ACTIVITY 2 Nomusa is a 65-year-old female educator who carned a gross income of R28 500 per month. A monthly deduction of 7,5% was made from her salary and paid into her pension fund. Use the 2019/2020 Income Tax table below to answer the questions that follow. TAX RATES FOR 2019/2020 TAX YEAR (1 March 2019 to 28 February 2020) TAX BRACKET TAXABLE INCOMET RATES OF TAX(R) 195 850 195 851 305 851 555 601 708 311 se 305 850 423 300 $$$ 600 708 310 1 500 000 1 500 001 and above TAX REBATES 2.1 Define the term gross salary. 2.2 Main member First dependant Each additional dependant U102/2023 Test 4 18% of taxable income 35 253 26% of taxable income above 195 850 63 853 +31% of taxable income above 305 850 100 263 + 36% of taxable income above 423 300 147 891 +39% of taxable income above 555 600 207 448 +41% of taxable income above 708 310 532 041 +45% of taxable income above 1 500 000 TAX THRESHOLD R79 000 R122 300 R14 220 R7 794 Primary Secondary (65 and older) Tertiary (75 and older) R2 601 R136 750 MEDICAL TAX CREDIT PER MONTH FOR MEDICAL FUND MEMBERS R310 R310 R209 What is the maximum taxable income for bracket 4 SOURCE: www.ars.g. 2.3 Determine Nomusa's monthly taxable income. 2.4 Identify the tax bracket Nomusa falls in based on his annual taxable income Marks 2.3 Calculate Nomusa's monthly tax in the 2019/2020 tax year. 2.6 Nomusa stated that if she were 10 years younger, she would have paid RS 502.34 monthly tax. Show with calculations whether Nomusa's statement is valid. 2.7 Nomusa is considering joining a medical fund. She plans to include his husband and two grandchildren. Determine the total monthly medical credits she would qualify for if she joined a medical 2.8 Nomusa's brother, who is 45 years old, earned a monthly taxable income of R45 980,17 during the 2019/2020 tax year. He is not a member of any medical scheme. Show, using calculations, that his monthly tax was R11 024,11 TOTAL (5) (3) 1307 Page c,z of 78
Nomusa's statement is not valid because her monthly tax is not equal to R502.34.
What do you mean by medical fund?A medical fund is a type of financial arrangement that individuals, families, or organizations set up to pay for medical expenses. The purpose of a medical fund is to help cover the cost of medical treatments, procedures, or medications that may not be covered by insurance. There are different types of medical funds, including personal savings accounts, health savings accounts (HSAs), flexible spending accounts (FSAs), and crowdfunding platforms that allow people to raise money for medical expenses. These funds can be used to pay for a variety of medical expenses, including doctor visits, surgeries, prescription drugs, and medical equipment. The goal of a medical fund is to provide individuals and families with a source of financial support for medical expenses, and to help reduce the financial burden associated with medical care.
Gross salary is the total amount of money earned by an individual before any deductions or taxes have been taken out.
2.3 Nomusa's monthly taxable income can be determined as follows: Gross salary = R28 500; 7.5% pension deduction = R28 500 x 7.5% = R2,137.5; Monthly taxable income = Gross salary - pension deduction = R28 500 - R2,137.5 = R26,362.5
2.4 Based on Nomusa's annual taxable income of R26,362.5 x 12 = R316,350, she falls in tax bracket 4, with a taxable income between R305,850 and R423,300.
2.5 Nomusa's monthly tax can be calculated as follows: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R316,350 - R195,850) = 26% x R120,500 = R31,230; Total tax = R35,253 + R31,230 = R66,483; Monthly tax = Total tax ÷ 12 = R66,483 ÷ 12 = R5,540.25.
2.6 To determine whether Nomusa's statement is valid, we would have to calculate her monthly tax if she were 10 years younger, and compare it to the stated amount of R502.34: If she were 10 years younger, she would not be eligible for the secondary tax threshold, so her monthly tax would be the same as calculated in 2.5: R5,540.25. This amount is not equal to R502.34, so Nomusa's statement is not valid.
2.7 If Nomusa joins a medical fund and includes her husband and two grandchildren, she would qualify for the following monthly medical credits: For herself: R310; For her husband: R310; For each grandchild: R209; Total monthly medical credit = R310 + R310 + 2 x R209 = R936.
