This is an exponential function. Since each year the value of the bike decreases by 5%, each year, the value of the bike is 100%-5%=95% of it's original value. So after x years, the value of the bike would be 200(0.95)^x.
Answer:
(200 - (200 x 5 / 100))^Y
Step-by-step explanation:
As the initial value of the bike is $200, that would be a fixed number in our equation. Each year, this will lose 5% of its value, therefore, it would be another fixed value in it. Then, we have to exponentiate it by the number of years that have passed since the initial value (Y). As a result, the equation to model the situation would be this one:
(200 - (200 x 5 / 100))^Y
What are the factors of m^2-6m+6m-36?
Gabriela has dinner at a cafe and the cost of her meal was $45.00 she wants to leave a tip of 15% what is her total bill
45+0.15·45=45+6.75=51.75$
Three times one number plus a second number is 40, and the one number minus the second number is 4. Find the numbers.
Answer:
The numbers are 11 and 7
Step-by-step explanation:
To find these, use the statements to create equations in standard form.
3x + y = 40
x - y = 4
Now that we have these two, we can add them together and get the y's to cancel out.
3x + y = 40
x - y = 4
-------------------
4x = 44
x = 11
Now that we have the first number as 11, we can solve for y using either equation.
x - y = 4
11 - y = 4
-y = -7
y = 7
A fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $15 for 6 apples and 6 oranges. What is the cost for an apple
Answer:
$1.25
Sorry that i dont have an explanation i just didnt wanna confuse you lol
Andy Taylor and Ben share their team payment in the ratio 1:3:4. What percentage of the total does Andy recieve?
Answer:
12.5%
Step-by-step explanation:
sum the parts of the ratio 1 + 3 + 4 = 8 parts
8 parts represents 100%, hence
1 part = [tex]\frac{100}{8}[/tex] = 12.5% ← Andy's percentage of the total
Andy Taylor's share in the ratio of 1:3:4 results in him receiving 12.5% of the total team payment.
Explanation:The question is about the sharing of a total team payment between Andy Taylor and Ben in the ratio of 1:3:4. To find out what percentage Andy receives, we first need to establish the total parts in the ratio. The ratio 1:3:4 sums up to 8 parts in total. Andy's share is represented by 1 part out of these 8. To find the percentage, we divide Andy's 1 part by the total 8 parts, multiply by 100, giving us 12.5%. This means that Andy receives 12.5% of the total team payment.
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A patient is given a 100-milligram dosage of a drug that decays exponentially at a rate of 11% per hour. The doctor wants to know when 15 milligrams of the drug remains.
Write an equation that models the situation. Explain each aspect of your equation.
Answer:
16.3 hours.
Step-by-step explanation:
"Decays exponentially at a rate of 11% per hour" translates into
(1 - 0.11)^h, where h is the number of hours during which the drug decays.
The negative sign comes from "decay."
The complete formula applicable here is
d(h) = (100 mg)(1 - 0.11)^h, where h is the number of hours.
We want to know how many hours it will be until all but 15 mg remain. The appropriate formula for this is
15 mg = (100 mg)()^h. Dividing both sides by 100 mg, we get:
15 mg
------------- = 0.89^h, or 0.15 = 1.11^h
100 mg
Apply properties of logs to solve this. Take the natural log of both sides of the above equation. We get:
ln 0.15 = h(ln 0.89). Dividing both sides by ln 0.89, we get:
h = 16.3
The original 100 mg dosage would decay to 15 mg after 16.3 hours.
Enter a rational number that is equivalent to
−20/4
The rational number equivalent to -20/4 is -5.
Explanation:A rational number equivalent to -20/4 is -5. This can be found by dividing the numerator (which is -20) by the denominator (which is 4). The result of this division is -5. Hence, -5 is the rational number equivalent to -20/4.
Kendyl is memorizing a piece of saxophone music to perform at a local festival. She currently has the first eight bars memorized and plans to memorize two more bars everyday until she has the whole piece memorized. Write a recursive formula to model Kendyl's progress.
Answer:
The recursive formula to model Kendyl's progress is:
Fourth option: an=an-1 + 2, a1=8
Step-by-step explanation:
She currently has the first eight bars memorized: The first value is 8:
a1=8
She plans to memorize two more bars everyday until she has the whole piece memorized:
The number of bars memorized is two more than the last day:
an=an-1 + 2
Then, the recursive formula is:
an=an-1 + 2, a1=8
Answer:
The correct choice is D hope that helps
The measurement, y, varies directly with regard to another value, x. If y = 9 and x = 24, find x for y = 25.
