Answer:
To determine how much you should invest to receive $100,000 on the maturity date, you will need to calculate the present value of the cash flows at the beginning of the investment. The present value is the amount of money you would need to invest today to receive a certain amount at a future date, taking into account the time value of money and the interest rate.
You can calculate the present value by using the formula:
PV = CF / (1 + r)^t
Where:
PV = present value
CF = cash flow (the amount you will receive at the maturity date)
r = interest rate
t = time (in years)
The first 18 months, the interest rate is 8% per year, which is equivalent to 8/12 = 0.67% per month.
The next 6 months, the interest rate is 1.5% per quarter, which is equivalent to 1.5/4 = 0.375% per month.
The last 12 months, the interest rate is 2% per semi-annual, which is equivalent to 2/2 = 1% per month.
For the first 18 months, the present value of the cash flow is:
PV = 100,000 / (1 + 0.0067)^(18/12) = 95,167
For the next 6 months, the present value of the cash flow is:
PV = 95,167 / (1 + 0.00375)^(6/12) = 94,853
For the last 12 months, the present value of the cash flow is:
PV = 94,853 / (1 + 0.01)^(12/12) = 94,853
So, to receive $100,000 on the maturity date, you should invest 94,853 dollars to the nearest dollar.
Six years ago,the sum of the ages of two brothers was 22, find the age of the older brother
The age of the older brother is 21 years
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Six years ago, the sum of the ages of two brothers was 22
x+y=22
The product of their ages is 21
xy=21
y=21/x
x+21/x=22
x²+21=22x
x²-22x+21=0
Factorize the equation
x²-21x-x+21=0
x(x-21)-(x-21)=0
(x-1)(x-21)=0
x=1 and x=21
21+y=22
y=1
Hence, the age of the older brother is 21 years
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Find the area of the figure. (Sides meet at right angles.)
Step-by-step explanation:
area of square=length×length
=5×5=25ft²
area of rectangle=length × breath
=2×9
18ft²
area of the figure=25 +18
=43ft²
You are a member of your local movie theater’s club. Every time you see a movie at the theater, you earn 4 advantage points. When you earn 100 points, you get a free movie pass. Currently, you have 36 advantage points.
1. Write an equation to model the number of movies, m, you must watch before you earn a free movie.
Solve the equation. Show your work
Answer:
4x + 36 = 100
Step-by-step explanation:
Considering how you have already earned 36 points, there will be no variable for it present. The x stands for the amount of times you go see a movie in the theater.
Answer:
You need to see 16 more movies to earn 100 points.
Step-by-step explanation:
you earn 4 advantage points every time you see a movie at the theater.
You need to earn 100 points to get a free movie pass.
Currently, you have 36 advantages points.
If you watch m movies you get = 4m points
You have 36 points so you need = 100 - 36 more points
So the equation will be = 4m = 100 - 36 [after combining like term]
4m = 64 [divide both side by 4]
m = 16
You need to see 16 more movies to earn 100 points.
NO LINKS!!
Rewrite the following definition of congruent segments as a biconditional statement:
Congruent segments have the same length.
Answer:
A segment is congruent to another segment if and only if they have the same length.
Answer:
Segments are congruent if and only if they have the same length.
Segments have the same length if and only if they are congruent.
Step-by-step explanation:
Biconditional statement
A biconditional statement is a combination of a conditional statement and its converse. It is conditional in both directions:
Hypothesis "if and only if" conclusion.Conclusion "if and only if" hypothesis.Write the given statement as a conditional statement:
If segments are congruent, then they have the same length.Write the given statement as a converse of the conditional statement:
If segments have the same length, then they are congruent.Both the conditional and converse statements must have the same truth value to produce a biconditional statement. Therefore, as both are true, we can write the biconditional statements:
Segments are congruent if and only if they have the same length.Segments have the same length if and only if they are congruent.Frederic scored 82¹/2 on his test. Express his score as an improper fraction.
Answer : 165/2
To do this, we just have to add 82 and 1/2. However, the question asks for an improper fraction, so we turn 82 into 164/2. Now, we add 1/2 to 165/2 which equals 164+1/2 = 165/2.
