Answer:
y/2
y*2
y-2
y+2
y%2
y^2
Operations on Algebraic Expressions: The three major components of an algebraic expression are variables, constants, and coefficients. Addition, subtraction, multiplication, and division are the four fundamental operations. We solve both difficult and straightforward equations using operations on algebraic expressions.There are three categories of algebraic expressions: monomial, binomial, and polynomial or multi-term expressions.These are the algebraic terms: Alphabetic letters alone or in combination with numbers or fractions are the variables.The numbers that are connected to the variables in a single term are called coefficients.Constants: Single integers or numbers that are typically connected to other terms through elementary operations.Examples include 8xyz, 25x+12y+9, 2yz23zy, and 3a+2b+5c.Algebraic Expression Types
There are three different categories for algebraic expressions. As follows:
Expressions with a monomial or single word. For instance, 4xy2, 3ab, 7p, 5xyz, etc., where 3,4,5,7 are the coefficients and x, y, z, a, b, p are the variables.Expressions with two terms or a binomial. For instance, 2xyx, pq5p2, etc.Multi-term or polynomial expressions. as in 2x+5y4, 2xy2+3y+1, etc.To learn more about Operations on Algebraic Expressions refer to:
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"y/2," "y*2," "y-2," "y+2," "y%2," and "y". Constants, coefficients, and variables make up the three main parts of an algebraic expression.
Procedures for Algebraic Expressions:Constants, coefficients, and variables make up the three main parts of an algebraic expression. These four operations—addition, subtraction, multiplication, and division—are known as the fundamental operations.By performing operations on algebraic expressions, we are able to solve both complex and simple equations.Polynomial or multi-term expressions, binomial expressions, and monomial expressions are the three types of algebraic expressions.The variables are either alphabetic letters alone or in combination with numbers or fractions.The term "coefficients" refers to the numbers that link the variables in a single term.Single integers or numbers known as constants are those that are often connected to other terms through simple mathematical procedures. There are more examples, such as 8xyz, 25x+12y+9, 2yz23zy, and 3a+2b+5c.Monomial expressions or single-word phrases. For instance, 4xy2, 3ab, 7p, 5xyz, etc., where 3,4,5,7 are the coefficients and x, y, z, a, b, p are the variables. two-term or binomial expressions pq5p2, for instance, or 2xyx. such as 2x+5y4, 2xy2+3y+1, etc., are examples of multi-term or polynomial expressions.To learn more about Algebraic expressions refer to:
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3. Pedro can pay 3 dollars for one T-shirt, or he can get 2 T-shirts for 5 dollars. Which is a better
deal? Why?
Answer:
Buying two T-shirts for 5 dollars is a better deal.
Step-by-step explanation:
If you bought one T-shirt for 3 dollars, that would be more than half of the money than two T-shirts. Therefore, it's a better deal to get 2 T-shirts for 5 dollars.
I don’t understand this any help please answer and explain please
Answer:
25.5 inches.
Step-by-step explanation:
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with legs of length 19 inches and 17 inches. The length of the hypotenuse is the square root of the sum of the squares of the other two sides. We can calculate this as follows:
hypotenuse = sqrt(19^2 + 17^2)
hypotenuse = sqrt(361 + 289)
hypotenuse = sqrt(650)
hypotenuse = 25.495097568 inches
Rounding to the nearest tenth, the length of the hypotenuse is 25.5 inches.
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read the whole question and then answer it!!
1a. No, the value of 60% of 400 is 240.
1b. No, the value of 60% of 200 is 120.
1c. No, the value of 60% of 120 is 72.
2. The equation the express the relation 60%, x, and 87 is 0.6x = 87. The value of x is 145.
3a.The equation is0.6c = 43.2. The value of c is 72.
3b. The equation is0.38e = 190. The value of e is 500.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
1.a
Compute the vale of 60% of 400.
Using the formula a% = a/100
60% of 400 = 60/100 of 400
Replace of by multiplication:
60% of 400 = (60/100) × 400
60% of 400 = 240.
1b.
Compute the vale of 60% of 200.
Using the formula a% = a/100
60% of 200 = 60/100 of 200
Replace of by multiplication:
60% of 200 = (60/100) ×2 00
60% of 400 = 120.
1c.
Compute the vale of 60% of 120.
Using the formula a% = a/100
60% of 120 = 60/100 of 120
Replace of by multiplication:
60% of 120 = (60/100) × 120
60% of 400 = 72.
2.
Given that 60% of x is 87.
Compute the vale of 60% of x.
