Elementary row operations are always applied to an augmented matrix after the solution has been found. So the option D is correct.
Elementary row operations:
1. It is possible to convert a system of linear equations into an equivalent system, or into a new system of equations that has the same solutions as the original system, using these straightforward techniques.
2. In order to convert a matrix to row echelon form, Gaussian elimination is used.
3. Simple row operations on an augmented matrix never alter the underlying linear system's solution set.
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What is the perimeter of a rectengular park that measure 20 1/4 yards by 32 5/8
The perimeter of the rectangular park is 423/4 units.
What precisely is a perimeter?The lengths of a shape's edges and sides are added to find its perimeter.
The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. That shape's perimeter is equal to the side lengths added together algebraically.
The perimeter of a shape is equal to the length of its boundary or whole circumference. The perimeter of a closed 2D form is the product of its sides.
Given : Length = 20 1/4
= 81/4
Width = 32 5/8
= 261/8
So, Perimeter = 2 ( L + B)
= 2 ( 81/4 + 261/8)
= 2 ( 423/8)
= 423/4 units.
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You are single and your gross pay for this week is $710. Using the
percentage method of withholding, what amount will you pay in federal
income tax if you claim 3 allowances. Each weekly allowance is $80.80.
(Use percentage method.)
The amount that you would have to pay in federal income tax if you claim 3 allowances would be: $65.46
How to solve for the claimable amountTo calculate the amount you will pay in federal income tax using the percentage method of withholding, you will need to know the withholding percentage for your gross pay and the number of allowances you are claiming.
If you claim 3 allowances, each allowance is $80.80, and you gross pay for the week is $710, your taxable income is:
$710 - 3*$80.8 = $710 - $242.4 = $467.6
To find the amount of federal income tax you will pay, you will need to use the withholding percentage for your taxable income. You can find this information by consulting the IRS Circular E (Employer's Tax Guide) or by using an online withholding calculator.
If we use the IRS Circular E, we can find that if you are single and claim 3 allowances, the withholding percentage for a taxable income of $467.6 is 14%.
So the amount you will pay in federal income tax is:
$467.6 * 14% = $65.46
Therefore, you will pay $65.46 in federal income tax if you claim 3 allowances, and your gross pay for the week is $710.
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xplain in words and write mathematically how the fundamental theorem of calculus is used to evaluate definite integrals.
Need help with question attached below in an image.
Average rate of change for the first 10 minutes after the soup was placed in the bowl is 200 .
How can I determine the graph's average rate of change?To get the slope of a graphed function, use the average rate of change formula. Divide the y-value change by the x-value change to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.Measure the temperature change every hour and compute the average rate of change. In order to achieve that, we calculate the temperature difference between 220 and 180 and divide it by the number of hours in that period.220 +180/2 = 200
average rate of change for the first 10 minutes after the soup was placed in the bowl 200.
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Which does not represent a way to show 3+3+3+3+3 with multiplication
The ways to represent 3+3+3+3+3 with multiplication are:
3 * 55*3What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, an expression 3+3+3+3+3
To represent this in multiplication terms,
We need to figure out what the expression tells us. So, there are 5 terms all terms have a value of 3.
Thus,
represent a way to show 3+3+3+3+3 with multiplication is either 3*5 or 5*3.
Therefore, The correct ways of representing the expression 3+3+3+3+3 are:
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Suppose that X and Y are integer valued random variables with joint probability mass function given by pX, Y(a, b) = {1/4a, for 1 > b > a > 4, otherwise. a. Show that this is indeed a joint probability mass function. b. Find the marginal probability mass function of X and Y. c. Find P(X = Y + 1).
The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.
To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:
PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:
PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.
P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12
So the probability that X is one more than Y is 5/12.
It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.
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Solve the initial value problem 2yy' + 3 = y^2 + 3x with y(0) = 9. 1. To solve this, we should use the substitution u = _____ With this substitution, y = _____
y' = _____
Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). 2. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. 3. The solution to the original initial value problem is described by the following equation in x, y.
The given initial value problem y(0)=8, solution is [tex]y=\sqrt{64e^x-3x}[/tex]
Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y. An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable is referred to as a differential equation in calculus (variables). The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. If y is a dependent variable, f is an unknown function, and x is an independent variable, then y=f(x) is a function.
