Margo will pay approximately $45.50 in interest on the loan.
What is interest?
Borrowers must pay lenders simple interest as a fee in exchange for a loan.
First, we need to calculate the interest that Margo will pay on the loan.
Interest = Principal x Rate x Time
where:
Principal = $1300
Rate = 3% per year (or 0.03)
Time = 14/12 years (since there are 12 months in a year)
Plugging in the values, we get:
Interest = $1300 x 0.03 x (14/12)
Interest ≈ $45.50
Therefore, Margo will pay approximately $45.50 in interest on the loan.
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A man went to a post office to buy some stamps. If he bought x, 50 cents stamps and y, 25 cents stamps, the total cost would have been $3.50. If, however, he bought twice as many 50 cents stamps and half as many 25 cents stamps, then the total cost would have been $4.75. Evaluate x and y.
find 3 consecutive even integers if three times the first integer is two times the third
Step-by-step explanation:
First = x
second = x + 2
third = x + 4
3 * x = 2 ( x+4)
3x = 2x+ 8
x = 8 8 10 and 12
HELP PLEASE ! 10+ POINTS! Social networking sites make some very accurate suggestions for people that you might know. Explain how trees are used to make these suggestions.
The circumference of the circular table is 72 π inches. What is the radius of the table
Answer: 36 inches
Step-by-step explanation:
The formula for the circumference of a circle is 2πr where r is the radius of the circle Therefore 2πr=72π so r=72/2 = 36 inches.
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
The average rate of change of P between t = 3 and t = 5 is -18 people/hour.
A possible value of people in line at t = 6, given the average rate of change would be 50.
How to find the average rate of change ?To find the average rate of change of P between t = 3 and t = 5, we can use the formula:
Average rate of change = (P(5) - P(3)) / (5 - 3)
From the table, we know P(3) = 85 and P(5) = 49.
Average rate of change = (49 - 85) / (5 - 3) = (-36) / 2 = -18 people/hour
To find the possible number of people at t = 6, Let P(6) = x. First, we will find the average rate of change between t = 3 and t = 6:
(P(6) - P(3)) / (6 - 3) = (x - 85) / 3
This value must be negative. Now, we will find the average rate of change between t = 5 and t = 6:
(P(6) - P(5)) / (6 - 5) = (x - 49) / 1
This value must be positive. Since (x - 49) is positive, we know that x > 49. Now we need to find a value for x that also satisfies the condition that the average rate of change between t = 3 and t = 6 is negative. Since (x - 85) / 3 is negative, we know that x < 85.
So, a possible value for P(6) is between 49 and 85. For example, we could choose P(6) = 50, which satisfies both conditions.
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Rieko is making bird houses for a craft fair she has 15 pounds of nails how many bird houses could rieko make if each bird house requires 1/4 pounds of nails
Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.
How many bird houses could rieko makeIf each bird house requires 1/4 pounds of nails and Rieko has 15 pounds of nails, we can use the following equation to determine the number of bird houses she can make:
number of bird houses = amount of nails / amount of nails per bird house
Plugging in the given values, we get:
number of bird houses = 15 / (1/4)
Simplifying the right-hand side by dividing 15 by 1/4, we get:
number of bird houses = 60
Therefore, Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.
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Mr Lim, Mr Bell and Mrs Walker paid for a meal. Mr Lim paid 1/5 of the amount Mr Bell and Mrs Walker paid together. Mr Bell paid 1/4 of the amount Mr Lim and Mrs Walker paid. A) What fraction of the total cost of the meal did Mrs Walker pay?
As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C)
what is fraction ?A fraction is a number that in mathematics represents a portion of a whole. It consists of a horizontal line between the numerator and denominator of two numbers. The denominator is the total number of equally sized components that make up the whole, whereas the numerator is the number of parts that are being taken into account. As an illustration, the fraction 3/4 denotes three of the four equal pieces. The denominator, 4, indicates that the entire is divided into four equal parts, while the numerator, 3, indicates that three parts are being taken into consideration.
given
Payment to Mr. Lim:
1/5(B + W) = (B + W)/5
Payment to Mr. Bell:
1/4(L + W) = (L + W)/4
These equations can be combined to find the value of W, or the amount Mrs. Walker paid:
(L + W)/4 + W + (B + W)/5 = C
To get rid of the fractions, multiply both sides by 20, which is the least common multiple of 5 and 4. This gives us:
20W + 4(B + W) + 5(L + W) = 20C
By enlarging and condensing, we obtain:
20C = 4B + 4W + 5L + 5W + 20W
9W + 4B + 5L = 20C
Now, we may change the expressions for the payments made to Mr. Lim and Mr. Bell to:
9W plus 4 (1/5 B + W) plus 5 (1/4 L + W) equals 20C.
