Initially I had 48 tokens initially
Solution:Given that , For every 8 tokens you have your friend has 3
Then, let us assume that, we have 8n tokens. Then our friend will have 3n tokens
After you give half of your tokens to your friend Your friend now has 18 more tokens than you.
We have to find how many tokens did you start with
Now, after giving away half of tokens we will have 8n/2 = 4n tokens
And our friend will have 4n + 3n = 7n tokens.
And according to given information
Friends tokens – my tokens = 18 tokens
7n – 4n = 18
3n = 18
n = 6
Then, I will have initially 8n = 8 x 6 = 48 tokens.
Hence, I had 48 tokens initially
Nancy is taking inventory in the pharmacy to make sure there is enough eye medication in the pharmacy. She counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in stock. Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes. Calculate how many boxes of each Nancy needs to order.
Answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy.
Step-by-step explanation:
Nancy counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in the stock.
So, there is a need to order (15 - 10) = 5 boxes of travoprost.
Again, Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes.
So, there is a need to order (12 - 3) = 9 boxes of latanoprost.
Therefore, Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy. (Answer)
Final answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost to fulfill the pharmacy's minimal stock requirement.
Explanation:
Nancy needs to order more boxes of eye medication to meet the pharmacy's minimal stock levels. For travoprost, the pharmacy requires 15 boxes but currently has only 10 boxes. So, Nancy needs to order:
15 boxes (required amount) - 10 boxes (current amount) = 5 boxes of travoprost.
For latanoprost, the pharmacy needs 12 boxes, but only has 3 boxes in stock, meaning Nancy needs to order:
12 boxes (required amount) - 3 boxes (current amount) = 9 boxes of latanoprost.
Jack ran 150 miles a week.Joanna ran 39 mote times than Jack.How many miles did Joanna run?
Answer:
5850 miles
Step-by-step explanation:
150 X 39 = 5850
We multiple because it says Joanna ran 39 more TIMES than Jack.
Joanna ran 5850 miles.
A tv cost $450. During a special sale, its marked 1/3 off. What's the sale price of the tv
1/3 off means it is selling for 2/3 the original price.
Multiply the price by 2/3:
450 x 2/3 = (450 x 2) /3 = 900/3 = 300
The sale price is $300
Answer:
$300
Step-by-step explanation:
The TV's regular price is 450 dollars, and we are looking for the sale price after a third of it gets marked off.
We first need to find 1/3 of 450.
[tex]\frac{1}{3}* 450 = \frac{450}{3}=150[/tex]
One third of the original price is $150.
Now, we need to subtract 150 from 450.
[tex]450-150=300[/tex]
So, the sales price of the TV would be $300.
Hope this helps!
Sheldon needs to buy 8 gallons of coleslaw for a family reunions the table shows the prices for different size of two brands of coleslaw use the table for exercises 11 and 12
3) 8p + 7q= 43
2p-7=-q
I need to solve using substitution. thanks.
Answer:
p=1, q=5. (1, 5).
Step-by-step explanation:
8p+7q=43
2p-7=-q
------------------
q=-2p+7=7-2p
8p+7(7-2p)=43
8p+49-14p=43
8p-14p=43-49
-6p=-6
6p=6
p=6/6=1
2(1)-7=-q
2-7=-5=-q
q=5
SINGLE AND DOUBLE REPLACEMENT
ASSIGNMENT 4
Balance the equations below:
1. Al +_HCI- H2 + AICI:
Answer:
gl hf
Step-by-step explanation:
Supposed charity received a donation of $23.9 million. If this represents 54% of the charity donated funds what is the total amount of its donated funds? round your answer to the nearest million dollars.
Total amount of funds is $44.26 million.
Step-by-step explanation:
Given,
Donation received = $23.9 million
As it represents 54% of charity.
Let,
Total amount = x
Therefore,
54% of x = 23.9 million
[tex]\frac{54}{100}*x=23.9\\0.54x=23.9[/tex]
Dividing both sides by 0.54
[tex]\frac{0.54x}{0.54}=\frac{23.9}{0.54}\\x=\$44.26\ millions[/tex]
Total amount of funds is $44.26 million.
