The amount that will be in the account in 25 years is $16,282.298.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
Given that,
Principal amount, P = $3000
Rate of interest, r = 7% = 0.07
Number of years, n = 25
The final amount in a compound interest where the interest is compounded annually is,
A = P (1 + r)ⁿ
Substituting the given values,
A = 3000 (1 + 0.07)²⁵
= 3000 (1.07)²⁵
= 16,282.298
Hence the final amount after 25 years is $16,282.298.
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Which of the following gives all the
prime numbers between 0 and 7?
Write an expression having only two terms that is
equivalent to 2x - 3. Explain how you wrote the
expression and how you can check that it iS equivalent.
Answer:
2X-3=0
2X=3
X=3/2
Step-by-step explanation:
Answer:
2x- 3 = 0
2x=3
x = 3/2
Step-by-step explanation: best of luck to you
kirans mother gets a restuarant bill for 25$ she has a coupon for 15% off what is the amount after the discount is applied
The amount after the discount is applied would be $21.25.
What is the percentage?
The percentage is defined as a ratio expressed as a fraction of 100.
As per the question, the given data as:
Bill amount = 25$
Coupon for 15% off
The amount after the discount can be calculated as:
⇒ 25$ - 15% of 25$
15% is expressed as 15/100 in fractional form
⇒ 25 - (15/100)(25)
15/100 is expressed as 0.15 in decimal form
⇒ 25 - (0.15)(25)
⇒ 25 - 3.75
⇒ 21.25
Thus, the final amount would be $21.25.
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Given the function
f
(
x
)
=
{
9
x
−
4
x
<
0
9
x
−
8
x
≥
0
The value of function at f(-1) = -13,
f(0) = -8 and f(2) = 10.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given equations,
f(x) = 9x - 4 where x < 0
f(x) = 9x - 8 where x ≥ 0
to find f(-1),
substitute value in equation f(x) = 9x - 4 where x < 0
f(x) = 9x - 4
f(-1) = 9(-1) - 4
f(-1) = -13
now f(0) and f(2), substitute in equation f(x) = 9x - 8 where x ≥ 0
f(x) = 9x - 8
f(0) = 9(0) - 8
f(0) = -8
f(2) = 9(2) - 8
f(2) = 10
Hence f(-1) = -13,
f(0) = -8 and f(2) = 10.
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There are 45
students in the University Travel Club. The following information and Venn diagram show how many students traveled to Germany, France, and Spain. How many students have been to Germany or Spain but not France?
20
members have visited Germany
20
have been to Spain
19
have visited France
10
have been to Germany and France
4
have only been to Germany
6
have only been to France
3
have been to only Spain and France
3
have been to all three countries
Some of the members have not been to any of the three
The number of students that have been to Germany or Spain but not France is given as follows:
18.
How to obtain the amounts?The amounts are obtained considering the Venn diagram in the problem.
For the 20 students that went to Spain, we have that:
x went only to Spain.3 have gone to Spain and France.3 have gone to Spain, Germany and France.6 have gone to Spain and Germany.Hence the value of x is obtained as follows:
x + 3 + 3 + 6 = 20
x + 12 = 20
x = 8.
The number of people who have gone to Spain or Germany but not France is given as follows:
6 + 4 + 10 = 18.
(or means at least one of Spain or Germany).
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evaluate the following 2x²+3x+4 if x=1
(x+y) (x+y) if x=2 and y=2
5x² +2x if x=2 and y=5
(x+y)³ if x=7 and y=3
The value of the expressions will be:
2x² + 3x + 4, when x=1 is equal to 9.
(x+y)², when x=2 and y=2 is equal to 16.
5x² + 2x, when x=2 is equal to 24.
(x+y)³, when x=7 and y=3 is equal to 1000.
How to calculate the expression2x² + 3x + 4, when x=1 is:
= 2(1)² + 3 + 4
= 2 + 3 + 4
= 9.
(x+y)², when x=2 and y=2 is equal to:
= (2 + 2)²
= 4²
= 16.
5x² + 2x, when x=2 is equal to:
= 5(2)² + 2(2)
= 20 + 4
= 24.
(x+y)³, when x=7 and y=3 is equal to:
= (7 + 3)³
= 10³
= 1000.
