A person placed $4080 in an investment
The compound interest comes into the picture when interest adds on the principal amount. The total value of $4080 after 4 years with a rate of interest of 5.7% is $4124.83.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount but after 1 year it will convert into $550.
As per the given,
Principle amount P = $4080
Rate of interest r = 5.7% = 0.057
Time period t = 4 years.
The formula for total value is given as,
V = P[tex]e^{rt}[/tex]
V = 4080[tex]e^{(0.057\times4)}[/tex]
V = $5124.83
Hence "The compound interest comes into the picture when interest adds on the principal amount. The total value of $4080 after 4 years with a rate of interest of 5.7% is $4124.83".
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The given question is incomplete complete question follows;
It is given that the equation (mx)²+ 5nx+4=0 has two equal real roots while the quadratic equation px²-x+m=0 has two distinct roots where m,n and p are constants. Express the range of n in terms of p
Given:
[tex](mx)^2+5nx+4=0\text{ has two equal real roots}[/tex][tex]px^2-x+m=0\text{ has distict roots. }[/tex]Taking the first equation:
[tex]a=m^2\text{ ; b=5n ; c=4 }[/tex][tex]b^2-4ac=0[/tex][tex]25n^2-4m^2(4)=0[/tex][tex](5n)^2-(4m)^2=0[/tex][tex](5n+4m)(5n-4m)=0[/tex][tex]5n+4m=0\text{ ; 5n-4m=0}[/tex][tex]m=-\frac{5}{4}n\text{ ; m=}\frac{5}{4}n[/tex][tex]4m=-5n\text{ ; 4m=5n}[/tex]Taking the second equation:
[tex]a=p\text{ ; b=-1 ; c=m}[/tex][tex]b^2-4ac>0[/tex][tex]1-4pm>0[/tex]If 4m=5n,
[tex]1-p(5n)>0[/tex][tex]1>p(5n)[/tex][tex]\frac{1}{5p}>n[/tex]If 4m=-5n,
[tex]1-p(-5n)>0[/tex][tex]1+5pn>0[/tex][tex]5pn>-1[/tex][tex]n>-\frac{1}{5p}[/tex]Range of n in terms of p:
[tex]\frac{1}{5p}>n>-\frac{1}{5p}[/tex][tex]-\frac{1}{5p}Which graph shows the solution to the inequality?
x - 4 ≤ -1
Answer:
[tex]x -4 \leq -1\\x -4 + 4 \leq -1 + 4\\x\leq -1 +4\\x\leq +3[/tex]
Answer:
x ≤ 3
Step-by-step explanation:
This is the answer because I say it is
¿What is the constant term missing in the perfect square that begins with x ^ 2-20xx
2
−20xx, squared, minus, 20, x?
Some of the terms of an equation that has missing terms will be eliminated.
100 is the missing term that transforms (x² - 20) into a perfect square.
What is a perfect square?
A perfect square is a number that can be written as the product of an integer multiplied by itself or as the integer's second exponent. For instance, the number 25, which is the product of the integer 5 multiplied by itself, is a perfect square because 5 x 5 = 25.
The missing term will be calculated in the next step.
Use k to represent the x-coefficient.
We thus have:
k = -20
Divide both sides by 2
k/2 = - 10
squaring both the sides,
(k/2)² = (- 10)²
=> (k/2)² = 100
This means that the term that is lacking is 100.
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Question:
What is the missing constant term in the perfect square that starts with x^2 -20x?
Solve for x :
ax+b=0 where a,b are any integers
Plus solution please
The solution for x of the given equation ax + b = 0 is x = -b/a.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
As per the given equation,
ax + b = 0
Add -b both side
ax + b - b = 0 - b
ax = -b
Divide by both side
ax/a = -b/a
x = -b/a
Hence "The solution for x of the given equation ax + b = 0 is x = -b/a".
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How do I know if these are true or false?For #9-12, True or False?9. In the construction of a frequency distribution, it is a not a good ideato have overlapping class limits such as 10 - 20, 20 ÷ 30, 30 - 40.10. It is not important to keep the with of each class the same in afrequency distribution. True11. In construction of a frequency polygon, the class limits are used forthe x-axis. ch12. Data collected over a period of time should be graphed by using apie chart. C
Question 9.