The given differential equation is,
[tex]2yy'+3=y^2+3x\\\\2y\frac{dy}{dx}=y^2+3x-3\\\\(3-y^2-3x)dx+2ydy=0\\\\compare, Mdx+Ndy=0\\\\M=3-y^2-3x\\\\N=2y[/tex]
The given equation is not exact but if we multiplied by [tex]e^{-x}[/tex]
[tex]The D.E.\\(3-y^2-3x)e^{-x}dx+2ye^{-x}dy=0\\\\then M_y=-2ye^{-x}=N_x\\The G.S,=y^2e^{-x}+3xe^{-x}=c\\\\y(0)=8\\c=64\\hence,\\y=\sqrt{64e^x-3x}[/tex]
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you drop a rock into a deep well. you can't see the rock's impact at the bottom, but you hear it after 6 seconds. the depth of the well is 285.9 feet. ignore air resistance. the time that passes after you drop the rock has two components: the time it takes the rock to reach the bottom of the well, and the time that it takes the sound of the impact to travel back to you. assume the speed of sound is 1100 feet per second. note: after seconds the rock has reached a depth of feet where
There is a distance of 656.088 feet to the bottom of the well.
What is Speed?
Speed is the ratio between the distance an object travels and the time it takes to cover that distance.
Since speed just has magnitude and no direction, it is a scalar quantity.
Because the amount of time that passes after you drop the rock is made up of both the amount of time it takes for it to fall to the bottom of the hole and the amount of time it takes for the sound of the impact to reach you,
Let t be the moment when a rock was attained at depth d, which is the well's bottom.
And this is the moment when you hear the sound of impact.
t + t' = 7 seconds
⇒ t' = 7 - t
Speed = Distance / Time
1100 feet per second = d / t'
d = 1100 t
Also d = 16t²
1100 t' = 16t²
1100 (7 - t) = 16t²
7700 - 1100t = 16t²
16t² + 1100t - 7700 = 0
4t² + 275t - 1925 = 0
This is a quadratic equation.
Discriminant = √(b² - 4ac) = √[275² - (4 × 4 × -1925)] = 326.228
t = (-275 ± 326.228) / (2 × 4)
t = 6.404 or t = -75.15
t = -75.15 is not possible because it is negative and t + t' = 7 seconds.
So t = 6.404 seconds
t' = 7 - 6.404 = 0.596 seconds
d = 16 × (6.404)² = 656.088 feet
Hence the distance from the well to the bottom is 656.088 feet.
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Aaliyah and Yohance are having a competition to see who can read
more pages over the coming weekend. Aaliyah has bet Ms. Solomon that
she'll read 50 more pages than Yohance. Both scholars read at an
average rate of 40 pages per hour. Yohance says that he's going to read
for 7.5 hours this weekend. How many hours will Aaliyah need to read in
order to fulfill her promise of reading 50 more pages than Yohance?
According to the information, Aaliyah is going to need 8.75 hours to read 50 more pages than Yohance.
How to calculate how many hour will Aaliyah need to read?To calculate how many hours Aaliyah will beed to read, we have to perform the following mathematical procedure
First, we have to calculate how many pages Yohance is going to read this week, so if she is going to read during 7.5 hours we have to multiply the number of pages she read per hour by time (7.5 hours).
40 * 7.5 = 300So, Yohance is going to read 300 pages. Now if we want to know how many hours needs Aaliyah to read 50 more pages we have to perform the following operation:
300 + 50 = 350350 / 40 = 8.75According to the above, Aaliyah needs to read for 8.75 hours to complete 50 more pages than Yohance.
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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and
d are integers.
1. x² - 8x + 15 = (ax + b)(cx + d)
2. 2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
3.6x² + 14x + 4 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
b
a
1. 1
2. 1
3.
Submit
Pass
-5
1
C
1
2
d
Question ID: 504360
-6
Save an
150
The values of variables a to d are
a = 1 and c = 1, b = -3 and d = -5a = 1 and c = 1, b = 2 and d = -6a = 1, b = 2. c = 6 and d = 2How to determine the values of the variablesPolynomial 1
This is given as
x² - 8x + 15 = (ax + b)(cx + d)
The factors of 15 that add up to -8 are
-3 and -5
This means that
b = -3 and d = -5
Because the coefficient of x² is 1, then
a = 1 and c = 1
Polynomial 2
This is given as
2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
Divide through by 2x
x² - 4x - 12 = (ax + b)(cx + d)
The factors of -12 that add up to -4 are
2 and -6
This means that
b = 2 and d = -6
Because the coefficient of x² is 1, then
a = 1 and c = 1
Polynomial 3
This is given as
6x² + 14x + 4 = (ax + b)(cx + d)
Factorize
(x + 2)(6x + 2) = (ax + b)(cx + d)
By comparison, we have
a = 1, b = 2. c = 6 and d = 2
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Find median for average life of a particular brand of a T.V sets from the following data
life in years : 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
No. of sets : 2 16 26 39 43 21 8 4
The median for average life of a particular brand of a T.V sets from the following data is given as follows:
17.5.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
The total number of observations in this problem is given as follows:
2 + 16 + 26 + 39 + 43 + 21 + 8 + 4 = 159.
