PLEASE HELP SO EASY !! ALGEBRA 2
The amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.
What is compound interest?Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, it's the interest earned on the principal amount plus any interest earned previously.
To calculate the amount after 5 years, we need to use the formula for compound interest:
A = P × {1 + r ÷ (n × 100)} ∧ (n × t)
where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $5000, r = 2.25% , n = 4 (since interest is compounded quarterly), and t = 5.
After applying these values, we get:
A = $5000 x (1 + 2.25/400) ⁴ ˣ ⁵
A = $5000 x (1.005625) ²⁰
A = $5000 x 1.1871955
A = $5593.60 (rounded off to 2 decimals)
Therefore, the amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.
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Suppose a(x) takes integers as inputs (so x=-4 is in the domain, but x=1/2 isn't, for example) and returns 1 if x is odd and 0 otherwise. Is a(x) a function? Is it a one-to-one function? Why?
Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function.
Describe function.A mathematical item called a function accepts an input and creates an output. It looks like an apparatus with an input and an output. A formula or a graph can both be used to express a function. For instance, the function f(x) = x² returns the square of an input x as output.
Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function. A(x) is not one-to-one, for instance, because a(1) and a(3) are both equal to 1.
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Apples $1.20 per pound how much would it cost for 2.5 pounds of apples?
Answer: $3.00
Step-by-step explanation:
To figure this out, we can use the following formula:
[tex]\textsf{Cost per pound x number of pounds we want to buy}[/tex]
In this case, we want to buy 2.5 pounds of apples, so we can multiply 2.5 by $1.20 to get the total cost:
[tex] \textsf{2.5 x 1.20 = 3} [/tex]
So, 2.5 pounds of apples will cost $3.00
Jungle John participates in a reality TV show that features fitness and agility competitions. In order to beat the competitors, John needs to swing from tree A to tree B, completing an arc of at least 60 feet with a central angle of 115∘.
What length of rope (radius) will he need to accomplish this activity?
Round your answer to the nearest foot, and please show your work.
The length of rope Jungle John will he need to accomplish this activity is 30 feet.
How do we calculate?
the formula for arc length is
L = rθ
where L = length of the arc,
r =e radius of the circle,
θ = central angle of the arc in radians.
θ = (115∘/180∘)π = 2.0089 radians
60 feet = r(2.0089 radians)
r = 60 feet / 2.0089 radians
r = 29.85 feet
r is approximated to 30 feet
Therefore, Jungle John will need a rope with a length of at least 30 feet to swing from tree A to tree B and complete an arc of at least 60 feet with a central angle of 115∘.
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Trigonometry help me please!
As per the question of trigonometry the another equation that describes the given graph is
y = -cos5x. And after verifying the equation given in the question as well as the new equation we conclude that both equations are equal.
In trigonometry what are the domain and range of the standard functions?The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental geometrical operations in trigonometry. These functions' domain and range are as follows:Sine Function (sin x): All real numbers are its domainRange: [-1, 1]The domain of the cosine function (cos x): all real numbersRange: [-1, 1]Domain: All real numbers, excluding x = (n + 1/2), where n is an integer. Tangent Function (tan x):the entire real number rangeDomain: All real numbers except for x = n, where n is an integer. Cotangent Function (cot x)the entire real number rangeDomain: All real numbers, excluding x = (n + 1/2), where n is an integer. Secant Function (sec x)Range: (-∞, -1] U [1, ∞)Domain: All real numbers except x = n, where n is an integer. What distinguishing characteristics can be found in the sine and cosine function graphs?The sine and cosine function graphs' main characteristics are:
The sine and cosine functions are both periodic, which means that their graphs repeat at regular intervals. The maximum distance between the function value and the horizontal axis is determined by the sine and cosine functions' amplitudes. Zeros: The positions where the sine and cosine functions intersect the horizontal axis are known as the zeros.The functions' maximum and minimum values occur at the period's endpoints. For charting and analyzing the behavior of the sine and cosine functions, it is crucial to comprehend these fundamental characteristics.a. We can use trigonometric identities to simplify the given equation in order to describe the graph using a different equation.
