Hence, the correct answer is (c)$1,055.10
What is simple interest?Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.
How to solve?We have,
Amount spent each month = $83.42
Interest rate, r = 1.8% = 0.018
Time, n = 3 years
Now,
The total amount collected at the end of the year = $83.42 × 12 = $1001.04
The value of the amount deposited in the bank after 3 years will be
Future value = Present value × ( 1 + r )ⁿ
on substituting the respective values,
we have
Future value = $1001.04 × ( 1 + 0.018 )³
or
Future value = $1,056.07
Hence,
The money he could have at the end of 3 more years will be $1,055.17
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What is the domain of the function f(x) = √(x+3)²?
Answer: Option 1
Step-by-step explanation:
The domain is the set of x values that make the radicand non-negative. Since the radicand is a perfect square, it will always be non-negative for any real value of x.
a rectangular fish tank is 50 cm long, 40 cm wide, and 30 cm high.
a) how many cubic centimeters of water will the tank hold?
b) how many milliliters of water will the tank hold?
c) how many liters of water will the tank hold?
Answer:
a) 60,000 cubic cm; b) 60,000 mL; c) 60 L
Step-by-step explanation:
a) V = l x w x h
V = 50 cm x 40 cm x 30 cm = 60,000 cubic cm
b) 1 cubic cm = 1 mL, therefore 60,000 cubic cm = 60,000 mL
c) 1000 mL = 1 L; 60,000 mL = 60 L
Your best friend is really struggling with their math class. You passed the same class last term with an A, so you’ve been helping them do practice problems and double-checking their homework. The professor has given them a take-home exam for their mid-term, and they want your help completing the exam. Is this an academic integrity violation? Why or why not? How would you handle this situation, and why would you handle it in that way?
Answer:
no
Step-by-step explanation:
you have done your part by helping in their study session,if you help them cheat you will suffer the consequences if he/she is caught,
This is an academic integrity violation because it is against honesty rules, the best would be to offer assistance to your friend.
Is this an academic integrity violation?Academic integrity encompasses principles of honesty, fairness, and trustworthiness in academic pursuits. It generally includes a commitment to originality and independent work. Assisting someone in completing an exam, especially a take-home exam, where individual effort and understanding are expected, would likely violate academic integrity policies.
Handling this situationHandling the situation ethically and responsibly would involve respecting the academic rules and ensuring fairness for all students. Instead of directly completing the exam for your friend, you can offer assistance by explaining concepts, providing guidance on problem-solving approaches, or reviewing their completed work to identify errors or areas for improvement. This way, you can help your friend learn the material and develop their own understanding, without compromising academic integrity.
Encourage your friend to seek additional help from their professor, teaching assistants, or tutoring services provided by the institution. They can also engage in group study sessions or form study groups with classmates, which promote collaborative learning while maintaining individual effort.
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(1 point) The matrix
6 4
-7 k
is invertible if and only if k is not equal to
Answer:
k ≠ -14/3
Step-by-step explanation:
A square matrix is invertible if and only if its determinant is not zero.
DeterminantThe determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:
det = (6)(k) -(-7)(4) = 6k +28
Restriction on kThe requirement that the determinant is not zero places a restriction on k.
6k +28 ≠ 0
k +14/3 ≠ 0 . . . . . . divide by 6
k ≠ -14/3 . . . . . . . . subtract 14/3
For the matrix to be invertible, the value of k must not be -14/3.
Please help!
If a student (represented by initials) was chosen at random, find P(HH|C).
P(HH|C)=2/5
P(HH|C)= 13/16
P(HH|C)=9/16
P(HH|C)=3/5
Answer:
a.) P(HH|C)=2/5
Explanation:
Given following:
P(HH) = 7P(C) = 10P(HH ∩ C) = 4P(HH ∪ C) = 13Solving steps:
[tex]\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}[/tex]
[tex]\sf P(HH|C) = \dfrac{4 }{10}[/tex]
[tex]\sf P(HH|C) = \dfrac{2 }{5}[/tex]
Im trying to figure out the answer
Step-by-step explanation:
[tex]\sqrt{35} =\sqrt{5} *\sqrt{7};[/tex]
all the details are in the attachment.
On a road, a bike sign in the shape of an isosceles trapezoid is to be painted. The sign and its dimensions are shown below. What is the area of the sign?
A right trapezoid is shown with height labeled 5 feet and one of the bases labeled as 9 feet, and the other base is labeled as 7 feet.
The area of the given right trapezoid is 40 ft².
