The amount of interest he has earned is $438
What is compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
A = P ( 1+r/100) ^t
A is the amount after year t
P is the principal and r is the rate
800 = P( 1+ 12/100)⁷
800 = P( 1+ 0.12)⁷
800 = P ( 1.12)⁷
800 = P( 2.21)
P = 800/2.21
P = $362
A = P+ 1
I = A-P
I =800 - 362
I = $438
therefore the interest he earned is $438
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please help me with this question
Answer:
f(x) = (x-5)(x+2)^2
Step-by-step explanation:
use desmos graphing calculator! it's very helpful and free :)
Answer:
From the graph,
The zeros of the function are at x= -2 and x= 5
But since at root -2,it doesn't cross the x axis, the root has even multiplicity
Ans:(x+2)^2 (x-5).....option B
Give the following angle as a bearing. 54
Answer:
Step-by-step explanation:
20 degees
a. Substitute 0 for x and, without using a calculator, find the country's population in
The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.
What are exponential function?An exponential function is a mathematical function that increases or decreases at a rate proportional to its current value. Exponential functions are used in a variety of sciences and everyday applications. For example, population growth is an exponential function of time because the population increases by a fixed percentage each year.
The exponential function f(x) = 565(1.026)ˣ models the population of a country, f(x), in millions, x years after 1970. Substituting 0 for x, the population of the country in 1970 was 565 million. Substituting 27 for x, the population of the country in 1997 was 1,118 million. The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.
It appears that the population of the country is growing by a factor of 3 every 27 years. This is evident from the fact that the population in 1997 is 3 times the population in 1970, and the population in 2024 is 3 times the population in 1997. This pattern is expected to continue with the population in 2051 being 3 times the population in 2024.
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what is the median? 0, 5, 10, 10, 12, 15, 15, 20, 25 30, 30, 35, 35, 45, 60
Answer:
The median of the given data is 20. To find the median, arrange the data in numerical order, and then take the middle value. In this case, the data is arranged in numerical order as 0, 5, 10, 10, 12, 15, 15, 20, 25, 30, 30, 35, 35, 45, 60. The middle value is 20, which is the median.
Answer:
17.5
Step-by-step explanation:
To find the median of a set of numbers, we need to arrange the numbers in order from smallest to largest and then find the middle value.
In this case, the numbers in the set arranged in ascending order are:
0, 5, 10, 10, 12, 15, 15, 20, 25, 30, 30, 35, 35, 45, 60
There are 15 numbers in the set, which means that the middle value is the eighth number. Since there are two numbers in the middle (15 and 20), we take the average of these two numbers to find the median:
median = (15 + 20) / 2 = 17.5
Therefore, the median of the set of numbers is 17.5.
Q.15. Bloom Pet Supplies makes a profit of $5.50 per bag on its line of dog food. Total expenses
associated with the sale of dog food stand at $2,500 per day. If the store wants to make a profit of
at least $5,225 per day, which inequality represents how many bags of dog food d the store must
sell to meet their goal?
A. 5.50d 2,500 ≥ 5,225
B. 5.50 2,500d ≥ 5,225
C. 5.50d +2,500 ≥ 5,225
D. 5.50 +2,500d ≥ 5,225
Answer:
Let's use option C to represent the relationship between the number of bags of dog food sold and the profit made:
Profit per bag of dog food = $5.50
Total expenses per day = $2,500
The store wants to make a profit of at least $5,225 per day.
If d represents the number of bags of dog food sold, then the profit made can be represented as:
Profit = Revenue - Expenses
Revenue = Profit + Expenses
Revenue = $5.50d + $2,500
To make a profit of at least $5,225 per day, we can set up the following inequality:
$5.50d + $2,500 ≥ $5,225
Simplifying:
$5.50d ≥ $2,725
Dividing both sides by $5.50:
d ≥ 500
Therefore, the store must sell at least 500 bags of dog food per day to make a profit of at least $5,225 per day.
The correct inequality that represents this relationship is option C: 5.50d +2,500 ≥ 5,225.
Mackenzie has $46. 13 less than Taylor. How would you show how
much money Mackenzie has?