Using the formula a% = a/100
60% of x = 60/100 of x
Replace of by multiplication:
60% of x = (60/100) × x
60% of x = 0.6x
Therefore the relationship is 0.6x = 87
Now divide both sides by 0.6:
x = 87/0.6
x = 145.
3a.
Given that 60% of c is 43.2.
Compute the vale of 60% of c.
Using the formula a% = a/100
60% of c = 60/100 of c
Replace of by multiplication:
60% of c = (60/100) × c
60% of c = 0.6c
Therefore the relationship is 0.6c = 43.2
Now divide both sides by 0.6:
c = 43.2/0.6
c =72.
3b.
Given that 38% of e is 190.
Compute the vale of 38% of e.
Using the formula a% = a/100
38% of e = 38/100 of e
Replace of by multiplication:
38% of e = (38/100) × e
38% of e = 0.38e
Therefore the relationship is 0.38e = 190
Now divide both sides by 0.38:
e = 190/0.38
e = 500.
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Find the measure of X
The measure of x = 64°
Vertical opposite angles:The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal.
Here we have
Three lines are intersected and formed a triangle
Let's assume that the triangle formed is ΔABC
In ΔABC, ∠C = 34°
Since Vertical opposite angles are equal
=> ∠B = 30°
As we know the sum of angles in a triangle = 180°
=> ∠A + ∠B + ∠C = 180°
=> ∠A = 180° - 30° - 34°
=> ∠A = 116
From the line CL [ observe the given picture ]
=> ∠A + x = 180°
=> 116° + x = 180°
=> x = 180° - 116°
=> x = 64°
Therefore,
The measure of x = 64°
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A sample of 200g of an isotope decays to another isotope according to the function A(t)= 200е⁻⁰⁰⁵⁴⁺ ,where t is the time in years
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
(a) After 25 years, about __g of the sample will be left.
(Round to the nearest hundredth as needed.)
The amount of initial sample will be left in the sample after 25 years is $771.49.
What is isotope decay?
An unstable atomic nucleus loses energy via radiation during the process of radioactive decay. A substance is regarded as radioactive if it has unstable nuclei. The three most frequent types of decay are alpha decay, beta decay, and gamma decay, all of which involve the emission of one or more particles.
Given:
A sample of 200g of an isotope decays to another isotope according to the function [tex]A(t) = 200e^-^0^.^0^5^4^t[/tex],where t is the time in years.
We have to find the amount of initial sample will be left in the sample after 25 years.
Plug t = 25 in the given equation.
[tex]A(25) = 200e^-^0^.^0^5^4^(^2^5^)\\A(25) = 771.4851\\A(25) = 771.49[/tex]
Hence, the amount of initial sample will be left in the sample after 25 years is $771.49.
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What is the slope of the line that contains these points? xxx 151515 171717 191919 212121 yyy -10−10minus, 10 222 141414 262626
According to the given information the slope of the linear function containing these points is of 1.
A linear function is what?The graph of a linear function is a horizontal line. The following is the form of a linear transformation. a + bx = y = f(x). One regression coefficient or one predictor variables make up a linear function.
Briefing:A linear function is modeled by:
y=mx+b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the value of y when x = 0.In this problem, the points given are: (-10, 22) and (14, 26), hence, the slope is given by:
[tex]y_2=26 ,y_1=22 ,x_2=14 , x_1=10\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\text { m }=\frac{26-22}{14-10}\\\\\m=1[/tex]
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PLEASE HELP ASAP!!!! FULL ANSWER ONLY!!!
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h = − 16 t^2 + 84 t + 72 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? ____________ feet
b) How many seconds does it take until the ball hits the ground? ____________ seconds
What is the maximum height of the ball 182.25 feet
How many seconds does it take until the ball hits the ground 6 seconds
How to find the maximum height of the ballThe maximum height will occur at the vertex v(h', k)
h' = -b/2a
From the equation h = − 16 t^2 + 84 t + 72
a = -16
b = 84
h' = -84/(2 * -16)
h' = t = 2.625
k = h = − 16 t^2 + 84 t + 72 at t = 2.625
= − 16 * 2.625^2 + 84 * 2.625 + 72
= 182.25 feet
The ball hits the ground when h = 0
0 = − 16 t^2 + 84 t + 72
solving the quadratic equation gives
t = 6 OR -3/4
Use the positive value
t = 6 seconds
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The graph below shows a transformation of y=2^x .
Write an equation of the form y=A . 2^x+k for the graph above.
y=
The graph showing the transformation of the function y = 2ˣ, with points (0, -1), and (1, -4), as well as an horizontal asymptote of y = 2, indicates that the equation of the graph in the form y = A·2ˣ + k is; y = -3·2ˣ + 2
What is an asymptote of a graph?The asymptote is a line that can be drawn on the graph such that the curve of the graph approaches the line without touching it as the values of the variables increase.
