Answer:
3
Step-by-step explanation:
14/2=7 6/2=3 7+3=10 which is also half of 20 (20 is how many fruits he has) He gave away 3 bananas
EB. Which statement does
Statements
Rowena is proving that AD
the represent in her proof?
A
Reasons
1. given
1. AB
ED: BC
DC
2. given
2. 2 CAD * ZCEB
3. AB = ED; BC = DC
3. def. of
segments
4. AB + BC = AC
ED + DC
4. segment addition
postulate
11
11
substitution property
ED + DC
Ο ΔACDe ΔECB
AACD = AEFD
Ο ΔΑΕΒ = ΔEED
6. AC = CE
6. substitution property
7. AC = CE
7. def. of
segments
AAFB
AECB
202C
8. reflexive property
9. ASA
Answer:it’s ACD=ECB
Step-by-step explanation:
The correct option is Segment Addition Postulate.
What is similarity theorem?Similarity of triangles. The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.
Here, we have,
The segment addition postulate states that where there are two points on a line A and C and a third point B can only be located on the line segment AB if and only if the the distances between point A and point B as well as the distance between point B and point C satisfy the equation AB + BC = AC
Therefore, given that in the figure, the point B is in between point A and point C on segment AC then AB + BC
Similarly, AD = AE + ED.
The correct option is Segment Addition Postulate.
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complete question:
BE || CD 1. Given 2. ∠A ≅ ∠A 2. Reflexive Property 3. ∠ACD ≅ ∠ABE 3. Corresponding angles formed by parallel lines and a transversal are ≅. 4. ∠ADC ≅ ∠AEB 4. Corresponding angles formed by parallel lines and a transversal are ≅. 5. ΔABE ∼ ΔACD 5. AA Similarity Postulate 6. AC AB = AD AE 6. Definition of Similar Triangles 7. AC = AB + BC, AD = AE + ED 7. ??? 8. AB + BC AB = AE + ED AE 8. Substitution 9. AB AB + BC AB = AE AE + ED AE 9. Addition 10. BC AB = ED AE 10. Subtraction Fill in the missing reason for the proof. A) Transitive Property B) Subtraction Property C) SSS Similarity Theorem D) Segment Addition Postulate
A(n)__________function will MULTIPLY the same number each time.
A. Exponential
B. Neither
C. Linear
The true statement is an exponential function will MULTIPLY the same number each time.
How to determine the complete statementA linear function is represented as:
y = mx + b
An exponential function is represented as:
[tex]y = ab^x[/tex]
The factor [tex]b^x[/tex] means that the number b is multiplied by itself x times
Hence, the word that completes the blank is (a) exponential
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Exponential functions multiply a constant number each time to show growth or decay.
Explanation:Exponential functions will multiply the same number each time. They model exponential growth or decay where the value increases or decreases at a constant rate over time.
For example, if you multiply 2 by itself multiple times: 2^1, 2^2, 2^3, the result will keep growing exponentially.
In math, exponential functions are denoted as f(x) = a*b^x, where 'b' is the constant multiplied each time for growth or decay.
The expression -10y²+54y+36 represents the profits made by a company when it increases the price of the product by y dollars. Factor this expression to find the price increase that results in a profit of 0
Answer:
− 2( 5 y + 3 ) ( y − 6 )
Step-by-step explanation:
hope it helps
Callie is comparing the costs of two options for her college education.
Option A: Complete the first two years of schooling at a community college and then transfer to a university.
Option B: Complete all four years of schooling at the university.
Community College Financial Analysis
Costs per Year
Financial Aid Package per Year
Tuition & Fees
Scholarships & Grants
$2,900
$800
Room & Board
$1,250
University Financial Analysis
Costs per Year
Financial Aid Package per Year
Tuition & Fees
Scholarships & Grants
$9,500
$10,000
Room & Board
Work-Study
$11,500
$2,000
Which statement about the cost of the options is true?
She would save $1,000 by choosing option B.
She would save $5,650 by choosing option A.
She would save $11,200 by choosing option B.
She would save $11,300 by choosing option A.
Answer:
Callie's comparison of two options for college education
The true statement is:
She would save $11,300 by choosing option A.
