Answer:
Original Price = $500
Step-by-step explanation:
The discount is 36%
and the discount amount is $180
Thus,
we can say that 180 is 36% of what number?
We let that number be "x" (original price). So we can say:
180 is 36% of x
In equation that will be:
180=36%*x
180=(36/100)*x
180=0.36x
So,
x = 180/0.36
x = $500
This is the original price.
What is the value of the expression below? (27^5/3) ^1/5
Answer:
The correct answer is 3.
Step-by-step explanation:
1. Let's resolve the expression below:
(27^5/3) ^1/5
( ∛ 27 ⁵ ) ^ 1/5 ⇒ ∛ 27 ⁵ = 27^5/3
( ∛ 3³ ⁵ ) ^ 1/5 ⇒ ∛ 3³ ⁵ = ∛ 27 ⁵
( 3 ⁵) ^ 1/5
⁵√ 3 ⁵ ⇒ ( 3 ⁵) ^ 1/5 = ⁵√ 3 ⁵
3
After making all the calculations and applying all the exponent rules, the final result is 3.
Answer:
B. 3
Step-by-step explanation:
A rectangular garden has a width of 90 feet. The perimeter of the garden is 500 feet. What is the length
Answer: 160ft.
Step-by-step explanation:
i need help
In a recent year, 17.7% of households watched the finals of popular reality series. There are 110.2 million households in the United States. How many households watched the finals?
195050400
hi, i am not giving an explanation because i am trying to get points. Please understand me
adam swam 1500m in 19 minutes. if swimming at a rate of 4.5km/h burns 600 calories, how many calories did adam burn
Adam burnt 631.6 calories approximately
Solution:Given that, Adam swam 1500m in 19 minutes.
If swimming at a rate of 4.5km/h burns 600 calories,
we have to find how many calories did adam burn?
Now, let us find his rate of swimming
Distance travelled = speed rate x time taken
[tex]\begin{array}{l}{1500 \mathrm{m}=\text { rate } \times 19 \text { minutes }} \\\\ {1500 \times 1 \mathrm{m}=\text { rate } \times 19 \times 1 \text { minute }}\end{array}[/tex]
We know that 1 hour = 60 minutes and also 1 kilometer = 1000 meter
[tex]\begin{array}{l}{1500 \times \frac{1}{1000} \mathrm{km}=\text { rate } \times 19 \times \frac{1}{60} \text { hour }} \\\\ {\frac{1500}{1000}=r a t e \times \frac{19}{60}} \\\\ {\text { Rate }=\frac{60}{19} \times \frac{3}{2}} \\\\ {\text { Rate }=\frac{30}{19} \times 3} \\\\ {\text { Rate }=\frac{90}{19}=4.736 \mathrm{km} / \mathrm{h}}\end{array}[/tex]
Now, we know that, swimming at a rate of 4.5km/h burns 600 calories,
Let "n" be the calories burnt when adam swam 1500 meter in 19 minutes
[tex]\begin{array}{l}{4.5 \mathrm{km} / \mathrm{h} \rightarrow 600 \text { calories }} \\\\ {\text {Then, } 4.736 \mathrm{km} / \mathrm{h} \rightarrow \text { n calories. }}\end{array}[/tex]
Now, by criss cross multiplication method,
[tex]\begin{array}{l}{4.5 \times n=4.736 \times 600} \\\\ {\rightarrow 4.5 n=2842.1052} \\\\ {\rightarrow n=631.578}\end{array}[/tex]
Hence, adam burnt 631.6 calories approximately.
Simplify the expression.
Answer:
[tex]-\frac{4z}{9}-3[/tex]
Step-by-step explanation:
Combine like terms, [tex]\frac{7}{9}z-\frac{6}{9}z-\frac{5} {9}z= -\frac{4z}{9}[/tex]
and 3-6= -3
The sum of John and Sally’s ages is 24. John is 6 years older than Sally. Which system of equations below represents this relationship and what are their ages? ASAP
J+S=24 and J=S+6 represents the relationship between ages.
