The total amount that she will have to pay back at the end of 10 months is $11,385.864.
We have Sophia .who borrowed $11,020.
We have to determine the total amount that she will have to pay back at the end of 10 months.
What is the formula to calculate the Simple Interest ?The Simple interest can be calculated using the formula -
S.I. = (P x R x T)
where -
P = Principle amount
R = Rate of interest
T = time in years
According to the question -
P = $11020
R = 4%
T = 10 months = 0.83 years
Therefore -
Interest = (P x R x T) = (11020 x 0.04 x 0.83) = $365.864
Now -
Interest = Total amount - Principle
Total Amount = Interest + Principle = 11020 + 365.864 = $11,385.864
Hence, the total amount that she will have to pay back at the end of 10 months is $11,385.864.
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A (-2,y) B (4,-6), gradient: -1/6
Find y using the cross-multiply method
We use the slope equation to solve for the slope/gradient of a line:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
m = the slope[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points that fall on the lineSolving the Question
We're given:
A (-2,y)B (4,-6)Gradient = [tex]-\dfrac{1}{6}[/tex][tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the given information:
[tex]-\dfrac{1}{6}=\dfrac{-6-y}{4-(-2)}\\\\-\dfrac{1}{6}=\dfrac{-6-y}{4+2}\\\\-\dfrac{1}{6}=\dfrac{-6-y}{6}[/tex]
Cross multiply (by multiplying the numerators by the opposite denominators):
[tex]-\dfrac{1}{6}=\dfrac{-6-y}{6}\\\\-1\times 6=6(-6-y)\\-6=-36-6y\\30=-6y\\y=-5[/tex]
Answery = -5
what the answerr need help asap
The answer is B
since sqrt x = x ^1/2 one being the power of the x and two being the number of radical
in this case 7sqrt x^3 = x ^ 3/7 which is B
Solve the equation for x.
2(x+5)+5=6x-4(-5+x)
Answer:
No solution.
Step-by-step explanation:
Simplify the equation.
2(x + 5) + 5 = 6x - 4(-5 + x) {Use distributive property}
2*x + 2*5 + 5 = 6x - 4*(-5) + (-4) * x
2x + 10 + 5 = 6x + 20 - 4x
2x + 10 + 5 = 6x - 4x + 20 {Combine like terms}
2x + 15 = 2x + 20
This equation has no solution.
suppose you won $15 on a lotto ticket at the local 7-eleven and decided to spend all the winnings on candy bars and bags of peanuts. candy bars cost $0.75 each while bags of peanuts cost $1.50 each.
The slope of a line is defined as the ratio of the difference between the y-coordinate and x-coordinate of the two points m= y₂-y₁/x₂-x₁
We have total spending = $15
So the equation of the budget line will be
PсQс+ PрQр = 15
Where, Pс and Qс is the price of unit candy and quantity of candy respectively. Pр and Qр is the price of unit peanuts and quantity of peanuts respectively.
Part A:Goods A B C D E F Candy Bars 0 4 8 12 16 20Bag of peanuts 10 8 6 4 2 0
Part B :Graph of Budget line
Budget line The slope of a budget is -2 i.e ratio of the prices.
Opportunity costs remain constant as each additional unit of the product is purchased.
The opportunity cost of one more candy bar is 0.5 bags of peanuts.
The opportunity costs of one more bag of peanuts are 2 candy bars.
Part C: No, it tells only what is possible.
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How do i do this? ive been working on it for a long time
Find the rule. _____, -9, ______, 3, 9 ...
The rule of arithmetic progression is -15, -9, - 3, 3, 9, 15.
What do w mean by Arithmetic progression?An arithmetic progression is a sequence of numbers that has a fixed common difference between any two consecutive numbers (A.P.). A.P.'s example is 3,6,9,12,15,18,21,...So, to find the rule:
Given: _____, -9, ______, 3, 9Then, 9 - 3 = 6So, the difference is 6.Therefore, the rule is -15, -9, - 3, 3, 9, 15.
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researchers collect continuous data with values ranging from 0-100. in the analysis phase of their research they decide to categorize the values in different ways. given the way the researchers are examining the data - determine if the data would be considered nominal, ordinal or ratio (you may use choices more than once).
The data in the given three questions can be considered as nominal, ordinal and ratio, respectively.