[tex]cos((a+b)/2) = 2 cos(sin(a-b)) sin((a-b)/2)[/tex][tex]Sin((a+b)/2) = cos(a) - cos(b) sin((a-b)/2)[/tex]Using this identity, the given equation can be made simpler:[tex][(2 cos(5x) sin(-4x))/(-2 sin(5x) sin(-4x)] gives y.\\y = -cos(5x)[/tex]So, the equation [tex]y = -cos(5x)[/tex] can be used to describe the graph.b. We can simplify the following equation and compare it with [tex]y = -cos(5x)[/tex]to see if the two equations are equivalent.
We obtain this by applying the same trigonometric identity as before.
Y is equal to [tex][((sinx - sin9x)/(cosx - cos9x)][/tex]Y is equal to [tex][(2 cos5x sin(-4x))/(-2 sin5x sin(-4x)][/tex] (using the identities [tex]cos(a) - cos(b) and sin(a) - sin(b))[/tex][tex]y = -cos5x[/tex]As we can see, the following equation's shortened form is equal.To know more about trigonometric functions visit:
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find the values of variables, then find the lengths of the sides of each quadrilateral
The variables are as follows:
x = 4
y = 4.8
The lengths of the sides of the kites are 4.5 and 6.8 units.
How to find the side of a kite?A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.
The non vertex angles are congruent.
Therefore,
x + 0.5 = 2x - 3.5
2x - x = 0.5 + 3.5
x = 4
y + 2 = 2y - 2.8
2y - y = 2 + 2.8
y = 4.8
Hence,
length of one pair = 4 + 0.5 = 4.5 units
length of the other pair = 4.8 + 2 = 6.8 units
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Y can represent the distance Frog B hopped as y=x+ 8/3 x. Now rewrite the equation using the distributive property.
The rewritten expression of y = x + 8/3x using the distributive property is y = x(1 + 8/3)
Rewriting the equation using the distributive property.From the question, we have the following parameters that can be used in our computation:
Y can represent the distance Frog B hopped as y=x+ 8/3 x.
This means that
y = x + 8/3x
Factor out x from the equation
So, we have
y = x(1 + 8/3)
The above equation has been rewritten using the distributive property.
Hence, the rewritten expression using the distributive property is y = x(1 + 8/3)
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50 Points! Multiple choice algebra question. Find the inverse of f(x)=3+5x. Photo attached. Thank you!
the inverse of the function f(x) = 3 + 5x is f^(-1)(x) = (x - 3) / 5.To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x).
what is inverse of the function ?
The inverse of a function is a new function that "undoes" the effect of the original function, meaning that if we apply the inverse function to the output of the original function, we get back the input.
In the given question,
To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x). The steps to find the inverse are as follows:
Step 1: Replace f(x) with y.
y = 3 + 5x
Step 2: Solve for x in terms of y.
y - 3 = 5x
x = (y - 3) / 5
Step 3: Replace x with f⁻¹(x) to get the inverse function.
f⁻¹(x) = (x - 3) / 5
Therefore, the inverse of the function f(x) = 3 + 5x is f⁻¹(x) = (x - 3) / 5.
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An area of land measures 735 metres by 756 metres. It is to be divided up into
square plots of equal size.
(a) What is the area of the largest squares that will fit on it?
(b) How many squares will fit on it?
a) The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.
b) The number of squares that will fit on the land is 61773.
Explain square
A square is a geometric shape with four sides of equal length and four right angles. It is a type of rectangle, but all of its sides are the same length. Squares are used in mathematics to represent and calculate areas and volumes, and they also have applications in architecture and art.
According to the given information
(a) To find the area of the largest squares that will fit on the land, we need to find the greatest common divisor (GCD) of the dimensions 735 and 756, and then square it.