John is 15 years old and Sally is 9 years old.
Step-by-step explanation:
Let,
John's age = J
Sally's age = S
According to given statement, the sum of their ages is 24;
[tex]J+S=24[/tex] Eqn 1
John is 6 years older than Sally means we will add 6 in Sally's age;
[tex]J=S+6[/tex] Eqn 2
Putting value of J from Eqn 2 in Eqn 1;
[tex](S+6)+S=24\\S+6+S=24\\2S=24-6\\2S=18[/tex]
Dividing both sides by 2
[tex]\frac{2S}{2}=\frac{18}{2}\\S=9[/tex]
Putting S=9 in Eqn 2
[tex]J=9+6\\J=15[/tex]
J+S=24 and J=S+6 represents the relationship between ages.
John is 15 years old and Sally is 9 years old.
Keywords: linear equation, substitution method
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It took Nora 10 hours to walk a 30 mile trail. How long did it take her to walk 9 miles at the same speed
Answer: 3 hours
Step-by-step explanation: 30 miles/10 hours=3 miles per hour. 9 miles/3 miles per hour= 3 hours.
Ashley had 5.6 pounds of fruit. She gave Aliyah 1.3
pounds of strawberries, Brendan 2.4 pounds of
grapes and Arley 1.2 pounds of bananas. How much
fruit does Ashley have left?
Answer:
0.7 pounds of fruit
Step-by-step explanation:
Step 1. Add all fruit Ashley has been given to Aliyah, Brendan and Arley
Find the sum of;
1.3 pounds for Aliyah
2.4 pounds for Berndan
1.2 pounds for Arley
4.9 pounds of fruits
Step 2. Subtract the total pounds given from the total pounds of fruit Ashley had.
5.6 pounds - 4.9 pounds = 0.7 pounds left
Answer; Ashley has 0.7 pounds of fruits left
A basketball team sells tickets that cost $10, $20 or for VIP seats $30. The team has sold 3239 tickets overall. It has sold 282 more $20 tickets than $10 tickets. The total sales are $63,720. How many tickets of each kind have been sold?
Answer:
The number of tickets that cost $ 10 is 923
The number of tickets that cost $ 20 is 1205
The number of tickets that cost $ 30 is 1111
Step-by-step explanation:
Given as :
The total number of three different tickets cost $ 10 , $ 20 and VIP seats $ 30
The total number of all tickets sold = 3239
The sale price for the tickets = $ 63720
Let The type of ticket for $ 10 = x
And The type of ticket for $ 20 = y
And The type of VIP ticket = v
According to question
The number of $ 20 tickets = The number of $ 10 tickets + 282
I.e y = x + 282
And x + y + v = 3239
Or, v = 3239 - ( x + y )
I.e v = 3239 - ( x + x +282 )
Or, v = 2957 - 2 x
Now ,
x × $ 10 + y × $ 20 = v × $ 30
Or, x × $ 10 + ( x + 282 ) × $ 20 = ( 2957 - 2 x ) × $ 30
or, 10 x + 20 x + 5640 = 88710 - 60 x
Or, 30 x + 60 x = 88710 - 5640
or, 90 x = 83070
∴ x = [tex]\frac{83070}{90}[/tex]
I.e x = 923
So, The number of tickets that cost $ 10 = x = 923
Similarly
y = x + 282
or, y = 923 + 282
I.e y = 1205
So, The number of tickets that cost $ 10 = y = 1205
And
v = 2957 - 2 x
∴ v = 2957 - 2 × 923
I.e v = 1111
So, The number of tickets that cost $ 30 = v = 1111
Hence
The number of tickets that cost $ 10 is 923
The number of tickets that cost $ 20 is 1205
The number of tickets that cost $ 30 is 1111
Answer
Answer:
1021 of the $10 tickets, 1303 of the $20 tickets and 915 of the $30 tickets.
Step-by-step explanation:
We have 3 types of tickets:
ones that cost $10, others that cost $20 and others that cost $30.