Please solve ASAP PLEASE
Answer:
Step-by-step explanation:
46+13 = 59
Answer:
Let Mackenzie have x
and Taylor have y
Then, since Mackenzie has 46.13 less than Taylor,
x = y - 46.13
Therefore, to show how much money Mackenzie has we will use the equation
x = y - 46.13
remember Makenzie has $x.
Taylor has $y
Makenzie money is less than Taylor's money by 46.13
so we take away 46.13 from Taylor's money to get that of Makenzie
Makenzie's money x = Taylor's money y - 46.13
x = y - 46.13
Step-by-step explanation:
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(5) mean about George's new store?
Answer:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.The total amount of profit 5 months after the store has been open is $5,400.Step-by-step explanation:
Given functions:
[tex]r(x)=x^2+5x+14[/tex]
[tex]c(x)=x^2-4x+5[/tex]
where:
r(x) is the store's revenue each month (in hundreds of dollars).c(x) is the store's expenses each month (in hundreds of dollars).x is the number of months since the store has been open.Profit is calculated by subtracting expenses from revenue.
Therefore, the composite function for profit is:
r(x) - c(x) = (r - c)(x)Since x represents the number of months the store has been open:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.
To calculate the total amount of profit in the first 5 months, substitute x = 5 into the composite function:
[tex]\begin{aligned}\implies (r-c)(5)&=r(5)-c(5)\\&=(5^2+5(5)+14)-(5^2-4(5)+5)\\&=(25+25+14)-(25-20+5)\\&=(50+14)-(5+5)\\&=64-10\\&=54\end{aligned}[/tex]
Since the revenue and expenses functions are measured in hundred of dollars, so too is the profit function. Therefore, the amount of profit generated in 5 months is $5,400.
dibuja una línea desde cada ecuación hasta la propiedad de igualdad que ilustra
By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.
What does Property of Equality means?The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.
As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.
Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"
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the sum is -7 and the difference is 14
Answer:
please give more information like what to find
3.5, -10.5
Step-by-step explanation:
Need help on parabola problem
Answer:
x = 4
Step-by-step explanation:
What is the radius of a sphere that has a surface area of 2903.33 in2?
7.6 in
15.2 in
13.5 in
8.6 in
Answer:
B. 15.2 inches.
Explain why y−7x−5=2/6.
Answer:
the expression
y -7/x-5 = 1/3 or 2/6
Step-by-step explanation:
Cross multiplying both sides:
3(y-7) = x - 5
3y - 21 = x - 5
3y - x = 21 - 5
3y - x = 16
The simplified equation is 3y-x=16.
A parking space shaped like a parallelogram has a base of 17 feet and a height is 9 feet a car parked in the space is 16 feet long and 6 feet wide how much of the parking space is not covered by the car
Answer:
40) sorry if I'm wrong :<
I am perplexed about how to calculate this:
For someone with a foot length of 29 cm, identify the 95% prediction interval estimate of their height and write a statement interpreting that interval.
CORRECT ANSWER: 177 cm < y < 200 cm
The 95% prediction interval for the height is given by the inequality 177 cm < y < 200 cm.
The interpretation is that we are 95% sure that the height of a person with a foot length of 29 cm is greater than 177 cm and less than 200 cm.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.In this problem, the bounds of the interval are given as follows:
y > 177cm -> greater than 177 cm.y < 200 cm -> less than 200 cm.We have a compound inequality, hence both conditions have to be respected simultaneously.
Missing InformationThere is not enough information to obtain the interval, hence we just interpret the given interval.