In the construction of a frequency distribution, it is NOT a good idea to have overlaping class limits such as 10-20, 20-30, 30-40.
Let's determine if the above statement is true or false.
A frequency distribution shows a representation of the num ber of observations within a given interval either in tabular or grahical format.
In the construction of a frequency distribution, the class limits should be made very clear in order for each observation to fall into only one class.
It is not a good idea to have ovelaping class limits like 20-30, 30-40. This is because overlaping limits such as this would make it dificult to determine the class where 30 is located.
Therefore, this statement ''it is NOT a good idea to have overlaping class limits such as 10-20, 20-30, 30-40'' is TRUE.
ANSWER:
True.
Class 7. Fractions & decimals
1/2 of 2 3/4
Answer:
11/8 or 1.375
Step-by-step explanation:
2 3/4 => 11/4
1/2 x 11/4 = 11/8
Which of these is most commonly a role of the government in the United States economy?
Answer:
The most obvious way the government is involved in the U.S. economy is providing public goods and services like education, military protection, national parks and federal highways.
Step-by-step explanation:
please help me I don't get this
Answer:
(10, 1) is a solution to this equation.
Answer: your answer will be (10, 1)
Step-by-step explanation:
i just watch a mathematics video
answer this solve 2k+6k=h for k
The value of the variable k in the equation given as 2k + 6k = h is k = h/8
How to determine the solution for k?From the question, the equation is given as
2k + 6k = h
Evaluate the like terms
i.e. We add 2k and 6k together.
This gives 8k
So, we have the following equation
8k = h
Divide both sides of the equation by 87
So, we have the following equation
8k/8 = h/8
Evaluate the quotient in the equation
k = h/8
The equation cannot be further simplified
Hence, the solution for k is k = h/8
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Which graph best represents Sarah total earnings for babysitting
Answer:
Sarah earned $10 per hour for babysitting
Step-by-step explanation:
help quick 10 points
Answer:
-x+6
Step-by-step explanation:
the slope is negative because the line is moving down. the y intercept is positive 6 because the line goes through the line (0,6)
lect the correct answer.The equation of a line is y=-3x - 2. What are the slope and the y-Intercept of the line?
Given the equation of a line as shown below :
[tex]y=-3x-2[/tex]To determine the slope and the y - intercept of the line, compare the equation with straight line equation
[tex]y\text{ = mx+c}[/tex]After comparing the equation of a line
[tex]\begin{gathered} m\text{ = slope} \\ c\text{ = y-intercept} \end{gathered}[/tex][tex]\begin{gathered} y\text{ = -3x-2 } \\ y=mx+c \\ m\text{ = -3 } \\ c\text{ = -2} \end{gathered}[/tex]Therefore slope = -3 and y - intercept = -2
= 18cm
c1 =
cm
XÑ
b1 = 25cm
Material Type
6²
163
c2=
b2 = 40cm
b3 = 55cm
b4 = 75cm
Quantity
c3 =
Total:
cm
Length (total)
Answer:
7.08661
Step-by-step explanation:
Find CX. C(6,-4), X(1, -2)
The value of CX as asked will be √29 when two points are given as (6,-4) and (1,-2) by using the distance formula √((x2-x1)²+(y2-y1)²).
What is point?In geometry, a point is a place. It is completely empty, meaning it has no width, length, or depth. A dot indicates a point. A line is described as a collection of points that extends in both directions indefinitely. It has a single length dimension.
What is distance?Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here,
distance formula =√((x2-x1)²+(y2-y1)²)
CX=√((x2-x1)²+(y2-y1)²)
=√((1-6)²+(-2+4)²)
=√(25+4)
=√29
When two points are given as (6,-4) and (1,-2) by the distance formula √((x2-x1)²+(y2-y1)²), the value of CX as asked will be 29.
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(7a
3
−2a−2)+(−5a+3)
Answer: 14a + 1
Step-by-step explanation:
( 7a x 3 - 2a - 2 ) + ( -5a + 3 )
( 21a - 2a - 2 ) + ( -5a + 3 )
21a - 2a - 2 - 5a + 3
14a + 1
What is the value of x?
Answer:
x = 20°
I hope it helps!