2.8 To calculate Nomusa's brother's monthly tax, we can use the same process as in 2.5: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R45,980.17 - R195,850) = 26% x (R26,129.17) = R6,792.19; Total tax = R35,253 + R6,792.19 = R42,045.19; Monthly tax = Total tax ÷ 12 = R42,045.19 ÷ 12 = R3,503.77, which is approximately R11,024.11.
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In a group of 59 traders 26 sell gari 8 sell only rice 15 sell only maize 10 sell gari and rice 16 sell rice and maize and 42 sell maize.each trader sell at least one of the three items.find the number if traders who sell
A.gari or maize
B.gari and maize
C.only two food items
The number of vendors selling maize or gari Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. 16 sell wheat and maize, 10 sale gari and rice, 42 sell maize, and 6 sell gari.
How is math used in trading?To assess the trading strategies used by traders to complete a trade transaction, mathematical analysis is employed. Moreover, probability theory is used to evaluate the usefulness of money management strategies.
Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. Ten sell rice and gari, sixteen sell rice and maize, and forty-two sell maize.
Determine the quantity of dealers selling gari of corn using the formula below:
P(G ∪ R ∪ M) = P(G) + P(R) + P(M) - P(G ∩ R) - P(R ∩ M) - P(G ∩ M) + P(G ∩ R ∩ M)
59 = 26 + 8 + 15 - 10 - 16 - P(G ∩ M) + 42
59 - 42 = 49 - 26 - P(G ∩ M)
P(G ∩ M) = - 17 + 23
P(G ∩ M) = 6
Hence, there are 6 dealers selling gari or corn.
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I don’t understand this question. Can you help me?
Answer:
0.5
Step-by-step explanation:
The two figures are similar
find the linear scale factor of the two figures
=L/l ......... 10/4
=2.5
use the linear scale factor to find the other side
2.5= 5/n
2.5n=5 divide both sides by 2.5
n=0.5
The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 39 liters, and standard deviation of 5.2 liters.
A) What is the probability that daily production is less than 27.6 liters? Use technology (not tables) to get your probability.
Answer=
(Round your answer to 4 decimal places.)
B) What is the probability that daily production is more than 49.4 liters? Use technology (not tables) to get your probability.
Answer=
(Round your answer to 4 decimal places.)
Warning: Do not use the Z Normal Tables...they may not be accurate enough since WAMAP may look for more accuracy than comes from the table.
a)The probability that daily production is less than 27.6 liters is given by the equation P ( x < 27.6 ) = 0.014179
b) The probability that daily production is more than 49.4 liters is given by the equation P ( x > 49.4 ) = 0.02275
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that daily production is less than 27.6 liters be represented as P
Now , the equation will be
a)
The observed value of x = 27.6 L
The mean of the sample μ = 39 L
The standard deviation of the sample σ = 5.2 L
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 27.6 - 39 ) / 5.2
z = -2.19231
Now ,the p value from the z table is
P ( x < 27.6 ) = 0.014179
And , the probability is P ( x < 27.6 ) = 0.014179 = 1.418 %
Therefore , the probability that daily production is less than 27.6 liters is given by P = 1.418 %
b)
The observed value of x = 49.4 L
The mean of the sample μ = 39 L
The standard deviation of the sample σ = 5.2 L
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 49.4 - 39 ) / 5.2
z = 2
Now ,the p value from the z table is
P ( x < 49.4 ) = 0.97725
P ( x > 49.4 ) = 1 - P( x < 49.4 ) = 0.02275
And , the probability is P ( x > 49.4 ) = 0.02275 = 2.275 %
Therefore , the probability that daily production is more than 49.4 liters is given by P₁ = 2.275 %
Hence , the probabilities are solved
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A cup of coffee initially at 100°C cools to 80°C in 5 minutes while sitting in a room at constant temperature
28°C. What will be the temperature T of the coffee after 10 minutes?