If we simplify, we get:
9W + 4B + 4W + 4W + 4W + 5L + 5W = 20C.
When we multiply both sides by 20 to once more get rid of the fractions, we get:
400C = 180W + 16B + 16W + 25L + 25W
20C = 4B + 4W + 5L + 5W + 20W
9W + 4B + 5L = 20C
Now, we may change the expressions for the payments made to Mr. Lim
If we simplify, we get:
61W + 16B + 25L = 400C
We may now determine W:
W = (400C - 16B - 25L) / 61
We can divide W by the overall cost C to determine the portion of the cost of the lunch that Mrs. Walker covered:
W/C = (400C - 16B - 25L) / (61C)
W/C = 400/61 - (16B + 25L) / (simplified) (61C)
As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C) .
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if someone knows the answer please tell me
Answer:
Step-by-step explanation:
first graph
y = 5x + 2
2 = y-intercept
5 = slope
the first graph is y = 5x+2 because the y-intercept is 2 and it rises 5 and goes over 1
second graph:
y = 2x + 3
third graph:
y = 3x + 3
The box plot above summarizes the resting heart rates, in beats per minute, of the members at a gym.
Which of the following could be the range of resting heart rates, in beats per minute ?
The range of resting heart rates is 70 beats per minute. Subtracting the lowest value from the highest value will give us the range.
What is range?It is a set of data which is the difference between the highest and lowest values.
The range of resting heart rates, in beats per minute, is calculated by subtracting the minimum value of the data set from the maximum value. In this case, the minimum value = 35
and the maximum value = 105,
so the range of resting heart rates = 105 - 35
= 70 beats per minute
The other answers cannot be the range of the resting heart rates because they are not calculated correctly.
The answer 16 beats per minute (105 - 89 = 16) is the difference between the maximum and the 90th percentile, and the answer 31 beats per minute (85 - 54 = 31) is the difference between the 85th percentile and the median.
The answer 62 beats per minute (95 - 33 = 62) is the difference between the 95th percentile and the minimum.
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Question:
or children between the ages of 5 and 13 years, the Ehrenberg equation ln � = ln 2.4 + 1.84 ℎ gives the relationship between the weight � (in kilograms) and the height ℎ (in meters) of the child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.1 m.
We can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
What is differential?A differential equatiοn is an equatiοn that includes an unknοwn functiοn and its derivative. A differential equatiοn describes a relatiοnship between a functiοn and changes in the functiοn.
The given equatiοn relating weight (W) and height (h) fοr children between 5 and 13 years οld is:
ln(W) = ln(2.4) + 1.84h
We want tο estimate the change in weight when a child grοws frοm a height οf 1 m tο 1.1 m.
First, we need tο calculate the weight at h = 1 m and h = 1.1 m.
At h = 1 m, we have:
ln(W1) = ln(2.4) + 1.84(1)
ln(W1) = ln(2.4) + 1.84
ln(W1) ≈ 2.684
Sο the weight at h = 1 m is apprοximately W1 ≈ e².684 ≈ 14.66 kg.
Similarly, at h = 1.1 m, we have:
ln(W2) = ln(2.4) + 1.84(1.1)
ln(W2) = ln(2.4) + 2.024
ln(W2) ≈ 2.807
Sο the weight at h = 1.1 m is apprοximately W2 ≈ e².807 ≈ 16.59 kg.
Tο estimate the change in weight when the height increases frοm 1 m tο 1.1 m, we can use the differential οf the equatiοn:
dln(W) = 1.84dh
Using differentials, we can apprοximate the change in weight as:
dW ≈ W2 - W1
dW ≈ e².807 - e².684
dW ≈ 1.93 kg
Therefοre, we can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
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An account pays 2.4% compounded monthly. Suppose you invest $150 a month for 8 years, then leave the money in the account, without making additional payments, for another 12 years. a. How much will you have at the end of the 20 years? b. How much interest did you earn?