Keywords: percentage, division
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Given the equation square root of quantity 3x plus 6 end quantity equals 3, solve for x and identify if it is an extraneous solution. 1; solution is extraneous 1; solution is not extraneous 3; solution is extraneous 3; solution is not extraneous
Answer:
1; solution is not extraneous
Step-by-step explanation:
the value 3=3 is true, meaning its not extraneous and also I got it correct on the test
The value of x is 1, and the solution is not extraneous.
Given that,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
We have to determine,
The value of x and identify if it is an extraneous solution.
According to the question,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
To find the value of the x following all the steps given below.
Squaring both the sides to solve the equation,
[tex]\sqrt{3x+6 } = 3\\\\(\sqrt{3x + 6 })^2= 3^2\\\\3x + 6 = 9\\\\3x = 9-6\\\\3x = 3\\\\x = \dfrac{1}{1}\\\\x = 1[/tex]
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, The solution is not extraneous.
Hence, The value of x is 1, and the solution is not extraneous.
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Raffle tickets are sold and 6 prizes are available for the lucky draw. A total of 1,356 raffle tickets are sold for 4/5 dollars each and the 6 prizes cost 8 3/10 each. How much money was raise from the raffle tickets?
Answer:
US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Number of raffle tickets sold = 1,356
Cost of each raffle ticket = US$ 4/5
Number of prizes = 6
Cost of each prize = US$ 8 3/10
2. How much money was raised from the raffle tickets?
For easier calculation, let's convert the fraction numbers to decimal numbers:
Cost of each raffle ticket = US$ 4/5 = US$ 0.80
Cost of each prize = US$ 8 3/10 = US$ 8 + 0.30 = US$ 8.30
Now, we use this formula to calculate how much money was raised and the profits:
Profits = (Number of tickets sold * Cost of each ticket) - (Number of prizes * Cost of each prize)
Replacing with the real values, we have:
Profits = 1,356 * 0.80 - 6 * 8.30
Profits = 1,084.80 - 49.80
Profits = 1,035
US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.
Final answer:
The total amount of money raised from the sale of 1,356 raffle tickets, priced at 4/5 dollars each, is $1,084.8.
Explanation:
To determine how much money was raised from the raffle tickets, we first need to calculate the total cost of each ticket and then multiply it by the total number of tickets sold. The question states that each raffle ticket is sold for 4/5 dollars. Since a total of 1,356 raffle tickets were sold, the total amount raised can be calculated as follows:
Total amount raised = Price per ticket × Total number of tickets
= (4/5) × 1,356
= 1,084.8 dollars
Therefore, the total amount of money raised from the raffle tickets is $1,084.8.
14. Carla needs 1,600 beads to make
8 necklaces. She divides the beads
equally. How many beads does Carla use
for each necklace? What basic fact did
you use?
Answer:I don’t know
I thought you won’t grieve me he answer straight up
Step-by-step explanation:
QUICK!!! WILL GIVE BRAINLIEST!!!!
The table represents a linear function.
A two column table with six rows. The first row, x, has the entries negative 4, negative 2, negative 1, 1, 2. The second column, y, has the entries, negative 2, negative 10, negative 14, negative 22, negative 26.
What is the slope of the function?
–8
–4
2
5
Answer:
-4
Step-by-step explanation:
You can tell because every time the slope decreases by 5.
Answer:
-4
Step-by-step explanation:
Take the first two sets of points (-4,-2) and (-2,-10)
Then use the formula Y2 - Y1 / X2 - X1 to find the slope
-10 + 2 / -2 + 4 = -8/2 which can be reduced to -4
The graph of f(x) = 'is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
) Intro
Done
Answer:
the functions have the same domains
Step-by-step explanation:
because since the functions f(x) and g(x) have the same (x)
The only value that is in the domains of both functions is 0.
and the range of g(x) is all values less than or equal to 0 are correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The original function is f(x)=√x
As this is condition for √x function, x≥ 0
Domain= [0, infinity)
Range= [0, infinity)
After the reflection across x-axis and y-axis, we get a function,
g(x)=-√-x
-x≥ 0 means x≤ 0,
So,
Domain= (-infinity, 0]
Range= (-infinity, 0]
From this you can see that the only value that is in the domains of both functions is 0.
The range of g(x) is all values less than or equal to 0.