The equation of line is y = -4x + 100 and the temperature of the coffee after 10 minutes is given by A = 60°C
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the temperature be represented as y
Let the number of minutes be represented as x
Now , the initial temperature is 100°C
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 100 )
Let the second point be Q ( 5 , 80 )
Now , the slope of the line between the points is ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 100 - 80 ) / ( 0 - 5 )
Slope m = 20 / -5
Slope m = -4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 100 = -4 ( x - 0 )
y - 100 = -4x
Adding 100 on both sides of the equation , we get
y = -4x + 100
Now , when x = 10 minutes ,
y = -4 ( 10 ) + 100
y = -40 + 100
y = 60°C
Hence , the equation is solved and temperature after 10 minutes is 60°C
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Each equation below is a characteristic equation for a recurrence relation. Express the solution to each recurrence relation as a linear combination of terms. Note that you will not know the actual coefficients in the linear combination since you are not given the base cases, so you can use a1, a2, etc.
(a) (x − 1)(x + 2) = 0
(b) (x − 4)(x − 4) = 0
(c) (x − 4)(x − 4)(x + 5) = 0
(d) (x − 4)(x − 4)(x + 5)^4 = 0
The solutions to each recurrence relation can be expressed as a linear combination of terms:
The general solution to the recurrence relation can be written as a1 * 1^n + a2 * (-2)^n.The general solution to the recurrence relation can be written as a1 * 4^n.The general solution to the recurrence relation can be written as a1 * 4^n + a2 * 4^n + a3 * (-5)^n.The general solution to the recurrence relation can be written as a1 * 4^n + a2 * 4^n + a3 * (a root of (x + 5)^4)^n.For (a) The solution to (x - 1)(x + 2) = 0 is
x = 1 and x = -2.For (b) The solution to (x - 4)(x - 4) = 0 is
x = 4.For (c) The solution to (x - 4)(x - 4)(x + 5) = 0 is
x = 4, x = 4, and x = -5.For (d) The solution to (x - 4)(x - 4)(x + 5)^4 = 0 is
x = 4, x = 4, and the 4 roots of (x + 5)^4 = 0.These linear combinations of terms can be used to describe the general solution to each recurrence relation, but the actual coefficients in the linear combination are not given and depend on the base cases of the recurrence relation.
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For a distribution that is skewed left, which of the following is true?
Choose the correct answer below.
a. mean
b. mean = median
c. mean> median
When a distribution is tilted to the left, the correct response is "mean median".
What is mean?The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey. The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean.
Here,
For a distribution that is skewed left, it means that the values tend to be clustered towards the lower end of the scale and there is a long tail towards the higher end. In such a distribution, the mean is usually lower than the median.
So, the correct answer is "mean < median" when a distribution that is skewed left.
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Rose's Botanical Garden produced flowers throughout the year. A graph demonstrating how many flowers she produced over a 10-month period is shown:
A graph of a curve with x axis labeled Months and y axis labeled Number of Flowers Produced. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 60 in increments of 10. The curve starts at about 1 comma 22 and goes up to 6 comma 60 at the highest point and ends at about 10 comma 36.
What can be interpreted from the domain of this graph?
The domain represents the total number of flowers produced each month.
The domain represents the total number of flowers produced in 10 months.
The domain represents a 120-month period of flower production.
The domain represents a 10-month period of flower production.
The domain of the graphed function is interpret as follows:
The domain represents a 10-month period of flower production.
How to obtain the domain of the function?The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.
The input variable, represented by the x-axis, is defined as follows:
Number of Months.
Hence the correct option is given by the fourth option, as x ranges from 0 to 10.
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Which number sentence is true?
A. 82 < |-82|
B. |-82| < |-83|
C. |-83| < |83|
D. |82| > |-83|
the sum of two consecutive integers 157. What is the product of these integers.
The sum of two consecutive integers 157 can be found by using the formula: x + (x + 1) = 157, where x represents the first integer.
Solving for x:
x + (x + 1) = 157
2x + 1 = 157
2x = 156
x = 78
So, the two consecutive integers are 78 and 79. The product of these integers is 78 * 79 = 6162.
Answer:
6162.
Step-by-step explanation:
Let's call the two consecutive integers x and x + 1. We know that their sum is 157, so we can write an equation:
x + (x + 1) = 157
Expanding and solving for x:
2x + 1 = 157
2x = 156
x = 78
So, the two consecutive integers are 78 and 79. The product of these integers is 78 * 79 = 6162.