Population and Water
This activity will help you meet this educational goal:
Content Standards—You will explain why scarcity and choice are basic economic problems faced by every society.
Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work.
Activity
Think about the video you watched earlier and answer these questions.
Part A
What was the scarce resource in the video?
Part B
What are three uses for this scarce resource?
Part C
What examples can you give from the video that show how Mexico City residents are adapting to water scarcity?
Part D
If you were an adviser to the Mexican government, what would you suggest to alleviate the water problem?
Part E
Think about scarcity. What scarce resource might prevent the Mexican government from implementing your suggestions?
a. Water was the scarce resource in the video.
b. Water is used for drinking, farming, and electricity.
c. Mexicans depend on trucks to deliver water. They also started buying water from small water shops that are open to meet the water demand.
d. The government could focus on improving water delivery and plumbing. It could also provide bottled water to residents at a discounted rate.
e. The Mexican government may face a scarcity of time, money, or labor
What is a scarce resource?When the demand for a natural resource exceeds the supply, resource scarcity results, which causes the stock of those resources to decrease. As prices rise and the resource becomes less accessible to those who are least well-off, this could result in unsustainable growth and a rise in inequality.
Natural resources are inherently scarce, including gold, oil, silver, and other fossil fuels. These resources become scarce and their prices may rise when demand outpaces supply. Due to their scarcity and market dominance, some commodities, like diamonds, command a high price. Based on the information Illustrated as answers, water is this scarce resource.
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A local salesman receives a base salary of $850 monthly. He also receives a commission of 11% on all sales over $500. How much would he have to sell in a month if he needed to have a monthly income of $3000?
He would need to sell $
to reach his needed monthly income needs.
For the local salesman to have a monthly income of $3,000, using mathematical operations, he would need to sell $20,045 worth.
How the total sales are determined?The sales revenue that the local salesman should generate to reach his monthly income target is determined by working backward with the mathematical operations of subtraction, division, multiplication, and addition.
Firstly, the base salary is deducted from the expected monthly earnings to obtain the amount of the sales commission.
The sales commission is equated to its commission percentage through division and multiplication operations.
The result is added to $500 to arrive at the expected sales revenue.
The monthly base salary = $850
Commission = 11% on sales above $500
Needed monthly income = $3,000
Sales commission = $2,150 ($3,000 - $850)
11% = $2,150
100% = $19,545 ($2,150/11% x 100%)
$19,545 = Sales above $500
Total target sales = $20,045 ($19,545 + $500)
Thus, if the salesman expects a monthly income of $3,000, he must generate monthly sales revenue of at least $20,045.
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Describe fully the single transformation that maps shape P onto shape Q. 14 16 x
Reasons:
The give figure shows;
The preimage figure = P
The image figure = Q
The image P is larger than the preimage Q, therefore, the figure, Q is a
dilation of the preimage P
The center of dilation is found with the formula;
[tex]& x_0=\frac{\mathbf{k} \cdot \mathbf{x}_1-\mathbf{x}_2}{\mathbf{k}-1} \\[/tex]
[tex]& y_0=\frac{\mathbf{k} \cdot \mathbf{y}_1-\mathbf{y}_2}{\mathbf{k}-\mathbf{1}}[/tex]
Where;
[tex]$\left(x_1, y_1\right)=$[/tex]A point on the preimage, [tex]$P=(2,3)$[/tex]
[tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)=$[/tex]The corresponding point on the dilated image, [tex]$\left.Q=\mathbf{( 4}, \mathbf{9}\right)$[/tex]
k= The scale factor
Therefore;
[tex]x_0=\frac{3 \times 2-4}{3-1}=1[/tex]
[tex]$y_0=\frac{3 \times 3-9}{3-1}=0$[/tex]
The center of dilation, [tex]$\left(x_0, y_0\right)=(1,0)$[/tex]
Therefore;
Shape P is transformed into shape Q through a single transformation that involves dilation by a scale factor of 3 with a center of dilatation at (1,0).
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Use the FOIL method to find the product below.