If A is the number of $10 tickets sold, B is the number of $20 tickets sold and C is the number of $30 tickets sold we have that:
A + B + C = 3239
B = A + 282
A*10 + B*20 + C*30 = 63720
We need to solve this system of equations.
From the second equation we have B isolated, we can replace it in the other equations:
A + (A + 282) + C = 3239
A*10 + (A + 282)*20 + C*30 = 63720
Now we can isolate one of the variables in the first equation and replace it in the second, lets isolate C.
C = 3239 - 2*A - 282 = 2957 - 2*A
the third equation is now:
A*10 + (A + 286)*20 + (2957 - 2*A)*30 = 63720
Now we solve it for A:
A*10 + A*20 - A*60 + 282*20 + 2957*30 = 63720
-A*30 + 94350 = 63720
A*30 = - 63720 + 94350 = 30630
A = 30639/30 = 1021
So they sold 1021 tickets of $10.
Now we can replace it in the equation:
C = 2957 - 2*A = 2957 - 2*1021 = 915
They sold 915 $30 tickets
They sold 1303 tickets of $20.
B = A + 282 = 1021 + 282 = 1303.
Simplify using the distributive property:
2a + 4(a+5) - 7
Answer:
6a + 13
Step-by-step explanation:
Given
2a + 4(a + 5) - 7 ← distribute parenthesis
= 2a + 4a + 20 - 7 ← collect like terms
= 6a + 13
Answer: 6a + 13
Step-by-step explanation: here you go: 2a + 4*(a+5) - 7
first we simplify the brackets (distributive property, you multiply 4 "a" times plus 5 times): 2a + 4a + 20 - 7
then you add those that multiply the variable separately from those that don't: 6a + 13
What is the perimeter of the figure?
A, 68 1/2 yd
B. 68 5/14 yd
C. 67 1/2 yd
D. 67 5/14 yd
Which expression is equivalent to 16d-64
Answer:
16(d-4)
Step-by-step explanation:
16d-64=16(d-4)
I NEED HELP ON THIS ASAP PLEASE I HAVE A TEST ON THIS TOMORROW
Ellie Mae has a jar that contains quarters and nickels. There are 15 more nickels than quarters. The total value is $2.55. How many nickels are in the jar?
There are 21 nickels in the jar
Step-by-step explanation:
Ellie Mae has a jar that contains quarters and nickels
There are 15 more nickels than quartersThe total value is $2.55We need to find the number of the nickles in the jar
Assume that the number of nickles is x
∵ There x nickles in the jar
∵ There are 15 more nickels than quarters
∴ The number of quarters = x - 15
∵ 1 nickle = 5 cents
∵ 1 quarter = 25 cents
∵ 1 dollar = 100 cents
∵ The total value is $2.55
- Change the total value to cents
∴ The total value = 2.55 × 100 = 255 cents
∵ 5 x + 25(x - 15) = 255
- Simplify it
∵ 5x + 25x - 375 = 255
- Add like terms
∴ 30x - 375 = 255
- Add 375 to both sides
∴ 30x = 630
- Divide both sides 30
∴ x = 21
There are 21 nickels in the jar
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Someone help me please
Answer: C
Step-by-step explanation:
5x+3y=13
+(-5x-12y=23)
---------------------
-9y=36
y=-4
To find x plug in y into any equation.
5x+3(-4)=13
5x=25
x=5
What is the 2010th letter in the following sequence: ABCDEDCBA.
Please answer ASAP. This is due tomorrow.
Answer:
B
Step-by-step explanation:
The sequence is ABCDEDCBABCDEDCBABCDEDCBA....
⇒The main sequence is the repitition of the sub-sequence ABCDEDCB
2010 when divided by 8 gives a quotient of 251 and a remainder of 2
251×8 = 2008
This means that after the sub-sequence ABCDEDCB is repeated for 251 times, it's last letter B is the [tex]2008^{th}[/tex] letter of the main sequence
Even after that, the sub-sequence ABCDEDCB keeps repeating and the [tex]2010^{th}[/tex] letter in the main sequence is the [tex]2^{nd}[/tex] letter of the sub-sequence ABCDEDCB, that is "B"
Final answer:
To find the 2010th letter in the repeating sequence ABCDEDCBA, divide 2010 by 9 and use the remainder to identify the letter's position in the pattern. The 2010th letter is C.