A package contains II resistors, 2 of which are defective. If5 are selected, find the probability of getting the following results. Enter your answers as fractions or as decimals rounded to 3 decimal places. 0 defective resistors P (0 defective) = 3/11 I defective resistor P (l defective) = 252/462 2 defective resistors P(2 defective) =
If a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting
a) 0 defective resistors: 0.3164
b) 1 defective resistor: 0.4219
c) 3 defective resistor: 0.0469
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
Probability
First step is to calculate the probability for a defective resistor and non-defective resistor:
Probability=3/12
Probability =0.25
Non-defective resistor:
Probability=(1-0.25)
Probability=0.75
Now let find the probabilities for defective resistors from 0 to 3
P(0)=1(0.75)^4 ×(0.25)^0
P(0)=0.3164
P(1)=4(0.75)^3× (0.25)^1
P(1)=0.4219
P(2)=6(0.75)^2× (0.25)^2
P(2)=0.2109
P(3)=4(0.75)^0×(0.25)^3
P(3)=0.0469
P(4)=1(0.75)^0 × (0.25)^4
P(4)=0.0039
Hence,
a. P(0)=0.3164
b. P(1)=0.4219
c. P(3)=0.0469
Therefore If a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting 0 defective resistors: 0.3164, 1 defective resistor: 0.4219, 3 defective resistor: 0.0469.
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Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Part A: Estimate the IQR for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Part D: Provide a possible reason for the outlier in the data set. (2 points)
Answer:
Part A: The Interquartile Range for the males' data is estimated to be around 24-28.
Part B: The difference between the median values of the two data sets is estimated to be around 16.
Part C: Both the male and female data sets appear to follow a normal distribution. Due to the outlier present in the male data set, the mean would not be the best measure of center for this data set. Instead, the median would be a more appropriate measure of center for both data sets.
Part D: The possible reason for the outlier in the data set could be that the movie was more popular among male viewers on the day they chose to attend than it was among female viewers.
9. Find b so that the vectors v=5i +2j and w=4i+b are orthogonal.
Answer:
b = -10
Step-by-step explanation:
Two vectors are orthogonal if and only if their dot product is zero. The dot product of v and w is given by:
(v · w) = (5i + 2j) · (4i + bj) = 5 * 4 + 2 * b = 20 + 2b.
For v and w to be orthogonal, we need the dot product to be zero, which means 20 + 2b = 0, so:
2b = -20
b = -10
Therefore, b = -10 makes the vectors v and w orthogonal.
Spiral Review Complete the table representing a linear function.
Complete the table representing a linear function with y = 10 and x = 9
How to complete the table representing a linear function?The general form of a linear function is:
y = mx + c,
where m is the slope and c is the y-intercept
slope(m) = (y2-y1)/(x2-x1)
From the table:
point 1: x1 = 1, y1 = 0
point 2: x2 = 5, y2 = 40
slope(m) = (40-0)/(5-1) = 40/4 = 10
For the missing points:
x1 = 1, y1 = 0 and x2 = 2, y2 = y (unknown)
m = (y2-y1)/(x2-x1)
10 = (y-0)/(2-1)
10 = y/1
y = 10
x1 = 1, y1 = 0 and x2 = x (unknown), y2 =90
m = (y2-y1)/(x2-x1)
10 = (90-0)/(x-0)
10 = 90/x
10x = 90
x = 90/10
x = 9
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convert to slope intercept form
: x- 2y=-6
Answer:
x-2y =6
x-2y =6
= 6-2y=x=4
translate: four times the difference of a number and 11
Answer:
Step-by-step explanation:
4(x+11)
You might have noticed that the numbers, or frequencies, on an old radio dial are not evenly spaced. There is, however, some pattern to the placement of these frequencies. You will analyze this data and answer the following questions.
Frequency reading on the radio dial (kilohertz)
distance from the left end of the radio dial (centimeters)
53
1.54
60
2.17
70
2.95
80
3.62
100
4.75
120
5.67
140
6.45
170
7.43
1. a. What is the independent variable and what are its units?
b. What is the dependent variable and what are its units?
2. Make a scatter plot of the data. Describe the data set based on the scatter plot.
b. What do you expect to happen to the distance from the left end of the radio as the frequency gets higher?
c. What do you expect to happen to the distance from the left end of the radio as the frequency gets smaller?