If yοu invest $150 a mοnth fοr 8 years, then leave the mοney in the accοunt, withοut making additiοnal payments, fοr anοther 12 years.
a) Yοu will have yοu will have apprοximately $59,073.95 at the end οf 20 years.$59,073.95 at the end οf 20 years.
b) Earned apprοximately $26,673.95 in interest οver the 20-year periοd.
What Is the Future Value οf an Annuity?The wοrth οf a series οf recurrent payments at a specific future date, assuming a specific rate οf return, οr discοunt rate, is the future value οf annuity.
Let's first calculate the tοtal number οf mοnths in 20 years:
20 years x 12 mοnths/year = 240 mοnths
a. we can use the fοrmula fοr the future value οf an annuity:
[tex]FV = PMT x (((1 + r/n)^(n*t) - 1) / (r/n))[/tex]
where:
PMT = the mοnthly payment ($150)
r = the annual interest rate (2.4% οr 0.024)
n = the number οf times the interest is cοmpοunded per year (12)
t = the tοtal number οf years (20)
FV = 150 x (((1 + 0.024/12)^(12*20) - 1) / (0.024/12))
FV ≈ $59,073.95
Therefοre, yοu will have apprοximately $59,073.95 at the end οf 20 years.
b. Tο calculate the amοunt οf interest yοu earned, we can subtract the tοtal amοunt οf mοney yοu invested frοm the future value:
Interest = FV - Tοtal amοunt invested
Interest = $59,073.95 - ($150 x 12 x 8 x 12)
Interest ≈ $26,673.95
Therefοre, yοu earned apprοximately $26,673.95 in interest οver the 20-year periοd.
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The perimeter of a rectangle is
360cm. find the breadth if its
length is 80cm.
Answer:
4.5 cm.
Step-by-step explanation:
Divide the length by the width to get the perimeter: 360 / 80 = 4.5 cm.
PLEASE MARK ME BRAIN LISTHOPE IT HELP YOU
Find the derivative of f(x)=−148x+1−−−−−√7
.
Answer: f(x) is -74(x+1/7)^(-1/2)
Step-by-step explanation:
To find the derivative of f(x), we can use the power rule and the chain rule.
First, let's rewrite f(x) as:
f(x) = -148(x+1/7)^(1/2)
Now, we can apply the power rule:
f'(x) = -148 * (1/2) * (x+1/7)^(-1/2)
Finally, we can use the chain rule:
f'(x) = -148 * (1/2) * (x+1/7)^(-1/2) * 1
f'(x) = -74(x+1/7)^(-1/2)
Therefore, the derivative of f(x) is -74(x+1/7)^(-1/2).
PLEASE HELP!!
x^2=7y-4+9x^2
A cone has a base area of 24 square inches and a height of 8 inches. What is the area of a cross-section of the cone
that is parallel to the base and 3 inches from the vertex?
The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is
Square inches.
Write the answer in friction
Answer:
Step-by-step explanation:
Cone height h = 8
Cone base r = sqrt( 24/pi) = 2.764
AB = h - 3 = 5
BC = 5 / tan(β) = 1.727
FB = FC - BC = 1.036482449 ( FB is the radius of cross-section circle)
Area of a cross-section is: (FB)2 * pi = 3.375 in2
ssume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1800 fish. Absent constraints, the population would grow by 180% per year.
If the starting population is given by
p
0
=
100
, then after one breeding season the population of the pond is given by
p
1
=
After two breeding seasons the population of the pond is given by
p
2
=
he is literally hitting the gritty
x – 19 ≤ 81, if x = 110
The inequality x - 19 ≤ 81 is not satisfied when x = 110.
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The given inequality is X – 19 ≤ 81, and we are asked to evaluate it when X = 110. To do so, we substitute X with 110 and simplify the expression. In this case, we get 110 - 19 ≤ 81, which simplifies to 91 ≤ 81. Since this statement is false, we conclude that the inequality X – 19 ≤ 81 is not satisfied when X = 110.
we can substitute x = 110 and simplify:x - 19 ≤ 81
110 - 19 ≤ 81
91 ≤ 81
This statement is false, since 91 is not less than or equal to 81.
Therefore, the inequality x - 19 ≤ 81 is not satisfied when x = 110.
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An observer views a rocket take off from a distance of N miles from the launch pad, and tracks the angle of elevation.
a) Express the height of the rocket as a function of the angle of elevation, Θ.
b) Express the angle of elevation as a function of the height, h, of the rocket.
c) When the angle of elevation is A degrees, find the height of the rocket.