The required form of the exponential equation is; y = A·2ˣ + k
Where;
k = The horizontal asymptote
The graph included in the question indicates that an horizontal asymptote is indicated by the line y = 2
= 2
Points on the graph of the transformed function are (1, -4), (0, -1)
When x = 0, y = -1, therefore;
-1 = A·2⁰ + 2
A·2⁰ + 2 = -1 - 2 = -3
A = -3
The equation for the graph is therefore;
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Jenna had fifty pieces of laundry to wash. First, she removed her ten favorite shirts, which she will wash by hand. Then she divided the rest into piles of 8 to wash in the machine. How many piles does she have for the machine? Show all work.
Using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, we know that:
Jenna has 50 pieces of laundry.
She removed her 10 favorite shirts.
50 - 10 = 40
She divided the rest into 8 piles.
40/8 = 5
Therefore, using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.
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PLEASE HELP ME SLOVE FOR X
Answer:
x = 5
Step-by-step explanation:
Since the lines with red arrows are parallel, we can use the ratios
(28 - 12)/28 = 4x/35
35(16) = 28(4x)
560 = 112x
x = 560/112
x = 5
[tex]4c^2+10c+4[/tex]
Answer:
Factor for this problem is
2(2c+1)(c+2)
Answer:(c+2)(4c+2)
Step-by-step explanation:
Factor by grouping
(c+2)(4c+2)
Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?
The number of handshakes that occur in Tom's workshop is 105
Given: Number of people in the workshop is 15 and Every person shakes hands once with every other person
To find: Number of handshakes
Since every person has to meet the other person only once and shake hands only once. So every handshake has only one possible combination.
Total number of combinations (handshakes) that can be possible with 15 people = [tex]15C_2[/tex]
The formula for a combination is
[tex]nC_r = \frac{n!}{r!(n-r)!}[/tex]
where n is the number of items and r is the unique arrangements.
Plugging in our numbers of n = 15 and r = 2, we get
[tex]15C_2= \frac{15!}{2!(15-2)!}\\= \frac{15!}{2! \times 13!} \\=\frac{15 \times 14 \times 13!}{2! \times 13!}\\[/tex]
On cancelling out 13! from numerator and denominator , we get
[tex]15C_2=\frac{15 \times 14}{2 \times 1}= 15 \times 7=105[/tex]
What is combination?A combination is a method of picking things from a collection in which the order of selection is irrelevant. Assume we have three numbers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.
It is feasible to count the number of combinations in smaller collections, but the possibilities of a set of combination increases with the number of groups of elements or sets. As a result, a formula has been developed to determine the number of things that can be selected.
The formula is
[tex]nC_r = \frac{n!}{r!(n-r)!} \, when \, n > r\\nC_r = 0 \, when \, n < r[/tex]
Where n = number of distinct objects to choose from
C = Combination
r = spaces to fill
The number of handshakes that occur in Tom's workshop is 105
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One angle measures 160°, and another angle measures (3k + 61)°. If the angles are vertical angles, determine the value of k.
k = 14
k = 33
k = 74
k = 160
Answer:
Therefore, the value of k is 1.
Step-by-step explanation:
Vertical angles are pairs of angles that are opposite each other and are formed by two intersecting lines. If one angle measures 160°, the other angle must measure 180° - 160° = 20°. Therefore, if the other angle measures (3k + 61)°, we can set up the equation 20 = 3k + 61. Solving for k, we get k = -41. However, since the value of k must be a positive integer, the only possible value of k is k = 1. Therefore, the value of k is 1.
Answer:
k = 33
Step-by-step explanation:
The figure below is reflected over the y-axis. What are the coordinates of the image of point R after this transformation?
Solve for a.
a+(−7)=−17
Answer: a= (-10)
Step-by-step explanation:
step 1- move the -7 to the other side of the equal sign to combine with -17.
step 2- to do this we need to make -7 positive so instead of (-17) -7, it would be (-17) +7.
step 3- leaving you with
a= (-10) hope this helped :)
[tex]3x^{2} +x -5=0[/tex]
The two solutions of the quadratic equation are:
x = 1.135
x= -1.468
How to solve the quadratic equation?
