On solving the provided question, the capital that is placed at 25% for 3 years, to obtain an interest of $ 1620 will be $3,164.06
Explain what compound interest is.interest you receive is equal to as - compound interest. Using simple math, you can see how this works: if you have $100 and it earns 5% interest annually, you will have = $105 at the end of the 1st year. You'll have = $110.25 at the conclusion of the 2ndyear.
To calculate, we will use the following
[tex]First, convert R as a percent to r as a decimal[/tex]
r = R/100
r = 25/100
r = 0.25 rate per year,
Then solve the equation for A
[tex]A = P(1 + r/n)^{(nt)}[/tex]
[tex]A = 1,620.00(1 + 0.25/1)^{(1)(3)}[/tex]
A = 1,620.00(1 + 0.25)(3)
A = $3,164.06
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A, B, C and D lie on a circle.
AC and BD intersect at X.
The angles BAX and CDX are equal and the length of CX is 8.2 cm.
What are angles?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Given that, the points A, B, C, D lie on a circle and AC and BD intersect at X.
The angles BAX and CDX, they are subtended by the same arc AD, hence, according to the property of angles subtended by the same arc, they are equal.
Thus ∠BAX = ∠CDX
Since, corresponding sides opposite to the equal angles are proportional.
CX/BX = CD/AB
⇒ CX/3.84 = 9.40/4.40
⇒ CX = (9.40*3.84)/4.40
⇒ CX = 8.2
Thus, length of CX is 8.2cm
The angles BAX and CDX are equal and the length of CX is 8.2 cm
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please help me!!!! i need it done right
The solution of the system of equations is y = 5 and x = 3, and the difference x - y gives:
x - y = -2
How to solve the system of equations?Here we have the system of equations:
5x + 3y = 30
-5x - 2y = -25
If we add the two equations we will get:
(5x + 3y) + (-5x - 2y) = 30 + (-25)
y = 5
So just by doing that we found the value of the variable y.
To find the value of x, we can replace the known value of y on one of the equations, doing that we will get:
5x + 3y = 30
5x + 3*5 = 30
5x + 15 = 30
5x = 30 - 15 = 15
x = 15/5 = 3
x = 3
Then the difference x - y gives:
x - y = 3 - 5 = -2
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It takes Elijah 8 minutes to run 4 laps how many minutes does it take him to run 1 lap?
Topic is unit rate
Answer:
2 minutes
Step-by-step explanation:
8 : 4 = x : 1
x = 8/4
x = 2
Step-by-step explanation: To find the time it takes Elijah to run 1 lap, we need to divide the time it takes him to run 4 laps by the number of laps he runs in that time. Since it takes Elijah 8 minutes to run 4 laps, the time it takes him to run 1 lap is 8 minutes / 4 laps = ${2}$ minutes per lap.
This calculation illustrates the concept of unit rate, which is the rate at which a quantity changes over a given unit of time or distance. In this case, the unit rate is the time it takes Elijah to run 1 lap, which is 2 minutes per lap. This unit rate allows us to compare the time it takes Elijah to run different distances, and to determine how long it would take him to run a given distance at the same pace.
One person calls 3 people. The next day, those people each call
3 people. The third day, those people each call 3 people. Write
an expression using exponents for the number of calls made on
the third day.
Answer:
3³
Step-by-step explanation:
You want an expression using an exponent to represent the number 3·3·3.
Repeated multiplicationAs you know, a coefficient is used to represent repeated addition:
a + a + a = 3a
The coefficient 3 in the above expression signifies that 'a' appears in the sum 3 times.
Likewise, repeated multiplication can be represented using a specific notation. An exponent signifies the number of times a factor appears in a product:
a · a · a = a³ . . . . . 'a' is a factor 3 times
ApplicationYou have a sequence of numbers of telephone calls:
3 the first day
3·3 the second day
3·3·3 the third day
The calls on the third day can be represented using an exponent:
3³
__
Additional comment
When superscript formatting is not available for the exponent, it is signified by a caret (^). The same number is 3^3 when written in plain text.
As you might expect, a plain text exponent must be enclosed in parentheses if it is other than a single letter or number.
At a grocery store, a customer pays a total of $11.10 for 1.6 pounds of chicken
and 2 pounds of fish. Another customer pays a total of $12.15 for 2.4 pounds of
chicken and 1.8 pounds of fish. How much does each cost per pound?
Each pound of fish and chicken will cost $3.75 and $2.25 respectively
How to determine how much each cost per pound?
A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Given that:
1. A customer pays a total of $11.10 for 1.6 pounds of chicken
and 2 pounds of fish.