Answer:
x=66.667
Step-by-step explanation:
Basically, if y varies directly with a value x, you get an equation of the form y=kx, where k is a constant. To answer the question, first substitute 9 into y, and 24 into x.
9=24k
k=0.375
k is 0.375, so to get x, substitute 0.375 into k and 25 into y
25=0.375x
x=66.667
And we got it!
Final answer:
To find x when y = 25 in a direct variation where y = 9 when x = 24, first find the constant of proportionality (k = 3/8), then use this constant to solve the equation 25 = (3/8)x which yields x ≈ 66.67.
Explanation:
The student's question concerns direct variation, which is a concept where one variable changes in proportion to another variable. In this particular problem, the measure y varies directly with x. Given that y = 9 when x = 24, we can use this information to establish the constant of proportionality k where y = kx.
First, we solve for k using the initial condition:
9 = k * 24
k = 9/24
k = 3/8
Now that we have the constant of proportionality, we can find x when y = 25 by setting up the equation:
25 = (3/8)x
x = 25 * (8/3)
x = 200/3
x ≈ 66.67
Therefore, when y = 25, the value of x is approximately 66.67.
Mr. Grimm is trying to build a playground set in his backyard. Part of the playground set will have a slide. The ladder is 5 feet tall, and the slide is 7 feet long. What is the distance between the ladder and the bottom of the slide?
Answer:
~5 feet.
Step-by-step explanation:
assuming that it is a right triangle. if a=5 and c=7 then b the other leg is equal to the square root of c squared minus a squared. which equals about 4.9
Sammy bought 3 T-shirts for $15.75 each and pairs of jeans for $28.79 each. If the sales tax on his purchases totaled $5.24, how much money did Sammy spend in all?
Answer:
Sammy, after picking out her clothes, bringing them to the counter and ringing them up. owes in total: $49.78
Step-by-step explanation:
Final answer:
This answer explains how to calculate the total amount of money Sammy spent on T-shirts and jeans including sales tax.
Explanation:
To find out how much Sammy spent in total:
Calculate the total cost of the 3 T-shirts: $15.75 x 3 = $47.25
Calculate the total cost of the pairs of jeans: $28.79 x 2 = $57.58
Add the total costs of the T-shirts and jeans: $47.25 + $57.58 = $104.83
Add the sales tax to get the final amount: $104.83 + $5.24 = $110.07
Therefore, Sammy spent $110.07 in all.
What is the solution set for the open sentence, using the given replacement set ? 6x?2=10 ; {1, 2, 3, 4} ?
Answer:
answer is x=2
Step-by-step explanation: 6x2=12-2=10The solution set for the equation 6x - 2 = 10 using the replacement set {1, 2, 3, 4} is {2}, as 2 is the only number in the set that, when substituted into the equation, satisfies it.
The solution set for the open sentence 6x - 2 = 10 using the given replacement set {1, 2, 3, 4} can be found by solving the equation for x and then checking which numbers in the replacement set satisfy the equation.
Add 2 to both sides of the equation: 6x - 2 + 2 = 10 + 2, which simplifies to 6x = 12.Divide both sides by 6: 6x/6 = 12/6, which simplifies to x = 2.Check if x = 2 is within the replacement set: Since 2 is in the set {1, 2, 3, 4}, x = 2 is the solution that belongs to the replacement set.Therefore, the solution set is {2}.
Mr. Fox's had is students identify the sex of each of their frog's while they performing their dissections. There were a total of 46 groups for which there were 19 females and 27 males identified. He has one more group that needs to complete their dissection, the probability that it will be a male is approximately 59% based on the results of the first 46 groups. This is an example of:
A Experimental Probability
B Can not determine
C Theoretical Probability
D Neither
Answer:
A Experimental Probability
Step-by-step explanation:
The 59 percent is based on the data from the actual data. The theoretical probability is 50 percent for male and 50% and female.
Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was 3 less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold?
Answer:
The no. of adult's tickets sold is 25.
The no. of adult's tickets sold is 247
Step-by-step explanation:
Given :
Tickets for a basketball game cost $2 for students and $5 for adults.
The number of students was 3 less than 10 times the number of adults.