Step-by-step explanation:
80+a=180
a=100
a=2x+3x
100=5x
x=20
PLEASE HELP! I ONLY HAVE A FEW MINUTES!! The amount of money put in the cash register, y, after selling x hotdogs at the snack shack. The slope is 2 1/4 and the y-intercept is 10
Explain what the slope and the y-intercept mean in this situation.
The interpretations are
Slope = Amount per hot dogIntercept = Initial amount of moneyHow to explain the slope and the y-intercept?The slope
From the question, the slope is given as
Slope = 2 1/4
From the question, we have
y = Amount of money
x =Number of hot dogs
This means that the amount of money per 1 hot dog is $ 2 1/4
The y-intercept
From the question, the y-intercept is given as
y-intercept = 10
From the question, we have
y = Amount of money
x =Number of hot dogs
This means that the initial amount of money is $10
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Work out the following calculations and give your answer to the nearest 10. A)23x46 b)25x68
Answer:
A) 1060 (corrected to the nearest 10) B) 1700
Step-by-step explanation:
A) the answer is 1058 which taken to the nearest 10 is 1060
B) the answer is 1700 which does not need to be corrected
I really need help, I’m struggling with the problem in the picture bellow
Please can someone help me soon
The x and y coordinates of Q are negative according to the transformation rule of a 90 degree counterclockwise rotation about the origin, which is (x, y)→ (-y, x).
C) Both x and y are negative.
A function translation is:When a function is transferred without undergoing any form or rotation changes, it has been "translated." A function may be translated both horizontally and vertically. Dilation, reflection, as well as rotation are additional "transformations" of a function that are feasible.
According to the given data:The following is the transformation formula for a 90° counterclockwise rotation about the origin:
(x, y) → (-y, x)
the triangle is then reflected across the x-axis,
the following transformation rule:
(x, y) → (x, -y)
So, we have:
(x, y) → (-y, -x)
From the graph, we have:
Q = (1,2)
So,
the coordinates of Q" are
Q" = (-2, -1)
Both the x and y coordinates of Q " are negative.
Therefore,
the correct answer is option:
C) Both x and y are negative.
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I understand that the question you are looking for is:
Triangle PQR is rotated 90 degrees counterclockwise about the origin to form the image triangle P'Q'R' (not shown). Then triangle P'Q'R' is reflected across the x-axis to form triangle P"Q"R" (not shown). What are the signs of the coordinates (x, y) of Point Q"?
A) Both x and y are positive
B) x is negative and y is positive
C) Both x and y are negative
D) x is positive and y is negative
1.1 Complete the table.
Length (cm) Length (mm)
4
12
50
88.49
What is the constant of proportionality?
The constant of proportionality in the given representation is 3 .
The proportionality constant is the ratio that connects two given numbers in a connection that is thought to be proportional. The proportionate constant is also known as constant ratio, unit rate, variable of variation, and even rate of change.
The proportionality constant is calculated by a proportionality constant illustration.
Finding the proportionality constant begins with identifying the x and y elements. To figure out the weight to stick ratio, x will stand for size and Y for the number of butter sticks. We use the equations k = y/ x to calculate the proportionality constant.
Given the value of x is 4 and the value of y is 12
therefore using the equation we get
k= 12 / 4 = 3 .
Therefore the complete table will be
length (x) (y)
4 12
50 150
88.49 265.47
Hence the proportionality constant is 3 .
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“A falcata is formed by taking a quadrant of a circle and removing a semicircle from it (see diagram).If the radius of the original circle is 2 units long, find the exact area of the falcata.”hello!! please help me out! i’m begging. this assignment is kicking my teeth in!!
step 1
Find out the area of the complete quadrant of the circle (1/4 of the complete circle)
[tex]A=\frac{1}{4}*pi*r^2[/tex]where
r=2 units
substitute
[tex]\begin{gathered} A=\frac{1}{4}*pi*2^2 \\ A=pi\text{ unit}^2 \end{gathered}[/tex]step 2
Find out the area of the semicircle removed
[tex]A=\frac{1}{2}*pi*r^2[/tex]where the radius of the semicircle removed is half of the radius of the circle
so
r=2/2=1 unit
[tex]\begin{gathered} A=\frac{1}{2}*pi*1^2 \\ A=\frac{pi}{2}\text{ unit}^2 \end{gathered}[/tex]therefore
to find out the area of the falcata, subtract the area of the removed semicircle from the area of the quadrant of the circle
The area of the falcata is
A=pi-pi/2=pi/2 unit2
the area of the falcata is pi/2 square unitssarah, the yearbook editor, and mrs. moore, the yearbook sponsor, are reviewing costs to produce the yearbook new yearbook design software costs $800, and it costs $15 to print each yearbook.
