Answer:
Okay, let's think through this step-by-step:
• Janelle Monae obtained a $3,500 loan at 8.5% interest for 1 year.
• 8.5% interest for 1 year = 8.5% of $3,500 = $297.50 in interest
• The loan amount ($3,500) plus interest ($297.50) = $3,797.50 total paid back
•Monthly payments = $3,797.50 / 12 months = $285.55
• So the interest amount in the first payment is $297.50 (calculated above as 8.5% of the $3,500 loan amount)
The choices do not match this:
A. $297.50 - This is the correct choice. This is the interest amount paid over the full loan.
B. $291.67 - This is too low. Calculated interest over 1 year at 8.5% is $297.50.
C. $24.79 - This is way too low. The interest amount due is $297.50 per the working.
D. $35.00 - This is also too low and does not make sense based on the loan details provided.
In summary, to find the interest in just the first payment, we calculate:
Interest over full loan ($297.50) / Number of payments (12) = $24.79
So the interest amount in just the first monthly payment is $24.79.
But the total interest paid over the life of the loan (1 year) is $297.50.
Does this help explain the steps and reasoning? Let me know if any part of the working or explanation is unclear. I can also provide additional examples if needed.
Let me know if you have any other questions!
Step-by-step explanation:
Martin made a stick pattern such that each successive stick is twice as long as the one before it. If the shortest stick in the pattern is long, and there are sticks in total, which is closest to the combined length of the sticks in Martin's pattern?
-7 4/5 divided by X = -5 1/5
The value of the variable is 3/2
What is a fraction?A fraction cam simply be described as an expression that is being used to represent the part of a whole number, a whole variable or element.
There are different types of fractions. They are listed as;
Improper fractionsProper fractionsComplex fractionsSimple fractionsMixed fractionsFrom the information given, we have that;
-7 4/5 divided by X = -5 1/5
convert to improper fractions, we have;
-39/5/x = -26/5
Now, cross multiply the values, we have;
-39/5 = -26x/5
cross multiply
-130x = -195
Divide both sides
x = -195/-130
x = 39/26 = 3/2
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____ are characteristics of samples, whereas ______ are characteristic of populations.
AConcepts; statistics
BParameters; statistics
CStatistics; parameters
DParameters; estimations
Find the surface area of the following figure. Round your final answer to the nearest
tenth.
The surface area is approximately 41.7 square units.
The rectangle has dimensions 18 units by 6 units, so its area is:
A(rectangle) = l x h = 18 x 6 = 108 square units
The semicircle has a radius of 5 units, so its area is half that of a full circle:
A(semicircle)
= 1/2 x π x r²
= 1/2 x π x 5²
= 1/2 x 25π
= 12.5π
To find the total surface area, we need to add the areas of the rectangle and the semicircle. However, since the semicircle is attached to the top of the rectangle, we need to subtract the area of the portion of the circle that overlaps with the rectangle. This overlapping area is equal to the width of the rectangle (18 units) times half the circumference of the circle (1/2 x π x r), or:
A(overlap)
= w x 1/2 x π x r
= 18 x 1/2 x π x 5
= 45π
Therefore, the total surface area is:
Surface area = A(rectangle) + A(semicircle) - A(overlap) = 108 + 12.5π - 45π ≈ 41.7 square units
Rounding to the nearest tenth, the surface area is approximately 41.7 square units.
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equivalent equation for (4x • 7)(5x • 9)
Another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.
What are Equivalent equations?Equivalent equations in algebra are those that have equivalent roots or solutions.
In order to produce an equivalent equation, the same quantity or expression must be added to or subtracted from both sides of the original equation.
If you multiply or divide an equation's two sides by the same non-zero number, the results are identical.
If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4.
So, we have the equation:
(4x • 7)(5x • 9)
Then, another equation that will be equivalent to the given equation can be:
(4x • 7)(5x • 9)
(28x)(45x )
Then,
28x(45x)
So,
(4x • 7)(5x • 9) = 28x(45x)
Therefore, another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.