To find the GCD, we can use the Euclidean algorithm:
GCD(735, 756) = GCD(735, 756 - 735) = GCD(735, 21) = GCD(21, 735 - 21 * 35) = GCD(21, 210) = GCD(21, 210 - 21 * 10) = GCD(21, 90) = GCD(21, 90 - 21 * 4) = GCD(21, 6) = GCD(6, 21 - 6 * 3) = GCD(6, 3) = 3
Therefore, the GCD of 735 and 756 is 3. The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.
(b) To find how many squares will fit on the land, we need to divide the total area of the land by the area of each square. The total area of the land is:
735 * 756 = 555960 square meters
The area of each square is 9 square meters, as we found in part (a). Therefore, the number of squares that will fit on the land is:
555960 / 9 = 61773.333...
Since we can't have a fractional number of squares, we need to round down to the nearest integer. Therefore, the number of squares that will fit on the land is 61773.
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A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results.
Annual income vs. age group
Less than
$
50
,
000
$50,000dollar sign, 50, comma, 000 At least
$
50
,
000
$50,000dollar sign, 50, comma, 000 Total
Ages
44
4444 and under
148
148148
68
6868
216
216216
Ages
45
4545 and above
38
3838
94
9494
132
132132
Total
186
186186
162
162162
348
348348
Which of the following statements is true of those polled?
According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.
How to find the correct sentence?To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.
According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).
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100 Points! Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Photo attached. Please show as much work as possible. Thank you!
f(4) = 537. and f(-3) = 363. To find f(-3), we replace x with -3 in the expression similarly for x=4.
what is expression ?
In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.
In the given question,
To find f(-3), we replace x with -3 in the expression:
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
= 3(81) - 4(-27) + 3(9) + 15 - 3
= 243 + 108 + 15 - 3
= 363
Therefore, f(-3) = 363.
To find f(4), we replace x with 4 in the expression:
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
= 3(256) - 4(64) + 3(16) - 20 - 3
= 768 - 256 + 48 - 23
= 537
Therefore, f(4) = 537.
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Given the piecewise function below, evaluate the function as indicated
The evaluation of the functions using piecewise function gives:
f(-9) = 8
f(0) = 2
f(6) = 7
f(-6) = 4
f(3) = 4.5
f(9) = -6
How to evaluate the functions using piecewise function?
To evaluate the functions using piecewise function, we have to the condition they satisfy. That is:
For f(-9), x = -9. Thus, x≤ -6. So use f(x) = (-4/3)x - 4 to evaluate f(-9). That is:
f(-9) = (-4/3)*(-9) - 4
f(-9) = 8
For f(0), x = 0. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(0). That is:
f(0) = (5/6)*0 + 2
f(0) = 2
For f(6), x = 6. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(6). That is:
f(6) = (5/6)*6 + 2
f(6) = 7
For f(-6), f(x) = (-4/3)x - 4:
f(-6) = (-4/3)*(-6) - 4
f(-6) = 4
For f(3), f(x) = (5/6)x + 2:
f(3) = (5/6)*3 + 2
f(3) = 4.5
For f(9), x = 9. Thus, x > 6. Use f(x) = -2x + 12:
f(9) = -2*9 + 12
f(9) = -6
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5 cubic cm
pls help help help
The value of 5 cubic cm in liters, can be converted to be
How to convert cubic centimeters to liters ?To convert cubic centimeters (cm³) to liters (L), we can use the following conversion factor:
1 L = 1000 cm³
This means that 1 liter is equal to 1000 cubic centimeters. To convert cubic centimeters to liters, we can divide the number of cubic centimeters by 1000.
For example, to convert 5 cubic cm to liters:
5 cm³ ÷ 1000 = 0.005 L
Therefore, 5 cubic cm is equal to 0.005 liters (or 5 mL).
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Full question:
5 cubic cm to Liters
Let m, n, and p be real numbers.
Name the property of equality that the statement illustrates.
m(n-p) = mn - mp
The property of equality that the statement m(n-p) = mn - mp illustrates is (d) the distributive property
Naming the property of equality that the statement illustrates.Given that
m(n-p) = mn - mp
The above property is the distributive property
The distributive property states that
a(b - c) = ab - ac
This case
a = m
b = n
p = c
Substitute the known values in the above equation, so, we have the following representation
m(n-p) = mn - mp
Hence, the property of equality that the statement illustrates is the distributive property
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In a spring, the tension (Tnewtons) is directly proportional to its extension ( x cm). When the tension is 150 newtons, the extension is 6 cm. (a) Find a formula for T' in terms of x. T = AD
The formula for tension (T) in terms of extension (x) is T = 25x.
