prove each of the given statements, assuming that a, b, c, d, and n are integers with n > 1 and that a ≡ c (mod n) and b ≡ d (mod n).
a. (a + b) ≡ (c + d) (mod n)
b. (a − b) ≡ (c − d) (mod n)
Answers
Since k and l are integers, k + l is also an integer, this proves that (a + b) ≡ (c + d) (mod n).
Since k and l are integers, k − l is also an integer, this proves that (a − b) ≡ (c − d) (mod n)
How to prove (a + b) ≡ (c + d) (mod n)?a. To prove that (a + b) ≡ (c + d) (mod n), we need to show that n divides (a + b) − (c + d), or equivalently, that (a + b) − (c + d) is an integer multiple of n. We have:
(a + b) − (c + d) = a − c + (b − d)
Since a ≡ c (mod n) and b ≡ d (mod n), we can write a = c + kn and b = d + ln for some integers k and l. Substituting these into the above equation, we get:
(a + b) − (c + d) = (c + kn) + (d + ln) − c − d = kn + ln = (k + l)n
Since k and l are integers, k + l is also an integer, and therefore, (a + b) − (c + d) is an integer multiple of n. This proves that (a + b) ≡ (c + d) (mod n).
How to prove (a − b) ≡ (c − d) (mod n)?b. To prove that (a − b) ≡ (c − d) (mod n), we need to show that n divides (a − b) − (c − d), or equivalently, that (a − b) − (c − d) is an integer multiple of n. We have:
(a − b) − (c − d) = a − c − (b − d)
Since a ≡ c (mod n) and b ≡ d (mod n), we can write a = c + kn and b = d + ln for some integers k and l. Substituting these into the above equation, we get:
(a − b) − (c − d) = (c + kn) − (d + ln) − c + d = kn − ln = (k − l)n
Since k and l are integers, k − l is also an integer, and therefore, (a − b) − (c − d) is an integer multiple of n. This proves that (a − b) ≡ (c − d) (mod n).
Learn more about integers
brainly.com/question/15276410
#SPJ11
Related Questions
Answer the questions below and show all of your
1. A toy is shaped as a triangular prism. The toy has a
base of 108 square inches. What is the height of the toy it
the volume is 729 cubic inches?
Answers
Answer:
6.75
Step-by-step explanation:
729=1/2*216h
729=108h
h=6.75
I think idrk
For altitudes up to 36,000 feet, the relationship between ground temperature and atmospheric temperature can be described by the formula t = −0.0035a + g, in which t is the atmospheric temperature in degrees Fahrenheit, a is the altitude, in feet, at which the atmospheric temperature is measured, and g is the ground temperature in degrees Fahrenheit. Determine the altitude in feet when t is −14.6 °F and g is 40 °F.
The altitude will be ____ feet.
Answers
The altitude in feet when t is −14.6 °F and g is 40 °F is -15600 feet.
What is altitude?Altitude or height is a distance measurement between a reference datum and a point or object, usually in the vertical or "up" direction. The precise definition and reference datum vary depending on the circumstance.
Like height, altitude is the distance above sea level. Areas are sometimes referred to as "high-altitude" if they extend at least 2,400 meters (8,000 feet) into the atmosphere. Mount Everest, located in the Himalayan mountain range on the boundary of Nepal and the Chinese territory of Tibet, is the highest point on Earth.
From the information, the temperature can be described by the formula t = −0.0035a + g.
The altitude in feet when t is −14.6 °F and g is 40 °F will be:
t = −0.0035a + g.
t = atmospheric temperature
a = altitude
g = ground temperature in degrees Fahrenheit
This will be illustrated as:
-14.6 = 0.0035a + 40
Collect like terms
0.0035a = -14.6 - 40
0.0035a = -54.6
Divide
a = -54.6 / 0.0035
a = -15600 feet
The altitude is -15600 feet.
Learn more about altitude on:
https://brainly.com/question/1159693
#SPJ1
How do you find Cosine when using trig?
Answers
Answer:
cosine= adjacent
hypotenuse
Answer:
adjacend/hypotonus
Step-by-step explanation:
When you want to find the cosine of an angle, you would divide the ajasent side by the hypotonus. You can remember soh cah toa for all the trig funtions. Hope this helps!