What is the area of the trapezium?Area of the trapezium = ½(a + b) × h
Given;
base 1 = 9 feet
base 2 = 7 feet
Height h = 5 feet
Area of the trapezium = ½(a + b) × h
Area = (9 + 7) x 5/2
Area = 16 x 5/2
Area = 8 x 5
Area = 40 Square feet.
Hence, the area of the given trapezium is 40 ft².
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a²-b when a = 8 and b = 7
Answer:
[tex]57[/tex]
Step-by-step explanation:
You just plug in 8 as a, and 7 as b. This gives you the following equation: [tex](8)^2-7[/tex] which becomes [tex]64-7[/tex] by squaring the 8, Then subtract 7 and you get [tex]57[/tex]
Answer:
57
Step-by-step explanation:
a = 8
b = 7
a² - b
= 8² - 7
= (8*8) - 7
= 64 - 7
= 57
Will is 30% taller than Wanda, so Will's height is ____% of Wanda's height.
Will's height is % of Wanda's height.
Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.
Will is 34% taller than Wanda, so Will's height is 134% of Wanda's height.
If Will is 34% of Wanda's height, we can conclude that he has all of Wanda's height plus 34% of that height.
All the height of Wanda represents 100% as it is referring to a complete system.
What is the height?
Height is a way to measure someone or something from base to top or head to toe.
From this, we can conclude that Will is 100% more than 34% of Wanda's height.
Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.
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The maximum capacity of a bird's lungs varies directly with it size. If a robin with a mass of 310 grams has a lung capacity of 46,5 mL, how much lung capacity does a 1270-gram hawk have? round it to the nearest tenth.
Thus, the required capacity lung capacity of hawk is 190.5ml.
robin with a mass of 310 grams has a lung capacity of 46.5 mL
let lung capacity of a 1270-gram hawk = x
Volume, is defined as the ratio of the mass of object to its density.
Here,
The maximum capacity of a bird's lungs varies directly with it size.
So the proportion can be given as
⇒ 310/46.5 = 1270/x
= 190.5
Thus, the required capacity lung capacity of hawk is 190.5ml.
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Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4 ? (2 points) graph of 2 x plus 4, with discontinuity at negative 2, 0 graph of 2 x plus 4, with discontinuity at 2, 8 graph of 2 x minus 4, with discontinuity at negative 2, negative 8 graph of 2 x minus 4, with discontinuity at 2, 0
We can simplify the given rational function into a linear one, the graph is below.
Which graph represents the function?
Here we have the rational function:
[tex]f(x) = \frac{4x^2 - 16}{2x - 4}[/tex]
Factorization the numerator, we get:
4x² - 16 = 0
4x² = 16
x² = 16/4 = 4
x = ±√4 = ±2
Then the numerator can be written as:
4*(x - 2)*(x + 2)
And the denominator can be rewritten as:
2x - 4 = 2*(x - 2)
Then the function becomes:
[tex]f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4[/tex]
So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.
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I need some help please
Please help me answer this question in khan academy
The interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].
Option D) is the correct answer.
Over which interval does f have a positive rate of change?To determine whether the average rate of change is positive, f(max) - f(min) must be greater than zero.
Given the function; f(x) = x³ - 9x
We determine f(max) - f(min)
At interval [ -2, 1 ]
(x³ - 9x) - ( x³ - 9x )
( (1)³ - 9(1) ) - ((-2)³ - 9(-2))= -8 - 10 = -18 NOT POSITIVE
At interval [ -2, 3 ]
(x³ - 9x) - ( x³ - 9x )
( (3)³ - 9(3) ) - ((-3)³ - 9(-3))= 0 - 0 = 0 NOT POSITIVE
At interval [ -1, 2 ]
(x³ - 9x) - ( x³ - 9x )
( (2)³ - 9(2) ) - ((-1)³ - 9(-1))= -10 - 8 = -18 NOT POSITIVE
At interval [ -4, -1 ]
(x³ - 9x) - ( x³ - 9x )
( (-1)³ - 9(-1) ) - ((-4)³ - 9(-4))= 8 - (-28) = 36 POSITIVE
Therefore, the interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].
Option D) is the correct answer.
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Whats the correct answer answer asap for brainlist
A bank loaned out $11,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled $1500, how much was loaned at
The amount loaned at 8% is $4800.
The amount loaned at 18% is $6,200.