The frequency (or absolute frequency) of an event in statistics is the number of times the observation occurred or was recorded in an experiment or research.Within a variable, nominal data is data that may be labelled or categorized into mutually exclusive groups. These categories cannot be meaningfully arranged.Ordinal data is a sort of categorical, statistical data in which the variables have natural, ordered categories but the distances between them are unknown.Two categories ( low vs high): frequency of values between 0-49 and frequency of values between 50-100 : nominal Three frequency (count) categories (low, medium, and high) of values ranging from 0 to 25, 26 to 74, and 75 to 100 : ordinalAnalyze each number in the set individually : ratioTo learn more about frequency, visit :
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The sum of 3 consecutive positive integers is 9 less than the product of the largest and smallest of the same 3 integers.
What is the smallest of these 3 integers?
The smallest integer is 4.
How to calculate the value?Let the numbers be x, x+1 and.x + 2.
Therefore, the expression will be:
x + x + 1 + x + 2 = x(x + 2) - 9
3x + 3 = x² + 2x - 9
Collect like terms
x² + 2x - 9 - 3x - 3
x² - x - 12 = 0
x² -4x + 3x - 12
x(x - 4) + 3(x - 4)
x - 4 = 0
x = 0 + 4 = 4
The smallest number is 4.
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The graph of f(x) = x has been horizontally shrunk by a factor of 4. If no other transformations of the function have occurred, which point lies on the new graph?
(–1, –4)
(–4, –1)
(1, StartFraction one-fourth EndFraction )
(1, negative StartFraction one-fourth EndFraction )
Using translation concepts, the point that lies on the new graph is given by: (-1, -4).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The equivalent translation to an horizontal shrink by a factor of a a function f(x) is given by:
f(ax).
Hence, in this problem, for the horizontal shrink by a factor of 4, the function will be given by:
g(x) = f(4x) = 4x.
Then when x = -1, the output is given by:
g(-1) = 4(-1) = -4.
The point that lies on the new graph is given by: (-1, -4).
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4 ten thousand 9 thousands divided by 10
Answer:
Step-by-step explanation:
49000/ 10 = 4900
what would be the cost of renting 2 lawn mowers for 5 hours?
Answer:
35 dollars
Step-by-step explanation:
thats the answer
ax + by = 12
2x + 8y = 60
In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a/b
?
Answer:
1/4
Step-by-step explanation:
If the system has infinitely many solutions, then
[tex]\sf \boxed{\bf \dfrac{a_1}{b_1}= \dfrac{a_2}{b_2}= \dfrac{c_1}{c_2}}[/tex]
ax + by = 12 ⇒ a₁ = a ; b₁ = b ; c₁ = 12
2x + 8y =60 ⇒ a₂ = 2 ; b₂ = 8 ; c₂ = 60
[tex]\sf \dfrac{a}{2}= \dfrac{b}{8}= \dfrac{12}{60}\\\\\\ \dfrac{a}{2}= \dfrac{12}{60}\\\\a = \dfrac{12}{60}*2\\\\a = \dfrac{2}{5}[/tex]
[tex]\sf \dfrac{b}{8}= \dfrac{12}{60}\\\\ b = \dfrac{12}{60}*8\\\\b = \dfrac{8}{5}\\[/tex]
[tex]\sf \dfrac{a}{b}= \dfrac{ \dfrac{2}{5}}{ \dfrac{8}{5}}\\\\[/tex]
[tex]\sf = \dfrac{2}{5}* \dfrac{5}{8}\\\\ = \dfrac{1}{4}[/tex]
ou have a tv that is 30 inches tall and 40 inches wide. what is the length of the diagonal of the tv.
The length of the diagonal of the TV is 50 inches
Given that the TV is 30 inches tall and 40 inches wide.
So length of the TV, l = 30 inches
and Width of the TV = 40 inches
The angle between the length and width of the TV is right angle. So we can use Pythagoras Law here.
That is, square of the hypotenuse is equal to the sum of the squares of the base and altitude of the right triangle.
i.e., If 'd' is the diagonal of the TV, then,
[tex]d^2 = l^2 +b^2 = 30^2+40^2 = 2500[/tex]
This implies that [tex]d=\sqrt{2500}=50[/tex] inches.
So the diagonal of the TV is 50 inches long.
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Answer:
50 inches
Step-by-step explanation:
Hope this helps
Mia completed the chart by first estimating the measurement around three objects in her house and then finding the actual measurement with her meter strip. What is the difference between the longest and shortest measurement
Using the subtraction between two amounts, it is found that:
The difference between the longest and shortest measurement is of 33 cm.