Step-by-step explanation:
Cost Analyses:
Option A: Community College + University Total Expenses
Tuition & Fees $5,800 ($2,900 x 2) + $19,000 ($9,500 x 2) = $24,800
Scholarships ($1,600) ($800 x 2) + ($20,000) ($10,000 x 2)=($21,600)
Room & Board $2,500 ($1,250 x 2) + $23,000 ($11,500 x 2) = $25,500
Work-Study + ($4,000) ($2,000 x 2) = ($4,000)
Total Cost $6,700 + $18,000 = $24,700
Option B: 4 years' University
Tuition & Fees $38,000 ($9,500 x 4)
Scholarships ($40,000) ($10,000 x 4)
Room & Board $46,000 ($11,500 x 4)
Work-Study ($8,000) ($2,000 x 4)
Total Cost $36,000
Difference between the two options = $11,300 ($36,000 - $24,700
Answer: She would save $11,300 by choosing option A
Step-by-step explanation:
Community College Financial Analysis:
Tuition and fees = 2900
Scholarship and grant = 800
Rooms and board = 1250
University Financial Analysis:
Tuition and fees = 9500
Scholarship and grant = 10000
Rooms and board = 11500
Work study - 2000
Option A :
First two years at college :2 × (2900 + 1250 - 800)
2 × (3350) = $6700
2 years at university : 2 × (9500 +11500 - 2000 - 10000)
2 × 9000 = 18000
Option A total = $(18,000 + 6700) = $24,700
Option B :
4 years at university : 4 × (9500 +11500 - 2000 - 10000)
4 × 9000 = $ 36000
She would be saving $(36,000 - 24,700) = $11,300 by choosing option A
Solve this problem
how far apart are these planes?
Answer:
9.433 miles
Step-by-step explanation:
c^2 = a^2 + b^2
The distance between the planes ABC is the square root of 89 miles, which is approximately 9.43 miles.
The distance between the planes ABC can be found using the Pythagorean theorem since the relationship between the sides AB, BC, and AC forms a right triangle. Given that AB is 5 miles, BC is 8 miles, and AC is the hypotenuse, the distance between the planes ABC can be calculated as follows:
[tex]$$ AC^2 = AB^2 + BC^2 $$[/tex]
Substitute the given values:
[tex]$$ AC^2 = 5^2 + 8^2 $$[/tex]
[tex]$$ AC^2 = 25 + 64 $$[/tex]
[tex]$$ AC^2 = 89 $$[/tex]
Therefore, the distance between the planes ABC is the square root of 89 miles, which is approximately 9.43 miles.
Bryan's mom spent $46.20 filling up her gas tank if her gas tank can hold 12 gallons of gas how much did each gallon cost
Answer: Each gallon costs $3.85
Step-by-step explanation:
We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:
$46.20 ÷ 12 = $3.85
Each gallon costs $3.85
I hope this helps!
Answer:
Each gallon costs $3.85
Step-by-step explanation: We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:$46.20 ÷ 12 = $3.85Each gallon costs $3.85I hope this helps!
What is the difference between a measure of center and a measure of variability?
Answer:
Step-by-step explanation:
The measure of center of a group of data is a single central value such as the mean and the median.
The mean is the arithmetical average of the sum of the data and the median is the middle value of the data when placed in ascending sequence.
The measure of variability gives an indication of the spread of the data about the mean. Examples are the Standard Deviation and the Interquartile Range.
Explaining the difference between a measure of center and a measure of variability.
What is the measure?The measure is an estimate or assesses the extent, quality, value, or effect of (something).
Determining:The measure of the center of a group of data is a single central value such as the mean and the median.
The mean is the arithmetical average of the sum of the data and the median is the middle value of the data when placed in ascending sequence.
The measure of variability gives an indication of the spread of the data about the mean. Examples are the Standard Deviation and the Interquartile Range.
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If a woman making $35 an hour gets a 10% raise (35 x 0.10 = 3.50 so $35 + $3.50 = $38.50/hour), how much will she now make in a 6 hour work day? (multiply by 6!) *
Which of the following statements is true?
O A) The number 135 is not divisible by 3 or 5.
OB) The number 135 is divisible by 3, 5 and 9.
OC) The number 135 is divisible by 3 and 5, but not by 9.
OD) The number 135 is divisible by 3 and 9, but not by 5.
Answer:
B)
Step-by-step explanation:
If you try to divide 135 with each number,every number is divisible by 135 XD
What is the best first step in solving Negative 4 x + two-fifths greater-than StartFraction 5 over 10 EndFraction? Add Two-fifths to both sides. Subtract Two-fifths from both sides. Multiply both sides by Negative 4 and reverse the inequality symbol. Divide both sides by 10 and reverse the inequality symbol.
Answer:
(B) Subtract 2/5 from both sides.
Step-by-step explanation:
What is the best first step in solving Negative 4 x + two-fifths greater-than StartFraction 5 over 10 EndFraction?