Body Mass Index (BMI) is the ratio of a person's body weight to volume. Extreme high values are associated with obesity, and extreme low values are associated with malnutrition. The Centers for Disease Control (CDC) uses percentiles, rather than fixed cutoffs, to categorize the weight status of individuals. Percentiles convey information about a person's relative standing over time in relation to others of the same age and gender. The CDC uses the table below to classify children from ages 2 to 20.
Weight status Percentile range
Underweight Less than the 5th percentile
Healthy weight 5th percentile to less than the 85th percentile
Overweight 85th to less than the 95th percentile
Obese Equal to or greater than the 95th percentile
One of the following statements is true. Select the true statement.
a. Approximately 85% of people have BMIs that are classified as overweight.
b. Approximately 10% of people have BMIs that are classified as overweight.
c. More than twice as many people are classified as obese than as underweight.
d. Approximately 95% of people have BMIs that are classified as overweight.
e. Approximately 5% of people have BMIs that are classified as overweight.
Answers
The required answer is e. Approximately 5% of people have BMIs that are classified as overweight. - This statement is true as less than 5% of people have BMIs that are classified as overweight.
Body mass index (BMI) is the ratio of a person's body weight to volume. Extreme high values are associated with obesity, and extreme low values are associated with malnutrition. The Centers for Disease Control (CDC) uses percentiles to categorize the weight status of individuals. The CDC uses the table below to classify children from ages 2 to 20.
The true statement among the following statements is:Approximately 5% of people have BMIs that are classified as overweight.
We have the following options:
a. Approximately 85% of people have BMIs that are classified as overweight. - This statement is false as only 18.5% to 24.9% of people have BMIs that are classified as healthy weight. Thus, less than 85% of people have BMIs that are classified as overweight.
b. Approximately 10% of people have BMIs that are classified as overweight. - This statement is false as more than 30% of people have BMIs that are classified as overweight.
c. More than twice as many people are classified as obese than as underweight. - This statement may be true, but it cannot be determined from the information given in the table.
d. Approximately 95% of people have BMIs that are classified as overweight. - This statement is false as less than 95% of people have BMIs that are classified as overweight.
e. Approximately 5% of people have BMIs that are classified as overweight. - This statement is true as less than 5% of people have BMIs that are classified as overweight.
Learn more about BMIs here https://brainly.com/question/32255368
#SPJ11
what is 9+10 i am giving away my points
Answers
Answer:
19
Step-by-step explanation:
hope this helps
thanks
Answer:
The answer is 109.
Because 10 + 9 =
10<--9
10<-9
109
Step-by-step explanation:
Hope this helps! Pls consider giving me Brainliest! It would mean a lot!
A group of 500 middle school students were randomly selected and asked about their preferred frozen yogurt flavor. A circle graph was created from the data collected.
a circle graph titled preferred frozen yogurt flavor with five sections labeled Dutch chocolate 21.5 percent, country vanilla 28.5 percent, sweet coconut 13 percent, espresso 10 percent, and cake batter
How many middle school students preferred cake batter-flavored frozen yogurt?
27
50
72
135
Answers
Answer: 135
Step-by-step explanation:
dutch chocolate: 107.5
country vanilla: 142.5
sweet coconut: 65
espresso: 50
107.5 + 142.5 + 65 + 50 = 365
500 - 365 = 135
cake batter sounds good
Someone help I’m LAAAAZYYYY
Answers
Answer:
It is 8,7
Hope this helps!
Step-by-step explanation:
Donte simplified the expression below. 4 (1 3 i) minus (8 minus 5 i). 4 3 i minus 8 5 i. negative 4 8 i. what mistake did donte make?
Answers
Donte made the mistake of not applying the distributive property correctly for the expression 4(1 + 3i). So, correct option is A.
The distributive property states that when a number is multiplied by a sum of terms, it should be distributed to each term individually. In this case, the number 4 should be multiplied by both 1 and 3i.
However, Donte incorrectly multiplied only the real part, 4, with 1, resulting in 4, and did not multiply the imaginary part, 3i, by 4. This mistake led to an incorrect simplified expression.