What are the measurements?The measurements are given as follows:
Orange: 36 cm.Mini Basketball: 41 cm.Bottom of a glue bottle: 8 cm.How to find the difference between the longest and shortest measurement?To find the difference between difference between the longest and shortest measurement, we have to subtracted the longest measurement by the shortest measures.
From the measurements given, we have that:
The longest measurement is of 41 cm, as 41 > 33 and 41 > 8.The shortest measurement is of 8 cm, as 8 < 33 and 8 < 41.Hence, the subtraction is given as follows:
41 cm - 8 cm = 33 cm.
The difference between the longest and shortest measurement is of 33 cm.
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if -16 is added to a number and the sum is doubled, the result is 1 less than the number. find the number.
The unknown number will be 31, if -16 is added to it and the sum is doubled, the result is 1 less than the number.
Let the unkown number be x.
Now according to the given question.
If -16 is added to the unknown number and the sum is doubled, the result is 1 less than the number.
⇒ (x + (-16))2 = x - 1
⇒ 2x - 32 = x - 1
⇒ 2x - x = -1 + 32
⇒ x = 31
Hence, the unknown number will be 31, if if -16 is added to it and the sum is doubled, the result is 1 less than the number.
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Question 4
Find the values of x, y and z.
100⁰ X
B..
y
N
Answer:
y=x=70
hope this helps
Step-by-step explanation:
In parallelogram the adjacent angles are supplementary
∠TBE+y=180
110+y=180
y=70
Also, opposite angles of a parallelogram are equal.
z=∠TSE=110
y=x=70
Factorize the following completely
1. 4p+2pr+6pz
2. ax + bx + cx
Answer:
1. 2p(2 + r + 3z)
2. x(a + b + c)
Step-by-step explanation:
1. The greatest common factor is 2p.
4p+2pr+6pz = 2p(2 + r + 3z)
2. The greatest common factor is x.
ax + bx + cx = x(a + b + c)
3(3x+5)-4x+5= -15 solve for x
Answer:
x = -7
Step-by-step explanation:
Solve for x:
5 - 4 x + 3 (3 x + 5) = -15
3 (3 x + 5) = 9 x + 15:
(9 x + 15) - 4 x + 5 = -15
Grouping like terms, 9 x - 4 x + 5 + 15 = (-4 x + 9 x) + (5 + 15):
((-4 x + 9 x) + (5 + 15)) = -15
9 x - 4 x = 5 x:
5 x + (5 + 15) = -15
5 + 15 = 20:
5 x + 20 = -15
Subtract 20 from both sides:
5 x + (20 - 20) = -20 - 15
20 - 20 = 0:
5 x = -20 - 15
-20 - 15 = -35:
5 x = -35
Divide both sides of 5 x = -35 by 5:
(5 x)/5 = (-35)/5
5/5 = 1:
x = (-35)/5
The gcd of -35 and 5 is 5, so (-35)/5 = (5 (-7))/(5×1) = 5/5×-7 = -7:
Answer: x = -7
Answer:
x = -7
--------------------------
Hope this helps!
Have a great day and God bless! :)
g(x)=4x^2-3x+5, g(x) - g(2)
Solve the question.
f
(
4
x
2
−
5
)
=
12
x
2
−
20
Step-by-step explanation:
whats an equivalent expression to 3(x+5)
Answer:
3x+15
Multiply the single term 33 by each term of the polynomial (x+5)
3x+15
Simplify expressions with distribution
4(5y + 2z) + 8z - 4(5z - 2y)
Answer:
28y - 4z
Step-by-step explanation:
Hey there!
In order to simplify this, we need to first distribute the numbers outside of the parentheses to the numbers inside the parentheses:
20y + 8z + 8z - 20z + 8y
Now we combine like terms:
28y - 4z
Type the expression that results from the following series of steps:
Start with
g
, times by 7, then subtract
f
Marina mixed almonds and walnuts to take on her camping trip. Almonds cost $3.00 per pound and walnuts cost $4.20 per pound. If she ended up with three pounds of a mixture that costs $3.36 per pound, how many pounds of each kind of nut did she use?
Out of mixture of 3 pounds with cost $3.36 per pound ,pounds each kind of nuts used by Marina are almonds 2.1 and walnuts 0.9 pounds.