(x+5)(x²-3x)
O A. x³ + 2x²-15
OB. x³+2x2-15x
OC. x³ +5x2-15x
OD. x³ + 5x2-15
SUBM
The FOIL method to find the product (x + 5)(x² - 3x) is x³ + 2x² - 15
How to use the foil method?You should note the following about FOIL method
It stands for "First, Outer, Inner, Last"
It is the sum of:
· multiplying the First terms,
· multiplying the Outer terms,
· multiplying the Inner terms, and
· multiplying the Last terms
That is (a+b)(c+d) = ac + ad + bc + bd
Use FOIL (First, Outside, Inside, Last)
The give expression is
x(x²) = x³
x(-3x) = -3x²
5(x²) = 5x²
5(-3x) = -15x
Combine like terms:
x³ - 3x² + 5x² - 15x
x³ + 2x² - 15
Therefore the FOIL method is x³ + 2x² - 15
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(2%)Find the solution set ofx^2+4x-21≤0.
Answer:
The solution set of x^2 + 4x - 21 ≤ 0 is (-7, -3)
Step-by-step explanation:
To solve this inequality, we first set x^2 + 4x - 21 = 0 and factor it to get (x + 7)(x - 3) = 0. This gives us x = -7 and x = 3 as the solutions.
To find the solution set of x^2 + 4x - 21 ≤ 0, we need to determine the values of x that make the expression on the left-hand side non-positive. Since x^2 + 4x - 21 is a quadratic function, it is non-positive when x is less than -3 or x is greater than -7.
Therefore, the solution set of x^2 + 4x - 21 ≤ 0 is the set of all x such that x ∈ (-7, -3).
Cameron owes his parents money that he narrowed to buy a bicycle. He plans on paying them back by giving them amount of money each month.
The amount that Cameron plans to give his parents every month as a way to pay them back for the bicycle is called an Installment.
What is a loan installment ?A loan installment is a fixed payment that a borrower makes to a lender over a period of time, usually on a regular basis, until the loan is fully paid off. The payment typically includes both the principal amount borrowed and the interest charged on the loan.
Loan installments are related to annuities in that they are both financial products that involve a series of regular payments. An annuity is a financial contract in which an individual gives an insurance company a lump sum of money or a series of payments in exchange for a stream of payments over a period of time.
This means therefore, that the amount that Cameron plans to pay his parents every month for the money borrowed to buy a bicycle, is called a loan installment.
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The full question is:
Cameron owes his parents money that he narrowed to buy a bicycle. He plans on paying them back by giving them amount of money each month. What is this amount called?
given side BC is congruent with side DC and side AC is congruent with EC, prove triangle bca is congruent with triangle dce
Answer:
Given side BC is congruent with side DC and side AC is congruent with EC, we can prove that triangle BCA is congruent with triangle DCE using the following steps:
Step 1: By using the definition of congruent, we know that if two sides of a triangle are congruent, then the angles opposite to those sides are also congruent. Therefore, angle BCA is congruent to angle DCE, and angle BAC is congruent to angle DEC.
Step 2: Since we have two pairs of congruent angles, we can use the angle-angle similarity postulate to prove that triangle BCA is similar to triangle DCE.
Step 3: Since both of the triangles are similar, we can use the third congruent side AC which is congruent to EC, to prove that the two triangles are congruent.
Step 4: Now, we can use the side-side-side postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Therefore, we can conclude that triangle BCA is congruent to triangle DCE.
Proof:
By the definition of congruence, we know:
-BC is congruent to DC
-AC is congruent to EC
By the angle-angle similarity postulate, we know that:
-angle BCA is congruent to angle DCE
-angle BAC is congruent to angle DEC
By the side-side-side postulate, we know that:
-triangle BCA is congruent to triangle DCE
Therefore, we can prove that triangle BCA is congruent to triangle DCE.
find the property
plssss help
Subtract 7 from both sides. Subtract 7 from 23 to get 16. Divide both sides by 4. Divide 16 by 4 to get 4.
What Is Angle Congruence’s Symmetric Property?According to the symmetric property, if one geometric form is congruent to another, the second shape is likewise congruent to the first. The symmetric property of congruence states that for all angles A and B, if AB A B then BA B A.Transitive Property of Congruence. “If two shapes are congruent to the third shape, then all the shapes are congruent to each other,” asserts the transitive property of congruence.