(A) Add Two-fifths to both sides.
(B) Subtract Two-fifths from both sides. <<<<<-------Correct Answer
(C) Multiply both sides by Negative 4 and reverse the inequality symbol.
(D) Divide both sides by 10 and reverse the inequality symbol.
The solution is Option B.
Subtract Two-fifths from both sides and the inequality equation is x < -1/40
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( -4x ) + 2/5 > 5/10
On simplifying the equation , we get
-4x + 2/5 > 1/2
Subtracting 2/5 on both sides of the equation , we get
-4x > ( 1/2 ) - ( 2/5 )
-4x > 1/10
On further simplification , we get
4x < - ( 1/10 )
Divide by 4 on both sides of the equation , we get
x < - ( 1/40 )
Hence , the inequality is x < - ( 1/40 )
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Ella’s geometry teacher asked each student to devise a problem and write out its solution. Here is Ella’s work:
A triangle has side lengths of 10, 11, and 15. What type of triangle is it?
Procedure:
102 ?? 112 + 152
100 ?? 121 + 225
100 < 346
Conclusion:
This triangle is an acute triangle.
Which statement best summarizes Ella’s work?
Ella’s procedure and conclusion are correct.
Ella’s procedure is correct, but her conclusion is incorrect.
Ella’s procedure is incorrect, but her conclusion is correct.
Ella’s procedure and conclusion are incorrect.
Answer:Ella's Procedure And Conclusion are incorrect
Step-by-step explanation:
Answer:
Ellas procedure and conclusion are incorrect
Step-by-step explanation:
Ahmed found the volume of a cone having both a height and a diameter of 6 centimeters. His work is shown below. Step 1 Find the radius. radius = StartFraction 6 Over 2 EndFraction = 3 centimeters Step 2 Find the area of the base. Area of base = Pi (3) squared = 9 pi centimeters squared Step 3 Multiply the area of the base by the height. 9 pi times 6 = 54 centimeters cubed Step 4 Divide 54 by 3 to find the volume of the cone. Volume of the cone = StartFraction 54 Over 3 EndFraction = 18 centimeters cubed What was Ahmed’s first error? In Step 1, the radius should be found by multiplying the diameter by 2. In Step 2, the formula 2 pi r should be used to find the area of the circle. In Step 3, the resulting area should be in terms of pi. In Step 4, the units of the resulting volume should be Centimeters squared.
Ahmed's first error was in step 3 where he failed to express 54 in terms of π.
What is Volume?Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.
We have,
Diameter = 6 cm
1. Radius = diameter/2
= 6/2
= 3cm
2. Area of base = π × 3²
= 9π cm²
3. Multiply the area of the base by the height
= 9π x 6
= 54π cm³
4. Divide 54π by 3 to find the volume of the cone
= 54π/3
= 18π cm³
So, the volume of the cone is 18π cm³.
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The measures of angle Y is 45 degrees and the measures of angle Z is 70 whg is the measure of angle W
Answer:
65 degrees
Step-by-step explanation:
I assume this shape is a triangle. The sum of the three angles in a triangle always equals 180 degrees. So, you add the angles that we have the measurements of and subtract it from 180 to get your answer of 65 degrees. hope this helps:)
g An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 4.8 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 4.9 psi, is there sufficient evidence at the 0.1 level that the valve performs below the specifications
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 4.9
For the alternative hypothesis,
µ < 4.9
This is a left tailed test.
If the population variance is 0.36, the population standard deviation would be √0.36 = 0.6 psi
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 4.9
x = 4.8
σ = 0.6
n = 210
z = (4.8 - 4.9)/(0.6/√210) = - 2.42
Looking at the normal distribution table, the probability corresponding to the z score is 0.0078
Since alpha, 0.1 > than the p value, 0.0078, then we would reject the null hypothesis. Therefore, there is sufficient evidence at the 0.1 level that the valve performs below the specifications.
If anyone could answer this for me I would very much appreciate it
Answer:
a3 = 45
Step-by-step explanation:
a1 = 20
an = a(n-1) *3/2 where n is the term number
a2 = a(2-1) *3/2
a1 *3/2
We know a1 = 20
a2 = 20*3/2 = 30
a3 = a(3-1) *3/2
= a2 *3/2
We know a2 = 30
= 30*3/2 = 45
A 50% tip for a $30 taxi cap ride
Answer:
15 dollars
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
We multiply the tip percentage by the amount billed
50% * 30
Change to decimal form
.50 * 30
15
What is the surface area of the cone? 17cm 10cm use 3.14 for pie
Gio is solving the quadratic equation by completing the square. 5x2 + 15x – 4 = 0 What should Gio do first?