The correct application of the distributive property would yield 4 multiplied by both 1 and 3i, resulting in 4 + 12i. Therefore, the correct simplified expression would be:
4(1 + 3i) - (8 - 5i) = 4 + 12i - 8 + 5i = -4 + 17i.
So, the mistake Donte made was not applying the distributive property correctly for 4(1 + 3i). So, correct option is A.
To learn more about expression click on,
https://brainly.com/question/27963677
#SPJ4
Complete question is:
Donte simplified the expression below.
4 (1 + 3 i) minus (8 minus 5 i). 4 + 3 i minus 8 + 5 i. Negative 4 + 8 i.
What mistake did Donte make?
He did not apply the distributive property correctly for 4(1 + 3i).
He did not distribute the subtraction sign correctly for 8 – 5i.
He added the real number and coefficient of i in 4(1 + 3i).
He added the two complex numbers instead of subtracted.
The absolute value of -1/4 is
Answers
Answer: 1/4
Explanation: Remember that the absolute value of a number is just the positive version of that number. So the absolute value of -1/4 is 1/4.
Find the shaded area of each figure, round your answer to one decimal place if necessary
Answers
Step-by-step explanation:
radius of circle = 5 yd ------ ( given )
height of triangle = 16 yd --- ( given )
base of triangle = 16 yd ----- ( given )
area of triangle = 1/2 × base × height
= 1/2 × 16 × 16
= 128 yd²
area of circle = π × radius²
= 3.14 × 5 × 5 --- ( π = 3.14 )
= 78.5 yd²
---------------------------------------area of shaded portion = area of triangle - area of circle
area of shaded portion= 128 yd²-78.5 yd²
area of shaded portion = 49.5 yd²
--------------------------------------PLEASE FOLLOW MEFind the area of the region bounded by the graphs of f(x)= x^3 + x^2 -6x and
g(x) = 2x - x^2.
A. (20/3)
B. 36
C.(148/3)
D. (256/3)
Answers
a sphere has a radius of 6 units. if the radius is tripled, by what factor does the volume increase?
Answers
Answer:
Original volume = (4/3)π(6^3) = 288π
New volume = (4/3)π(18^3) = 7,776π
7,776π ÷ 28π = 27
When the radius of a sphere is tripled, the volume of the new sphere is 27 times the volume of the old sphere.
A school fundraiser sells 1,200 raffle tickets. Each ticket costs $2. There is one grand prize worth $100 and 5 smaller prizes worth $20 each. What is the expected gain or loss for buying 1 ticket? loss of $1.91 loss of $1.83 gain of $2.16 loss of $1.99
Answers
Answer:
loss of $1.83
Step-by-step explanation:
The average prize per ticket is ...
($100 +5($20))/1200 = $200/1200 ≈ $0.1667 ≈ $.17
You pay $2.00 for a ticket, so your expected value is ...
-$2.00 +0.17 = -$1.83 . . . . a loss of $1.83
Answer:
loss of 1.83
Step-by-step explanation:
iready test
Find the nth term of this quadratic sequence
2, 8, 18, 32, 50, ...
Answers
Answer:
nth term = 2n^2
Step-by-step explanation:
The computation of the nth term of the quadratic sequence is as follows;
The given sequence is 2,8,18,32,50
Now
The first term, n = 1 = 2 × 1 × 1 = 2
Second term, n =2 = 2 × 2 × 2 = 8
Third, n =3 = 2 × 3 × 3 = 18
fourth term, n = 4, = 2 × 4 × 4 = 32
fifth term, n =5, = 2 × 5 × 5 = 50
Now finally For nth term, = 2 × n × n = 2n^2
Therefore nth term = 2n^2
Can some one help me with this question its hard :( down below ill give brainliest and plz explain
Answers
Answer:
1 is the answer
Step-by-step explanation:
10^0 on the calculator is 1
How many positive integers between 1000 and 9999 inclusive are divisible by 5 and 7?
Answers
If a number is divisible by 5 and 7, then that number is divisible by LCM(5, 7) = 35. So count the multiples of 35 in the range.
Since
9999 = 35•285 + 24
we know there are 285 multiples of 35 among the positive integers 1-9999. We also have
1000 = 35•28 + 20
so there are 28 multiplies of 35 less than 1000.
Then there are 285 - 28 = 257 multiples of 35 in the given range.