The given statement is T = kx, where T is the tension, x is the extension, and k is the proportionality constant.
To solve this problem, we need to find the value of k. We can do that by substituting the given values of T and x into the equation:
T = kx
150 = k×6
k = 25
Therefore, the formula for tension (T) in terms of extension (x) is T = 25x.
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ANSWER ASAPP!!!!!!
AAAA
If f(x)= e³x, then d/dx(e³x)=? A. 3e³x B. e³x C.ex D. 9e³x
Answer:
the answer is D. 9e³x.
Step-by-step explanation:
If f(x) = e³x, then we can find its derivative using the chain rule of differentiation as follows:
d/dx(e³x) = 3e³x * d/dx(3x) = 3e³x * 3 = 9e³x
= D. 9e³x.
Answer:
A
Step-by-step explanation:
Question 7 (3 points)
The graph and table below represent the constant rate for the amount of time it takes for a given
number of gallons of water to flow from a hose.
a. Find the rate of both the graph and table. Be sure to show all work.
b. Which one has the greater rate? Explain how you know.
The rate of water flow is 6 gallons per unit of time.
What is slope?
Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.
a. To find the rate, we need to calculate the amount of water that flows per unit of time.
Method 1: Using the Graph
First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.
From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.
So, the slope of the line is:
slope = change in y-values / change in x-values
= (60 - 30) / (10 - 5)
= 6
Therefore, the rate of water flow is 6 gallons per unit of time.
Method 2: Using the Table
We can also find the rate by calculating the differences in y-values and x-values in the table.
x y Difference in y Difference in x Rate (y/x)
-------------------------------------------------------
5 30 - - -
7 42 12 2 6
10 60 18 3 6
From the table, we can see that the rate of water flow is 6 gallons per unit of time.
b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.
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1 Suppose another student says he spends $29 each
week on entertainment. Will the mean and median
increase or decrease?
decreas
2 What is the new mean when the value from problem 1
is included in the data set?
Show your work. For elementary kids
Answer:
Step-by-step explanation:
The ratio of apples to pears at a farm stand is 5:3. What is the percentage of the fruit to apples?
The length of a rectangle is 4 meters less than 2 inches times width. The perimeter is 34 meters. Find the width
Answer:
7
Let's call the width = x
width : x
so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7
3x = 21
x = 7
so x is 7
During a sale the regular price of a pair of running shoes is reduced by 20%. If the sales price is $64 what is the regular price of the running shoes
The regular price of the running shoes is $80.
Let's denote the regular price of the running shoes as P. We know that during the sale, the price is reduced by 20%, which means the sales price is 80% (100% - 20%) of the regular price.
Given that the sales price is $64, we can set up the equation:
0.8P = $64
To find the regular price P, we divide both sides of the equation by 0.8:
P = $64 / 0.8
P = $80
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What is the total payment required to pay off a promissory note issued for $500.00 at 8% ordinary interest and a 90-day term? A. $507.20 C. $508.00 B. $540.00 D. $510.00
The total payment required to pay off the promissory note debt of 90 days term is D. $510.00.
The promissory note issued is for $500.
The interest rate is 8%.
Furthermore, the time frame is 90 days.
So the total payment is
= $500 + ($500 × 8% × 90 days ÷ 360 days)
= $500 + ($500 × 8% × 1/4)
= $500 + 10
= $510
Promissory notes are sometimes known as an IOU, a loan arrangement, or simply a note. It is a legal lending contract in which the borrower pledges to return the lender a specific amount of money within a specific time frame.
This type of document is legally binding and imposes a legal duty to repay the loan. Mortgages, school loans, car loans, company loans, and personal loans between family and friends all use promissory notes.
