The payment amount rate required to pay off the loan in 2 years is k = $4,266.67 and the total interest paid during the two-year period is $2,142.66. This is calculated by using the formula for continuous compounding to solve for k and the formula for calculating interest to solve for I.
1. Calculate the payment rate required to pay off the loan in 2 years:
k = P/(1 - e^(-rt))
= 7506/(1 - e^(-0.15*2))
= 7506/(1 - 0.8698)
= 4,266.67
2. Calculate the total interest paid during the two-year period:
I = P(e^(rt) - 1)
= 7506(e^(0.15*2) - 1)
= 7506(1.3302 - 1)
= 2,142.66
Payment rate required to pay off the loan in 2 years: K = $5,062.89. The amount of interest paid during the 2-year period is $1,506.11. The borrower pays back a total of $9,012.89 over the 2-year period. The interest rate of 15% is continuously compounded and the payments are made at a continuous rate of K dollars per year.
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What is the reading of each thermometer? Pls help!!!
Answer:
celsius is 100 Fahrenheit is 42 kelvin is 30045
2x -3y > -9 in standard form
Answer:
2x-3y>-9
Step-by-step explanation:
Standard Form = Ax+By=C
2x-3y>-9 is already in standard form.
Hope this helps :)
Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = sin(x) + 9 0 < x < 2Ï€ increasing decreasing
The function is increasing on the open interval (0, 2Ï€) and decreasing on the open interval (-2Ï€, 0).
The derivative of a function tells us the slope of the function at any given point, and the sign of the derivative tells us whether the function is increasing or decreasing at that point. If the derivative is positive, the function is increasing at that point, and if the derivative is negative, the function is decreasing at that point.
The function f(x) = sin(x) + 9 is increasing on the interval (0, 2π) because the derivative of sin(x) is positive on this interval. The derivative of sin(x) is cos(x), which is positive for all values of x except for multiples of π.
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Sara earns a 15% commission on furniture that she sells. How much commission
would she earn if she sells a dining room set for $850?
well, how much is 15% of 850?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 850}}{\left( \cfrac{15}{100} \right)850}\implies 127.5[/tex]
What is the measure of∠A in the triangle shown?
Answer:
23
Step-by-step explanation:
Answer:
m∠A = 70°
Step-by-step explanation:
The dashes on line segments AB and AC mean that they are equal in length. Therefore, the triangle is an isosceles triangle. This means that the two base angles, ∠B and ∠C are congruent.
Interior angles of a triangle sum to 180°. Therefore:
⇒ m∠A + m∠B + m∠C = 180°
⇒ m∠A + 55° + 55° = 180°
⇒ m∠A + 110° = 180°
⇒ m∠A + 110° - 110° = 180° - 110°
⇒ m∠A = 70°
Help would be greatly appreciated’
The solution of the give inequality is n < 6
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given is an inequality, 3-2(n-4) > -1
On solving, we get,
3-2(n-4) > -1
3-2n+8 > -1
-2n+11 > -1
2n-11 < 1
2n < 12
n < 6
Hence, the value of the inequality is n < 6
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Find the circumferences of of both circles to the nearest hundredth.
The circumference of the yellow circle is about | 69.12 × ft.
The circumference of the purple circle is about | 25.13 × ft
a. The circumference of the yellow circle is 43.96 ft.
b. The circumference of the purple circle is 28.26 ft.
What is the circumference of a circle?A circle is a figure that is bounded by a curved path called circumference. Thus a circumference if the boundary of a given circle. It can be determined by;
circumference of a circle = 2πr
where r is the radius of the circle.
In the diagram given in the question, we have;
a. diameter of the purple circle = 9 ft, so that;
r = d/2
= 9/2 = 4.5 ft
Circumference of the purple circle = 2πr
= 2*3.14*4.5
= 28.26
Circumference of the purple circle is 28.26 ft.
b. diameter of the yellow circle = 2.5 + 9 + 2.5
= 14
So that;
r = d/2
= 14/2 = 7 ft
Circumference of the yellow circle = 2πr
= 2*3.14*7
= 43.96
The circumference of the yellow circle is 43.96 ft.