A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.
Explain the variables in mathematics?A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.
A symbol (typically a letter) used in algebra to represent an unknowable numerical value in an equation. X and Y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are examples of frequently used variables (arc length).
The price to produce x yearbooks will be 15x.
Additionally, software has a fixed cost of $800.
So the total price would be:
y = 800 + 15x
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a) The sum of the three dimensions of a cuboid is 48 cm and the ratio among the lengths of its dimensions is 5: 4:3, Find its area. (grade 6)
Answer:
588 cm
Step-by-step explanation:
Michael is driving to Hollywood, California. Hollywood is 1,375 miles from Michael's. home. If Michael spends 4 days driving to Hollywood, what is the fewest number of miles he can drive each day?
Answer:
343.75
Step-by-step explanation:
dividing the number of miles by the number days to get fewest equal number miles per each day
A city advertises that the average number of runners over the past two decades in their annual road race is 800.
The difference between the average number of runners and the greatest number of runners is the same as the difference between the average number of runners and the least number of runners. The greatest number of runners in a race was 920.
What absolute value equation can be written to determine the least number of runners, and what is this value?
Enter your answers in the boxes.
Absolute value equation: |x- ___| = ___
The least number of runners in a race was ___
Step-by-step explanation:
Absolute value equation:
[tex] |x - 120| = 920[/tex]
least no of runners = 800 - ( 920 - 800) = 680
A triangle has side lengths of (10f+6)(10f+6) centimeters, (2f-4)(2f−4) centimeters, and (9g+1)(9g+1) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
The formula predicts that the triangle's perimeter will be 12f+9g+3.
What is a triangle?
A triangle is a polygon with three sides and three angles. The triangle has angles that add up to 180 degrees.The perimeter of the triangle is determined by adding together all of its sides.The sides of a triangle are (10f +6) centimetres, (2f-4) centimetres, and (9g+1) centimetres long, respectively.
The expression for the triangle's perimeter will be
P = (10f+6) + (2f- 4) + (9g+1)
P = 12f+9g+3
The formula predicts that the triangle's perimeter will be 12f+9g+3.
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A quadratic function passes through the points (−1,−1), (2,−19), and (3,−33).
What is the equation of the function in standard form?
A) f(x)=−2x^2−4x−3
B) f(x)=−2x^2+4x−3
C) f(x)=−2x^2−4x+3
D) f(x)=−2x^2+4x+3
The quadratic function has an equation of f(x) = -2x² - 4x - 3
How to determine the equation of the functionFrom the question, the ordered pairs are given as
(−1,−1), (2,−19), and (3,−33).
A quadratic function is represented as
f(x) = ax²+ bx + c
Using the point (-1, -1), we have
a(-1)²+ b(-1) + c = -1
So, we have
a - b + c = -1
Using the point (2, -19), we have
a(2)²+ b(2) + c = -19
So, we have
4a + 2b + c = -19
Using the point (3, -33), we have
a(3)²+ b(3) + c = -33
So, we have
9a + 3b + c = -33
So, we have
a - b + c = -1
4a + 2b + c = -19
9a + 3b + c = -33
Using a graphing tool, we have
a = -2, b = -4 and c = -3
Substitute a = -2, b = -4 and c = -3 in f(x) = ax²+ bx + c
So, we have
f(x) = -2x² - 4x - 3
Hence, the equation is f(x) = -2x² - 4x - 3
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a square has side lengths. How long is each diagonal?
Answer:the same as sid length
Step-by-step explanation:all sides are the same
can someone help me solve this math problem with solution?? TYY! you
Answer: n + 3
Step-by-step explanation:
Solution
n+3
Evaluate
(n 2 +n−6)
(n−2)
Remove the parentheses
n−2n 2 +n−6
Factor the expression
n−2
(n+3)(n−2)