This is an odd cardinality, hence the median is found in the class when the counter hits:
(159 + 1)/2 = 80.
Which is the class 15-20, as 2 + 16 + 26 < 80 and 2 + 16 + 26 + 39 > 80, and the median value is given as follows:
(15 + 20)/2 = 17.5.
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Given f(x)=9/5 x + 32, find the folwing.
The inverse of the function as it has been written is f(x) = (x - 32) 5/9.
What is the inverse of the function?We know that the inverse of a function can easily be obtained as long as we have the function as we do in the question here. The function has been given to us as; f(x)=9/5 x + 32.
Let y = f(x)
Hence;
y=9/5 x + 32
y - 32 + 5/9 = x
We would then have the inverse of the function as;
f(x) = (x - 32) 5/9
This is the procedure that would help us to obtain the inverse of the function that have been given here.
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Missing parts;
Given f(x)=9/5 x + 32, find the following;
Inverse of the function
help for brainliested
Answer:
Jade will be farther by 0.6 or .6 miles in 3 hours
Step-by-step explanation:
Jade walks at a speed of 3 miles per hour so 3×3=9 miles per hour
Elena walks at a speed of 2.8 miles per hour so 2.8×3=8.4 miles per hour
Next,the question is how much farther will Jade walk after 3 hours so that means 9-8.4 which is 0.6 or .6 in decimals and we read it as six tenths
hope it helps you
a. suppose there are 10 lab sections of a statistics class that each have the same number of students enrolled. a class evaluation is about to be administered to some of the students. it has been decided to randomly select 4 of the 10 lab sections and give the evaluation to all the students in those sections.
The type of sampling design is used: simple random sample
The correct answer is an option (a)
We know that in data analysis, the sampling is nothing but the selecting the group or subset of the population to make statistical inferences.
The types of probability sampling are:
Simple random sampling, Systematic sampling, Stratified sampling and Cluster sampling.
In simple random sampling, the researcher randomly selects a subset of data from the population.
In Stratified random sampling, the population is divided into smaller subgroups called as strata.
In case of clustered random sampling, the population is divided into clusters, and then we randomly select some of these clusters as sample.
As we know multistage sampling is a type of cluster sampling.
Here, it has been decided to randomly select 4 of the 10 lab sections.
This means, simple random sampling design is used in given scenario.
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The complete question is:
a. suppose there are 10 lab sections of a statistics class that each have the same number of students enrolled. a class evaluation is about to be administered to some of the students. it has been decided to randomly select 4 of the 10 lab sections and give the evaluation to all the students in those sections. What type of sampleing design is used?
a) Simple random sample
b) Stratified random sample
c) Clustered random sample
d) Multistage sample
Please help me, I really need this so bad.
Answer:
slope = 1/2
Step-by-step explanation:
rise = 3
run = 6
rise/run
3/6 = 1/2
Answer:
The slope is 1/2
Step-by-step explanation:
The slope is rise over run, from point 1 to point 2 the line rises 3.
The run from point 1 to point 2 is 6.
That means that rise over run is 3/6
Simplify this so that it is in the simplest form to get 1/2.
The image shows the rise and the run.
I hope this helps you out :D
(12 - 31) + (7 + 31)
Find E(X) and Var(X) for a continuous random variable X with a pdf f(x) = 4x³,0 < x < 1.
Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E(X)=xP is the formula's notation (x).
How do you find ex and Var X?It is common to refer to the long-term average or mean (symbolized as ) as the expected value of a discrete random variable X, denoted by the symbol E(X). Thus, if you conducted an experiment again throughout time, you could anticipate this average result. If you toss three fair coins, for instance, let X be the number of heads you receive. The expected value of X is the average number of heads you would anticipate receiving after three fair coin tosses if you were to perform this experiment a significant number of times.f(x) = 4x³,0 < x < 1
Domain of f(x) = 4x³,0 < x < 1 : Solution : 0 < x < 1
Interval notation : (0,1)
Range of 4x³ ,0 < x < 1;
Solution : 0 < f(x) < 4
Interval Notation : (0,4)
Axis interception points of 4x³,0 <x <1.