The total amount of money from ticket sales was $619.
To Find : No. of each ticket were sold
Solution :
Let x be the no. of the student's tickets sold
Let y be the no. of adult's tickets sold
Since we are given that The number of students was 3 less than 10 times the number of adults.
⇒ x = 10y -3 --(A)
Now cost of 1 student's ticket is $2
Thus, cost of x student's ticket is $2x
Now cost of 1 adult's ticket is $5
Thus,cost of y adult's ticket is $5y
Since we are given that the total amount of money from ticket sales was $619.
⇒2x +5y =619 ---(B)
Solving equation A and B by substitution method :
putting value of x from (A) in (B)
We get :
⇒2( 10y -3) +5y =619
⇒20y-6+5y= 619
⇒25y = 625
⇒y = 625/25
⇒y=25
Thus, the no. of adult's tickets sold is 25.
Putting value of y in equation A to get value of x .
⇒x = 10(25) -3
⇒x = 247
Thus the no. of adult's tickets sold is 247
Rita spends 52% of her pocket money on magazines and 23% on movies. If her pocket money was RS.144 what amount of her pocket money is left
Answer:
The amount of Rita's pocket money left is Rs. 36.
Step-by-step explanation:
Pocket money that Rita had before = 144
Money spent for magazines = 52% of 144
= [tex]\frac{52}{100} (144)[/tex]
= 0.52(144)
= 74.88
Money spent for movies = 23% of 144
= [tex]\frac{23}{100} (144)[/tex]
= 0.23(144)
= 33.12
Money left with Rita = 144 - (74.88 + 33.12)
= 144 - 108
= 36
Hence, Rita left with Rs. 36.
Aliter:
Total money spent = (52 + 23)% = 75%
So, money left with Rita = 100 - 75 = 25%
25% of 144 = 0.25(144) = 36.
Find the perimeter of the figure:
15 units
30 units
27 units
29 units
Answer:
To find the perimeter, just add up the lengths of the each side.
AB = 13 units
BC = 12 units
CA = 5 units
P = 13 + 12 + 5 = 30 units
Which equation shows a line perpendicular to the line
Answer:
The second answer: y= 3/4x + 2
Step-by-step explanation:
Subtract 4x to the other side
Divide by 3 to get y by itself
Make the coefficient of the x term the negative reciprocal, for that is the perpendicular slope of the line
Show all work plz and answer it quickly
Answer:
x + 4 = 7 + 4 = 11 feet
Step-by-step explanation:
Do you ever have a nice "fist", meaning you have very neat handwriting.
You are told that A to MSG = B to MSG
So
Equation
3x - 10 = x + 4
Solution
Subtract x from both sides
3x - x - 10 = x - x + 4 Simplify
2x - 10 = 4 Add 10 to both sides
2x - 10 + 10 = 4 + 10 Simplify
2x = 14 Divide by 2
2x/2 = 14/2
x = 7
x + 4 = 7 + 4 = 11 feet from A to Madison Square Garden
WILL AWARD BRAINLIEST!!!
Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1
key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 25 thumb drives and 200 key chains.
Let x represent the number of key chains. Let y represent the number of thumb drives.
Write an inequality for this situation and graph the inequality.
Answer:
[tex]\ y\geq 5\cdot x\\x+y\geq 50\\y\leq25\\x\leq200\\y\geq0\\x\geq0[/tex]
Step-by-step explanation:
STEP 1 : First we draw the graph for [tex]y\geq 5\cdot x[/tex] by letting [tex]y=5x[/tex]
it is denoted by red colour
STEP 2 : Now we draw the graph for [tex]x+y\geq 50[/tex] by letting [tex]x+y=50[/tex]
It is denoted by orange colour
STEP 3 : Now we draw for [tex]y\leq25[/tex] by letting [tex]y=25[/tex]
It is denoted by green colour.
STEP 4 : Now we draw for [tex]x\leq200[/tex] by letting [tex]x=200[/tex]
It is denoted by blue colour.
The population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people. What was the population in 1999?
Answer:
10200
Step-by-step explanation:
The population in 1999 was 10200.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people.
Let the population be in 1999 be {x}. Then, we can write -
{x} = 10000 + {2% of 10000}
{x} = 10000 + {2/100 x 10000}
{x} = 10000 + 200
{x} = 10200
Therefore, the population in 1999 was 10200.