As given,
Cost per pound
Almonds=$3.00
Walnuts=$4.20
Total mixture=3 pounds
Cost of mixture=$ 3.36 per pound
Let x amount of almonds and y walnuts Marina use
According to condition,
x +y=3 __(1)
3x +4.20y =3 ×3.36 __(2)
Multiply 3 to (1) and subtract from (2)
3x +4.20y=10.08
3x +3y= 9
1.2y=1.08
⇒y=0.9
Substitute y=0.9 in (1),
x=2.1
Therefore, pounds of each kind of nuts used by Marina are almonds 2.1 and walnuts 0.9 pounds.
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what is the range of h(x) = |x| − 2??? please help
Answer:
it's C_67$-$(?9
Step-by-step explanation:
it's )3)384((3(# 920
select the correct answer from each drop-down menu. determine the number and type of solutions for the following quadratic equations using the discriminant. equation number and type of solutions
Equation [tex]y=x^{2} +7x-11[/tex] has two real solutions.
Here are the coefficients: a=1,b=7,c=11
The discriminating party is: [tex]7^{2}[/tex] -4(1)(-11)=93
Positive, so there are two viable options.
According to the discriminant:
[tex]y=-3x^{2} +x+12[/tex] has two real solutions.
[tex]y=2x^{2} -6x+5[/tex] has zero real solutions.
[tex]y=x^{2} +7x-11[/tex] has two real solutions.
[tex]y=-x^{2} -8x-16[/tex] has one real solution.
What are the benefits of discriminant equation ?Quadratic functions occupy a special place in the academic curriculum. They are small improvements over linear functions and offer a major break from attachment to straight lines because their values may be readily derived from input values.
The discriminant informs you of the number of quadratic equation solutions or x intercepts for a parabola.
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I need help 15/4+(-4/1/3
The expression is simplified to -33/4
What are fractions?
Fractions are simply defined as the part of a whole set.
There are different types of fractions, which includes;
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsGiven the expression;
15/4+(-4/1/3)
To simply the expression, we need to take the following steps;
First, we need to expand the bracket, we have;
15/ 4 - 4/ 1/ 3
Now, take the inverse of the divisor and multiply
15/ 4 - 4 × 3/ 1
15/ 4 - 12
Find the lowest common multiple
15 - 48/4
-33/4
Thus, the expression is simplified to -33/4
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27040 in scientific notation
The midpoint of \overline{\text{AB}} AB is M(2, -2)M(2,−2). If the coordinates of AA are (-2, 1)(−2,1), what are the coordinates of BB?
The coordinate of point B from the given coordinates is (6, -9)
Midpoint of a coordinateThe formula for calculating the midpoint of coordinates is expressed according to the formula:
M(x, y) = {(x₁+x₂)/2, (y₁+y₂)/2}
Given the coordinate points M (2, -2) and A (-2, 1)
Substitute
2 = (x₁+x₂)/2
2 = -2+x₂/2
4 = -2 + x₂
x₂ = 6
Similarly;
Substitute
-2 = (1+y₂)/2
-4 = 1+x₂/2
-8 = 1 + y₂
y₂ = -9
Hence the coordinate of point B from the given coordinates is (6, -9)
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Answer:(6,-5)
Step-by-step explanation:deta math
Find the difference. –8 – (–11)
Answer:
3.Step-by-step explanation:
Subtract:
-8 - (-11)= -8 + 11 or 11 + (-8)= 3.The diagram below shows part of the graph of the equation y=[tex]2x^{2}+ax+b.[/tex] the graph intersects the x-axis at the points [tex](-\frac{7}{2}, 0) and (2,0)[/tex]. Find the value of a and the value of b
The value of a is 3.
The value of b is -14.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The function of the graph is,
y = 2x² + ax + b
The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).
Now,
Since, The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).
Hence, The points must satisfy the graph of the function.
So, Points (-7/2, 0) and (2, 0) are satisfy the function y = 2x² + ax + b.
When point (-7/2, 0) satisfy the function y = 2x² + ax + b
Then,
0 = 2 × (-7/2)² + a × (-7/2) + b
0 = 49/2 - 7a/2 + b
7a/2 - b = 49/2 .... (i)
And, When point (2, 0) satisfy the function y = 2x² + ax + b
Then,
0 = 2 × (2)² + a×2 + b
2a + b = -8 .... (ii)
Add equation (i) and (ii) we get;
7a/2 - b + 2a - b = 49/2 + (-8)
11a/2 = 33/2
11a = 33
a = 3
And, 2a + b = -8
2 × 3 + b = -8
b = -8 - 6
b = -14
Hence, The value of a is 3.
The value of b is -14.
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