We can solve an equation by applying the four equality properties: addition, subtraction, multiplication, and division. To get the value of an unknown variable, we simply add, subtract, multiply, or divide both sides of an equation.
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40 people or 10% of a group of people were aged 55 or older how many people were younger than 55 in that group?
Answer: 360
Step-by-step explanation:
If 10% of people were 55 or older, than 90% of people were younger than 55.
This is 9 times the number of people that were 55 or older.
Therefore, the answer is 360.
During a review game, Mr. Pai's class correctly answered 67 questions on the first try. If there were 74 questions in the game, at what rate were questions answered correctly on the first try? Express your answer as a decimal. Round to the nearest thousandth.
A. 0.905
B. 0.095
C. 1.104
D. 0.091
Answer:
The answer is option A.
Step-by-step explanation:
To find the rate at which the questions were answered correctly on the first try, we can divide the number of questions answered correctly by the total number of questions.
Let's call the rate of correct answers on the first try as R
R = (number of questions answered correctly) / (total number of questions)
Substituting the given values:
R = 67 / 74
R = 0.905
So, the rate of correct answers on the first try is 0.905.
Answer:
Step-by-step explanation:
The question answered correctly in fraction will be 67/74.
67/74 equals 67÷74, which is 0.9054054054...
0.9054054054... round to the nearest thousand is 0.905.
So the answer is A, 0.905.
Six years ago,the sum of the ages of two brothers was 22, find the age of the older brother
The age of the older brother is 13
How to determine the age of the elder brotherFrom the information given, let their ages by x and y
This is represented as;
x + y = 22
(x - 6) (y -6) = 21
From equation (1), make x, the subject of formula
x = 22 - y (3)
Substitute equation (3) in equation (2), we get;
(22 - y- 6)(y - 6) = 21
expand the brackets
(16 - y)(y-6) = 21
16y - 96 - y² +6y = 21
collect iike terms
-y² + 22y - 96 - 21 = 0
subtract like terms
-y² + 22y - 117 = 0
y²- 22y + 117 = 0
Find the pairs factors of 117 and substitute the values
y² - 13y - 9y + 117 = 0
(y² - 22y) - (9y + 117) = 0
factorize
y(y - 22) - 9(y - 22) = 0
Then y = 9 and y = 22
The older brothers age = x = 22 - y = 22- 9 = 13
Hence, the value is 13
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The complete question:
The sum of the ages of two brothers is 22 years. Six years ago, the product of their ages was 21 years. What is the age of the elder brother?
231. At noon, my odometer read 6852 miles. At 3:30 pm, it read 7034 miles.
(a) What was my average rate of change during these three and a half hours?
(b) Let t represent the number of hours I have been driving since noon and y represent my
odometer reading. Write an equation that relates y and t. Assume constant speed.
(c) Graph your equation.
(d) Show that the point (5,7112) is on your line, and then interpret this point in the context
of this problem.
Average rate of change of reading = [tex]\frac{7034 - 6852}{3.5} = 52[/tex] miles per hour
The equation representing t in hrs and odometer reading after noon in y is
y = 6852 + 52t
What is an equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
The reading in odometer =6852 miles at 12:00
The reading in odometer = 7034 miles at 3 :30 pm
Average rate of change of reading = [tex]\frac{7034 - 6852}{3.5} = 52[/tex] miles per hour
An equation representing t in hrs and odometer reading after noon in y is
y = 6852 + 52t
The point is (5,7112)
for t = 5
y = 6852 + 52*5 = 7112 (proved)
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Please help me with this question.
The solution of the given differential initial value problem is
y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.
Given is the initial value problem -
y' = y² - 6y + 5
We can write the -
y' = y² - 6y + 5
Dividing both sides by {y² - 6y + 5}, we get -
y'/y² - 6y + 5 = 1
Integrating -
∫(y'/y² - 6y + 5) dx = ∫1 dx
- 1/4 log(1 - y) + 1/4 log (5 - y) = x + c{1}
Solving for y{x}, we can write -
y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}
The given differential equation can be solved and written as -
y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}
Therefore, the solution of the given differential initial value problem is
y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}.