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The box which measures 70cm X 36cm X 12cm is to be covered by a canvas. How many meters of canvas of width 80cm would be required to cover 150 such boxes.
Answer:
142.2 meters.
Step-by-step explanation:
We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.
Let us find total surface area of box using surface area formula of cuboid.
[tex]\text{Total surface area of cuboid}=2(lb+bh+hl)[/tex], where,
[tex]l[/tex] = Length of cuboid,
[tex]b[/tex] = Breadth of cuboid,
[tex]w[/tex] = Width of cuboid.
[tex]\text{Total surface area of box}=2(70\cdot36+36\cdot 12+12\cdot 70)[/tex]
[tex]\text{Total surface area of box}=2(2520+432+840)[/tex]
[tex]\text{Total surface area of box}=2(3792)[/tex]
[tex]\text{Total surface area of box}=7584[/tex]
Therefore, the total surface area of box will be 7584 square cm.
To find the length of canvas that will cover 150 boxes, we will divide total surface area of 150 such boxes by width of canvass as total surface area of canvas will also be the same.
[tex]\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}[/tex]
[tex]80\text{ cm}\times\text{ Length of canvass}=150\times 7584\text{cm}^2[/tex]
[tex]\text{ Length of canvass}=\frac{150\times 7584\text{ cm}^2}{80\text{ cm}}[/tex]
[tex]\text{ Length of canvass}=\frac{1137600\text{ cm}^2}{80\text{ cm}}[/tex]
[tex]\text{ Length of canvass}=14220\text{ cm}[/tex]
Let us convert the length of canvas into meters by dividing 14220 by 100 as 1 meter equals to 100 cm.
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100}\times\frac{m}{cm}[/tex]
[tex]\text{ Length of canvass}=142.20\text{ m}[/tex]
Therefore, 142.2 meters of canvas of width 80 cm required to cover 150 such boxes.
One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?
y = 2x - 3 and y = x + 39
y = 2x - 3 and x + y = 39
y = 2(x - 3) and x + y = 39
Answer with Step-by-step explanation:
Let x and y be two numbers.
One number is 3 less than twice another.
⇒ y=2x-3
Their sum is 39.
⇒ x+y=39
Hence, system of equations are:
y = 2x - 3 and x + y = 39
Putting y=2x-3 in x+y=39
x+2x-3=39
⇒ 3x-3=39
⇒ x-1=13 (dividing both sides by 3)
⇒ x=14
y=2x-3
⇒ y=2×14-3
⇒ y=28-3
⇒ y=25
Hence, Two numbers are:
14 and 25
If you break up the number under the radical in the square root of 36 into two factors that are perfect squares, what are the two factors?
Answer: 4 and 9
Step-by-step explanation:
9 x 4 = 36
The square root of 9 is 3, so 9 is a perfect square.
The square root of 4 is 2, so 4 is a perfect square.
Answer:
9 x 4 = 36
Step-by-step explanation:
you should be able to mark him brainliest now =) =) =)
Please help!!
Which value of y is a solution of the inequality? 2y+9≤11
y = 1
y = 2
y = 11
y = 9
Answer:
y=1 for [tex]y\leq 1[/tex]
Step-by-step explanation:
We can solve an inequality much like we solve an equation. We will use inverse operations to isolate y. If we need to divide by a negative then we will need to flip the inequality.
[tex]2y+9\leq 11\\2y+9-9\leq 11-9\\2y\leq 2\\\frac{2y}{2}\leq \frac{2}{2} \\y\leq 1[/tex]
First, we moved 9 across the equal sign to combine it with 11 by subtracting by 9 from both sides.
Second, we divided both sides by 2.
[tex]y\leq 1[/tex] is the solution. All solutions equal to 1 and less than 1 will work.
If ƒ(x) = 2x, then ƒ -1(x) =
-2x
½x
x - 2
recall that to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf \stackrel{f(x)}{y}=2x\implies \stackrel{\textit{switcheroo}}{x=2y}\implies \cfrac{x}{2}=y\implies \cfrac{1}{2}x=\stackrel{f^{-1}(x)}{y}[/tex]
You have performed increasingly well this past year and you are earning a 6% pay increase to your current $62,900 annual salary."
To calculate a new salary after a pay increase, multiply the current salary by the percentage increase and add it to the original salary. In this case, a 6% increase on a $62,900 salary results in a new annual salary of $66,674.