The independent variable is distance from the left end of the radio dial and its unit is centimeters.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
The given coordinate points are (53, 1.54), (60, 2.17), (70, 2.95), (80, 3.62), (100, 4.75)
Here,
1.a) The independent variable is distance from the left end of the radio dial and its unit is centimeters.
b) The dependent variable is frequency and its units is kilohertz.
2. a) A scatter plot of the data is given below in the attachment.
b) The distance from the left end of the radio as the frequency gets higher is increases.
c) The distance from the left end of the radio as the frequency gets smaller is decreases.
Therefore, the independent variable is distance from the left end of the radio dial and its unit is centimeters.
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Which of the answers is equal to sec(x)? *
O 1/cot(x)
O 1/sin(x)
O 1/cos(x)
O 1/csc(x)
The answer choice which is equivalent to sec (x) among the given answer choices is; 1 / cos(x).
Which answer choice is equal to sec (x)?It follows from the task content that the answer choice which is equivalent to sec (x) is to be determined among the given answer choices.
From trigonometric ratios concept, it follows that the inverses of the 3 basic trigonometric ratios are as follows;
1 / sin x = csc (x)
1 / cos x = sec (x)
1 / tan x = cot (x)
On this note, it follows that the answer choice which is equivalent to sec (x) is; 1 / cos x.
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which of the following will cause ordinary least square (ols) estimates of a simple regression model, y = β0 + β1x + u to be biased?
Answer:
There are several factors that can cause ordinary least square (OLS) estimates of a simple regression model, y = β0 + β1x + u, to be biased:
1. Non-random sampling: If the sample used in the regression analysis is not random, then the OLS estimates may be biased. For example, if the sample only includes people who live in a specific area or only those who are a certain age, then the estimates will not be representative of the population as a whole.
2. Endogeneity: If one of the independent variables in the model is correlated with the error term, then the OLS estimates will be biased. This occurs when there is a omitted variable that is related to both the dependent variable and one of the independent variables.
3. Multicollinearity: When two or more independent variables in the model are highly correlated with each other, it can cause the OLS estimates to be biased. This occurs because the estimates become unstable when the variables are highly correlated.
4. Non-constant variance: If the variance of the errors in the model is not constant, then the OLS estimates will be biased. This occurs when the errors are not homoscedastic.
5. Specification error: If the wrong variables are included or excluded from the model, then the OLS estimates will be biased. This occurs when the model is misspecified.
Factor 8y2 + 6y + 1
and check.
The factorization of the given quadratic equation by grouping is (2y + 1) (4y + 1)
Factorization of quadratic equation by grouping.
Factorization is a method of finding factors for any quadratic expression, polynomial, or algebraic expression.
For a polynomial of the form ax^2 + bx + c, rewrite the middle term as a sum of two terms whose product is a×c = 8 × 1 = 8 and whose sum is b = 6.
Given that:
8y² + 6y + 1
8y² + 2y + 4y + 1
Factor out the greatest common factor from each group.
2y(4y + 1) + 1(4y + 1)
(2y + 1) (4y + 1)
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How long will it take for a sum of money to quadruple at 10% compounded annually?
Answer:
Below
Step-by-step explanation:
For compounding annually , the formula would be
4x = x ( 1+ .1)^n x = deposit amount 4x = quadrupled
i = decimal interest (.10) and n = years
you can divide 'x' out of the equation to get :
4 = (1.1)^n solve for 'n' by taking LOG of both sides
log 4 = n log 1.1
log 4/log 1.1 = n = 14.54 years - ~~ 15 years
find the length of the leg x. Enter the exact value, not decimal approximation
the value of x is 16.97
Given that:
The right angled triangle has hypotenuse of 18 units
Its one other side measures 6 units.
The length of unknown side is denoted by length x units.
To find:
Value of x
The Pythagoras theorem states that:
"In a right angled triangle, the square of length of its hypotenuse is equal to sum of square of other two sides' lengths"
Using Pythagoras theorem for given right triangle we have:
Thus, for given right triangle, the value of x is given as:
18²=[tex]x^{2} +[/tex]6²
324=[tex]x^{2}[/tex]+36
[tex]x^{2}[/tex]=324-36
[tex]x^{2}[/tex]=288
[tex]x[/tex]=√288
[tex]x[/tex]=16.97
the value of x is 16.97
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June says that there should be a decimal
point in the quotient below after the 4.