Hence, the only value that is in the domains of both functions is 0.
and the range of g(x) is all values less than or equal to 0 are correct.
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The graph of f(x) =sqrt of x is reflected across the x-axis and then across the y-axis to create the graph of function g(x). Which statements about the functions f(x) and g(x) are true? Check all that apply. The functions have the same range. The functions have the same domains. The only value that is in the domains of both functions is 0. There are no values that are in the ranges of both functions. The domain of g(x) is all values greater than or equal to 0. The range of g(x) is all values less than or equal to 0.
A shipping company is loading cube shaped crates into a larger cube shaped container the smaller cubes have side lengths 21/2 feet,and the larger shipping container has side lengths of 10 feet. How many crates will fit in the largest shipping container?Explain your reasoning
Answer:
64 crates
Step-by-step explanation:
Smaller Cube Side Length = 2 1/2 feet, or, 2.5 feet
Larger Container (Cube) Side Length = 10 feet
We find volume of larger container and find volume of small crates. We divide the large volume by volume of each crate. This will give us number of crates we can fit.
Volume of Cube = x^3
Where x is the side length of the cube
Now,
Small Crate Volume = (2.5)^3 = 15.625 cubic feet
Large Container Volume = 10^3 = 1000 cubic feet
Number of crates that would fit = 1000/15.625 = 64
So, 64 crates will fit in the largest shipping container
64 crates will fit into the largest shipping container.
1. Calculate the volume of each crate:
Volume [tex]\( V_{\text{crate}} \)[/tex] of a cube with side length s:
[tex]\[ V_{\text{crate}} = s^3 = (2.5)^3 \] \[ V_{\text{crate}} = 2.5 \times 2.5 \times 2.5 \] \[ V_{\text{crate}} = 15.625 \text{ cubic feet} \][/tex]
2. Calculate the volume of the larger container:
Volume [tex]\( V_{\text{container}} \)[/tex] of the larger cube-shaped container:
[tex]\[ V_{\text{container}} = (10)^3 = 1000 \text{ cubic feet} \][/tex]
3. Determine the maximum number of crates that can fit:
To find out how many crates can fit into the container, divide the volume of the container by the volume of one crate:
[tex]\[ \text{Number of crates} = \frac{V_{\text{container}}}{V_{\text{crate}}} \] \[ \text{Number of crates} = \frac{1000}{15.625} \] \[ \text{Number of crates} \approx 64 \][/tex]
What’s the LCM of 6 and 9
Answer:
Step-by-step explanation:
The answer is 18
Answer: The LCM of 6 and 9 is 18.
Step-by-step explanation: Using your basic multiplication facts, you know that 6 and 9 are both multiples of 18. Check to make sure 18 is the LCM.
Which of the following expressions could be used to represent "three less than half a number"?
A. 3 - 1/2n
B. 1/2n - 3
C. 3n - 1/2
D. 1/2 - 3n
Answer:
B. 1/2n - 3
Step-by-step explanation:
One way to get half a number is to multiply it by 1/2.
The phrase "a number less than an other number" often indicates subtraction.
[tex]\frac{1}{2}n-3[/tex]
Answer:1/2n-3
Step-by-step explanation:
because three less than half of a number means half minus three
In one year , Melinda’s parents spend 2,440.90 on cable and internet service . If they spend the same amount each month , estimate with the monthly fee is for cable and internet .
Answer:
The monthly fee for cable and internet is 200.
Step-by-step explanation:
Given:
Amount spend on one year for cable and internet service is 2440.90.
Now, to get the monthly fee for same amount spend on a year, by dividing the amount spend on a year with 12. As in one year there are 12 months.
So, [tex]2440.90\div 12[/tex]
=[tex]203.41[/tex]
By estimating the amount we get 200. As estimating means to round off the number to the nearest of whole number.
Therefore, the monthly fee for cable and internet is 200.
i need help with my math
Answer:
12 hours
Step-by-step explanation:
Let the cruise ship travel x hours before the container ship caught up and the container ship starts y hour after the cruise ship starts.
So, the distance traveled by the cruise ship in x hours = distance traveled by the container ship in (x - y) hours.
So, x - y = 10 ........ (1) (Given)
And 5x = 6(x - y)
⇒ x = 6y .......... (2)
Now, solving equations (1) and (2, we get 5y = 10, ⇒ y = 2 hours.
