Answer:
multiply the number of meters by 100
Bill purchases new furniture for her first apartment. The furniture costs $1,426.25 (including the tax and delivery). If the furniture place is offering an annual rate of 15.45% to finance the purchase with a SI (simple interest) add-on loan with a term of 4 years, what are the monthly payments?
$48.07 would be the monthly payments on the loan.
We must first determine the total amount of interest charged over the course of the 4-year term in order to determine the monthly payments on a basic interest add-on loan.
The formula for simple interest is:
I = P * r * t
where I is the interest charged, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.
In this case, P = $1,426.25, r = 0.1545 (15.45% expressed as a decimal), and t = 4 years. So, the total amount of interest charged is:
I = $1,426.25 * 0.1545 * 4
I = $881.25
Adding the interest to the principal, we get the total amount paid over the 4-year term:
Total amount = $1,426.25 + $881.25
Total amount = $2,307.50
We must divide the sum by the number of months left in the loan term in order to get the monthly installments. As the loan period is 4 years long, there are 48 months:
Monthly payment = Total amount / Number of months
Monthly payment = $2,307.50 / 48
Monthly payment = $48.07
Therefore, the monthly payments on the loan would be $48.07.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The correct statements regarding the scatter plot are given as follows:
The line of best fit gives the best approximation between the SAT score and the GPA.The line of best fit can be used to predict the GPA based on the SAT score.A reasonable prediction of GPA for a SAT score of 2100 is a GPA of 3.5.What is the scatter plot?The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:
(SAT score, GPA).
There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.
For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.
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The entire graph of the function g is shown in the figure below. Write the domain and range of g using interval notation.
Answer:g=g(9)
Step-by-step explanation:
A store is selling USA Spirit T-shirts. The shirts are available in red blue and white shirts of each color are available in size a small, medium, large and extra-large. Amie will randomly select one shirt from the shelf if the shelf contains equal numbers of shirts in each color and size in combination. What is the probability that Amie will select a large shirt?
The probability that Amie will select a large shirt is 0.25 or 25%.
Given information:
USA Spirit T-shirts are available for purchase in a shop.
The shirts are available in red, blue, and white, with sizes ranging from small to medium to large to extra-large.
Amie will choose one shirt at random from the shelf if the shelf includes an equal number of shirts in each color and size combination.
There are three colors and four sizes, so there are a total of 3 x 4 = 12 shirts on the shelf.
Since there are an equal number of shirts of each size and color, there are 12/4 = 3 large shirts.
The probability of selecting a large shirt is the number of large shirts divided by the total number of shirts, which is:
3/12 = 1/4 = 0.25.
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Order the numbers from greatest to least based on their absolute value.
|−25
|, |0.5|, |−34
|, |0.35|
Responses
A |0.5| > |0.35| > |−25
| > |−34
||0.5| > |0.35| > |− 2 5 | > |− 3 4 |
B |0.5| > |−25
| > |−34
| > |0.35|,|0.5| > |− 2 5 | > |− 3 4 | > |0.35|,
C |−34
| > |−25
| > |0.35| > |0.5||− 3 4 | > |− 2 5 | > |0.35| > |0.5|
D |−34
| > |0.5| > |−25
| > |0.35||− 3 4 | > |0.5| > |− 2 5 | > |0.35|
The numbers arranged from greatest to least based on their absolute value is; |-34|, |-25|, |0.5|, |0.35|
What are absolute values?The absolute value of a number is the expression or value of the distance of the number from 0 on the number line.
The numbers are; |-25|, |0.5|, |-34|, |0.35|
The absolute value of a number is positive, which indicates;
|-25| = 25
|0.5| = 0.5
|-34| = 34
|0.35| = 0.35
The above numbers arranged from greatest to least is therefore;
34 > 25 > 0.5 > 0.35
The numbers arranged from greatest to least based on their absolute value is therefore;
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What is the approximate value of the upper quartile
A 18
B 20
C 25
D 27
The approximate value of the median is 25
The median is the middle number in a sorted, ascending, or descending, list of numbers and can be more descriptive of that data set than the average.