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What is 6 5/6-5 1/2
6 5
6
-
5 1
2
The difference between 6 5/6 and 5 1/2 is 4/3 .
How to subtract these mixed numbers?To subtract these mixed numbers, we need to first convert them into improper fractions:
6 5/6 = (6 x 6 + 5)/6 = 41/6
5 1/2 = (5 x 2 + 1)/2 = 11/2
Now we can subtract:
41/6 - 11/2
To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:
11/2 = (11 x 3)/(2 x 3) = 33/6
Now we can subtract the fractions with the same denominator:
41/6 - 33/6 = 8/6
Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:
8/6 = 4/3
As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..
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The complete question is:
What is the rule for the sequence
5/6, 1 1/2, 2 1/6, 2 5/6.....
A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
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50 Points! Multiple choice algebra graphing question. The related graph of a quadratic equation is shown at the right. Use the graph to determine the solutions of the equation. Photo attached. Thank you!
Answer:
(C) {-3, 2} is the correct answer.
please help pleaseee i need dis good grade
Answer:62.8 units
Step-by-step explanation:
What is the measure of angle x?
Enter your answer in the box.
Answer:
43
Step-by-step explanation:
at the upper horizontal plane the angles add up to 180 degrees so you add the right angle with the 47 degrees and then you subtract the answer from180 degrees.the value you obtain is oppositely equal to the value of x hence,43
The factorization of x2 – 6x – 72 is:
Step-by-step explanation:
x^2 -6x - 72 = ( x-12)(x+6)
If you can't do this 'in your head' you can always use Quadratic Formula
with a = 1 b= - 6 and c= -72
to find roots x = 12 and -6 then write the equation as above
A triangular building is bounded by three streets. The building measures approximately 94 feet on the first street, 188 feet on the second street, and 168 feet on the third street. Approximate the ground area K covered by the building.
Answer: To find the area of a triangle, we can use the formula:
Area = (base x height) / 2
However, in this problem, we don't have the height of the triangle directly. Instead, we have the lengths of three sides of the triangle.
To find the height, we can use Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides:
Area = √(s(s-a)(s-b)(s-c))
where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter (half of the perimeter) of the triangle:
s = (a + b + c) / 2
Once we have the area of the triangle, we can use the given price per square foot to calculate the cost of the lot.
So, to apply this to the problem at hand, we can first calculate the semi-perimeter of the triangle:
s = (94 + 188 + 168) / 2 = 250
Next, we can use Heron's formula to find the area of the triangle:
Area = √(250(250-94)(250-188)(250-168)) ≈ 7329.53 square feet
Finally, we can calculate the cost of the lot by multiplying the area by the price per square foot:
Cost = 7329.53 x $3 = $21,988.59
Therefore, the approximate cost of the triangular lot is $21,988.59.
Step-by-step explanation:
Find the sum of 401-137 then use estimation to see if your answer is reasonable
Since 260 is close to 264, our answer of 264 is reasonable.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
The sum of 401-137 can be found by subtracting 137 from 401:
401 - 137 = 264
Therefore, the sum of 401-137 is 264.
To estimate whether this answer is reasonable, we can use rounding. We can round 401 to 400 and 137 to 140, which makes the subtraction easier to estimate mentally:
400 - 140 ≈ 260
Since 260 is close to 264, our answer of 264 is reasonable.
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x = sin t, y = 3 cos t
Answer:
16.39 square units.
Step-by-step explanation:
The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.
To see this, we can use the Pythagorean identity for sine and cosine:
sin^2 t + cos^2 t = 1
Multiplying both sides by 9, we get:
9 sin^2 t + 9 cos^2 t = 9
Substituting x = sin t and y = 3 cos t, we get:
9 x^2 + y^2/3 = 9
This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.