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PLS HELP THIS IS DUE TODAY
1. PM:MQ and KM:ML (Given)
2. KM/MQ = PM/ML (Property of cross multiplication)
3. ∠ PMK = ∠ LMQ (vertical angles are congruent)
4. ΔPMK ~ ΔLMQ (SAS~)
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Given,
PM:MQ and KM:ML
To prove
ΔPMK ~ ΔLMQ
By the figure,
PM:MQ = KM:ML (Given)
Cross multiplying
KM/MQ = PM/ML
∠ PMK = ∠ LMQ (vertical angles)
Using Side - Angle - Side theorem
ΔPMK ~ ΔLMQ
Hence,
1. PM:MQ = KM:ML , since its given
2. KM/MQ = PM/ML using cross multiplication
3. ∠ PMK = ∠ LMQ both are vertical angles
4. ΔPMK ~ ΔLMQ using side-angle-side theorem of similarity
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Find the mean for the number of hours of sleep: 6 7 5 8 6 7 6 8
66
6.7
7
6.625
66.25
The mean of the numbers is 22.625
How to find the mean?The average of all the data in a set. The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
The mean or average of the set of the data is calculated thus
(6+7+5+8+6+7+6+8)/8
181/8 = 22.625
Therefore, the mean for the number of hours of sleep: 6 7 5 8 6 7 6 8 is 22.625
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Find the scale factor.
ABCD~EFGH
Answer:
0.67
Step-by-step explanation:
10/15＝0.666666......
＝0.67
consider the expression 1/2x2 +x+7 complete 2 descriptions of the parts of the exprssion
The description of the parts of the expression are:
The coefficient of x² is 1/2.
The coefficient of x is 1.
The constant is 7.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(1/2)x² + x + 7
Now,
The coefficient of x² is 1/2.
The coefficient of x is 1.
The constant is 7.
Thus,
The description of the expression is given above.
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Answer:
The description of the parts of the expression are:The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.Example: 2 + 3x + 4y = 7 is an expression.We have,(1/2)x² + x + 7Now,The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.Thus,The description of the expression is given above.Learn more about expressions here:brainly.com/question/3118662#SPJ1The description of the parts of the expression are:The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.Example: 2 + 3x + 4y = 7 is an expression.We have,(1/2)x² + x + 7Now,The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.Thus,The description of the expression is given above.Learn more about expressions here:brainly.com/question/3118662#SPJ1
Step-by-step explanation:
How many gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution so that the resulting mixture is an 18% sugar solution?
On solving the provided question, we can say that by percentage 9.6 gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
by percentage
mix with 96 gallons of a 10% sugar solution
the resulting mixture is an 18%
10/100 X 96 = 9.6
9.6 gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution
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What is the surface area of the right rectangular prism? 125 m 2 75 m 2 250 m 2 200 m 2
The surface area of a right rectangular prism is 250 m².
Option C is the correct answer.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
From the figure,
Width = w = 5 m
Height = h = 5 m
Length = l = 10 m
The surface area of a right rectangular prism.
= 2 (lw + lh + wh)
= 2 (10 x 5 + 10 x 5 + 5 x 5)
= 2 (50 + 50 + 25)
= 2 (125)
= 2 x 125
= 250 m²
Thus,
250 m² is the surface area of a right rectangular prism.
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Answer:
250m 2
I hope this helps <3
solve the following inequalities sketch a number line - (x + 5 +) greater than 2 (1 - x)
When graphed, a linear equation always produces a straight line since each element in the equation has an exponent of 1.
What are examples of linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
What three types of linear equations are there?The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Given, 3x−2<2x+1
⇒3x−2x<1+2
⇒x<3 or x∈(−∞,3)
At x=3, the lines y=3x-2 and y=2x+1 will both intersect.
The dark line unmistakably depicts the 3x-2<2x+1 solution.
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Is j = 1 a solution to the inequality below? 4 > j
Answer:
yes
Step-by-step explanation:
4 > j ( substitute j = 1 )
4 > 1 ← is a true statement
so j = 1 is a solution to the inequality
Figure A is a scale image of Figure B, as shown.
1³/
Figure A
Figure B
The scale that maps Figure A onto Figure B is 1 : 71
Enter the value of z.
Therefore , the solution of the given problem of linear equation comes out to be x = 21.75.
A linear equation is precisely what?A linear regression curve is built on the equation y=mx+b. The y-intercept is m, and the slope is B. The previous sentence is sometimes referred as a "mathematical equation merging multiple variables," even if y or y are independent parts. The only variables in bivariate linear equations are two. There are no known solutions to application issues involving linear equations. Y=mx+b, also written as mx+b, is the expression for a straightforward system of equations.
Here,
Given :
From a mixed number, you must convert it to a decimal number. You can do this by following the instructions below:
In order to start, you must reduce the fraction's denominator by its numerator.
Step 2: You must now multiply the resulting quotient by the whole number component.