A general quadratic equation:
a*x^2 + b*x + c = 0
Has solutions of the form:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here the quadratic equation is:
3*x^2 + x - 5 = 0
So the values are:
a = 3
b = 1
c = -5
Replacing that in the quadratic formula for the solutions we will get:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*3*(-5)} }{2*3}\\\\x = \frac{-1 \pm 7.81 }{6}[/tex]
Thus, the two solutions are:
x = (-1 + 7.81)/6 = 1.135
x = (-1 - 7.81)/6 = -1.468
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Find the probability of royal flush poker hand when 5 cards are dealt from an ordinary deck. Enter your answer as a fraction. P(royal flush) - )
Probability p(Royal flush)= 4/2598960 = 1/649740
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
A royal rush in Poker Card is five of each of the following: ace, king, queen, jack, and ten.
The ten, Jack, Queen, King, and Ace of a single suit make up a royal flush. These hands come in fours.
Total no. of ways = selecting 5 cards out of 52 cards = 52 C5 = 2598960
So, P(royal flush)= 4/2598960 = 1/649740
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Q4 Two consecutive numbers are such that the larger number when
added twice the smaller number gives a sum of 70. Find the two numbers.
Answer:
The answer is in the picture
Step-by-step explanation:
The explanation is in the picture
Suppose you have a group of 20 people, 7
are women and the remaining people are
men. What is the probability you select 4
women from the group?
The probability of select 4 women from the group is, P = 35.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given: You have a group of 20 people, 7 are women and the remaining people are men.
7 are women then 13 are men.
No. of ways in which 4 women can be chosen from 7 women are 7C4.
So, the probability of select 4 women from the group is,
[tex]P = {7_C_4} \\P = \frac{7!}{4!*(7-4)!} \\P=\frac{7!}{4!*3!} \\P = 35[/tex]
Hence, the probability of select 4 women from the group is, P = 35.
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Stem and leaf plots
And box
Pls help I have no idea what this is
Answer:
61 is the mode.
Step-by-step explanation:
Remember, the mode is the most repeated number in the list. 6|1 is repeated the most times (twice).
Answer:
61 is the correct answer
R(x) = -40x^2 + 5000x
Determine the prices where the revenue is zero?
For each price where the revenue is zero, explain why the revenue is zero.
Answer:
The prices where the revenue is zero are $x = 0 and $x = 125.
When x = 0, the revenue is 0 since the function is equal to zero (R(0) = -40(0)^2 + 5000(0) = 0).
When x = 125, the revenue is 0 since the coefficient of the x^2 term is negative and the coefficient of the x term is positive. Since the equation is equal to zero, the two terms must cancel each other out, resulting in zero revenue (R(125) = -40(125)^2 + 5000(125) = 0).
Step-by-step explanation:
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is
μ=12.00
Mbps. The sample size is
n=25
and the test statistic is
t=2.376.
The p-value for the hypothesis test in this problem is given as follows:
0.0258.
How to obtain the p-value of the test?The first step in obtaining the p-value of the test is verifying the hypothesis that are test, to classify the test.
At the null hypothesis, it is tested if the mean carrier data speed is of 12 Mbps, that is:
[tex]H_0: \mu = 12[/tex]
At the alternative hypothesis, it is tested if the mean carrier data speed is different of 12 Mbps, that is:
[tex]H_1: \mu \neq 12[/tex]
Then we have a two-tailed test, as we are testing if the mean is different of a value, and the parameters are given as follows:
25 - 1 = 24 degrees of freedom.Test statistic of t = 2.376.Using a t-distribution calculator with these parameters, the p-value for the test is given as follows:
0.0258.
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A thermometer shows the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F). One day, it shows 87°F and 31°C. The next day, it shows 94°F and 34°C. Determine if there is a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.
No, there is not a proportional relationship because 87 over 31 does not equal 94 over 34.
Yes, there is a proportional relationship because 87 over 31 equals 94 over 34.
No, there is not a proportional relationship because degrees Celsius and degrees Fahrenheit are not the same measurement.
Yes, there is a proportional relationship because degrees Celsius and degrees Fahrenheit are the same measurement.
The values shown by the thermometer of 87 °F and 94 °F which in degrees Celsius are 31 °C and 34 °C indicates that the relationship is not a proportional relationship. The correct option is therefore;
No, there is not a proportional relationship because 87 over 31 does not equal 94 over 34.What is a proportional relationship?A proportional relationship is one in which one variable is a constant multiple of the other, such that the ratio of each data pair is a constant.
The temperature it shows on the first day = 87 °F and 31°CThe temperature it shows on the next day = 94 °F and 34 °CThe ratio of the two temperatures are therefore;
[tex]\dfrac{87}{31}[/tex] and [tex]\dfrac{94}{34}[/tex]
31 is a prime number, therefore'
[tex]\dfrac{87}{31} \neq \dfrac{94}{34}[/tex]
The ratio of the ordered pair of a proportional relationship is constant, the ratio of the specified values is not constant, therefore, the relationship is not a proportional relationship.