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find the perimeter of P and area of A of triangle JKL J(-5,-7),K(2,3),L(-1,-7)
Answer: To find the perimeter of triangle JKL, we need to find the length of each side and add them up. We can use the distance formula to find the length of each side:
Side JK = sqrt[(2 - (-5))^2 + (3 - (-7))^2] = sqrt[7^2 + 10^2] = sqrt[149]
Side KL = sqrt[(-1 - 2)^2 + (-7 - 3)^2] = sqrt[(-3)^2 + (-10)^2] = sqrt[109]
Side LJ = sqrt[(-1 - (-5))^2 + (-7 - (-7))^2] = sqrt[4^2] = 4
Therefore, the perimeter of triangle JKL is:
P = JK + KL + LJ = sqrt[149] + sqrt[109] + 4
To find the area of triangle JKL, we can use the formula:
A = 1/2 * base * height
We can choose any side as the base, and the corresponding height will be the perpendicular distance from the opposite vertex to the base. Let's choose side KL as the base. The height from vertex J to side KL is the perpendicular distance between J and the line containing KL. We can find this distance using the formula for the distance between a point and a line:
Area = 1/2 * KL * h
where h = |(2 - (-1))( -7 - 3) - (-5 - 2)(-1 - 3)| / sqrt[(-1 - 2)^2 + (-7 - 3)^2]
Simplifying the above expression, we get:
h = 24 / sqrt[109]
Therefore, the area of triangle JKL is:
A = 1/2 * KL * h = 1/2 * sqrt[109] * 24 / sqrt[109] = 12
So, the perimeter of triangle JKL is sqrt[149] + sqrt[109] + 4, and the area of triangle JKL is 12.
Step-by-step explanation:
determine whether the pair of functions and inverse functions f(x)=6x-15 and g(x)=1/6x+5/2
The pair of functions are inverses, as their compositions result in x.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
If two functions are inverse, the composites f(g(x)) and g(f(x)) both result in x.
The composite functions for this problem are given as follows:
f(g(x)) = f(x/6 + 5/2) = 6(x/6 + 2.5) - 15 = x + 15 - 15 = x.g(f(x)) = g(6x - 15) = 1/6(6x - 15) + 2.5 = x - 2.5 + 2.5 = x.Hence they are inverses.
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I’ll give BRAINLIEST if correct as well as 5star ratings
Answer:x=-4,-2
Step-by-step explanation:it is
the telephone line transfers 5760 KB data in 240 seconds what is the transfer rate per second
The data transfer rate per second is found as: 24 KB / sec.
Explain about the rate of change?Slope is also known as constant rate of change. Divide the change in y-values by both the change in x-values to determine that average rate of change. Identifying changes in measurable parameters like maximum pace or average velocity calls for the knowledge of the average fluctuation rate.Data transfer: 5760 KB
Time : 240 seconds
Rate per second = Data transfer / Time
Rate per second = 5760/ 240
Rate per second = 24
Thus, the data transfer rate per second is found as: 24 KB / sec.
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A real estate agent has 19 properties that she shows. She feels that there is a 30 % chance of selling any one property during a
week. The chance of selling any one property is independent of selling another property. Compute the probability of selling at
least 5 properties in one week. Round your answer to four decimal places.
Answer: This is a binomial probability problem. Let X be the number of properties sold during a week, then X has a binomial distribution with parameters n=19 and p=0.3.
The probability of selling at least 5 properties is:
P(X ≥ 5) = 1 - P(X < 5)
To calculate P(X < 5), we can use the binomial cumulative distribution function or the normal approximation to the binomial distribution.
Using the binomial cumulative distribution function, we have:
P(X < 5) = Σ P(X = k) for k = 0 to 4
Using the formula for the binomial probability mass function, we get:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= (0.7)^19 + 19(0.3)(0.7)^18 + 171(0.3)^2(0.7)^17 + 969(0.3)^3(0.7)^16 + 3876(0.3)^4(0.7)^15
Using a calculator or statistical software, we get:
P(X < 5) = 0.95044
Therefore, the probability of selling at least 5 properties in one week is:
P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.95044 = 0.0496 (rounded to four decimal places).
So the probability of selling at least 5 properties in one week is approximately 0.0496 or 4.96%.
Step-by-step explanation:
A restaurant offers a 13% discount on all of its food. What is the new total after the discount has
been applied to a bill of £39?
Give your answer in pounds and include the £ sign.
Answer:
£33.93
Step-by-step explanation:
A 13% discount means that the new price will be 87% of the original, as 100 - 13 = 87.
This can be calculated by converting the percentage into a decimal, then multiplying by the decimal:
87 / 100 = 0.87
39 * 0.87 = 33.93
Write the equation of a rational function that has been reflected, shifted down 6, right 8, and stretched by a factor of 4.