2. Another customer pays a total of $12.15 for 2.4 pounds of
chicken and 1.8 pounds of fish
Let C and F represent the cost of one pound of chicken and fish respectively
Statement 1:
1.6C + 2F = 11.10 ---- (1)
Statement 2:
2.4C + 1.8F = 12.15 ---- (2)
we have simultaneous equations now, let's solve using the elimination method:
1.6C + 2F = 11.10 ---- (1)
2.4C + 1.8F = 12.15 ---- (2)
2.4 × (1.6C + 2F = 11.10) = 3.84C + 4.8F = 26.64
1.6 × (2.4C + 1.8F = 12.15) = 3.84C + 2.88F = 19.44
..........................................
1.92F = 7.2
Thus, 1.92F = 7.2
F = 7.2/1.92 = $3.75
Put F = $3.75 into (1):
1.6C + 2F = 11.10
1.6C + 2(3.75) = 11.10
1.6C + 7.5 = 11.10
1.6C = 11.10 - 7.5
1.6C = 3.6
C = 3.6/1.6 = $2.25
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function rule to find f(–11).
Answer:
f(-11) = -16
Step-by-step explanation:
We are given a function
f(x) = x-5
Substitute the value of x = -11 into the function
f(-11) = -11-5
= -16
Answer:
-16
Step-by-step explanation:
Given that,
f ( x ) = x - 5
To find the value of f ( -11 ), you have to replace x with -11 & solve it.
Let us solve it now.
f ( -11 ) = x - 5
f ( -11 ) = -11 - 5
f ( -11 ) = -16
A group of friends were working on a student film that had budget of $400. They used 23% of their budget on equipment. How much money did they spend on equipment?
Answer: they must have used up around 40% of the money if I’m wrong I’m so sorry
Step-by-step explanation: Good luck!
hello could someone explain the law of sines to me?
Answer:The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
Step-by-step explanation:
Isaac has $89,535 in a savings account that earns 8% annually. The interest is not
compounded. To the nearest dollar, how much will he have in total in 4 years?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years..
Round your answer to the nearest dollar.
Answer:
Step-by-step explanation:
Help please!! This is actually so confusing
Answer: [tex]\frac{\sqrt{55}}{8}[/tex]
This is the same as writing sqrt(55)/8 where the 8 is not inside the square root.
=====================================================
Explanation:
Draw a right triangle in the quadrant Q1, which is in the northeast corner.
We're given [tex]\cos(\theta) = 3/8[/tex]. Recall that cosine is the ratio of adjacent over hypotenuse.
[tex]\cos(\text{angle}) = \text{adjacent/hypotenuse}[/tex]
This right triangle will have an adjacent side of 3 and hypotenuse of 8.
Refer to the diagram below.
Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to find the missing side is exactly [tex]\sqrt{55}[/tex], which is the opposite side of angle theta.
Then as one last step, we would say:
[tex]\sin(\text{angle}) = \text{opposite/hypotenuse}\\\\\\\sin(\theta) = \frac{\sqrt{55}}{8}[/tex]
--------------
A very similar approach is to use the pythagorean trig identity
[tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex]
Solving for sine gets us
[tex]\sin(\theta)=\sqrt{1-\cos^2(\theta) }[/tex]
Sine is positive in Q1.
Then plug in [tex]\cos(\theta) = 3/8[/tex] and simplify. You should get the answer mentioned above.
tickets for a high school dance cost $4.00 each if purchased in advance, but $5.00 at the door. If 225 tickets were sold and $950 was collected, how many tickets were sold in advance and how many were sold at the door?
50 tickets were thus sold at the door. As a result, there were 175 advance sales of tickets and 50 at the door.
What is a linear equation?A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".
Tickets for a high school dance were provided.
Purchases made before the dance cost $4.00 apiece.
If purchased at the door, they would cost $5 apiece.
225 tickets were sold, bringing in $950.
It's time to locate the advance-purchase and door-purchase tickets.
Let the quantity of advance tickets sold equal x.
And the quantity of tickets sold at the door will be equal to y.
hence, the overall quantity of tickets sold
[tex]x+y = 225\\y = 225 - x[/tex]......(1)
Now,
4x + 5y = 950
[tex]4x + 5y = 950\\4x + 5(225-x) = 950\\4x + 1125 - 5x = 950\\-x = -175\\x= 175\\y=50[/tex]
50 tickets were thus sold at the door.
As a result, there were 175 advance sales of tickets and 50 at the door.