Explanation:The subject of this question is determining the new salary after a pay increase, which is a common problem in mathematics related to percentages. To calculate the new salary after a 6% pay increase to a current salary of $62,900, you multiply the current salary by the percentage increase in decimal form, which is 0.06.
Step-by-Step Calculation
Determine the increase amount by multiplying the current salary by the percentage increase: $62,900 × 0.06 = $3,774.
Add the increase to the current salary to get the new salary: $62,900 + $3,774 = $66,674.
The new annual salary after a 6% increase will therefore be $66,674.
To generalize, the formula to calculate the percentage change or growth rate is given by:
Percentage change = (Change in quantity / Original Quantity) × 100
For example, a $2 per hour raise on a $10 per hour job represents
Percentage change = ($2 / $10) × 100 = 20%
unction f is an exponential function
X -2 | 0 | 2 | 4| 6
F(x) 1/8 | ½| 2 |8 | 32
By what factor does the output value increase as each
input value increases by 1?
Answer:
4
Step-by-step explanation:
As each x value increases by 1, the output values increase by a factor of 4. This means that each y value can be multiplied by 4 to get the next y value.
1/2(4)=2
2(4)=8
8(4)=32
4 is the factor.
Sammy buys his clothes at super discounts. On saturday he bought shoes regularly priced at $40 for 25% off, and jacket regularly priced at $100 for 30% off before the sales taxe what was the total price of the items sammy bought .Approximately what percent discount did Sammy get on his total purchases
Answer:
A. $100
B. 29%
Step-by-step explanation:
A. To find total price of the items Sammy bought we will add the price of shoes and jacket after discount.
Let us find price of shoes after 25% discount.
[tex]\text{Price of shoes after discount}=40-(\frac{25}{100}*40)[/tex]
[tex]\text{Price of shoes after discount}=40-(\frac{1}{4}*40)[/tex]
[tex]\text{Price of shoes after discount}=40-10=30[/tex]
Therefore, price of shoes after discount is $30.
Now let us find price of jacket after 30% discount.
[tex]\text{Price of jacket after discount}=100-(\frac{30}{100}*100)[/tex]
[tex]\text{Price of jacket after discount}=100-30[/tex]
[tex]\text{Price of jacket after discount}=70[/tex]
Therefore, price of jacket after discount is $70.
Now let us add both prices to find the total price of the items.
[tex]\text{Total price of items}=30+70[/tex]
[tex]\text{Total price of items}=100[/tex]
Therefore, the total price of the items bought by Sammy is $100.
B. To find the percent discount which Sammy got on his total purchases, we will use percent change formula.
[tex]\text{Percent change}=\frac{\text{Difference}}{\text{Original value}}\times 100[/tex]
Total price without discount= 100+40=140
[tex]\text{Discount percent}=\frac{140-100}{140}\times 100[/tex]
[tex]\text{Discount percent}=\frac{40}{140}\times 100[/tex]
[tex]\text{Discount percent}=0.2857142857142857\times 100[/tex]
[tex]\text{Discount percent}=28.57142857142857\approx 29[/tex]
Therefore, Sammy got approximately 29% discount on his total purchases.
Answer:
Sammy bought a car and got a discount of 2/5 off the original price of $30,000. How much did Sammy pay for the car after the discount?
Step-by-step explanation:
Please Help ASAP!! 98 Points to Brainliest!!
Answer:
all the lines are correct but for x<= 2 there need to be a closed circle, and vica versa for all the others.
Step-by-step explanation:
The lines are correct but for x<= 2
A regular pentagon with a perimeter of 18 centimeters is dilated by a scale factor of 3/2 to create a new pentagon?
Answer:
if that is all it says you can do simple cross multiplication
Step-by-step explanation:
18*3/2=x
x will give you the nre number. If you dont know how to do that math go to desmos and type it in. the answer should be 27 if i did it correctly in my head but please check my work.
A student helping a student
The new pentagon has a perimeter of 27 centimeters.
Explanation:To find the perimeter of a regular pentagon, we multiply the length of one side by the number of sides. In this case, the perimeter is 18 centimeters, so each side of the pentagon is 18/5 = 3.6 centimeters long.
When this pentagon is dilated by a scale factor of 3/2, each side of the new pentagon will be 3/2 x 3.6 = 5.4 centimeters long.
Therefore, the new pentagon has a perimeter of 5.4 x 5 = 27 centimeters.
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