Answer: add 4 on both sides
Step-by-step explanation:
Answer:
Isolate the constant
Step-by-step explanation:
i just took it on edge A
According to a Gallup survey conducted in July 2011, 20% of Americans favor reducing the U.S. budget deficit by using spending cuts only, with no tax increases. An economics professor believes that fewer college students would favor deficit reduction through spending cuts only. The professor surveys 500 college students and finds that 75 of them favor reducing the deficit using only spending cuts. What is the test statistic?
Answer:
The test statistic is [tex]t = -62.5[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 0.2*500 = 100[/tex]
The alternate hypotesis is:
[tex]H_{1} < 0.2*500 < 100[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem:
[tex]X = 75, \mu = 100, \sigma = \sqrt{500*0.8*0.2} = 8.94, n = 500[/tex]
So
[tex]t = \frac{75 - 100}{\frac{8.94}{\sqrt{500}}}[/tex]
[tex]t = -62.5[/tex]
The test statistic is [tex]t = -62.5[/tex]
Answer:
[tex]z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{500}}}=-2.795[/tex]
Step-by-step explanation:
Data given by the problem
n=500 represent the random sample taken
X=75 represent the students in favor to reducing the deficit using only spending cuts
[tex]\hat p=\frac{75}{500}=0.15[/tex] estimated proportion of favor to reducing the deficit using only spending cuts
[tex]p_o=0.2[/tex] is the value that we want to check
z would represent the statistic
System of hypothesis
We want to cehck if the true proportion of students in favor to reducing the deficit using only spending cuts is less than 0.2.:
Null hypothesis:[tex]p\geq 0.2[/tex]
Alternative hypothesis:[tex]p < 0.2[/tex]
The statistic for this case is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info provided we got:
[tex]z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{500}}}=-2.795[/tex]
which shows the numbers from greatest to least? 9.5 9 3/8 9.125 9 3/4
Answer:
I think the answer is 9 3/4, 9.5, 9 3/8, 9.125
Kate baked some cookies. She put 12 cookies on each cookie sheet. If she baked 24 cookie sheets of cookies, how many cookies did she bake in all?
Answer:
She baked 288 cookies
Step-by-step explanation:
24 X 12 equals 288
Answer:
288 cookies
Step-by-step explanation:
A horticulturist working for a large plant nursery is conducting experiments on the growth rate of a new shrub. Based on previous research, the horticulturist feels the average weekly growth rate of the new shrub is 2cm per week. A random sample of 48 shrubs has an average growth of 1.80cm per week with a standard deviation of 0.50cm. Is there overwhelming evidence to support the claim that the growth rate of the new shrub is less than 2cm per week at a 0.010 significance level
Answer:
[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
And the p value would be:
[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week
Step-by-step explanation:
Information given
[tex]\bar X=1.8[/tex] represent the sample mean for the growth
[tex]s=0.5[/tex] represent the sample standard deviation
[tex]n=48[/tex] sample size
[tex]\mu_o =2[/tex] represent the value that we want to compare
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 2cm per week, the system of hypothesis are :
Null hypothesis:[tex]\mu \geq 2[/tex]
Alternative hypothesis:[tex]\mu < 2[/tex]
Since we don't know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
And the p value would be:
[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week
To pass science, a student must earn at least a grade of 70. How many students failed this science class? A histogram titled Science Grades has grades on the x-axis and number of students on the y-axis. 2 students received a score of 50 to 59; 5 students received a score of 60 to 69; 8 students received a score of 70 to 79; 5 students received a score of 80 to 89; 2 students received a score of 90 to 100.
Answer:
7 students
Step-by-step explanation:
Answer:
the answer is 7 people
Step-by-step explanation:
have a great day!
Área of panel 5ft by 16ft
In preparation for upcoming wage negotiations with the union, the managers for the Bevel Hardware Company want to establish the time required to assemble a kitchen cabinet. A first line supervisor believes that the job should take 40 minutes on average to complete. A random sample of 120 cabinets has an average assembly time of 42 minutes with a standard deviation of 8 minutes. Is there overwhelming evidence to contradict the first line supervisors belief at a 0.05 significance level
Answer:
[tex]t=\frac{42-40}{\frac{8}{\sqrt{120}}}=2.739[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(z>2.739)=0.0616[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.