And x = 6y = 12 hours.
So, the cruise ship travels for 12 hours before the container ship caught up. (Answer)
Factor the expression into an equivalent form. ab^2 - b
Answer:
ab² - b = b(ab -1)
Step-by-step explanation:
The variable b is common to both terms here. Thus,
ab² - b = b(ab -1)
F(x)= 5x^2+6, g(x)= 7x find (f o g)(x), find (g o f)(x), find f(g(-4)), fine g(f(5))
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x^2+6\\g(x) = 7x[/tex]
So
[tex](f o g)(x) = 5(7x)^2+6\\= 5(49x^2)+6\\=245x^2+6\\(g o f)(x) = 7(5x^2+6)\\= 35x^2+42\\(fog(x))=245x^2+6f(g(-4)) = 245(-4)^2+6 \\=245(16)+6\\=3920+6\\=3926\\g(f(x)) = 35x^2+42\\g(f(5)) = 35(5)^2+42\\=35(25)+42\\=875+42\\=917[/tex]
Hence,
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Keywords: functions, Function composition
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Will mark the brainliest.
Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
Answer:
The mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.
Explanation:
The figure attached represents the situation.
The triangle on the left and the triangle on the right are similar triangles because they are right triangles and the marked angles are congruent.
The distance between the mirror and the basketball goal is represented by the unknown x.
By similarity:
[tex]10/6=x/4[/tex]Solving:
[tex]x=40\times 10/6=40/6=20/3[/tex]Thus, the mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.
I am a two-digit even number. I am
a multiple of 5. My tens digit is 8
more than my units digit.
Decimal Operati
1. Find the sum of the expression.
0.975 + 3.8
Answer:
4.775
Step-by-step explanation:
Answer:
4.775
Step-by-step explanation:
Add
0.975
3.800 =
4.775
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation. What are the values a, b, and c in the following quadratic equation? −5x2 − 9x + 12 = 0
A:a = −9, b = 12, c = 0
B: a = −5, b = −9, c = 12
C: a = 5, b = 9, c = 12
D:a = 9, b = 12, c = 0
Answer:
B
Step-by-step explanation
Answer:
Option B. a = −5, b = −9, c = 12
Step-by-step explanation:
The general form of the quadratic equation is as following
ax² + bx + c = 0
Where a, b and c are constants.
And the given equation is −5x2 − 9x + 12 = 0
Comparing the given equation to the general form
ax² + bx + c = 0
−5x2 − 9x + 12 = 0
So, a = -5 , b = -9 and c = 12
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
So, the answer is option B: a = −5, b = −9, c = 12
When a 49 pound weight is attached to a spring, the spring stretches 7 inches. Assume that the length of the spring y varies directly
with the weight attached x. Write and solve a direct variation equation to
find the length of the spring when a 63 pound weight is attached.
Kaitlin's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Kaitlin $5.50 per pound, and type B coffee costs $4.25 per
pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $448.00. How many pounds of type A coffee were used?
Answer:
The quantity of Type A coffee were used is 32 pounds .
Step-by-step explanation:
Given as :
The cost of type A coffee = $ 5.50 per pound
The cost of type b coffee = $ 4.25 per pound
The total cost of coffee = $ 448.00
The quantity of coffee of type B is twice than type A
Let The quantity of type A coffee = x pound
So, The quantity of type B coffee = 2 × x pound
Now, According to question
x × $ 5.50 + 2 x × $ 4.25 = $ 448
Or, x × $ 5.50 + x × $ 8.5 = $ 448
Or, 14 x = 448
∴ x = [tex]\frac{448}{14}[/tex]
I.e x = 32
∴ The quantity of type A coffee = 32 pound
And, The quantity of type B coffee = 2 × 32 = 64 pound
Hence The quantity of Type A coffee were used is 32 pounds . Answer
Final answer:
By setting up an equation based on the costs per pound and the relationship between quantities of coffee types A and B, we find that Kaitlin used 32 pounds of type A coffee for her blend.
Explanation:
We need to determine how many pounds of type A coffee were used in the blend, given that twice as many pounds of type B were used and that the total cost was $448.00. Let x be the pounds of type A coffee. Then, 2x will represent the pounds of type B coffee since twice as much type B is used compared to type A.