N=Any given number
A=Any given angle
(My Open Math question)
Short Answers:
a)N*tan(Θ)
b)arctan(h/N)
c)N*tan(A)
Let * stand for multiplication
Hope this is helpful to someone:)
Theodore invests $15,000 into an account at an annual rate of 0.55% simple interest for 36 months.
1) What is the Principal in this scenario?
1) 0.0055
2) 0.55 %
3) $15,000
4) 3
2) What is the interest rate for this account?
1) 0.55 %
2) $15,000
3) 3
4) 0.0055
3) What number do you use to represent the interest rate in the simple interest formula?
1) 0.55 %
2) 3
3) $15,000
4) 0.0055
4) What is the length of time of this investment, in years?
1) 0.55 %
2) 3
3) $15,000
4)0.0055
5) Calculate the simple interest earned on this account.
Answer:
1)$15000
2)0.55%
3)0.55
4)3
5)24.75
Step-by-step explanation:
5)1500×0.55×3/100
Rewrite 300-4 in a different way, using the Commutative Law of Multiplication.
A) 30-40
B) 1200
C) 4.300
D) 3.100-4
Answer:
3x100-4
Step-by-step explanation:
3x100=300
(3x100)-4
300-4
help i forgot how to do this
1. The angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees. 2. the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.
Describe Cosine?In trigonometry, cosine (cos) is a trigonometric function that relates the adjacent side and the hypotenuse of a right triangle. It is defined as the ratio of the adjacent side to the hypotenuse. The cosine function is periodic with a period of 360 degrees or 2π radians, and it has a range of values between -1 and 1.
In other words, if we have a right triangle with an angle x, then the cosine of x is equal to the length of the adjacent side of the triangle divided by the length of the hypotenuse.
1.In a right-angled triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. Therefore, cos(x) = adjacent/hypotenuse = 37/39.
Using inverse cosine function on a calculator, we get x ≈ 23.6 degrees.
Therefore, the angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees.
2. Again, using the definition of cosine, we have cos(x) = adjacent/hypotenuse = 8/17.
Using inverse cosine function on a calculator, we get x ≈ 62.3 degrees.
Therefore, the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.
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I need help with this math problem. It’s from the course “Apply Math”.
The expected value of the gas grill is 6.50 million dollars if a development cost of $4 million is invested.
What is expected value?The expected value is the sum of all possible outcomes multiplied by their associated probabilities.
The expected value of the gas grill can be calculated as follows:
Expected value = (0.10 × 3) + (0.50 × 6) + (0.40 × 8)
= 0.30 + 3.00 + 3.20
= 6.50 million dollars
Therefore, the expected value of the gas grill is 6.50 million dollar.
This calculation allows investors to decide whether or not to invest in a specific project, as the expected return must be greater than the development cost.
In this case, the expected value of 6.50 million dollars is greater than the development cost of 4 million dollars, making the investment a viable option.
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Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.01q2 +5q-39, where q
is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in
thousands of dollars, from selling and producing a pairs of sunglasses.
A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your
answer.)
Answer: MP(q)
B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your
answer to three decimal places.)
Answer:
thousand pairs of sunglasses need to be sold.
C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your
answer to three decimal places.)
=
Answer:
thousand dollars of maximum profits can be expected.
Solving the quadratic equation, we get the maximum profit is 2451 thousand dollars.
What are quadratic equations?A second-degree algebraic equation in x is known as a quadratic equation. The quadratic equation is written as Ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
For an equation to be categorised as a quadratic equation, the coefficient of x2 must be a non-zero term (a 0).
The function is given as
P(q) = -0.01q2 +5q-39
We have
P(q) = -0.01q2 +5q-39
Differentiate
So, we have
P'(q) = -0.01q + 5
Set to 0
So, we have
-0.01q + 5
This gives:
-0.01q = -5
Evaluate
q = 500
Hence, 500 thousand pairs of sunglasses should be sold to maximize profits.
What is the maximum profit?
In (a), we have
q = 500
This gives:
P (500) = (-0.01)500×2 +5×500-39
Evaluating:
P (500) = -10 + 2500 -39
= 2451
Hence, the maximum profit is 2451 thousand dollars.
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When we solve the quadratic equation, we discover that the utmost profit is $2451 thousand dollars.