The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
To find the median, calculate the value mean by adding together the middle values and dividing them by two.
Hence, the approximate value of the median is Median
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What is the approximate value of the median?
A 18
B 20
C 25
D 27
Best represents the population
The equation that best represents the population of the town, which increases exponentially at the rate of 6% every year, after x years is C. y = 158,260(1.06)ˣ.
What is exponential growth?Exponential growth refers to a constant percentage or rate of growth per period.
The opposite of exponential growth is exponential decay and refers to the constant rate of decay in value per period.
The town's initial population = 158,260
Growth rate per year = 6%
Let x = the number of years of growth
Let y = the population after x years
Equation:y = 158,260(1 + 0.06)^x
Thus, the correct equation representing population growth after x years is Option C.
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Edouard Manet's Luncheon on the Grass was shown in the ___ after it was rejected for the annual salon.
A. World's Fair
B. Impressionist exhibition
C. salon d'automne
D. Osalon des refuses
Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.
Option D is the correct answer.
We have,
Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.
In response to this rejection,
Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).
Thus,
Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.
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Katy plans to invest $200
each quarter into a simple, ordinary annuity that earns 3.2%
interest compounded quarterly.
What will be the future value of her annuity after 6
years?
The requried future value of Katy's annuity after 6 years will be $5268.63.
We can start by calculating the number of compounding periods over 6 years. Since Katy is investing quarterly, there are 6 x 4 = 24 compounding periods.
Next, we can use the formula for the future value of an ordinary annuity:
[tex]FV = PMT \times ((1 + r)^n - 1) / r[/tex]
Where PMT is the periodic payment, r is the interest rate per period, and n is the total number of periods.
Plugging in the given values, we get:
[tex]FV = $200 \times ((1 + 0.032/4)^{24} - 1) / (0.032/4)[/tex]
FV = $200 x (1.23675 - 1) / 0.008
FV = $200 x 30.84375
FV = $5268.63
Therefore, the future value of Katy's annuity after 6 years will be $5268.63.
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There are ten cookies in the cookie jar. Three are Oreos. Two are peanut butter cookies.
Four are chocolate chip cookies. One is a sugar cookie. What fraction of the cookies
are peanut butter cookies?
The fraction of the cookies that are peanut butter cookies is 1/5
What fraction of the cookies are peanut butter cookies?From the question, we have the following parameters that can be used in our computation:
Total = 10
Peanut butter = 2
using the above as a guide, we have the following:
Fraction = Peanut butter /Total
So, we have
Fraction = 2/10
Evaluate
Fraction = 1/5
Hence, the fraction is 1/5
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Find the interest earned and the future value of an annuity with monthly payments of $200 for two years into an account that pays 6% interest per year compounded monthly.
The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43
What is the interest earned?Principal,P = $200
Time, t = 6%
Number of periods, n = 12
Interest rate, r = 6%
= 6/100
= 0.06 rate per year,
FV = P(1 + r/n)^nt
FV = 200.00(1 + 0.06/12)^(12)(2)
FV = 200.00(1 + 0.005)^(24)
FV = $225.43
Therefore,
Principal = $200.00
Interest = $25.43
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S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B = the number is Between 12 and 25
O = number is Odd
L = number is a Less than 25
Find the P(A and L) = [____] Round to 2 d.p
The probability of A and L is 0.25, rounded to two decimal places
To find the probability of A and L, we need to find the number of elements in the intersection of A and L and divide by the total number of elements in the set S.
A = {x ∈ S | x ≥ 21}
= {21, 23, 29, 30}
L = {x ∈ S | x < 25}
= {10, 11, 13, 19, 21, 23}
A ∩ L = {x ∈ S | x ≥ 21 and x < 25}
= {21, 23}
Therefore, the probability of A and L is:
P(A and L) = |A ∩ L|/|S|
= 2/8
= 0.25
Therefore, the required probability of A and L is 0.25, rounded to two decimal places
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The last customer of the day is a loyal customer who brings in a $15.00 off coupon. She purchases two paint brushes, one dozen colored pencils, and one sketch book.