Step-by-step explanation:
Information provided
[tex]\bar X=42[/tex] represent the sample mean for the assembly time
[tex]s=8[/tex] represent the sample deviation
[tex]n=120[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We want to conduct a hypothesis in order to see if the true mean is equal to 40 minutes or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu =40[/tex]
Alternative hypothesis:[tex]\mu \neq 40[/tex]
The statistic for this case is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{42-40}{\frac{8}{\sqrt{120}}}=2.739[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(z>2.739)=0.0616[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.
The hypothesis testing does not provide sufficient evidence to contradict the supervisor's belief that the job should take 40 minutes on average.
Explanation:The subject matter refers to the concept of hypothesis testing in statistics, where in context, we are checking whether the actual average assembly time of a kitchen cabinet contradicts the believed assembly time. Hypothesis testing works on a null hypothesis and an alternative hypothesis. In this case, the null hypothesis (H0) can be that the average assembly time equals 40 minutes. The alternative hypothesis (H1) would be that the average assembly time does not equal 40 minutes.
At a 0.05 significance level, we calculate the test statistic (z-score) which represents how many standard deviations a data-point (the sample mean) is from the mean (the supervisor's claimed mean). The z-score is calculated as:
(Sample Mean - Claimed Mean) / (Standard Deviation/ √Number of Observations)
In this case, this becomes: (42-40)/(8/√120) = 1.732. The corresponding p-value for this z-score is 0.083.
Since the p-value is greater than the significance level of 0.05, we cannot reject the null hypothesis. Hence, there isn't overwhelming evidence to contradict the supervisor's belief that the job should take 40 minutes on average.
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The number of fish caught by a fisherman was increased by 35% to 1080. What was the number of fish caught by the fisherman before the increase?
Answer:
800
Step-by-step explanation:
1.35x = 1080 -->
x = 1080/1.35 -->
800
Use the distributive property to write an equivalent expression without parentheses.
9 (a + 8)
Check all that apply.
Distribute 9, by multiplication, to the variable, a, and to the constant, 8.
Write the two multiplications, 9(a) + 9(8)
The expression 9(a) is written as 9a.
The expression 9(8) equals 72.
The equivalent expression is 9a + 8.
The equivalent expression is 9a + 72.
Answer:
A.Distribute 9, by multiplication, to the variable, a, and to the constant, 8.
B.Write the two multiplications, 9(a) + 9(8)
C.The expression 9(a) is written as 9a.
D.The expression 9(8) equals 72.
F.The equivalent expression is 9a + 72.
Step-by-step explanation:
or rather 9+72
Write an expression that means the sum of six and the product of three and d
Final answer:
The expression representing the sum of six and the product of three and a variable 'd' is written as 6 + 3d.
Explanation:
The expression that means the sum of six and the product of three and d is written as 6 + 3d.
This expression shows that you first multiply the number three by the variable d, and then add six to the result of that multiplication.
The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), instructs us to perform the multiplication before the addition.
Michael invests $2000 in an annuity that offers an interest rate of 4%
compounded quarterly for 5 years. What is the value of Michael's investment
after 5 years?
The future value of Michael's investment after 5 years is $44,038.01.
The future value of an annuity can be determined using the following formula:
[tex]FV=PV(1+r/n)^{n}[/tex]
FV = future value
PV = present value
r = annual interest rate
n = number of periods interest held
We can also compute the future value using an online finance calculator as follows:
N (# of periods) = 20 quarters (5 years x 4)
I/Y (Interest per year) = 4%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
FV = $2,440.38
Total Interest = $440.38
Thus, the value of Michael's investment after 5 years is $2,440.38.
Find the vector equations for medians from the vertices to the three midpoints of triangle ABC with vertices A(-1,5), B(5,-2) and C(3,5).
Answer:
The equation is
2y + 85x + 75 = 0
Step-by-step explanation:
Given vertices A(-1,5), B(5,-2) and C(3,5).
Suppose we want to find the median from A
First, we find the midpoint of side BC
Let the midpoint be M = ((x1 + x2)/2, (y1 + y2)/2)
= ((5+3)/2, (-2-5)/2)
= (8/2, -7/2)
= (4, -7/2)
Next, we write the equation of median with A(-1,5) and midpoint M(4,-7/2)
y = mx + c
The slope m = (y2 - y1)/(x2 - x1)
= (-7/2 - 5)/(4 + 1)
= (-17/2)/5
m = -85/2
We find the y-intercept, using A(-1,5)
x = -1, y = 5, m = -85/2
y = mx + c
5 = (-85/2)(-1) + c
c = 5- 85/2
= -75/2
y = -85x/2 - 75/2
Multiply through by 2
2y = -85x - 75
2y + 85x + 75 = 0
And this is the equation