You therefore obtain:
=> 7 1/4 = 7 + 0.25 = 7.25
The scale picture that transforms "Figure a" into "Figure b" is then: 1: 71
The specified length of the appropriate side of "Shape a" must then be multiplied by in order to determine the value of "z."
The outcome is as follows:
=>x = (3)(7.25)
=> x = 21.75
Therefore , the solution of the given problem of linear equation comes out to be x = 21.75.
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The complete question is "Figure a is a scale image of figure b the scale that maps figure a onto figure b is 1:7 1/4 enter the value of x
Both figures are triangles
Figure a is smaller than figure b
Figure a to the right has a 3
Figure b to the right has a x"
10. A truck travelling at x km/h, where 30 ≤x≤ 120, uses gasoline at the rate of r(x) L/100 km, where r(x) = 1(4900 + x). If fuel costs $1.15/L, what speed will result in the lowest fuel cost for a trip of 200 km? What is the lowest total cost for the trip?
The required lowest cost for the trip of 200km is given as $657.1.
What is the rate of change?Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
A truck travelling at x km/h, where 30 ≤x≤ 120, uses gasoline at the rate of r(x) L/100 km, where r(x) = 1/400(4900/x + x)
Since,
For r(x) maximum, r(x) = 0
1/400(4900/x + x) = 0
4900 = x²
x = 70 km/hr
Now,
Cost of the fuel for 200km = 200 / r(70) × $1.15/L
= 200/(1/400× (4900/70 + 70)) × 1.15
= $657.1
Thus, the required lowest cost for the trip of 200km is given as $657.1.
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On a math test there are multiple choice questions worth 4 points and open ended questions worth 6 points. Mr pills' first period class won a competition. and each student has 10 extra credit points added to their test score.
a. If Mai answered 13 mu tipple choice questions correctly and earned a total score of 92. how many open ended questions did she answer correctly?
b. If priya answered 4 open ended questions correctly and earned a total score of 94,how many multiple choice questions did she answer correctly?
c. Write an expression that will represent a students' score in first period who answers m multiple choice questions and e open ended correctly
A: Mai answered 5 open-ended questions correctly,
B: Priya answered 15 multiple-choice questions correctly,
C: expression for the condition is y = 10 + 4a + 6b.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given points on each multiple choice question = 4
points on each open-ended question = 6
extra credit for winners = 10 points
A. If Mai answered 13 multiple-choice questions correctly and earned a total score of 92,
the total score of multiple choice questions = 13*4
the total score of multiple choice questions = 52
score left = 92 - 52 - 10 (reducing 10 for extra points)
score left = 30
open-ended questions she answers correctly = 30/6
open-ended questions she answers correctly = 5
B: If Priya answered 4 open-ended questions correctly and earned a total score of 94,
the total score of open-ended questions = 4*6
the total score of open-ended questions = 24
the score left = 94 - 24 - 10 (reducing 10 for extra points)
score left = 60
multiple choice questions she answers correctly = 60/4
multiple choice questions she answers correctly = 15
C: an expression that will represent a student's score in first period,
let y be the total score,
a be the number of multiple choice questions answered,
the total score of multiple choice questions = 4a
and b be the number of open-ended questions answered,
the total score of open-ended questions = 6b
expression is,
y = 10 + 4a + 6b (adding 10 for extra points)
Hence Mai answered 5 open-ended questions correctly,
Priya answered 15 multiple-choice questions correctly,
and expression is y = 10 + 4a + 6b.
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ASSIGNMENT
1. Suppose the demand function for a product is given
by: Qa = 500 - 5P, compute the:
(a) quantity demanded at the unit price of Ghé 10
(b) price to sell 200 units
(c) price for zero demand
(d) quantity demanded at zero price
(e) the own-price elasticity of demand at the price for
which 200 units are sold.
The value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.
What is demand function?The link between the quantity demanded for a commodity (the dependent variable) and its price is represented by the demand function (independent variable).
a) At the price of Gh¢10 , then
Qd= 500 - 5P
Qd= 500 -5(10)
Qd= 500-50 = 450 units
The value of quantity demanded at unit price Gh¢10 is 450 units.
b) If there are 200 units,then
Qd= 500- 5P
200 = 500-5P
5P = 500-200
P= 300/5
P= Gh¢60
The price to sell 200 units is Gh¢60
c) if demand is zero, it mens Qd= 0
Qd= 500- 5P
0= 500-5P
5P= 500
P= Gh¢100
The price for 0 demand is Gh¢100.
d) If P= 0, then
Qd= 500-5P
Qd= 500-5(0)
Qd= 500 units
The quantity demanded at zero price is 500 units.
Hence, the value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.