What percent did she save by using her coupon?
~info of the art supplies~
*Paint brush- $10.50
*Colored pencils- $7.88
*Sketch Book- $16.12
The total cost of the art supplies without the coupon is:
2 paint brushes x $10.50 per brush = $21.00
1 dozen colored pencils x $7.88 per dozen = $7.88
1 sketch book x $16.12 per book = $16.12
Total cost without coupon = $21.00 + $7.88 + $16.12 = $45.00
With the $15.00 off coupon, the total cost becomes:
$45.00 - $15.00 = $30.00
The amount saved by using the coupon is:
$45.00 - $30.00 = $15.00
The percentage saved can be calculated as:
Percentage saved = (Amount saved / Total cost without coupon) x 100%
Percentage saved = ($15.00 / $45.00) x 100%
Percentage saved = 33.33%
Therefore, the customer saved 33.33% by using her coupon.
Two quadratic functions are represented below. Which function has the greater maximum value
A function which has the greater maximum value is: function f(x).
How to calculate the vertex and axis of symmetry of a quadratic function?In Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry (vertex), Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = -x² - 3x + 1, we have:
Axis of symmetry, Xmax = -(-3)/2(-1)
Axis of symmetry, Xmax = 3/-2 = -1.5.
For the value of k in vertex, we have:
f(x) = -x² - 3x + 1
f(-1.5) = -(1.5)² - 3(-1.5) + 1
f(-1.5) = 3.25
For g(x), the maximum value or vertex is 2 and as such, quadratic function f(x) has the greater maximum value.
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The function A = A0e
-0.0077x models the amount in pounds of a particular radioactive material
stored in a concrete vault, where x is the number of years since the material was put into the vault. If
300 pounds of the material are initially put into the vault, how many pounds will be left after 140
years
There will be about 105.28 pounds of radioactive material in the concrete vault after 140 years.
The function [tex]A = A_0e^{(-0.0077x)}[/tex] gives the amount A of the radioactive material, where A0 is the initial amount of the material, x is the number of years since it was put in the vault, and e is the mathematical constant approximately equal to 2.71828.
We are given that the initial amount of material put into the vault is 300 pounds.
Therefore, [tex]A_0 = 300[/tex].
We want to find the amount of material that will be left after 140 years. Therefore, x = 140.
Substituting these values into the function, we get:
[tex]A = A0e^{(-0.0077x)}\\A = 300e^{(-0.0077 * 140)}\\A = 105.28[/tex]
Therefore, after 140 years, approximately 105.28 pounds of radioactive material will be left in the concrete vault.
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Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter. Write four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon.
All the four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon are,
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Given that;
Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter.
Now,
Here are four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon:
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Hence, In each pair, the first number represents the side length of the pentagon, and the second number represents the perimeter of the pentagon.
And, If you add 1 to the side length in each pair, you'll see that the perimeter increases by 5, just as Fernando learned in math class.
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(3x-2y+7)-(x+8xy-1)+(10x-xy)
Simplifying the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), the solution we would get by combing like terms can be expressed as: 12x - 2y + 7xy + 6.
How to Simplify an Expression?Given the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), to simplify it, follow the steps shown below:
(3x - 2y + 7) - (x + 8xy - 1) + (10x - xy) [given]
Open the bracket by applying the distributive property:
3x - 2y + 7 - x + 8xy - 1 + 10x - xy
Combine like terms together:
3x - x + 10x - 2y + 8xy - xy + 7 - 1
12x - 2y + 7xy + 6
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The world record in the long jump is 29 feet 4 inches. How many inches short of 10 yards is the record long jump?
The record long jump is 8 inches short of 10 yards.