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Find the value of each variable in the parallelogram.
m= ?
n= ?
Answer:
i think the answers are m=4 and n=10
ANYONE PLEASE ANYONE WHO GOOD AT MATH PLEASE HELP
Answer:
f(g(f(1))) = 45 — needs to use the equationg(f(g(0))) = 3Step-by-step explanation:
You want to use the graph to evaluate the compositions ...
f(g(f(1)))g(f(g(0)))where f(x) = x² -2x -3, and g(x) = x -2.
Reading the graphTo find the value of a graphed function, locate the function argument on the x-axis and find the point of intersection of that vertical line with the graph. The y-coordinate of that point is the function value.
f(g(f(1)))Here, we're asked to read the graph to find f(1), use that value to find g(f(1)), then use that value to find f(g(f(1))). This last value is f(-6), which is off the top of the graph. We need to use the equation to find the value:
f(x) = (x -2)x -3
f(-6) = (-6 -2)(-6) -3 = 48 -3 = 45
The value of f(g(f(1))) is 45. The equation must be used for this.
g(f(g(0)))Reading the graph for g(0), we find the value to be -2. Then f(-2) is 5, and g(5) is 3.
The value of g(f(g(0))) is 3.
__
Additional comment
A suitable calculator or spreadsheet can evaluate these expressions for you.
23.5 x -0.3
How do I do 23.6 times -0.3 and what is the answer?
100 points
Answer: -7.05
Step-by-step explanation: a calculator is very helpful for problems like these if you can use one in your class!
Stock values for a certain company are recorded in the table.
I understand the first question and how to do the math not sure how to justify it. PLEASE HELP!
x (Weeks Since 5 Years Ago) y (Closing Price, in $)
most recent 260 67.06
7 days ago 259 67.00
1 month ago 256 66.24
6 months ago 234 60.04
1 year ago 208 54.69
3 years ago 104 47.31
5 years ago 0 28.09
Using a process similar to the one you used in part B, this exponential model was found as the best fit for this data:
y = 30.078(1.003)x.
Question 1
Question
Use the exponential model to make predictions about closing prices of this stock. Remember that x represents the number of weeks since the first data point, so the value of x today would be 260.
Type the correct answer in each box. If necessary, round the answers to the nearest cent.
One week from today, the stock is predicted to close at $
65,734.37
.
One month from today, the stock is predicted to close at $
66,327.75
.
One year from today, the stock is predicted to close at $
76,584.35
.
Question 2
Do you think the model is a good predictor of the future closing price of the stock? Justify your response in three to four sentences.
Answer:
Question 1
The model is an exponential model that describes the relationship between the number of weeks since the first data point and the closing price of the stock. It is calculated by using the given data points and finding the best fit for the data. The model can be used to make predictions about the closing prices of the stock by plugging in the value of x, which represents the number of weeks since the first data point.
One week from today, the stock is predicted to close at $67,034.37, one month from today, the stock is predicted to close at $66,327.75, and one year from today, the stock is predicted to close at $76,584.35 according to the model.
Question 2
It is difficult to say whether the model is a good predictor of the future closing price of the stock because it depends on how accurately the model describes the underlying relationship between x and y. However, since the model is based on historical data and has a high R-squared value, it could be a good predictor of the future closing price of the stock.
A new energy bar is being advertised as "high protein, low carb" with a ratio of 4:1
4
:
1
. You compare this new item to three other energy bars with the following protein-to-carb ratios.
Proteins (g) Carbs (g)
Product A
38
8
Product B
34
4
Product C
31
4
Write a ratio for each energy bar so that you can easily compare it to the new brand. (Create an equivalent ratio that has a 1
on the right side of the ratio.) Round your answer to the nearest hundredth, if necessary.
The ratio for each product, so that they can be compared to the new brand, is given as follows:
Product A: 4.75 : 1.Product B: 8.5 : 1.Product C: 7.75 : 1.How to obtain the ratios?The ratio of an amount A over an amount B is obtained applying the proportion of these amounts, that is, the division of A by B.
Hence, for the products in this problem, the ratio of protein to carbs is applied by the division of the amounts of protein by cards.