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ENRICHED: A random number generator is used to generate one integer between 70 and 200. Let J be the event of generating a multiple of 25, and let K be the event of generating a multiple of 70. What are the possible outcomes of each event?
J={ }
K= { }
J U K{ }
The possible outcomes for each event are given as follows:
J = {75, 100, 125, 150, 175, 200}.K = {70, 140}J U K = {70, 75, 100, 125, 140, 150, 175, 200}.How to obtain the possible outcomes for each event?
Event J is composed by the multiples of 25 that are between 70 and 200, hence we start at 75, as 25 x 3 = 75, and then keep adding 25 until we reach 200, as follows:
J = {75, 100, 125, 150, 175, 200}
Event K is composed by the multiples of 70 that are between 70 and 200, hence we start at 70, as 70 x 1 = 70, and then keep adding 70 until we reach 200, as follows:
K = {70, 140}.
The union set is composed by the elements that belong to at least one of these two sets, hence:
J U K = {70, 75, 100, 125, 140, 150, 175, 200}.
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The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 200 pounds of the new blend. The selling price of the new blend is to be $5.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?
The amount of Earl Grey tea to mix is 225 pounds.
The amount of Orange Pekoe tea to mix is 75 pounds.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let x be the amount of Earl Grey tea to mix.
So, the amount of Orange Pekoe tea to mix = 300-x
then, 6x+4 (300-x) = 5.5 x 300
6x+1200-4x=1650
2x=450
x=225
and, amount of Orange Pekoe tea to mix = 300-225=75
Thus, the amount of Earl Grey tea to mix = 225 pounds
and, the amount of Orange Pekoe tea to mix=75 pounds.
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Kendall wants to use a credit card to purchase new furniture. His standard
APR is 22.65%, but his credit card is offering a promotional rate of 3% for six
months. The cost of the furniture, including sales tax, is $1,014. Assume that
Kendall has a previous unpaid balance, and his monthly payments apply to that
balance. How much will the promotional rate save Kendall in finance charges
during the six-month period?
Answer:
$199.98
Step-by-step explanation:
To calculate the amount that Kendall will save in finance charges during the six-month promotional rate period, we need to calculate the finance charges he would have incurred with his standard APR and then compare it to the finance charges he will incur with the promotional rate.
First, let's calculate the monthly finance charges with the standard APR. To do this, we need to know the average daily balance for each month. Assuming Kendall has a previous unpaid balance, let's say it is $500. And assuming he makes no other purchases, his average daily balance for each month would be:
$1,014 + $500 = $1,514The finance charges for each month with the standard APR would be:
$1,514 * (22.65/100) / 12 = $38.37
So, the total finance charges for the six-month promotional rate period with the standard APR would be:
$38.37 * 6 = $230.22
Next, let's calculate the finance charges with the promotional rate:
$1,514 * (3/100) / 12 = $5.04
So, the total finance charges for the six-month promotional rate period with the promotional rate would be:
$5.04 * 6 = $30.24
Finally, we can calculate the amount that Kendall will save in finance charges during the six-month promotional rate period:
$230.22 - $30.24 = $199.98
Therefore, Kendall will save $199.98 in finance charges during the six-month promotional rate period.
I need a real answer with solution please help.
Answer:
A and D
Step-by-step explanation:
Given the function:
[tex]\displaystyle{f(x)=\sqrt{5-x^2}}[/tex]
In order to find the first-order derivative of square root function, we have to convert the form of surd to exponent form. Therefore:
[tex]\displaystyle{f(x)=\left(5-x^2\right)^{\frac{1}{2}}}[/tex]
Since the exponent is a constant and that the base is an expression with variable, we can apply the chain rule (power rule variation):
[tex]\displaystyle{f(x) = u^n \to f'(x) = nu^{n-1} \cdot \dfrac{du}{dx}}[/tex]
Therefore:
[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-1} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-\frac{2}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}[/tex]
Deriving 5 - x²:
[tex]\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = 0 - 2x^{2-1}}\\\\\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = -2x}[/tex]
Thus:
[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot (-2x)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}(-2x)\left(5-x^2\right)^{-\frac{1}{2}} }\\\\\displaystyle{f'(x)=-x\left(5-x^2\right)^{-\frac{1}{2}} }[/tex]
You can also convert to the square root form of:
[tex]\displaystyle{f'(x)= \dfrac{-x}{\sqrt{5-x^2}}}[/tex]
Therefore, A and D are correct.
if you invest $550 at a 4% interest rate will be the interest
Answer:
22
Step-by-step explanation:
550x4%=550x0.04=22
Answer:
$22
Step-by-step explanation:
550 x 4% = 550 x 0.04 = $22
A rectangular prism has a volume of 120 in³. What is the height of the prism? What is the
surface area of the prism?