We know that 1 yard is equal to 3 feet, so 10 yards is equal to 10 x 3 = 30 feet.
To find out how many inches short of 10 yards the record long jump is, we need to first convert 29 feet 4 inches to inches only.
We can do this by multiplying the number of feet by 12 (since there are 12 inches in a foot) and then adding the number of inches:
29 feet 4 inches = (29 x 12) + 4
= 348 + 4
= 352 inches
Now we can find out how many inches short of 10 yards the record long jump is:
30 feet = 30 x 12 = 360 inches
360 - 352 = 8
Therefore, the record long jump is 8 inches short of 10 yards.
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On the coordinate plane, plot the following points. Then, connect the points in order from A to E then back to A to form a figure. what is the area of the figure?
A (1, 2) B (1, 7) C (9, 7)
D (9, 3) E (6, 5)
The calculated area of the figure is 59/2 square units
Calculating the area of the figureFrom the question, we have the following coordinates that can be used in our computation:
A (1, 2) B (1, 7) C (9, 7) D (9, 3) E (6, 5)
The area is then calculated as
Area = 1/2 * | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |
So, we have
Area = 1/2 * | (1 * 7 + 1 * 7 + 9 * 3 + 9 * 5 + 6 * 1) - (2 * 1 + 7 * 9 + 7 * 9 + 3 * 6 + 5 * 1) |
Evaluate
Area = 1/2 * 59
So, we have
Area = 59/2
Hence, the area is 59/2 square units
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true are:
i. m∠5 + m∠6 = 180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
What is a triangle?A triangle is a shape which is bounded by just three sides, thus it has three internal angles whose measures add up to 180°. The internal angle of a triangle is the measure of the angle formed within the two lines forming the edge. While the exterior angles are angles that exist outside the boundary of the triangle when its sides are extended.
From the given question and information, the statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
The required diagram is attached to this answer as a guide
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The pairs of polygons below are similar. Give the scale factor, perimeter ratio, and area ratio of Figure A to Figure B
1.) The scale factor = 4
The perimeter ratio = 1:3
The area ratio = 1:16
How to calculate the scale factor of the given shapes?To calculate the scale factor of the given shapes, the formula that should be used would be ;
Scale factor = Bigger dimensions/ Smaller dimensions
Length of the bigger rectangle (B) = 16
Length of the smaller rectangle (A) = 4
The scale factor = 16/4 = 4
The perimeter = 2(l+w)
length B = 16
width B = 8
perimeter B = 2(16+8)
= 2(24) = 48
Length A = 4
width A = 2
perimeter A =2(4+2)
= 16
The perimeter ratio = A:B = 16:48 = 1:3
Area = length×width
length A = 4
width A = 2
Area A = 4×2 = 8
length B = 16
width B = 8
area B = 8×16= 128
Area ratio of A:B = 8:128 = 1:16
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The table represents a quadratic function f(x).
x f(x)
−4 7
−3 6
−2 7
−1 10
0 15
1 22
2 31
If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
A) 3
B) 6
C) 16
D) 22
Answer:
B) 6
Step-by-step explanation:
Calculate the value of c by substituting point (0, 15) into the quadratic equation formula:
[tex]f(x)=ax^2+bx+c[/tex]
[tex]\begin{aligned}f(0)=a(0)^2+b(0)+c&=15\\0+0+c&=15\\c&=15\end{aligned}[/tex]
Therefore:
[tex]f(x)=ax^2+bx+15[/tex]
Substitute the point (1, 22) into the formula and create an equation for a in terms of b:
[tex]\begin{aligned}f(1)=a(1)^2+b(1)+15&=22\\a+b+15&=22\\a+b&=7\\a&=7-b\end{aligned}[/tex]
Therefore:
[tex]f(x)=(7-b)x^2+bx+15[/tex]
Finally, substitute another point from the table (-3, 6) and solve for b:
[tex]\begin{aligned}f(-3)=(7-b)(-3)^2+b(-3)+15&=6\\(7-b)9-3b+15&=6\\63-9b-3b+15&=6\\78-12b&=6\\-12b&=-72\\b&=6\end{aligned}[/tex]
Therefore, the value of b is 6.