To write the equation of a rational function that has been reflected, shifted 6 down, 8 to the right and stretched by a factor of 4, we have to start with the basic rational function which is:
f(x)= 1/xThe reflected function we multiply it by -1 resulting in: g(x)= -1/xHow to shift a function?To shift it down by 6, we must subtract 6 from the function, so we have:
h(x) = -1/x-6To shift the function to the right by 8, we substitute x for (x-8), finding this result:
i(x)= -1/(x-8)-6To stretch the function by a factor of 4, we have to multiply the denominator by 4, which will result in:
j(x)= -1/4(x-8))-6Therefore, the equation of the rational function will be:
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Write and solve a problem involving money that can be solved with a division equation and has a solution of 1,350
The answer to this question is as follows equation As a result, each recipient will get $1,350.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
We must divide the total sum by three in order to distribute the funds among the three recipients equally. Let x represent the total sum that will be given to each recipient.
x = 4,050 / 3
x = 1,350
As a result, each recipient will get $1,350.
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Many mortgage lenders offer a way to lower your interest rate by paying some of the interest up front. This prepaid interest is known in the industry as points. Each point corresponds to 1% of the amount borrowed. In short, you're paying a fee to lower your interest rate. A lender offers you a 10 year fixed mortgage of 100,000 at 2.7% interest when you buy 1 point Find the monthly payment. Do not round intermediate calculations. Round your answer to the nearest cent.
We have the fοllοwing respοnse after answering the given questiοn: The equatiοn mοnthly payment, rοunded tο the next penny, is $959.49.
What is the equatiοn?In a mathematical equatiοn, the equals sign (=), which cοnnects twο claims and denοtes equality, is utilized. In algebra, an equatiοn is a mathematical statement that prοves the equality οf twο mathematical expressiοns.
Fοr instance, in equatiοn 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressiοns can be used tο describe the relatiοnship between the twο sentences οn either side οf a letter. The lοgο and the particular piece οf sοftware frequently cοrrespοnd. like, fοr instance, 2x - 4 = 2.
[tex]P = \frac{rP}{(1 - (1 + r)^{-n}}[/tex]
where P is the regular mοnthly payment, r is the interest rate each mοnth, n is the number οf payments, and P is the amοunt οf interest that has already been paid in dοllars.
r = 0.027 / 12 = 0.00225
The number οf payments must then be determined. There are 120 mοnthly payments fοr a 10-year mοrtgage.
n = 120
P = 1% * $100,000 = $1,000
Nοw that the data have been entered, we can cοmpute the monthly payment:
[tex]P = (0.00225 \times $99,000 / (1 - (1 + 0.00225)^{(-120)})) + $8.33[/tex]
where $8.33 represents the mοnthly charge fοr the prepaid interest and $99,000 represents the tοtal amοunt bοrrοwed after subtracting the prepaid interest.
If we cοndense this phrase, we get:
P = $959.49
Hence, The mοnthly payment, rοunded tο the next penny, is $959.49.
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The reading on a water meter in April and May are 417.8 kl and 430.4 kl. If there is a basic charge of 23 pesos and the cost per kl is 20 pesos, how much is the billing for water consumption between the two months?
Answer:
the billing for water consumption between April and May is 275 pesos.
Step-by-step explanation:
To find the billing for water consumption between April and May, we need to calculate the difference in the water usage as measured by the water meter.
The difference between the readings in April and May is:
430.4 kl - 417.8 kl = 12.6 kl
To calculate the cost of this water usage, we need to multiply the volume of water by the cost per kl and then add the basic charge.
The cost of the water usage is:
12.6 kl x 20 pesos/kl = 252 pesos
Adding the basic charge of 23 pesos, the total billing for water consumption between the two months is:
252 pesos + 23 pesos = 275 pesos
Therefore, the billing for water consumption between April and May is 275 pesos.
which ratios have a unit rate greater than 1? choose all that apply 2 1/2 miles:3 hours 9/8 miles:5/6 hour 1/3 mile: 2 3/8 hours 9/5 miles:3 hours 4 miles:3 1/3 hours 7 miles: 3/4
Answer: The ratios that have a unit rate is 9/8 miles:5/6hours and 7miles: 3/4 hours
Step-by-step explanation:
Unit rate is the ratio of the distance travelled o the time taken.