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Estimate the quotient of 42.4 ÷ 7.28.
Answer:
5 is the *estimate*
MPModel with Mathematics There are 8 seahorses and 8 fish in the water. How many seahorses and fish are there in all?
Answer:
they are 8 seahorse.becauce even seahorse are fish
Find the sum and express it in simplest form.
(6y³+ y2) + (-4y³ + 2y² + 1)
008
Clear all
Enter the correct answer.
180
?
DONE
Answer:
[tex]2y^3+3y^2+1[/tex]
Step-by-step explanation:
Given expression:
[tex](6y^3+y^2)+(-4y^3+2y^2+1)[/tex]
Remove the parentheses:
[tex]6y^3+y^2-4y^3+2y^2+1[/tex]
Collect like terms:
[tex]6y^3-4y^3+y^2+2y^2+1[/tex]
Combine like terms:
[tex]2y^3+3y^2+1[/tex]
-9+2a<3a…………………………..
For each of the following transformations of the parent function f(x) = x^3, graph both functions on the same set of axes, and evaluate the impact of the transformation on the number and location of the X-and y-intercepts, and on the symmetry of the function.
The graph of the functions f(x) = (-5x)³ and f(x) = x³ - 4 are drawn below.
How to draw the graph of the function?The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.
The parent function is given below.
f(x) = x³
The function is stretched by 5 units and gets reflected over the y-axis. Then the function is given as,
f(x) = (-5x)³
The function is shifted by 4 units downward then subtract 4 from the function. Then the function is given as,
f(x) = x³ - 4
The graph of the functions f(x) = (-5x)³ and f(x) = x³ - 4 are drawn below.
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Write an equation for a line parallel to y=−3x−5 and passing through the point (2,-10)
Considering the definition of parallel line, the equation for a line parallel to y=−3x−5 and passing through the point (2,-10) is y=-3x-4.
What is Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other.
Two lines are parallel if they have the same slope m and different y-intercepts b.
Equation of parallel line in this caseThe line is y= -3x -5
where
the slope m is -3the ordinate to the origin b is -5If two lines are parallel if they have the same slope, the parallel line has a slope of -3.
The line passes through the point (2, -10). Then:
-10= -3× (2) + b
-10= -6+ b
-10 + 6= b
-4 = b
Finally, the equation of parallel line is y= -3x - 4.
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Which of these events is not mutually exclusive?
A) the chance that you will get a heads or tails when you flip a coin once.
B) the chance that you will only study for the test alone or with a friend.
C) the chance that you will meet your friends for pizza or at a chinese restaurant for dinner today at 6.
D) the chance that you will answer the ringing phone or take a walk.
The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.
On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.
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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
this question is related to probability.
mutually exclusive
Mutually exclusive events are those events that do not occur at the same time.
For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.
probability
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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If matt and Jan each make 10 gallons of punch, how many more gallons of orange juice would Jan use than Matt?
If Matt and Jan each create 10 gallons of punch, Jan uses 2 liters more orange juice as a result than Matt.
what is unitary method ?Using the unitary approach, an issue can be resolved by first figuring out the value of a single unit, then multiplying that value by the number of units needed to solve the problem. The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.
given
For his 10-gallon punch, Matt uses gallons of orange juice, which adds up to 3x=3*2 = 6.
Using the formula Jan uses gallons of orange juice to create 10 gallons of punch and Matt uses gallons of orange juice to make 10 gallons of punch, we can calculate that Jan uses 2 gallons more orange juice than Matt.
If Matt and Jan each create 10 gallons of punch, Jan uses 2 liters more orange juice as a result than Matt.
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I’ll give BRAINLIEST if correct
Answer:
No, because (6,4) is on the line.