0.0007 in standard form
Answers
Answer:
very simple 0.0007 = 7 / 10000 lol
Step-by-step explanation:
hope this is helpful!
0.277 D Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.038 1.552 100 ANOVA df F Significance F 1.976 0.104 4 Regression Residual Total SS 19.042 228.918 247.960 MS 4.760 2.410 95 99 Intercept X1 Coefficients Standard Error 7.505 1.213 0.147 0.057 -0.105 0.055 0.001 0.001 0.095 0.311 t Stat 6.187 2.594 -1.902 с 0.305 P-value 0.000 0.011 0.060 0.063 0.761 Lower 95% Upper 95% 5.097 9.913 0.034 0.259 A B 0.000 0.002 -0.523 0.713 X2 X3 X4 A statistician wants to investigate a phenomenon using multiple regression analysis. She uses four independent variables: X1, X2, X3, and X4, and her dependent variable is Y. To estimate the multiple regression model, she uses the ordinary least squares estimator. The estimation results are given in the output table below. Answer the following questions: 1. (4 points) Interpret the parameter estimate of X1. Explain. 2. (4 points) X4 is a dummy variable. How would you interpret the parameter estimate of X4? Explain. 3. (3 points) Which parameter estimates are statistically significant at 5% level of significance. Interpret. 4. (4 points) Calculate the 95% confidence interval of X2 (A=? and B=?). Use t-value = 1.96 in your calculations. Write down the formula and how you calculate them. Explain. 5. (3 points) Test the hypothesis that whether the overall model is statistically significant. Which test do you use? What is the decision? Explain. 6. (3 points) Calculate the value of t-statistics (C=?) for X3. Write down the formula and explain. 7. (5 points) Calculate and interpret the R-squared of the model (D=?). Discuss if the fit is good or not. Explain.
Answers
The parameter estimate of X1 is 0.147. It means that, holding all other variables constant, a unit increase in X1 is associated with a 0.147 increase in Y.
X4 is a dummy variable, which takes the value of 1 if a certain condition is met and 0 otherwise. The parameter estimate of X4 is -0.105, which means that, on average, the value of Y decreases by 0.105 units when X4 equals 1 (compared to when X4 equals 0).
The parameter estimates that are statistically significant at 5% level of significance are X1 and X2. This can be determined by looking at the p-values in the table. The p-value for X1 is less than 0.05, which means that the parameter estimate for X1 is statistically significant.
Similarly, the p-value for X2 is less than 0.05, which means that the parameter estimate for X2 is statistically significant.
The 95% confidence interval for X2 can be calculated using the formula:
B ± t-value * SE(B)
where B is the parameter estimate for X2, t-value is 1.96 (for a 95% confidence interval), and SE(B) is the standard error of the parameter estimate for X2. From the table, the parameter estimate for X2 is 0.001 and the standard error is 0.001. Thus, the 95% confidence interval is:
0.001 ± 1.96 * 0.001 = (-0.001, 0.003)
This means that we can be 95% confident that the true value of the parameter estimate for X2 falls between -0.001 and 0.003.
To test whether the overall model is statistically significant, we use the F-test. The null hypothesis is that all the regression coefficients are zero (i.e., there is no linear relationship between the independent variables and the dependent variable).
The alternative hypothesis is that at least one of the regression coefficients is non-zero (i.e., there is a linear relationship between the independent variables and the dependent variable).
From the ANOVA table in the output, the F-statistic is 1.976 and the p-value is 0.104. Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the overall model is statistically significant.
The t-statistic for X3 can be calculated using the formula:
t = (B - 0) / SE(B)
where B is the parameter estimate for X3, and SE(B) is the standard error of the parameter estimate for X3. From the table, the parameter estimate for X3 is 0.095 and the standard error is 0.311. Thus, the t-statistic is:
t = (0.095 - 0) / 0.311 = 0.306
The R-squared of the model is 0.038, which means that only 3.8% of the variation in the dependent variable (Y) can be explained by the independent variables (X1, X2, X3, X4). This suggests that the fit is not very good, and there may be other factors that are influencing Y that are not captured by the model.
However, it is important to note that a low R-squared does not necessarily mean that the model is not useful or informative. It just means that there is a lot of unexplained variation in Y.