What are quadratic equations?A quadratic equation is an x-dependent second-degree algebraic problem. [tex]ax^{2} +bx+c=0[/tex], where x is the variable, a and b are the coefficients, and c is the constant element, is how the quadratic equation is expressed.
The coefficient of [tex]x^{2}[/tex] must not be negative for an equation to be categorized as a quadratic equation (a, 0).
The function is given as
P(q) = [tex]-0.01q^2[/tex] +5q-39
We have
P(q) = [tex]-0.01q^2[/tex] +5q-39
Differentiate
So, we have
P'(q) = -0.01q + 5
Set to 0
So, we have
-0.01q + 5
This gives:
-0.01q = -5
Evaluate
q = 500
So, in order to make the most money 500 000 sets of sunglasses should be sold.
In (a), we have
q = 500
This gives:
P (500) = (-0.01)500×2 +5×500-39
Evaluating:
P (500) = -10 + 2500 -39
= 2451
Therefore, the highest profit is $2451 thousand dollars.
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1+1 I don’t know I’m in 7 th grade
Answer:
2
Step-by-step explanation:
no explanation needed.
Pleas help, Will mark brainliest and if you don't know then don't answer
Answer: 10 pigs and 3 chickens
Step-by-step explanation:
So the farmer has seen 40 legs
Pigs have 4 legs & Chickens have 2
Pigs: 40/4= 10 pigs
Chickens: 40/2= 20 chickens
So with us know which answer is correct we choose 10 pigs
Then if we have 10 pigs we have 3 chickens
13-10= 3 chickens
In conclusion we have the 10 pigs & 3 chickens
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
the values of x are 13 and 1.
Step-by-step explanation:
x - 7 = +√36 or x - 7 = -√36
Therefore,
x - 7 = +6 or x - 7 = -6
=> x = 7 + 6 or x = 7 - 6
=> x = 13 or x = 1
Therefore, the values of x are 13 and 1.
Answer: x = 25
Step-by-step explanation:
(x – 7)2 = 36 (Given)
2(x -- 7) = 36 (Associative Property)
2x - 14 = 36 (Distributive Property)
2x - 14 + 14 = 36 + 14 (Addition Property of Equality)
2x = 50 (Simplification)
2x/2 = 50/2 (Division Property of Equality)
x = 25 (Simplification)
X follows Poisson distribution. This distribution was randomly sampled 40 times. The sum of these 40 numbers follows
a) Poisson distribution
b) Exponential distribution
c) Weibull distribution
d) Normal distribution
The sum of these 40 sampled numbers follows option D: normal distribution, if X follows Poisson distribution.
The likelihood that a certain number of events will occur in a specific period of time or space, provided that they do so with a known constant mean rate and the Poisson distribution describes the distribution of events, regardless of the time since the previous event. When the mean is high, the sum of the Poisson distribution resembles a normal distribution.
The "normal distribution," a continuous probability distribution that is symmetrical at the mean and has a bell-shaped curve. It is also known as the bell curve or the Gaussian distribution. Several natural phenomena, including height, weight, blood pressure, and others, have a normal distribution.
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Find the polynomial that represents the area of the square
The polynomial expression that represents the area of the given square is: 4x² + 28x + 49
What is the area of the square?The formula for the area of a square is expressed as:
Area = side * side
Now, we are given the dimensions of the square and we have:
Side length = x + 7 + x = 2x + 7
Thus:
Area of square = (2x + 7) * (2x + 7)
= 4x² + 14x + 14x + 49
= 4x² + 28x + 49
Thus, we conclude that expression represents the area of the square.
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w/ solution please
thank uuu
Roger and Rohan are partners of R&R Biscuit Company. Given below is details of items that appeared in their current account for the year ended December 31, 2019:
The net profit before appropriation is (d). $1,889,000.
How to solveTo calculate net profit before appropriation to R&R biscuit company by adding all the appropriation expense to share of profit after appropriation and deducting appropriation income.
In this case, interest on capital, drawings and partner's salary are appropriation expense while interest on drawings is appropriation income.
Now,
Net profit before appropriation
= ($650,000+$200,000+$100,000+$30,000-$20,000) + ($650,000+$150,000+$130,000+$25,000-$26,000)
= $960,000 + $929,000
= $1,889,000
So, the correct answer is (d). $1,889,000.
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