The area of an ellipse is given by the formula:
Area = pi * a * b
Substituting the values of a and b, we get:
Area = pi * 3 * sqrt(3) ≈ 16.39
Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.
PLEASE HELP QUICK How many clubs have at least 30 members?
A.5 clubs
B.6 clubs
C.8 clubs
D.9 clubs
Answer:
D. 9 clubs
Step-by-step explanation:
Given a stem-and-leaf plot of the number of members in clubs, you want to know the number of clubs with 30 or more members.
Stem and Leaf PlotThe plot shows the club membership to be ...
{10, 13, 15, 24, 26, 30, 36, 39, 50, 55, 59, 61, 66, 78}
The 9 clubs whose member numbers are in bold have at least 30 members.
The number of clubs with at least 30 members is ...
D. 9 clubs
<95141404393>
i need help please also need the answer.
The correct answer as a trinomial in descending degree order is -2x^2 + 6x + 4
How to solve
Here's the step-by-step solution with the figures:
(5x^2 + 10x - 5) - (7x^2 + 4x - 9)
= 5x^2 + 10x - 5 - 7x^2 - 4x + 9 (distribute the negative sign)
= (5x^2 - 7x^2) + (10x - 4x) + ( -5 + 9) (collect like terms)
= -2x^2 + 6x + 4 (simplify and arrange in descending degree order)
Therefore, the simplified expression in descending degree order is -2x^2 + 6x + 4.
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A slow pitch softball diamond is actually a square 60' on side how far is it from home to 2nd base
Answer:
The distance from home to second base is approximately 84.85 feet in a slow pitch softball diamond that is 60 feet on each side.
Step-by-step explanation:
In a softball diamond that is 60 feet on each side, the distance from home to second base is approximately 84.85 feet. This is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the distance from home to second base forms the hypotenuse of a right triangle with legs that are each 60 / sqrt(2) feet long. Using the Pythagorean theorem, we can calculate that the distance from home to second base is approximately 84.85 feet.
Write an equation of the line below.
You are going to start a business making chicken sandwiches and hamburgers. You have a budget of $750. The chicken sandwich costs $2.75 to make and the hamburger costs $1.95 to make. Which inequality models the situation?
A. 2.75x+1.95y ≤ 750, where x is # of chicken sandwiches and y is # of hamburgers
B. 2.75x+1.95y = 750, where x is # of chicken sandwiches and y is # of hamburgers
C. 2.75x+1.95y ≥ 750, where x is # of chicken sandwiches and y is # of hamburgers
The correct option is A, the inequality is:
2.75x + 1.95y ≤ 750
Which inequality models the situation?Let's define the variables we will be using:
x = number of chicken sandwiches
y = number of hamburgers.
We know that the budget is $750, and the chicken sandwich costs $2.75 to make and the hamburger costs $1.95 to make, then we can write the inequality:
"Total cost equal to or smaller than 750"
2.75x + 1.95y ≤ 750
That is what we can see in option A, so that is the correct one.
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HURRY DUE TONIGHT
Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
Brand B contains 3% saline solution by volume.
The correct option is B.
We have,
Brand A was a six gallon 18% saline solution.
Final, she 18 gallon 8% saline solution mixture.
let the percentage of saline solution in brand B be x.
So, volume of saline solution
= 18% of 6 gallons + x% of (18 - 6) gallons
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Thus, the percentage of saline solution in brand B is 3%.
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ms george baked 2 cakes of equal size each of her 12 guests at the same amount of cake, and no cake was left over.
a What fraction of a cake did each guest eat
b. How do you think ms george cut the cakes into equal pieces? Explain
Choose the scatterplot(s) that DO NOT suggest a linear relationship between x and y.
O a
O b
Oc
O d
y
y
y
y
2nd and 3rd scatterplot do not suggest a linear relationship between x and y.
What is scatterplot?