To know more about null hypothesis refer here:
https://brainly.com/question/28920252
#SPJ11
Problem 1 What is meant by the term 'Decision Analysis'? - Decision Analysis: The term decision analysis originated in 1964 by ROnald A. Howard, professor of Management Science and Engineering at Stanford University. - The objective of a decision analysis is to choose the most advantageous alternative from various alternative solutions of decision problems. - Decision analysis is systematic, quantitative and visual approach to addressing and evaluating important choices confronted by businesses. - Systematic approach means creating a constructive environment, investigating the situation, generating good solutions or alternatives, choosing the best solution and taking action. - Quantitative approach means to convert the problem into a mathematical model or formula to find the best solution. By using common quantitative tools. Decision tree, payback analysis and simulation. - Visual approach means to convert the problem into graphical charts to find the best solution.
Answers
Decision Analysis is a mathematical method for making decisions in uncertain environment.
What is environment ?
Environment refers to the surrounding conditions, resources and factors that can have an impact on an organism, community, or system. This can include physical factors such as weather, terrain, and pollution, as well as biological factors such as other living organisms, and social or economic factors such as culture, laws and economic conditions.
The process of Decision Analysis can be broken down into several steps:
1) Define the decision problem: Clearly state the problem and the decision maker's objectives.
2) Identify the decision alternatives: List all the feasible options available to the decision maker.
3) Specify the probability distribution of the uncertain parameters: Assign probabilities to the possible outcomes of the uncertain parameters.
4) Evaluate the expected value or expected loss for each alternative: Compute the expected value or expected loss for each alternative, using the probability distribution of the uncertain parameters.
5) Choose the alternative with the highest expected value or the lowest expected loss: Select the alternative that maximizes the expected value or minimizes the expected loss.
6) Sensitivity analysis: Check the robustness of the decision by studying the effect of small changes in the model's assumptions.
Decision Analysis is a mathematical method for making decisions in uncertain environment.
To learn more about environment visit : brainly.com/question/13107711
#SPJ4
text
Calibri
11
BIVA
co
WM
There are many different ways to write down an equation for a line like the one in the problem. Does
y-3/x-6=2represent the line? What about y-6/x-6=5What about y+5/x-1=2? Explain your reasoning
1.
2.
3.
Answers
Thislink has the answer: https://brainly.com/question/19701013?answering=true&answeringSource=greatJob%2FquestionPage%2F3
Answer:
Step-by-step explanation:
I need an answer for both of these
Answers
Answer:
1. x < -2
2. x < -9
Step-by-step explanation:
1. x + 15 < 13
Minus 15 on both sides.
x + 15 - 15 < 13 - 15
+15 - 15 makes a 0.
x < -2
2. x + 11 < 2
Minus 11 on both sides.
x + 11 - 11 < 2 - 11
+11 - 11 makes a 0.
x < -9
Answer:
1. x < -2
2. x < -9
3. x < 15
Step-by-step explanation:
Treat the < and > symbols as an equals sign to make it less confusing to solve. Then solve for x like you normally would.
1. x+ 15 = 13
subtract 15 from both sides
x=-2, or x < -2
2. x + 11 = 2
Subtract 11 from both sides.
x=-9, or x <-9
3. 19 > x + 4
19 = x + 4
Subtract 4.
15 > x, or x < 15
please help this one doesnt nee and explantion
Answers
Answer:
C.
Step-by-step explanation:
$159.99 × 0.25 is the amount of money she saved buying the CD player
Find the value of x in the triangle at 36° x° x° the right.
Answers
The required measure of the angle x is 72° in the triangle.
Given that,
The value of x in the triangle at 36°, x°, and x° is to be determined.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
For the triangle sum of the internal angle is 180°,
36 + x + x = 180
2x = 144
x = 72°
Thus, the required measure of the angle x is 72° in the triangle.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
Corporate triple a bond interest rates for 12 consecutive months are as follows:
9.6
9.2
9.3
9.7
9.8
9.7
9.7
10.6
9.9
9.6
9.4
9.7
if required, round your answer to two decimal places.
develop three-month and four-month moving averages for this time series. if required, round your answers to two decimal places.
enter the mean square errors for the three-month and four-month moving average forecasts. if needed, round your answer to three decimal digits.
what is the moving average forecast for the next month?