Explanation:
The sequence ABCDEDCBA consists of 9 letters. To find the 2010th letter in this pattern, we need to divide 2010 by the number of letters in the sequence. Dividing 2010 by 9 gives us 223 with a remainder of 7. This tells us that the 2010th letter is the same as the 7th letter of the sequence, because after every full repetition of 9 letters, the pattern starts over.
Let's map out the sequence: A(1), B(2), C(3), D(4), E(5), D(6), C(7), B(8), A(9). Using this mapping, the 7th letter corresponds to the letter C.
The 2010th letter in the sequence ABCDEDCBA is C.
A store is offering 25% off all shoes. Declan purchases shoes and clothes. The expression representing his total cost (including 8% tax) is c + (1 - 0.25)s + 0.08[c + (1 - 0.25s]. Which term represents the cost of the shoes after the discount
Answer:
39.5 = tax represents the cost of shoes after the discount
Step-by-step explanation:
c=(1- 0.25)+0.08 [c+(1-0.25s] +8% tax
c= cost
s=shoes
1- 0.25=0.75+0.08= $0.83
c=$0.83
[0.83+(1-0.25s]
1-0.25=0.75
0.83+0.75 =$1.58
x 25
___
39.5 = tax represents the cost of shoes after the discount
Correct me if i'm wrong :-D
Is 5 a solution to the equation 2x2 + 10 = 60?l
Answer:
14
Step-by-step explanation:
2x2=4
10+4= 14
Answer:Yes
Step-by-step explanation:5is the solution
Jacinta buys 4 pounds of turkey and 2 pounds of
ham. She pays a total of $30, and the turkey costs
$1.50 less per pound than the ham. What would
be the combined cost of 1 pound of turkey and 1
pound of ham?$6
The combined cost for 1 pound of turkey and 1 pound of ham is $10.5
Step-by-step explanation:
Let,
Turkey = x
Ham = y
According to given statement;
4x+2y=30 Eqn 1
x = y-1.50 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]4(y-1.50)+2y=30\\4y-6+2y=30\\6y=30+6\\6y=36[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{36}{6}\\y=6[/tex]
Putting y=6 in Eqn 2
[tex]x=6-1.50\\x=4.5[/tex]
1 turkey costs $4.5 and 1 ham costs $6.
Combined cost of 1 pound of turkey and ham each = 4.5+6=$10.5
The combined cost for 1 pound of turkey and 1 pound of ham is $10.5
Keywords: linear equations, subtraction
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347 students listed soccer as their favorite sport. This is 13 less
than three times the number of students who listed basketball.
Answer:
Step-by-step explanation:
347+13=360. 360 divided by 3 = 120 students signed up for basket ball
Using algebra, the number of students who listed basketball as their favorite sport is calculated to be 120, based on the information given that 347 students prefer soccer and that number is 13 less than three times the number of basketball fans.
Explanation:Calculating the Number of Basketball Fans
To find the number of students who listed basketball as their favorite sport, we can use algebra. Let's call the number of basketball students x. We know that 347 students listed soccer as their favorite sport, which is 13 less than three times the number of students who listed basketball. This information gives us the equation:
3x - 13 = 347
Adding 13 to both sides to isolate the term 3x on one side, we get:
3x = 360
Dividing both sides by 3 to solve for x, we get:
x = 120
Therefore, there are 120 students who listed basketball as their favorite sport.
A cell phone company mistakenly advertises that their data plan costs "0.02 cents" for every kilobyte of data
The cell phone company made a error in the conversion of cents to dollars in their advertisement. They advertised the cost as 0.02 cents/kilobyte, but they probably meant $0.02/kilobyte.