A scatter plot is a particular type of plot or mathematical diagram by using Cartesian coordinates to display values for typically two variables for a set of values. It represents the correlation between two sets of data which may be linear or non linear sometimes strongly positive linear sometimes it may be curvilinear sometimes it may be null.
In the first plot it visibly showing a graph for straight line that is strong positive linear scatter plot. Same for the last but there is a little difference that it is negative linear scatter plot.
For the second one there is a null scatter plot. So there is no correlation.
For the 3rd graph there is a curvilinear relation in the scatterplot.
Hence, 2nd and 3rd scatterplot do not suggest a linear relationship between x and y.
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Suppose that the function h is defined, for all real numbers, as follows.
h(x) =
-2 if x-2
-1 if x=-2
Find h(-5), h (-2), and h (5).
h(-5) =
h (-2) = 0
h (5) = 0
8
X
S
The given function h(x) is h(-5) = -2, h(-2) = -1 and h(5) = -2.
What is the defined function for all real numbers?The set of all possible inputs is the domain of a function. For instance, all real integers other than x=0 are in the domain of f(x)=x2 and g(x)=1/x, respectively. Additionally, custom functions with more restricted domains can be defined.
The definition of the function h(x) is as follows:
h(x) =
-2 if x < 2
-1 if x = -2
Using this definition, we can find the values of h(-5), h(-2), and h(5) as follows:
h(-5): Since -5 < 2, we use the first part of the definition and set h(-5) = -2.
h(-2): Since -2 = -2, we use the second part of the definition and set h(-2) = -1.
h(5): Since 5 > 2, we use the first part of the definition and set h(5) = -2.
Therefore, we have:
h(-5) = -2
h(-2) = -1
h(5) = -2
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what is the answer (x+80)(x-20)
Answer:
Using the FOIL method to multiply (x + 80)(x - 20), we get:
(x + 80)(x - 20) = x^2 - 20x + 80x - 1600
Simplifying the expression, we get:
(x + 80)(x - 20) = x^2 + 60x - 1600
Therefore, the answer is x^2 + 60x - 1600.
I really need help with this to find x value and need reasons
Answer:
x = 45 degrees
Step-by-step explanation:
All angles in a triangle will add up to 180 degrees. So far we have 57 degree of 180. We also see a supplementary angle, with one side being 102 degrees, so the other is 78 degrees, because it must add up to 180. We see that the arrows in the bases show that the corners are even, so now we know two corners: one with 57 degrees and the other with 78.
Now, follow this equation to find x:
57 + 78 + x = 180
135 + x = 180
-135 -135
x = 45
24. Which description describes the solutions to this inequality?
9 > 52
A. all the possible numbers that are smaller than twenty-five
B. all the positive numbers that are greater than ten
C. all the positive numbers that are larger than twenty-five
D. all the possible numbers that are smaller than ten
The description describes the solutions to this inequality in all the positive numbers that are greater than ten. The correct option is B.
What is inequality?Relationships between two expressions that aren't equal to one another are known as inequalities. Social justice theories are fundamentally based on the idea of inequality, which is the condition of not being equal, especially in terms of status, rights, and opportunities.
The given equation is 9 > 52.
everything that is positive and bigger than 10
Therefore, the correct option is B. All the positive numbers are greater than ten.
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Kamrie wants to paint her living room. The rectangular room measures 20 feet by 15 feet and has 10-foot ceilings. Along one of the long walls, there are three windows that each
measure 3 feet by 8 feet. Along one of the short walls, there are two windows that each measure 3 feet by 8 feet. Along the other long wall, there is a rectangular opening that measures
7 feet by 8 feet. The cans of paint Kamrie will purchase cover 415 square feet.
Part A: Determine the area of the walls. Show your work.
Part B: Determine the area of the doors, windows, and rectangular opening. Show your work.
Part C: Determine the area that Kamrie will paint and then determine how many cans of paint Kamrie needs to buy.
A) The area of the walls is 700 ft²
B) The area of the doors, windows, and rectangular opening is 226ft²
C) The area that Kamrie will paint is 474 ft², and she will need to purchase 2 cans of paint.