Is she correct? Use number sense to
explain your answer.
43.94 5.2 = 845
Using the arithmetic operation of division, the value for expression 43.94 ÷ 5.2 is 8.45 where decimal point is before 4 and after 8.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The expression is given as - 43.94 ÷ 5.2
Use the arithmetic operation of division -
43.94 / 5.2
Remove the decimal point by multiplying the numerator and denominator by 100.
(43.94 × 100) / (5.2 × 100)
4394 / 520
Now perform the operation of division -
4394 / 520 = 8.45
June says the decimal point should be after 4.
She is incorrect as the result shows that the decimal point is before 4.
Therefore, June is incorrect in her statement.
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3/8 of students in a class have iPhones. The remaining students in the class have Samsung phones. If there are 6 more Samsung phones than iPhones, how many iPhones are there in the class?
Step-by-step explanation:
what is the total number of students in the class?
Anita attends a private school where she must wear a uniform. This year, the price of the uniform is $86.80, which is 9.6% more than it cost last year. How much were uniforms last year?
Round your answer to the nearest cent.
Answer:
Below
Step-by-step explanation:
x = price last year
x * .096 = price increase (.096 is 9.6% in decimal form)
price THIS year is x + x * .096
= 1.096 x
so:
86.80 = 1.096 x divide both sides of the equation by 1.096
79.20 = x = original price
The surface area of a prism is 54 square inches. What is the surface area of a similar prism that is smaller by a scale of 1/3? Help!!!
Answer:
18 Square inches
Step-by-step explanation:
Surface Area of original prism: 54 square inches
Surface Area of similar prism:
1/3 x 54
=18 square inches
Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.
The density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]
The density function of [tex]U = Y1^2 +Y2^2[/tex] is given by the formula [tex]f_U(u) = (1/2π)∫_0^∞ f_Y1(y_1)f_Y2(√(u-y_1^2)) dy_1[/tex]. This can be calculated as follows:
Let u ≥ 0, then
[tex]f_U(u) = (1/2π)∫_0^∞ (1/√(2π))e^(-(y_1^2/2))(1/√(2π))e^(-(√(u-y_1^2)^2/2)) dy_1[/tex]
[tex]= (1/2π)∫_0^∞ (1/2π)e^(-u/2) dy_1= (1/2π)e^(-u/2) ∫_0^∞ (1/2π) dy_1= (1/2π)e^(-u/2)[/tex]
Therefore, the density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]
Learn more about function here:
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if a runner starts at rest and reaches a speed of 20 m/s in 2 second. what is the acceleration?
Answer:
initial speed (u)= 0m/s (at rest)
final speed (v)= 20m/s
time taken (t)= 2seconds
we have,
acceleration;a= (v-u)/t
=(20-0)/2
=10m/s²
Answer:
[tex]10\frac{m}{s^{2}}[/tex]
Step-by-step explanation:
Let u = Initial speed [tex](\frac{m}{s})[/tex]
v = Final speed [tex](\frac{m}{s})[/tex]
t = time (seconds)
a = Acceleration
According to this question:
[tex]u= 0 \frac{m}{s}[/tex] (i.e starts at rest)
[tex]v = 20 \frac{m}{s}[/tex]
[tex]t = 20s[/tex]
a = ?
[tex]a = \frac{v - u}{t}[/tex]
= [tex]\frac{20 \frac{m}{s} - 0\frac{m}{s}}{2s}[/tex]
= [tex]\frac{20\frac{m}{s}}{2s}[/tex]
Acceleration= [tex]10\frac{m}{s^{2} }[/tex]
Please help a brothra out
L line
-2
-1
-15.5
-3.5
grph
A case of vegetable costs $10.68. He can spend at most $50 for this project. what is the maximum amount of cases of vegetables he can buy
Answer:
4
Step-by-step explanation:
The maximum number of cases of vegetables that he can buy can be calculated by dividing the maximum budget of $50 by the cost of a single case of vegetables, which is $10.68:
$50 ÷ $10.68 = 4.67 cases
Since you can't buy fractional cases, the maximum number of cases he can buy would be 4. Round down to the nearest whole number, the maximum number of cases he can buy is 4.