The cost equation can be represented as:
5.50x + 4.25(2x) = 448
Solving for x:
5.50x + 8.50x = 448
14x = 448
x = 448 / 14
x = 32
Therefore, Kaitlin used 32 pounds of type A coffee for her blend.
Katelynn earned $1240 in two weeks at the recreation
center during a trap shooting tournament. She earned
$480 the first week and the rest the second week.
Write an algebraic equation to model the situation.
x = 1240-y can be used to model the situation where x is the amount earned in second week.
Step-by-step explanation:
Given,
Total amount earned = D = $1240
Amount earned in first week = y = $480
Let,
x be the amount earned in second week.
Therefore,
Total amount earned = Amount earned in 1st week + 2nd week amount
D = x + y
1240 = x + y
Solving for x;
[tex]x= 1240- y [/tex]
x = 1240-y can be used to model the situation where x is the amount earned in second week.
Keywords: linear equation, subtraction
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Anna's birthday is tomorrow. Her friend Emma decides to buy chocolate covered strawberries to take to the birthday party. Emma has $12.00 to spend on the strawberries. The strawberries are packaged in 3 different sizes that vary in price.
Small box -- 8 ounces --$4.50
Medium box -- 12 ounces -- for $6.50
Large box -- 1 pound -- $7.25
Choose all the statements that are TRUE .
A.The large box contains twice as many ounces of strawberries as the small box.
B.To get the maximum ounces for her money, Emma should buy 1 large and 1 small box of strawberries.
C.Emma spends a total of $11.00; therefore, she is purchasing 2 small boxes of strawberries.
D.Emma purchases a small box and a medium box of strawberries. The total purchase is $11.75.
CHECK ALL THAT APPLY PLS
Answer:
A.The large box contains twice as many ounces of strawberries as the small box. TRUE
B.To get the maximum ounces for her money, Emma should buy 1 large and 1 small box of strawberries. TRUE
C.Emma spends a total of $11.00; therefore, she is purchasing 2 small boxes of strawberries. FALSE
D.Emma purchases a small box and a medium box of strawberries. The total purchase is $11.75. FALSE
Step-by-step explanation:
Here, the amount Emma has to be spent = $12
According to the question:
Small box -- 8 ounces --$4.50
Medium box -- 12 ounces -- for $6.50
Large box -- 1 pound -- $7.25
Now, the given statements are:
A.The large box contains twice as many ounces of strawberries as the small box.
The amount of strawberry in large box = 1 pound
Amount of strawberry in small box = 8 ounce
Now, double of 8 ounce = 16 ounce = 1 pounds
So, the given statement is TRUE.
B.To get the maximum ounces for her money, Emma should buy 1 large and 1 small box of strawberries.
Total ounces in 1 large and 1 small box = 16 ounce + 8 = 22 ounces
The price total = $4.40 + $7.25 = $11.65
So, the given statement is TRUE.
C.Emma spends a total of $11.00; therefore, she is purchasing 2 small boxes of strawberries.
cost of 1 small box = $4.50
Cost of 2 small box = 2 x $4.50 = $9
The given statement is FALSE
D.Emma purchases a small box and a medium box of strawberries. The total purchase is $11.75.
cost of 1 small box = $4.50
Cost of 1 medium box = $6.50
So, the total cost is $4.50 + $6.50 = $11.00
So, the given statement is FALSE.
Write each percent as a fraction in lowest terms.
1. 15% Too 2. 36% tos
3. 44% 10
4. 45%
5. 8% 18o
- 6. 60%
Answer:
Step-by-step explanation:
1) 15%=15/100=3/20
2) 36%=36/100=9/25
3) 44%=44/100=11/25
4) 45%=45/100=9/20
5) 8%=8/100=2/25
6) 60%=60/100=6/10=3/5
What is the answer to this?
Answer:
6
Step-by-step explanation:
Split the numerator/ denominator into like factors, that is
= [tex]\frac{72}{12}[/tex] × [tex]\frac{x^2}{x^2}[/tex] ← cancel to give 1
= 6 × 1
= 6
Plz tell me the domain
Answer:
Step-by-step explanation:
this is an solution