How did we arrive at the above?Part A:
The area of each of the short walls is
10 ft x 15 ft
= 150 sq ft.
So, the total area of the four walls is:
2(200 sq ft) + 2(150 sq ft)
= 700 sq ft
Part B:
The area of the three windows along the long wall is
3 ft x 8 ft
= 24 sq ft each, so their total area is
3(24 sq ft)
= 72 sq ft
The area of the two windows along the short wall is also
3 ft x 8 ft = 24 sq ft each,
so their total area is
2(24 sq ft)
= 48 sq ft
The area of the rectangular opening along the other long wall =
7 ft x 8 ft = 56 sq ft.
So, the total area of the doors, windows, and rectangular opening is
72 sq ft + 48 sq ft + 56 sq ft
= 176 sq ft
Part C:
To determine the area that Kamrie will paint, we need to subtract the area of the doors, windows, and rectangular opening from the total area of the walls
700 sq ft - 176 sq ft
= 524 sq ft
To determine how many cans of paint Kamrie needs to buy, we divide the area to be painted by the coverage per can
524 sq ft ÷ 415 sq ft/can
≈ 1.26 cans
So Kamrie needs to buy at least 2 cans of paint to cover the entire living room.
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Hallar la ecuación de la parábola cuya directriz es la recta x= - 6 y su foco es F(0,0).
The required equation of the parabola is y² = 24x for focus (6,0) and directrix x= -6 .
The focus and directrix of the required parabola are as,
Focus (6, 0)
and, Directrix x = - 6
Since the focus of the parabola lies on the x- axis, the x- axis is said to be the axis of the parabola.
Therefore, the equation of the parabola is either of the form,
y² = 4ax
or, y2 = - 4ax
depending on which axis the parabola is in, that is whether negative or positive axis.
It is also seen that the directrix, x = - 6 which implies it is to the left of the y- axis while the focus is (6, 0) which implies it is to the right of the y-axis.
Hence, the parabola is of the form y² = 4ax.
Since, a = 6
Thus, the equation of the parabola is y² = 4(6)x
⇒ y² = 24x
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The segmented bar graph shows the relative frequencies regarding your arrival time to school using three different routes. How many times more likely are you to be on time than be late to school if you take Route C?
Therefore, you are three times more likely to be on time than be late if you take Route C to school.
What is relative frequency?Relative frequency is a statistical term that refers to the proportion or percentage of times an event or a particular value occurs within a larger set of data. It is calculated by dividing the number of times the event or value occurs by the total number of observations in the data set.
Here,
To determine how many times more likely you are to be on time than late if you take Route C, we need to compare the heights of the green and red bars for Route C. From the graph, we can see that the green bar (representing on-time arrivals) is approximately three times taller than the red bar (representing late arrivals) for Route C.
To calculate how many times more likely you are to be on time than late if you take Route C, we need to find the ratio of the heights of the green and red bars:
Ratio = height of green bar / height of red bar
Looking at the segmented bar graph, we can see that the height of the green bar for Route C is approximately 0.45, and the height of the red bar is approximately 0.15.
Ratio = 0.45 / 0.15
= 3
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Does anybody know this? I am a bit confused and please answer it right cause if you don't know it don't bother
The number of different passwords, considering 2 digits and 2 letters, is given as follows:
A. 6,760,000.
B. 3,276,000.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The password is composed by:
Four digits.Two letters.With repetition, we have that:
Each of the four digits have 10 possible outcomes.Each of the two letters have 26 possible outcomes.Hence the number of passwords is given as follows:
10^4 x 26² = 6,760,000.
Without repetition, we have that:
Digits: 10, 9, 8 and 7 outcomes.Letters: 26 and then 25 outcomes.Hence the number of passwords is given as follows:
10 x 9 x 8 x 7 x 26 x 25 = 3,276,000.
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