The correct option is therefore;
No there is not a proportional relationship because 87 over 31 does not equal 94 over 34
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Write an equation and solve for p. Show all work.
a) The equation is 10p + 80 = 180 and p = 10.
b) The three angles are 90°, 37°, 53°.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that, the angles of the triangles are 53°, 2p + 17°, and 8p + 10°.
The sum of all angles of a triangle is 53° + 2p + 17° + 8p + 10° = 80 + 10p
The sum of all angles of a triangle is 180°.
Therefore,
80 + 10p = 180
Subtract 80 from both sides:
10p = 100
divide both sides by 10:
p = 10.
Putting p = 10 in 2p + 17°, and 8p + 10°:
2p + 17° = 20° + 17° = 37°
8p + 10° = 80° + 10° = 90°
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solution set of a compound inequality
The solution of a compound inequality is the common region or intersection region of two inequalities.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
A sentence having two inequality statements connected by the words 'or' Or 'and' is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence.
For example, if in a compound inequality we get x > 3 and x > 5 so the final conclusion is x > 5.
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You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
(a) Loan you can afford is $143097.67. (b) Total money will you pay the loan company is $378000. (c) Interest amount is $234902.33.
What is Loan interest ?Loan interest is the additional cost that a borrower must pay on top of the principal amount of a loan. Interest is typically expressed as a percentage of the principal and is charged over a specific period of time. The rate of interest charged on a loan is determined by a variety of factors, including the borrower's creditworthiness and the type of loan. The purpose of interest is to compensate the lender for the risk and cost of providing the loan.
Given data:
Principal = $1050 per month
Time = 30 year
= 30 × 12
= 360 months
Interest rate = 8%
= 0.08/12
= 0.006667 monthly
(a) We get here first maximum amount of loan by present value of annuity as
Present value of annuity = principal × [tex]\frac{1-(1+rate)^{-t} }{rate}[/tex] .........(1)
Put here value we get
value of annuity = 1050 × [tex]\frac{1-(1+0.006667)^{-360} }{0.006667}[/tex]
value of annuity = $143097.67
(b) Total amount = principal × time period
= $1050 × 360
= $378000
(c) Total amount of interest paid will be
interest amount = total amount paid - loan amount
interest amount = $378000 - $143097.67
interest amount = $234902.33
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A new gaming chair costs $239.87. You have already saved $106.37 and earn $44.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
44.5w + 106.37 = 239.87; w = 3
44.5w − 106.37 = 239.87; w = 9
44.5w − 239.87 = 106.37; w = 9
44.5 + 106.37w = 239.87; w = 3
The equation will be 44.50 w + 106.37 = 239.87, and it will take 3 weeks to collect money for gaming chair.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the data provided in the question,
Cost of new gaming chair = $239
Savings for gaming chair = $106.37
Each week earning = $44.50
Then the expression will be,
44.50 w + 106.37 = 239.87
44.50 w = 239.87 - 106.37
w = 133.5/44.50
w = 3
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I need help asap
If anyone can help bro
The minimum length of the slanted poles needed to support the fly is 20 feet.
What is a Pythagoras theorem?
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
To find the minimum length of the slanted poles, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the slanted pole) is equal to the sum of the squares of the other two sides (the heights of the tent and fly).
We are given that the height of the tent is 12 feet and the height of the fly is 16 feet. The Pythagorean theorem can be written as follows:
c² = a² + b²
where c is the length of the slanted pole, a is the height of the tent, and b is the height of the fly.
Substituting in the given values, we get:
c² = 12² + 16²
= 144 + 256
= 400
Taking the square root of both sides gives:
c = √400
= 20
Therefore, the minimum length of the slanted poles needed to support the fly is 20 feet.
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2. Sandra gets 2 dollars for every 50 aluminum cans she recycles. What is the ratio of dollars to
cans? How much money does she make per can?
Answer:
1:25
$0.04 or 4 cents per can
Step-by-step explanation:
The ratio of dollars to can is 2:50 = 1:25.
$1/25 = $0.04
She gets $0.04 or 4 cents per can
The sum of 5 consecutive odd numbers
is 145.
What is the third number in this sequence?
Hello,
I hope you and your family are doing well!
The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. Since the sum of 5 consecutive odd numbers is 145, we can set up the equation:
(a + (a + 4)) / 2 * 5 = 145
where a is the first term in the sequence.
Solving this equation gives us:
a = -23
The third number in the sequence is the third odd number after a, which is a + 4. Substituting -23 for a gives us:
(-23) + 4 = -19
Therefore, the third number in the sequence is -19.
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