Show your work.
Given that the volume of the rectangular prism is 120 cubic inches, we can write the equation:
l * w * h = 120
where l, w, and h are the length, width, and height of the prism, respectively.
Since the length is 3 and the width is 10, we can plug in these values into the equation:
3 * 10 * h = 120
Solving for h, we get:
h = 120 / (3 * 10) = 120 / 30 = 4
So the height of the rectangular prism is 4 inches.
To find the surface area of the rectangular prism, we can add up the areas of all six faces:
2 * l * w + 2 * w * h + 2 * h * l
Plugging in the known dimensions, we get:
2 * 3 * 10 + 2 * 10 * 4 + 2 * 4 * 3 = 60 + 80 + 24 = 164 square inches
So the surface area of the rectangular prism is 164 square inches.
Answer: Hight 4 inch, surface area 164 square inch
Step-by-step explanation: multiply with l * w * h
* = x
Consider the following system of linear inequalities and corresponding graph:
y ≥ 2x - 4
x > -3
y < 5
Which of the following points is a solution to this system of linear inequalities?
A point that is a solution to this system of linear inequalities is (0, 1).
How to determine the point that is a solutionFrom the question, we have the following parameters that can be used in our computation:
y ≥ 2x - 4
x > -3
y < 5
Using the point (0, 1)
To see why this is a solution, we need to check if it satisfies each of the inequalities:
y ≥ 2x - 4: 1 ≥ 2 * 0 - 4, which is truex > -3: 0 > -3, which is truey < 5: 1 < 5, which is trueSince the point (0, 1) satisfies all of the inequalities, it is a solution to the system of linear inequalities.
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the team to win 3 games wins the playoffs. what is the probability of a team winning a 5 game playoff if it has 50% chance of winning each game
Therefore , the solution of the given problem of probability comes out to be probability of winning a 3 game out of 5 is 0.5 .
What specifically does the probability method entail?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any quantity between 0 and 1, whereby 1 frequently represents certainty range 1 and 0 normally denotes possibility, can be used to represent chance. A probability diagram illustrates the likelihood that a particular event will take place.
Here,
Given :
Since,
the probability to win a game is 50% .
So they have to win 3 games ,
and so , the probability to win the game is:
=> 1/2 * 1
=> 0.5
thus,
probability of winning a 3 game out of 5 :
=> 0.5
Therefore , the solution of the given problem of probability comes out to be probability of winning a 3 game out of 5 is 0.5 .
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If the terminal side of angle θ goes through the point (8/17,−15/17) on the unit circle, then what is cos(θ)?
The cosine of the angle θ is 8/17 whose terminal side passes through the given point
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent
Given here: The terminal side goes through the point (8/17, -15/17)
Thus we have cosθ =8/17 and sin θ =-15/17
now tan θ =sinθ /cosθ
tanθ = -15/8
θ = -61.9275
Hence, cosθ =8/17
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Can someone please help?
Answer: The annual premium for a 27-year-old female purchasing a 20-Year Endowment insurance policy with a face value of $25,000 is $42.67.
Step-by-step explanation:
1. Find Sn for the arithmetic series where a1= 3 , an= 42 , n= 14
2. Find sn for the arithmetic series where a1= −20 , n= 25 , an= 148
3. Find sn for the arithmetic series where a1=5 , d=1/2 , n=13
The value of the sum of the series is are 315, 1600 and 104
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
For the first series, we have
In this series, a1= 3 , an= 42 , n= 14
Plugging these values into the formula, we get:
Sn = 14/2 * (3 + 42)
Sn = 315
For the second series, we have
In this series, a1= −20 , n= 25 , an= 148
Plugging these values into the formula, we get:
Sn = 25/2 * (-20 + 148)
Sn = 1600
For the third series, we have
In this series, a1=5 , d=1/2 , n=13
So, we have
an = a + (n - 1)d = 5 + 12 * 1/2 = 11
Plugging these values into the formula, we get:
Sn = 13/2 * (5 + 11)
Sn = 104
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which direction does the graph of the equation shown below open v^2-4x+4y-4=0
The graph of the equation x^2 - 4x + 4y - 4 = 0 is a circle, so it doesn't have a direction of opening.
How to detemrine the directionFrom the question, we have the following parameters that can be used in our computation:
x^2 - 4x + 4y - 4 = 0
The equation x^2 - 4x + 4y - 4 = 0 is of a conic section
i.e. the equation of a circle
The equation of a circle does not have a particular direction it opens to
Hence, it is a closed shape
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