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Write the equation of the line in slope-intercept form (y=mx+b) for each of the following.
help ill brainlist
The linear equation that is modeled by the table is:
y = 2x + 1
How to write the linear equation?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we can use the first two points on the table (-3, -5) and (-1, -1), we will get the slope:
a = (-1 + 5)/(-1 + 3)
a = 4/2 = 2
Then the line is something like:
y = 2x + b
To find the value of b we can use one of the points (-3, -5), replacing these values we will get:
-5 = 2*-3 + b
-5 = -6 + b
-5 + 6 = b
1 = b
Then the linear equation is:
y = 2x + 1
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Let f(x)=x−4 and g(x)=−2x+4
Find g(f(2))
When f(x)=x4 and g(x)=2x+4 at x=2 for f(x) and x=-2 for g, the value of g(f(2)) is 8 (x).
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
Here,
f(x)=x-4
g(x)=-2x+4
f(2)=2-4
=-2
g(-2)=-2*-2+4
g(-2)=8
The value of g(f(2)) is 8 for f(x)=x−4 and g(x)=−2x+4 at x=2 for f(x) and x=-2 for g(x).
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The value of a company's equipment is $33,000 and decreases at a rate of 12% each year. Write an exponential decay function for the value of the equipment after t years.
Answer:
Below
Step-by-step explanation:
Value = 33000 ( .88)^t each year, t , the value is only 88% ( or in decimal: .88) of the prior year ( 12 % decrease leaves 88% )
Every hour, the population of a colony of bacteria increases by 4% of what the population was at the beginning of the hour. If the population is 2488 at 12 o'clock, what was the population 2 hours before that
The population 2 hours before that is 2691 if the population of a colony of bacteria increases by 4% of what the population was at the beginning of the hour.
What is meant by population?A population is a distinct group of individuals that can be distinguished for the purposes of data collection and analysis by at least one feature. Populations are used in statistics and other branches of mathematics. Data is typically collected from a sample while learning about a large population.
Between sample size and population, the population will always be larger in number. The entire group of individuals under study is referred to as the population. 250 persons make up the population in the illustration, which is the same size as the high school under consideration.
We have P₀=2488
Rate of increase=R=4%
Time=2 hours
Bacteria count =P
P=P₀[tex](1+(R/100)^{T}[/tex]
=2488×(1+(4/100))²
=2488×1.0816
=2691.0208≈2691
Therefore, the population 2 hours before that is 2691.
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Please help me with inequalitys
Answer:
n = -104
Step-by-step explanation:
You want to identify a solution to the inequality -5 +n/13 < -12.
SolutionAdding 5 we get ...
n/13 < -7
Multiplying by 13 gives ...
n < -91
Of the choices available, only -104 is less than -91.
n = -104
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there are 75 fifth graders and 125 fourth graders. They are going to be grouped in teams for field day with the same number of with the same number of teams if there must also be the same number of fifth graders on each team how many teams can there be at most?
Please Help
The 25 teams can there be at most.
What is the LCM?
Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers.
We have,
75 fifth graders
125 fourth graders.
They are going to be grouped in teams for a field day with the same number of students on each team.
the same number of teams if there must also be the same number of fifth graders on each team.
take the LCM of the 75 & 125 Which is the 25.
3 fifth graders each
5 fourth graders each
Hence, the 25 teams can there be at most.
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please help, giving brainliest!
Jaxon models the volume of a popcorn box as a right rectangular prism. Its dimensions are 2 3/4
in by 2 1/4 4 in by 55 in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.
Answer:
30.9 cubic inches
Step-by-step explanation:
This is a volume question. You multiply 2 3/4, 2 1/4, and 5 inches all together.
First you turn it into an improper fraction and multiply. 11/4*9/4 = 99/16
Then multiply this by 5: 99/16 * 5 = 30.9375
Round to nearest tenth: 30.9
A bag of flour weighs 4 pounds the flour is priced per ounce How many ounces of flour are in the bag
Answer: 64
Step-by-step explanation:
There are 16 ounces in a pound and there are 4 pounds and 4x 16 is 64
Answer:
64 oz.
Step-by-step explanation:
16 oz. = 1 lb.
16 oz. x 4 lbs. = 64 oz.
what simplify. 5x + 3 (x + 2) + 3
Answer:
8x + 9
Step-by-step explanation:
5x + 3x + 6 + 3
8x + 9
the quotient of -9and y
show work
Answer: -9/y
Step-by-step explanation: quotient is a fancy word for divide
-9/y
He turns 110 degrees and walks 270 yards until he arrives at the other end of the lake. Approximately how long is the lake?
The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.