Asymptotes of 4x³. 0 < x < 1;
Extreme Points of 4x³ . 0<x < 1:
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When lisa was born, her parents put 8000 into a college fund account
The initial deposit was $8000 and after 18 years the simple interest earned is $12960. So, the total amount for Melissa in college account is $20,960.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
The amount that was put in college fund for Melissa, P = $8000
The rate at which interest was earned is, R = 9%
The time period after which the account was checked, T = 18 years
The formula for Simple Interest is -
S.I. = (P R T)/100
Substitute the values into the equation -
S.I. = (P R T)/100
S.I. = (8000 × 9 × 18)/100
S.I. = 1296000/100
S.I. = 12960
The amount of interest earned in 18 years is $12960.
The total amount after 18 years will be -
Total Amount = Initial deposit + Interest earned
Total Amount = $8000 + $12960
Total Amount = $20960
Therefore, the total amount after 18 years is $ 20,960.
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When Melissa was born, her parents put $8,000 into a college fund account that earned 9% simple interest. After 18 years, she had $20,960 in the account. How did this happen?
Anything would be great!
The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:
C) Translation (x,y) -> (x + 7, y), and reflection over the x-axis.
What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The vertices of the original triangle are given as follows:
A(-3,-2), B(-6,-5) and C(-1,-4).
The vertices of the reflected triangle are given as follows:
A'(4,2), B'(1,5) and C'(6,4).
The composite rule for these two transformations is given as follows:
(x,y) -> (x + 7, -y).
The transformation y -> -y is a reflection over the x-axis, hence the correct option is given by option C.
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W तल दिइएका तथ्याङ्कको मध्यिका पत्ता लगाउनुहोस् । Find the median of the following data: 16, 15, 14, 18, 17, 20, 25 .00 16
Answer:
arrange in ascending order
14,15,16,17,18,20,25
there are odd number of terms so
median = (n+1/2) th observation
here n = 7 which is odd
therefore, 7+1/2 th observation
which is 4th observation
ans) 17
Simplify each expression by combining like terms
-9y-10y -2z
By Simplify expression -9y-10y -2z this we get - 19y - 2z.
What is the Simplify expression ?Expression simplification is a crucial skill to master if you want to comprehend algebra. We can convert a complicated expression into one that is more condensed and straightforward by simplifying it.When constants and variables are merged with the help of the operation symbols (+, -, x, and ), the result is an algebraic expression.The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible. There should be no more multiplying, dividing, adding, or subtracting to be done once everything is done.Examples :
-9y-10y -2z
Simplify
-9y - 10y - 2z : -19y - 2z
-9y - 10y - 2z
= - 19y - 2z.
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In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded. A regression line was generated and shown to be an appropriate description of the relationship. The results of the regression analysis are below. Depend Variable: Top Speed Variable Constant Weight Coefficient 107.58 0.8710 s.e. of Coeff 11.12 0.4146 t-ratio 9.67 2.10 prob 0.000 0.062 R squared = 30.6% R squared (adjusted) = 23.7% s = 10.42 with 12 - 2 = 10 degrees of freedom Part A: What is the LSRL based on the analysis provided? Make sure to identify what the variables represent in the context of the problem. (4 points) Part B: What is the predicted value for the top speed of a boat if its weight is 4 tons? Show your work.
Slope of regression is 0.8710 and at 4 tons top speed of boat is 111.064 mph.
What do you mean by linear regression?Linear regression is a data analysis technique that predicts the value of unknown data by using another related and known data value. It mathematically models the unknown or dependent variable and the known or independent variable as a linear equation.
Given, In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded.
Solution(a)
Given in the question
Dependent variable is top speed of a boat (in mph) Independent variable is weight of boat (in tons)
from the coefficient table of Enova summary we can write least square regression line as follows
Top speed = 107.58 +0.8710* Weight of boat
Here intercept of regression line = 107.58
Slope of regression line = 0.8710
Solution(b)
if X = 4 tons
than predictive value of the top speed of a boat can be calculated as
Top speed = 107.58 +0.8710 * 4 = 107.58 +3.484 = 111.064 mph predictive value of the top speed of a boat = 111.064 mph if its weigh It is 4 tons.
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Complete question:
a meter is about 1 1/10 yards about how many meters long is an automobile
The number of yards of the automobile of length 'x' meters will be 1.10x yeads.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
A meter is about 1 ¹/₁₀ yards.