What are the linear equations that represent the question?a + b - 11,000 equation 1
0.08a + 0.18b = 1500 equation 2
Where:
a = amount loaned at 8%
b = amount loaned at 18%
How much was loaned at 8 and 18%?Multiply equation 1 by 0.08
0.08a + 0.08b = 880 equation 3
Subtract equation 3 from equation 2
0.10b = 620
b = 620 / .10
b = $6200
a = 11,000 - 6200 = $4800
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
What does point H represent in this context?
CORRECT (SELECTED)
Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah
Explanation: Point HHH is on line aaa, so it represents Josiah's distance at a certain time. Point HHH is also on line bbb, so it represents the same distance and time for Chana.
The point that is labeled H on this graph is the point where Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah.
How to solve for the point H.At the point H, there is an intersection between the distance covered by both of these individuals.
This point is the point where we are shown that Chana has caught up with Josiah as they are skating.
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Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.
R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
The transformation was a 180° rotation about the origin.
We can solve this question by plotting the points R (1, 1)
S (3, 1) T (1, 6) and R' (–1, –1) S' (–3, –1) T' (–1, –6) on the graph as shown below.
As we can see from the graph, the original triangle RST which was in quadrant 1, now becomes triangle R’S’T’ in quadrant 3. Thus, when triangle RST was transformed using the rule (x, y) → (–x, –y), from quadrant 1 to quadrant 3 it is a 180° rotation about the origin.
Hence, the transformation was a 180° rotation about the origin.
Your question was incomplete. Please check below for full content.
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown. R (1, 1) S (3, 1) T (1, 6) R' (–1, –1) S' (–3, –1) T' (–1, –6)
Which best describes the transformation?
The transformation was a 90° rotation about the origin.
The transformation was a 180° rotation about the origin.
The transformation was a 270° rotation about the origin.
The transformation was a 360° rotation about the origin.
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What is the next whole number after 3355 in the base six system
Answer:
Ordinal, 3,355th. This number as US currency, three thousand three hundred fifty-five dollars ... 3355 is NOT a triangle number ... Base 6
Find the real numbers x and y.
27+yi= 11-x + 4i
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -16 [/tex]
[tex]\qquad \tt \rightarrow \: y =4 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 27 + yi = 11 - x + 4i[/tex]
[tex]\qquad \tt \rightarrow \: yi + x = 11 + 4i - 27[/tex]
[tex]\qquad \tt \rightarrow \: x + yi = - 16 + 4i[/tex]
By equating both equations we get :
[tex]\qquad \tt \rightarrow \: x = - 16[/tex]
[tex]\qquad \tt \rightarrow \: y = 4[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The distance between two towns on a
map is 6.25 cm.
The scale on the map is 1 cm = 30 miles.
What is the actual distance between the
two towns?
Answer:
Actual distance=187.5miles
Step-by-step explanation:
1cm=30miles
6.25cm=6.25*30miles
=187.5miles
The distance between the two towns using the map scale is 187.5 miles.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The distance between the towns on map is 1 cm.
And, the scale of map is 1 cm = 30 miles.
As per the problem the actual distance can be found by using the scale of the map as follows,
The distance between two towns is 6.25 × 30 = 187.5 miles.
Hence, the actual distance between the two towns is 187.5 miles.
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Find the solutions of each equation on the interval [0,2pi)
sin(3pi/2+ x)+sin(3pi/2 +x)= -2
Answer:
x=0
Step-by-step explanation:
You can combine the equation to get 2sin(3/2 +x) = -2
divide both sides by 2 and you get the equation equal to -1. sin is equal to -1 when the value inside is 3/2 so this is the answer.
You enter a room. 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.
How many legs are on the ground?
Answer:
36
Step-by-step explanation:
I think it’s a trick question because “legs” can also mean like chair legs that hold it up. Therefore:
2 dogs = 8 legs
4 horses = 16 legs
1 giraffe = 4 legs
And a bed: 4 legs(things that hold it up)
And a chair: 4 legs (things that hold it up)
This is assuming that the bed is a normal bed with stools holding it up
And the chair has 4 piles aswell as no missing legs in the animals… lol
PLS help!!! MARKING BRAINLIST IF ANSWER IS CORRECT( explanation required) What number should be placed in the box to help complete the division calculation?
.
Factor completely.
x^2+5x+6
Enter your answer in the box.