Explanation:The cell phone company is advertising their data plan costs at 0.02 cents per kilobyte but it seems like they may have meant $0.02/kilobyte which is different. Understanding the difference requires Mathematics concepts such as understanding of decimals and units conversion. If we take the advertised rate of 0.02 cents/kilobyte, it means for every 1 kilobyte of data, we will only be charged 0.0002 dollars. This is very cheap compared to charging $0.02/kilobyte. The error occurred because the company did not convert cents to dollars correctly, as $1 is equal to 100 cents, not 1 cent.
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What's 184 divided 9
Answer: 20.4444444 etc.
Step-by-step explanation:
Answer:
20.44
Step-by-step explanation:
184÷9= 20.44
How much water should be added to 6 gallons of pure acid in order to obtain the 24% acid solution?
HELP
Answer:
19 gallons
Step-by-step explanation:
Let x gallons be the amount of water which should be added to 6 gallons of pure acid in order to obtain the 24% acid solution.
Amount of water = x gallons
Amount of pure acid = 6 gallons
Amount of acid solution = x + 6 gallons
Amount of acid in acid solution = 24%
So, there are [tex]0.24(x+6)[/tex] gallons of acid in acid solution.
Hence,
[tex]0.24(x+6)=6[/tex]
Solve this equation. Multiply it by 100:
[tex]24(x+6)=600\\ \\24x+144=600\\ \\24x=600-144\\ \\24x=456\\ \\x=19\ gallons[/tex]
Answer:
19 gallons
Step-by-step explanation:
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if r + 9 = 42, does r + 9 - 9 = 42 + 9? Why or why not?
No, It is not true.
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ r + 9 = 42
⇒ r + 9 - 9 = 42 + 9
Now,
Since, The expression is,
⇒ r + 9 = 42
⇒ r + 9 - 9 = 42 + 9
It is not true, because if we subtract 9 then both side subtract as;
⇒ r + 9 - 9 = 42 - 9
⇒ r = 33
Thus, It is not true.
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Ace Hardware sells boxes of wrench (100) and hammers ($300). Howard ordered 40 boxes of wrenches and hammers for $8400. How many boxes of each are in the order?
Answer:
Howard's order will contain 15 boxes of hammers and 39 boxes of wrenches.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Price of box of wrenches = US$ 100
Price of box of hammers = US$ 300
Cost of the order = US$ 8,400
2. Let's find the exact amount of boxes of wrenches and hammers
Cost of the order = Price of box of wrenches * Number of boxes of wrenches + Price of box of hammers * Number of boxes of hammers
Replacing with the real values:
8,400 = 100 * 40 + 300 * Number of boxes of hammers
8,400 = 4,000 + 300 * Number of boxes of hammers
- 300 * Number of boxes of hammers = 4,000 - 8,400
- 300 * Number of boxes of hammers = -4,400
Number of boxes of hammers = -4,400/300 = 14.67 ≈ 15
For making a order without fractions or decimals of a box, it will contain just whole numbers, this way:
15 boxes of hammers + 39 boxes of wrenches
Cost of Howard's order = 15 * 300 + 39 * 100 = 4,500 + 3,900 = 8,400
Howard ordered 18 boxes of wrenches and 22 boxes of hammers. This solution was found by solving the system of equations derived from the total number of boxes and the total cost of the order.
Let's denote:
w as the number of boxes of wrenches Howard ordered.
h as the number of boxes of hammers Howard ordered.
Given:
1. Each box of wrenches costs $100.
2. Each box of hammers costs $300.
3. Howard ordered a total of 40 boxes.
4. The total cost of the order is $8400.
We can set up a system of equations based on the given information:
1. The total number of boxes ordered:
w + h = 40
2. The total cost of the order:
100w + 300h = 8400
Now, let's solve this system of equations.
