be calculated using the formula:
Perimeter = 2(length + width)
Substituting the values, the perimeter in terms of x is:
Perimeter = 2((2x - 1) + (5x + 3))
Simplifying further:
Perimeter = 2(7x + 2)
Perimeter = 14x + 4
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