Step-by-step explanation:
Inequality given is y > -1/2x + 7
Point given is (6, 4)
Substitute the x coordinate and y coordinate into the equation
4 > -1/2(6) + 7
4 > -3 + 7
4 > 4
(Statement is False, hence inequality does noit hold)
First part of the answer is No
Since both the left and right side of the inequality is the same at 4, the point (6,4) lies on the line.
Hence, second part is because (6, 4) is on the line.
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In the diagram below of triangle KLM, N is the midpoint of KM and O is
the midpoint of LM. If NO = 18 - 2x, and KL = 9x
measure of NO?
16, what is the
Measure on NO
Answer:
10 units
Step-by-step explanation:
2 * (18-2x) = 9x-16
36 - 4x = 9x -16
52 = 13x
x = 4 then NO = 18-2(4) = 10 units
⠀⠀⠀
Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions
to the nearest hundredth.
x² + 12x + 11 = 0
a.
b.
x = -11 or x = -1
x = 1 or x = 6
C.
d.
01:41:19
x = 10 or x = -3
x=0 or x = -6
The solution for the given quadratic equation is x = -11 or x = -1.
What is a quadratic equation?A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.
The standard form of a quadratic equation is ax² + bx + c = 0.
Where a, b and c are constants.
The given quadratic equation is,
x² + 12x + 11 = 0.
The graph of the equation is, plotted below.
From the graph,
The solutions are x = -1 and x = -11
The second approach to find the solution for the given quadratic equation is factorization method,
x² + 12x + 11 = 0
x² + 11x + x + 11 = 0
x(x + 11) + 1(x + 11) = 0
(x + 11) (x + 1) = 0
x = -11 or x = -1
So the required solution is x = -11 or x = -1.
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Elapsed time
Mary rented a movie. She started the movie at 10:29 PM and it ended at 1:49 AM. How long was the movie?
Answer:3 hours 20 mins
Answer:
3 hours 20 minutes is the length of the movie.
Michael Jordan made 7,327 of his 8,772 free-throw attempts, while Larry Bird made 3,960 of his
4,471 free-throw attempts.
a. Write the ratio of free throws made to attempts in fractional form for both players.
b. Are the two ratios proportional? Explain.
The ratio of free throws made to attempts in fractional form for both players are 1:1.2 and 1:1.1 respectively, the two ratios are not proportional
What is ratio?Ratio can be defined as the proportion of a number which can also be written as a fraction. On the other hand ratios show how many times a number is contained in another number.
The given numbers are
Michael Jordan made 7,327 of his 8,772 free-throw attemptsLarry Bird made 3,960 of his 4,471 free-throw attempts.The ratios are
Michael = 7327:8772 = 1:1.2
Larry - 3960:4471 = 1:1.1
To know if they are proportional
1/1.2 ≠1/1.1
In conclusion, from the calculations, the two ratios are not proportional
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Write 28+24 using gcf and distributive property
Answer:
4 x 13
Step-by-step explanation:
GCD of 28 and 24 is 4
28 = 4 x 7
24 = 4 x 6
4 (7 + 6)
4 x 13
1/5/2023
7:41PM
Answer: 4*(7+6), 4*7+4*6.
Step-by-step explanation:
The GCF, or greatest common factor, of 28 and 24, is 4.
So, what you would do is 4*(28/4+24/4)
You would get, 4*(7+6), 4*7+4*6.
A clock tower is 15 feet tall. How long is its shadow when the sun is at an altitude (angle above the horizon) of 60 degrees? Give your answer in feet.
The length of the shadow when the sun altitude is 60 degrees is 8.7 feet.
How to find the side of a right triangle?The clock tower is 15 feet tall. The length of the shadow when the sun is at an altitude of 60 degrees can be calculated as follows:
This situation forms a right angle triangle.