For us to know which of the ratios has a unit rate greater than 1, we need to divide the distance by the time as shown;
If distance = 9/8 miles and time = 5/6 hours
Hence the ratio that has a unit rate is 9/8 miles:5/6hours
If distance = 7 miles and time = 3/4 hours
Consider the parabola represented by this equation.
4x2 + 4x + 2y + 1 = 0
Which features are features of the parabola?
0
opens down
opens to the left
directrix at y = ㅎ
vertex at (-1,0)
directrix at x =
02/00
HELPPPP MEEEW
Answer:
a) opens down
c) directrix at y = 1/8
d) vertex at (-1/2,0)
Step-by-step explanation:
Starting from the given equation:
4x^2 + 4x + 2y + 1 = 0
We can rearrange to obtain the standard form of the equation of a parabola:
2(y + 1/2) = -4(x + 1/2)^2 + 1
(y + 1/2) = -2(x + 1/2)^2 + 1/2
Comparing to the standard form:
(y - k) = a(x - h)^2
We can see that the vertex of this parabola is at the point (-1/2, -1/2).
Next, we can find the axis of symmetry by noting that the parabola is symmetric about a vertical line passing through the vertex. This line is given by:
x = -1/2
We can also determine whether the parabola opens upward or downward by looking at the sign of the coefficient a. In this case, a = -2, so the parabola opens downward.
The distance between the vertex and the directrix is given by |1/(4a)|. Therefore, the distance between the vertex (-1/2, -1/2) and the directrix is:
|1/(4(-2))| = 1/8
So the directrix of the parabola is the horizontal line y = 1/8.
Therefore, the correct options are:
a) opens down
c) directrix at y = 1/8
d) vertex at (-1/2,0)
The other options are incorrect:
b) The parabola does not open to the left.
e) The directrix is not a vertical line at x = -3/8.
State whether this is a polynomial and give reason to your answer. X²-4X-32
Answer:
Yes, it's a polynomial
Step-by-step explanation:
A polynomial is an expression that only involves operations of addition, subtraction, multiplication, and positive integer powers and variables.
Your expression fits the criteria. You could also make this into a binomial and get (x-8)(x+4).
Please answer my question that I posted. I'm stuck and I really need help.
A parking garage opens at 8am Some cars are parked parked in the garage overnight T he graph shows the total number of cars in the garage. What is the slope for this graph?
A. 1
B. 2
C. 3
D. 5
You make party favors for an event. You tie 9 inches of ribbon around each party favor. Write an expression for the number of inches of ribbon needed for n party favors.
The ribbon costs $3 for each yard. Write an expression for the total cost (in dollars) of the ribbon.
As a result, the price of the ribbons is proportional to the number of party favours, with each Favour costing (3/4) dollars.
What are quantity and example?A measurable quality such as weight, length, time, volume, or pressure is referred to as quantity. A unit is a unit of measurement that is used to measure other quantities (for example, a gramme, a second, a liter, or a pascal are unit of the above quantities). Chemists employ a wide range of measurements.
The amount of ribbon required for n party favours is calculated as follows:
19n inches (since each party Favour requires 9 inches of ribbon)
As the price is stated in dollars per yard, we must first convert the amount of inches to yards before we can determine the ribbon's total cost. Since there are 36 inches in every yard, we can calculate the number of yards by dividing the total amount of inches by 36:
Total yards of ribbon = (9n) / 36 = (n) / 4
Thus, the following phrase represents the ribbon's overall cost:
3 × (n/4) = (3n) / 4 dollars
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Please provide steps for the answer
This represents the number of small rolls the club sold.
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides.
To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
In the equation 3s + 135 = 4.5 (s+10)
The equation 3s + 135 = 4.5(s + 10) can be used to represent this situation, where s represents the number of small rolls the club sold.
Hence, represents the number of small rolls the club sold.
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