We can use the first equation to express one of the variables in terms of the other:
h = 40 - w
Substitute this expression for h into the second equation:
100w + 300(40 - w) = 8400
Now, let's solve for w:
100w + 12000 - 300w = 8400
-200w = 8400 - 12000
-200w = -3600
w = 3600 ÷ 200
w = 18
Now, we can find h using the first equation:
h = 40 - w
= 40 - 18
= 22
So, Howard ordered 18 boxes of wrenches and 22 boxes of hammers.
14 points! Any help is appreciated... Thank you!
The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for each flower. The October price was a 20% increase in the September price.
Part A
What was the price of the flowers in September?
$__
Part B
The seventh-grade class earned 40% of the selling price of each flower.
In September, they sold 900 flowers.
In October, they sold 700 flowers.
Select a choice from each drop-down menu to make a true statement.
The seventh-grade class earned more money in (October/September)______ by (amount of money)_____
Answer:
The seventh-grade class earned more money in September by $36
Step-by-step explanation:
a)
The price of flowers in September was $1.50. In October, the price went up 20%
The increase in the price was 20*1.50/100=$0.30. So the new price is $1.80
$1.80
b) In September, the seventh-grade class sold 900 flowers for
900*1.50 = $1,350. They earned 40% of it, that is
40*1,350/100 = $540
In October they sold 700 flowers for
700*1.80 = $1260. They earned 40% of it
40*1260/100 = $504
The difference was $540-$504=$36
The seventh-grade class earned more money in September by $36
The roof of a high rise is in the shape of an isosceles triangle with a base of 89 feet. The perimeter of the roof is 281 feet. How long is each of the equal sides of the roof?
Answer:
96 ft
Step-by-step explanation:
Perimeter= a (base)+b (side)+c (side)
281 = 89 +b + c
281 -89 = b + c
192 = b+ c ( however in an iscoceles triangle, 2 sides aree equal therefore b and c will be equal)
So: 192/2 = 96
Answer:
Each of the equal sides of the roof is 96 ft long
Explanation:
Let the length of each of equal sides of given isosceles triangle be x, we know that perimeter of a triangle is equal to sum of sides of the triangle, we are given the base side to be equal to 89 feet and perimeter of the triangle equal to 281 feet.
so we can say that x + x + 89 =281 feet.
=> 2 x + 89 = 281 feet
=> 2 x = 192
=> x = 96
So, each of the equal sides is equal to 96 feet.
mr smith 6 hours earned 267. how much did he earn per hour
Answer: $44.50 per hour
Step-by-step explanation:
so easy
6hrs=$267
divide by 6 on both sides
1hr=$44.50
5. Mackenzie and Roger both leave the park at the same time walking in opposite
directions. Mackenzie walks 5 miles per hour, and Roger walks 6 miles per hour.
Which equation represents the distance d between them t hours after they have
left the park?
Answer:
d =11t
Step-by-step explanation:
Which best describes the strength of the model?
The table shows the number of calories in four meals and
the cost of each meal.
Cost of Meal and Number of Calories
Number of calories Cost of
in the meal the meal
550=$12
1,250=$11
780=$13
650=$10
A.a weak positive correlation
B.a strong positive correlation
C.a weak negative correlation
D.a strong negative correlation
Answer: Option C
Step-by-step explanation: A Positive correlation means that as one variable increases, also does the other variable.
In this case, if we put the data in order we have:
$10 ----- 650 calories
$11 ----- 1250 calores (here we have an increase)
$12 ----- 550 calories (here we have a decrease)
$13 ---- 780 calories (here we have an increase)
The correlation can be calculated with a calculator, and it yields to:
C = (∑(x-x')(y-y'))/√(∑(x-x')^2*∑(y-y')^2) = -0.12924
(where y' and x' are the means of the variables x and y)
So whe can see that the correltion is negative and close to zero, so this is a weak negative correlation.
Answer:
The answer is C. a weak negative correlation
on EDGE
Step-by-step explanation:
2022
Jayda is mixing pink paint by mixing 3.5 quarts of red paint with three-quarter cup of white paint how much red paint should be mixed with 6 cups of white paint to make her shade of pink?