Hence, using trigonometric ratios,
tan 60 = opposite / adjacent
where
opposite side = 15 feet
adjacent side = x
tan 60 = 15 / x
cross multiply
x tan 60° = 15
divide both sides by tan 60
x = 15 / tan 60
x = 15 / 1.73205080757
x = 8.65800865801
x = 8.7 feet
Therefore,
length of shadow = 8.7 feet.
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What is .622 as a percent
Answer:
62.2%
Step-by-step explanation:
0.622 x 100 = 62.2%
an open tank is 3 M long 2 m wide and 1 m 50 cm deep how much amount of paint is required to paint its inside and outside if 1 kg of paint covers 20 Sq m
First, calculate the surface area of the inside of the tank by multiplying the length, width, and height: 3 m * 2 m * 1.5 m = 9 m^2.
Then, calculate the surface area of the outside of the tank by adding the surface area of all 6 sides: 2 * (3 m * 1.5 m + 2 m * 1.5 m + 3 m * 2 m) = 24 m^2.
Finally, add the surface area of the inside and outside to get the total surface area: 9 m^2 + 24 m^2 = 33 m^2.
To find the amount of paint required, divide the total surface area by the coverage per kg of paint: 33 m^2 / 20 m^2/kg = 1.65 kg.
What’s the correct answer answer asap for brainlist
Answer:
Hope is the thing with feathers
Step-by-step explanation:
this is because this phrase expresses how hope moves through someone
How do you change 5/8 to an equivalent fraction with a denominator of 100
We can multiply both the numerator and denominator by 12.5 to get the equivalent fraction:
5/8 = 62.5/100
How to find the equivalent fraction?We want to rewrite 5/8 as an equivalent fraction with a denominator of 100.
Remember that if we multiply both the numerator and denominator of a fraction by the same number, then we will get an equivalent fraction.
So if that number is x, we can write:
5/8 = (5*x)/(8*x)
First, we want a denominator of 100, then the value of x must be such that:
8*x = 100
x = 100/8
x = 12.5
Then the equivalent fraction is:
(5*12.5/8*12.5) = 62.5/100
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Which of the following tables represents a proportional relationship?
Answer: Choice D
Step-by-step explanation:
When we think of proportional relationships, we can think of ratios. The x and y value will be multiplied by the same ratio throughout the table to create equivalent points. The easiest way to do this is to turn the points into fractions and see if they all simplify to the first point, which in this case is 2/3.
4/6 / 2/2 = 2/3
6/9 / 3/3 = 2/3
8/12 / 4/4 = 2/3
2 is being added to the x value each time and 3 is being added to the y value each time. hope this helps!
Translate the sentence into an equation.
Three less than the product of 9 and a number equals 2.
The translation of the sentence to an equation is 9x - 3 =2
How to translate the sentence to an equationFrom the question, we have the following parameters that can be used in our computation:
Three less than the product of 9 and a number equals 2.
Represent the number with x
So, we have the following representation
Three less than the product of 9 and x equals 2.
The product of 9 and x means 9x
So, we have
Three less than 9x equals 2.
Three less than means -3
So, we have
9x - 3 equals 2
Lastly, we have
9x - 3 =2
Hence, the equation is 9x - 3 =2
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Shady Grove Middle School is having an outdoor activity day. Each grade can have several teams, but the size of the team must be the same for each grade. There are 108 seventh graders and 102 eighth graders. How many students can be on each team?
Simplify each expression by combining like terms. NO SPACES in your answer.
−5.2t+8.2−7.8t
What is the answer in simpelest form?
The simplification of the expression -5.2t+8.2-7.8t is 8.2-13t
What is simplification of expression?Simplification of expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
For example, 2x+5y-8x + y can be simplified by collecting like terms. The variables here are x and y
therefore 2x-8x+5y+y = 6y - 6x = 6( y-x)
Similarly, simplifying -5.2t+8.2-7.8t, we collect the term of t' together.
-5.2t-7.8t+8.2= -13t+8.2
= 8.2-13t
therefore the simplification of -5.2t+8.2-7.8t is 8.2-13t
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