Answer:
6
Step-by-step explanation:
What is the name of this shape?
A shape is shown with 4 sides of different lengths. Each side is not equal to the other.
A.
quadrilateral
B.
pentagon
C.
triangle
D.
hexagon
An initial population of 820 quail increases at an annual rate of
23%. Write an exponential function C to model the quail population. What will the approximate population be after 3 years?
The approximate population after 3 years is 1526.
Given that, principal=820, rate of interest=23% and time period=3 years.
If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.
Here, population after 3 years is 820(1+23/100)³
= 820×1.23³
= 820×1.860867
= 1525.91094
≈ 1526
Therefore, the approximate population after 3 years is 1526.
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Use the long division method to find the result when 4x³ + 8x² + 13x + 15 is
divided by 2x + 3.
Answer:
2x2+x+5
Step-by-step explanation:
Two ramps are placed back to back as shown. What is the length of the ramp labeled x?
The value of the x as shown in the graph will be 16.61 ft.
From the sine rule in the triangle,
In a triangle ABC, where a, b, and c are the side lengths opposite to the angles A, B, and C respectively, and where the opposite angles A, B, and C are opposite to sides a, b, and c respectively, the Sine Rule states:
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
Use the Law Of Sines to solve this:
(Sin 7)/9 = (Sin 13)/x
Cross multiply...
x(Sin 7) = 9(Sin 13)
Divide both sides by Sin 7
x = [9(Sin 13)]/(Sin 7)
x = 16.61254121
therefore, for the ramp, the value of the x will be 16.612 ft.
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The volume of the triangular pyramid below is 240 units. Find the value of a.
Answer: =
12
Submit Answer
15
مومی مرده
The value of x in the triangular pyramid is 8 units.
How to find the height of a pyramid?The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.
volume of the pyramid = 1 / 3 ×base area × height
Therefore,
base area = 1 / 2 bh
base area = 1 / 2 × 12 × x
base area = 6x
Therefore,
volume of the pyramid = 1 / 3 × 6x × 15
240 = 30x
divide both sides by 30
x = 240 / 30
x = 8 units
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2x^2+5x+10=0 Find the best method to solve this equation.
x = -5±-55i/5 is the solution and the best method to solve is by using the general formula.
Solving quadratic equation using the general formulaGiven the quadratic equation below;
2x^2+5x+10=0
The best method to solve the equation is by using the completing the square method as shown below:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
From the equation;
a = 2
b = 5
c = 10
Substitute into the formula to have:
x = -5±√5²-4(2)(10)/2(2)
x = -5±√25-80/4
x = -5±√-55/5
x = -5±-55i/5
Hence the solution to the given system of equation is x = -5±-55i/5
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A line of best fit predicts that when x equals 33, y will equal 31.65, but y
actually equals 31. What is the residual in this case?
A. -0.65
B. 1.35
C. 0.65
D. 2
Find the area of the shaded region in the figure below if the radius of the outer circle is 14 and the radius of the inner circle is 6. Keep your answer in terms of π.
The area of "shaded-region" formed between the two circles having radius as 14 and 6, is 160π square units.
The area of region between "two-circles" can be calculated as area of the "larger-circle" minus area of "smaller-circle".
The "larger-circle" is having radius of = 14 units;
The "smaller-circle" is having radius = 6 units;
So, we can find the area of the region as:
Area = π(14)² - π(6)²;
Area = π(196 - 36),
Area = π(160),
Therefore, area of the region between the two circles is 160π square units.
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The given question is incomplete, the complete question is
Find the area of the shaded region in the figure below if the radius of the outer circle is 14 and the radius of the inner circle is 6. Keep your answer in terms of π.