Answers
The mean square errors for the three-month and four-month moving average forecasts shown below.
What is mean square errors?How closely a regression line resembles a set of data points is determined by the Mean Squared Error. It is a risk function that corresponds to the squared error loss's expected value. The average, more particularly the mean, of errors squared from data related to a function is used to determine mean square error.
Given:
According to the Given data we construct a table as
Month Sales 3- month 4- month 3- month 4- month
moving moving squared squared
averages averages error error
1 9.6
2 9.2
3 9.3
4 9.2 9.367 0.111
5 9.2 9.400 9.450 0.160 0.123
6 9.2 9.500 9.500 0.010 0.140
7 9.2 9.733 9.625 0.001 0.006
8 9.2 9.733 9.725 0.751 0.776
9 9.2 10.000 9.950 0.010 0.002
10 9.2 10.067 9.975 0.218 0.141
11 9.2 10.033 9.950 0.401 0.322
12 9.2 9.633 9.975 0.004 0.031
13 9.567 9.650
MSE 0.185 0.176
Learn more about mean square errors here:
https://brainly.com/question/29662026
#SPJ4
Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answers
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.
On the cross country team, 7th graders are required to run x number of miles each morning. 8th graders are required to run 15% more then 7th graders which expression represents the number of miles an 8th grader has to run (ALSO I AM NOT A HIGH SCHOOLER IM IN 7TH GRADE )
Answers
Answer:
Step-by-step explanation:
7g = x miles
7 grade is x miles
8g = 7g + 15%
8 grad is 15% more than 7 grade
put what 7g is equal to into the 8g equation
8g = x + 15%
The expression represents the no. of miles an 8th grader
has to run 1.15x miles.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, 7th graders are required to run x number of miles, 8th graders are required to run 15% more than 7th graders.
∴ The expression represents the no. of miles an 8th grader has to run is,
= [ x + (15/100)x ] miles.
= x + 0.15x miles.
= 1.15x miles.
learn more about percentages here :
https://brainly.com/question/24159063
#SPJ2
which value is a solutions of 7/4x^2 -2 = 0.5 x+4
Answers
Answer:
x= 2 x= -1 5/7
Step-by-step explanation:
I believe this is the answer I used a math site.
PLEASE HELP URGENT!! DONT LINK FILES!!! HELP!!
The face of triangular-shaped guitar has an area of 52 square inches and the height of 13 inches. What is the length
of the guitar?
Answers
Answer:
Base = 8
Step-by-step explanation:
Area of a triangle can be calculated as:
Area = 0.5 x Base x Height
The values of the area and the height are given in order to find the length.
A= 52 in^2
Height= 13
First we have to find the base or the length. Using the values above we can set up the equation as:
1. 52= (0.5)(13)(b)
2. 52/0.5(13)
3. b=8
Answer: The length of the guitar or the base would be 8 inches.
I hope this helps and for future problems regarding this topic use the formula above!!
Formula: 0.5 x Base x Height
Please help me I need to finish this :)
Answers
You inherit RM300,000 from your parents and want to use the money to supplement your retirement. You receive the money on your 65 th birthday, the day you retire. You want to withdraw equal amounts at the end of each of the next 20 years. What constant amount can you withdraw each year and have nothing remaining at the end of 20 years if you are earning 7% interest per year?
A. RM15,000
B. RM28,318
C. RM33,574
D. RM39,113
Answers
To determine the constant amount that can be withdrawn each year for 20 years, we need to calculate the annuity payment using the present value of an annuity formula.
Inherited amount: RM300,000
Interest rate: 7% per year
Number of years: 20
Using the present value of an annuity formula:
PV = P * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value (inherited amount)
P = Annuity payment (constant amount to be withdrawn each year)
r = Interest rate per period (7% or 0.07)
n = Number of periods (20 years)
Plugging in the values:
300,000 = P * [(1 - (1 + 0.07)^(-20)) / 0.07]
Solving this equation, we find that the constant amount that can be withdrawn each year is approximately RM15,000.
Therefore, the correct answer is A. RM15,000.
To know more about interest click here: brainly.com/question/30393144
#SPJ11