For each product, the ratios are obtained as follows:
Product A: 4.75 : 1, as 38/8 = 4.75.Product B: 8.5 : 1, as 34/4 = 8.5.Product C: 7.75 : 1, as 31/4 = 7.75.Hence they can be compared to the new product, as all the ratios have a denominator of one.
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Topic = nth term
For the sequence u = 2n² - 5n+ 3, determine:
Find the value of n for which u = 45
Answer:
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
u = 2n² - 5n + 3
u = 45
2n² - 5n + 3 = 45
2n² - 5n - 42 = 0
(2n - 7)(n + 6) = 0
2n - 7 = 0 or n - 6 = 0
n = 7/2 or n = 6
Answer: 6
find the simple interest earned for principal of $2,000 at and 8% rate for 5 years
Answer:
Amount = $ [tex]2080[/tex]
Step-by-step explanation:
Given ,
Principal of $2,0008% rate5 yearsTo Find : The Amount
We can derive the SI i.e the Simple Interest by the formula,
[tex]SI = \frac{PRT}{100}[/tex]
Applying the values into the given equation we get,
[tex]SI = \frac{2000X8X5}{100}[/tex]
Substituting we get,
[tex]SI = 80$[/tex]
[tex]Amount =[/tex] [tex]SI + Principal[/tex]
[tex]Amount = 80 + 2000[/tex]
[tex]Amount = $2080[/tex]
i will mark brainliest!!
Does the following system have a unique solution? why?
The required system of equation has no solution.
When the system of equation has unique solution.The more physical interpretation of the idea of two linear equations having a linear equation is that it will always have a singular solution regardless of whether the lines are parallel or coinciding.
According to question:We have,
4x + 10y = 57---------------(1)
2x + 5y = 38
Multiply 2
4x + 10y = 76----------(2)
So, above equation (1) and (2) has no solution.as values of x and y are not same for both the equation.
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Which of these equations is a quadratic function?
Answer:
B
Step-by-step explanation:
Quadratic Function:A quadratic function is a polynomial function which has a degree of 2, and is generally expressed in standard form: [tex]ax^2+bx+c\text{ where }a\ne 0[/tex]. The degree of a polynomial function can be determined by looking at which term has the largest exponent.
By looking at both options, B would be the correct option as it is a polynomial function with degree 2, while option A is a polynomial function with degree 1, also known as a linear equation.
The 6th term of an AP is 32 while the 10th term is 48. find the common difference and the 1st term
Answer:
d = 4 and a₁ = 12
Step-by-step explanation:
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₆ = 32 and a₁₀ = 48 , then
a₁ + 5d = 32 → (1)
a₁ + 9d = 48 → (2)
subtract (1) from (2) term by term to eliminate a₁
0 + 4d = 16
4d = 16 ( divide both sides by 4 )
d = 4
substitute d = 4 into (1) and solve for a₁
a₁ + 5(4) = 32
a₁ + 20 = 32 ( subtract 20 from both sides )
a₁ = 12
Find the arithmetic mean of the set of data 6,1,5,and 1
Answer:
3.25
Step-by-step explanation:
To find the arithmetic mean of a set of data, you add up all of the values in the set and then divide by the total number of values.
In this case, the set of data is {6, 1, 5, 1} and the total number of values is 4.
To find the arithmetic mean, we add up all the values:
6 + 1 + 5 + 1 = 13
then divide by the total number of values:
13 / 4 = 3.25
So the arithmetic mean of the set of data {6, 1, 5, 1} is 3.25.
For what values of the variable does each of the following expressions make sense? We call the set of this values the domain of the expression. sqaure root of -(6-x)
The square root of a number is only defined for non-negative numbers, since the square root of a negative number is not a real number.
For the expression sqaure root of -(6-x) to make sense mathematically, the expression inside the square root must be non-negative.
So, we need to find the values of x that make -(6-x) non-negative.
-(6-x) is non-negative when -(6-x) ≥ 0
Simplifying this inequality, we get 6-x ≤ 0
x ≤ 6
So, for x ≤ 6, the expression sqaure root of -(6-x) is defined and makes sense mathematically. This is the domain of the expression.
In summary, the domain of the expression sqaure root of -(6-x) is x ≤ 6.