Given : b = 245 yards, c= 270 yards,
To find: The length of the lake which is the value of x
To find [tex]\angle A[/tex], we know that [tex]110^o\, and\, \angle A[/tex] lie on straight line. So
[tex]110^o + \angle A = 180^o\\\\\angle A = 180^o - 110^o = 70^o[/tex]
Using law of cosines
[tex]a^2 = b^2 +c^2 - 2bc\cdot cosA[/tex]
Plugging the values of b , c and A into the equation, we get
[tex]a^2 =245 ^2 +270^2 - 2\times 245 \times 270 \times \cos 70^o \\[/tex]
The value of [tex]\cos 70^o[/tex] is 0.342 approximately
On substituting this in the equation, we get
a = 296.1 yards
What is law of cosines?Every triangle has three vertices and three sides. If in a triangle, the three vertices are A, B, and C, then, the sides opposite these vertices are a, b, and c, respectively. The angle at each vertex is given the same name as the vertex. Therefore, the three angles are also named A, B, and C. To solve such a triangle is to find the lengths of each of its sides and all its angles.
The sine rule or law of sines is used when we are given either
a) two angles and one side
or
b) two sides and the angle that is not included between these two sides.
[tex]\frac{\sin A}{a} =\frac{\sin B}{b} =\frac{\sin C}{c}[/tex]
The cosine rule or law of cosines is used when we are given either
a) three sides (SSS)
or
b) two sides and the included angle (SAS)
[tex]c^2=a^2+b^2-2ab\cdot\ cosC \\ b^2=a^2+c^2-2ac\cdot\ cosB\\ a^2=b^2+c^2-2bc\cdot\ cosA\\[/tex]
The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.
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Last month, Paulina earned $520.60. This month, she works overtime and earns $601.30. What is the percent of increase in Paulina’s earnings? Round to the nearest tenth if necessary.
The percent of the increase in Paulina’s earnings is 15.55%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Last month, she earned $520.60. This month, she works overtime and earns $601.30.
The percent of increase = ($601.30 - $520.60)/520.60 x 100%
The percent of increase = (80.7)/520.60 x 100%
The percent of increase = 0.15501 x 100%
Apply the multiplication operation,
The percent of increase = 15.55 %
Thus, the percentage of the increase in Paulina’s earnings is 15.55%.
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If the following series continues the same pattern. What is the next number in the series 1, 10, 7, 16?.
Answer:
Step-by-step explanation:
28
Each number within a sequence is called an arithmetic sequence.
True false question.
True
False
Answer: True
Step-by-step explanation: Take a number on the list minus the previous one, and it shows a constant, then it is an arithmetic sequence.
Jen wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Jen can pay $52 per month, plus $3 for each group class she attends. Alternately, she can get the second membership plan and pay $31 per month plus $4 per class. If Jen attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that? What is that total amount?
ITS DUE TODAY HELP PLEASE
The number of classes per month that had same total amount paid was 21
The total amount is $115
How to find the total amountlet the number of group class be represented by x
first membership plan, Jen can pay $52 per month, plus $3 for each group class she attends
= $52 + $3x
second membership plan, Jen can pay $31 per month plus $4 per class
= $31 + $4x
when the total amount are equal
$52 + $3x = $31 + $4x
52 - 31 = 4x - 3x
21 = x
The total amount
= $52 + $3 * 21
= $115
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A company bought a van that had a value of £12 000
Each year the value of the van depreciates by 25%.
Work out the value of the van at the end of three years.
Answer:
The value of the car at the end of 3 years will be £5,062.50.
Write an equation of the line that passes through (2,-5) and is parallel to the line 2y=3x+10 .
Answer: [tex]y+5=\frac{3}{2}(x-2)[/tex]
Step-by-step explanation:
[tex]2y=3x+10 \implies y=\frac{3}{2}x+5[/tex]
Parallel lines have the same slope, so the slope of the line we need to find is 3/2.
Substituting into point-slope form, the equation is [tex]y+5=\frac{3}{2}(x-2)[/tex].
Question 4
Is this a function? Explain, why or why not!
Edit View Insert Format Tools Table
12pt Paragraph BIUA 2 TV 00
2 pts
DI
By using the concept of function, it can be seen that the given figure does not represents a function.
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the values on the x axis represents the domain and the values on the y axis represents the Range.
From the figure it can be seen that
For x = 2, there are three points on the y axis.
So the point x = 2 maps to different points on the y axis
So this is not a function
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6. (3x + 1)(x - 2) =
7. (x − 3)(2x - 1) =
8. (x-3y) (2x - y) =
9. (2x - y)(x-2y) =
Hello is there a tutor who can help
Answer:
6 (3x + 1)(x - 2) = 3x^2 - 2x + x - 2 = 3x^2 - x - 2
7 (x − 3)(2x - 1) = 2x^2 - x - 3x + 3 = 2x^2 - 4x + 3
8 (x-3y) (2x - y) = 2x^2 - yx - 3xy + 3y^2 = 2x^2 - 4xy + 3y^2
9 (2x - y)(x-2y) = x^2 - 3xy + 2y^2 = x^2 - 3xy + 2y^2