Answer:
(x+3)(x+2)
Step-by-step explanation:
x^2 + 5x+6
To factor this problem, we need to determine which two numbers multiply to 6 and add to 5
3*2 = 6
3+2 -5
(x+3)(x+2)
Step-by-step explanation:
x² + 5x + 6
= x² + 2x + 3x + 6
= x ( x + 2 ) + 3 ( x + 2 )
= ( x + 2 ) ( x + 3 )
Hence factorized.
x+6y=28, solve for y
Answer:
[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]
Step-by-step explanation:
So when you're solving for y you want to get y by it self meaning there should be nothing with y, including any coefficients. The first step is to usually move any terms to the other side and then divide by the coefficient of y so y "technically doesn't" have a coefficient, while it does, but that coefficient 1, so it doesn't really mean much.
Subtract x from both sides
[tex]6y = -x+28[/tex]
Divide both sides by 6
[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]
The given equation solved for y as y = (28 - x)/6.
The given equation is x+6y=28.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved for y as follows
Here, x+6y=28
⇒ 6y = 28 - x
⇒ y = (28 - x)/6
Therefore, the given equation solved for y as y = (28 - x)/6.
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Mr. Zuro finds the mean height of all 15 students in his statistics class to be 67.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 63.8 inches tall. What is the mean height of the 16 students in the class?
Answer: 66.8
Step-by-step explanation:
Let the mean height of 16 students in the class = X
Therefore,
[tex]\frac{15*67+63.8}{16} =X[/tex]
[tex]X=\frac{334}{5}[/tex]
X = 66.8
Cindy has decided to lease a car. the lease includes a money factor of 0.00354. what interest rate is cindy being charged in her lease? a. 0.85% b. 8.5% c. 1.475% d. 14.75% please select the best answer from the choices provided a b c d
The interest rate Cindy will be charged with money factor 0.00354 is approximately 8.5% which is option b.
Given The factor included in lease is 0.00354.
Interest is the amount that a bank or person who gives loan charges from loan taker.
Money factor is a method for finding the financing charges on a lease with monthly payments. The money factor can be translated into the annual percentage rate by multiplying the money factor by 2400.
Money factor=0.00354.
So the interest rate that Cindy will charge is equal to 2400*0.00354
The interest rate Cindy will be charged =8.496%
=8.5%
Hence the interest rate charged is approximately 8.5%.
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Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
Distance formula: √(x₂-x₁)² + (V2 - V₁)²
O(x-4)² + y² = 100
O(x-4)2 + y² = 10
O x² + (y-4)² = 10
O x² + (y-4)² = 100
Answer:
(x-4)² + y² = 100
Step-by-step explanation:
The only circles that have a center at (4 , 0) are :
(x-4)² + y² = 100
(x-4)² + y² = 10
……………………
• (-2 - 4)² + 8² = (-6)² + 64 = 36 + 64 = 100 ≠ 10
Then
The circle (x-4)² + y² = 10 doesn’t contain the point (-2, 8)
• (-2 - 4)² + 8² = 100
Then
The circle (x-4)² + y² = 100 contains the point (-2, 8)
Write an equation of the line that passes through a pair of points:
(2, 3), (4, negative 2)
a.
y = Negative five-halvesx – StartFraction 1 Over 8 EndFraction
c.
y = Negative five-halvesx + 8
b.
y = Negative five-halvesx – 8
d.
y = Five-halvesx + 8
The equation of line that passes through a pair of points: (2, 3), (4, -2).is option B. y = -5/2 x + 8.
What is the equation of a line passing through two given points in 2 dimensional plane?Suppose the given points are (x_1, y_1) and (x_2, y_2),
then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
We need to find the equation of the line that passes through a pair of points: (2, 3), (4, -2).
So, the equation would be
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
[tex](y - 3) = \dfrac{-2 - 3}{4- 2} (x -2)\\\\\\(y - 3) = \dfrac{-5}{2} (x -2)\\\\\\2(y - 3) = -5 (x -2)\\\\2y - 6 = -5x + 10\\\\2y = -5x + 16\\\\y = -5/2 x + 8[/tex]
Hence, the equation of line is option B. y = -5/2 x + 8.
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Answer:B
Step-by-step explanation:
0.2 was divided into a particular number. this quotient was the multiplied by 7, and 2.8 was taken from that product. if the previous operation resulted in -499.8 find the initial number
Answer:
(x/0.2)(7)-2.8=-499.8
x=-14.2
Step-by-step explanation:
(x/0.2)(7)-2.8=-499.8
7x/0.2 -2.8 = -499.8
35x -2.8 = -499.8
35x = -499.8 +2.8
35x = -497
35x/35 = -497/35
x = -14.2
you probably already got it solved, but at least this can help anyone else!