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Fred's science class is going to the Ancient Dig adventure park. His teacher got the school group package, which costs $308. The package covers the entrance fee for the group, a private dig site, and an activity guide. Fred's teacher upgraded the package to include a fossil tool kit for each of the 22 students, bringing the total to $440. Which equation can you use to find k, the cost of each tool kit?
Answer: (440-308) ÷ 22 = The cost of each tool kit is 6 dollars
Step-by-step explanation:
The original price of the field trip was $308 after the price fof each tool kit was added the price was $440.
The total costs of all the tool kits was 132
440-308=132
the total cost of the tool kits divided by the number of kids will get the price of each tool kit
132÷22 =
K=
What is 5a^2b + 15ab^2 factories fully
Answer:
[tex]5 {a}^{2} b + 15a {b}^{2} = [/tex]
[tex]5ab(a + 3b)[/tex]
The depth of water at a dock can be modeled as y = 3 sin(x) +7. At low tide, the water is 4 feet
deep. What is the depth of water at high tide (its maximum point)?
Step-by-step explanation:
At low tide depth = (3)(-1) + 7 = 4
at HIGH tide depth = (3) (+1) + 7 = 10 feet
find the value of x and y in simplest radical form. An explanation on how you got an answer would be appreciated.
EDIT: I got the answer, but I'll give points to anyone who wants them.
The value of the variables 'x' and 'y' will be 8√2 cm and 9√2 cm, respectively.
Given that:
Area of a small triangle, A = 72 square cm
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The equation is given as,
x² / (32)² = y² / (36)² = 72 / (1/2 x 32 x 36)
The value of 'x' is calculated as,
x² / (32)² = 72 / (1/2 x 32 x 36)
x = 8√2 cm
The value of 'y' is calculated as,
y² / (36)² = 72 / (1/2 x 32 x 36)
y = 9√2 cm
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which equation can be used to find the value of x x=60 + 40
Answer:
x = 50
Step-by-step explanation:
2x = 60+40
simply 60 + 40 to 100
so 2x = 100
and then divide 2 to get it to the other side.
like this = x = 100/2
then divide 100 by 2 and get 50
so x=50
23
A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.
Jake finds out that the track is 270 km long.
He assumes that the track has been measured correct to the nearest 10 km.
Could the average speed of the train have been greater than 160 km/h?
You must show how you get your answer.
Answer: To answer this question, we need to calculate the maximum possible speed of the train based on the given information and check if it is greater than 160 km/h.
First, let's use the given information to find the range of possible speeds of the train. The time taken by the train is given as 110 minutes, correct to the nearest 5 minutes. This means that the actual time taken by the train could be anywhere between 107.5 minutes and 112.5 minutes.
Converting the time to hours, we get:
Lower bound of time = 107.5 minutes = 107.5/60 hours = 1.792 hours
Upper bound of time = 112.5 minutes = 112.5/60 hours = 1.875 hours
Now, let's use the given distance of 270 km, correct to the nearest 10 km, to find the range of possible average speeds of the train. The lower bound of the distance is 265 km, and the upper bound is 275 km.
Lower bound of speed = 265 km / 1.875 hours = 141.3 km/h
Upper bound of speed = 275 km / 1.792 hours = 153.5 km/h
Therefore, based on the given information, the maximum possible speed of the train is 153.5 km/h, which is less than 160 km/h.
So, we can conclude that the average speed of the train could not have been greater than 160 km/h.
Step-by-step explanation:
Write a quadratic function with zeroes – 1 and 6. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer:
If the zeroes of a quadratic function are -1 and 6, then its factored form is:
(x + 1)(x - 6) = 0
Expanding the left side:
x^2 - 5x - 6 = 0
So the quadratic function in standard form is:
f(x) = x^2 - 5x - 6
Answer:
f(x) = x^2 - 5x - 6
Step-by-step explanation:
To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:
(x + 1)(x - 6) = 0
Expanding the factors, we get:
x^2 - 5x - 6 = 0
This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:
f(x) = x^2 - 5x - 6
This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.