Convert the mixed fraction number to a decimal number. Then we have
1 meter = 1 ¹/₁₀ yards
1 meter = 1 + ¹/₁₀ yards
1 meter = 11 / 10 yards
1 meter = 1.10 yards
Let the length of the automobile be 'x' meters. Then the number of yards in 'x' meters is given as,
⇒ x × (1.10)
⇒ 1.10x yards
The number of yards of the automobile of length 'x' meters will be 1.10x yeads.
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Solve this system of linear equations. Separate
the x- and y-values with a comma.
2x + 2y = -8
-13x + 7y = -48
Enter the correct answer.
Answer:
x = 1, y = - 5
Step-by-step explanation:
2x + 2y = - 8 → (1)
- 13x + 7y = - 48 → (2)
multiplying (1) by 7 and (2) by - 2 and adding will eliminate y
14x + 14y = - 56 → (3)
26x - 14y = 96 → (4)
add (3) and (4) term by term to eliminate y
40x + 0 = 40
40x = 40 ( divide both sides by 40 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
2(1) + 2y = - 8
2 + 2y = - 8 ( subtract 2 from both sides )
2y = - 10 ( divide both sides by 2 )
y = - 5
then solution is x = 1, y = - 5
For each value below, enter the number to four decimal places Suppose an arrow is shot upward on the moon with a velocity of 60m / s then its height in meters after seconds is given by h(t) = 60t - 0.83t ^ 2 Find the average velocity over the given time intervals [4, 4, 5]; (4,4,1) 2; [4,4,01]:; [4,4,001]:
Average speed is determined by dividing the total distance you traveled by the total time,
How fast is it moving on average?In order to calculate average velocity, divide the change in position or displacement (x) by the time intervals (t) during which the displacement takes place. Depending on the displacement's sign, the average velocity can either be positive or negative. The SI unit for average speed is meters per second (m/s or ms-1).
Average speed is determined by dividing the total distance you traveled by the total time, whereas average velocity is determined by dividing your displacement, which is a vector pointing from your initial location to your end position, by the whole time.
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In a certain year, a movie and its sequel grossed a combined total of $1518 million. If the sequel grossed $116 million more than the movie, then how much did each movie gross?
The movie gross is $701
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,
Total amount earned from the movie and the sequel = $1518
Amount earned from the movie = x
Amount earned from the sequel = x + $116
Now,
x + (x + 116) = 1518
2x + 116 = 1518
2x = 1518 - 116
2x = 1402
x = 1402/2
x = 701
Now,
x = $701
x + 116 = 701 + 116 = $817
Thus,
The movie gross is $701
The sequel gross is $817
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a freshly poured cup of coffee from mcdonald’s is measured to be 185 degrees fahrenheit. if left alone in a cup, the temperature of the coffee decreases by about 3.2% each minute. what would be the temperature if left alone in the cup for 20 minutes? round to the nearest degree
The temperature of the cup if it is left alone for 20 minutes, can be found to be 97 degrees Fahrenheit
How to find the temperature of the cup ?To find the tempertature of the cup, the formula would be:
= Beginning temperature x ( 1 - rate of decrease per minute ) ^ number of minutes
Beginning temperature = 185 degrees fahrenheit
rate of decrease per minute = 3.2% each minute
number of minutes = 20 minutes
The temperature is:
= 185 x ( 1 - 3 .2 %) ²⁰
= 97 degrees Fahrenheit
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Find a number that
has exactly 7 different prime factors.
Explain how you found it.
Answer:
957,697,598
Step-by-step explanation:
You want a number that has 7 different prime factors.
PrimesIf we choose 7 primes at random from the first 20, we might have the list ...
{2, 11, 13, 23, 41, 53, 67}
The product of these primes will have 7 different prime factors.
2 × 11 × 13 × 23 × 41 × 53 × 67 = 957,697,598
The number 957,697,598 has exactly 7 different prime factors.
__
Additional comment
Any of these factors might have a power greater than 1 without changing the number of different primes. We chose to keep it simple.
The second attachment shows the first 20 prime numbers.
if matrix a is symmetric show that any two eigenvectors of a correspond to different eigenvalues are orthogonal
A symmetric matrix is a square matrix that is equal to transpose of itself. If A is a symmetric matrix, then it satisfies the condition: A = AT. (AT is the inverse of A )
A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.
Suppose λ and μ are 2 distinct values of matrix A.
For the matrix to be Symmetric,
( Ax,y)=(x,Ay)
condition needs to be satisfied.
Here, ( x,y) is dot product between vectors x and y
λ (u,v) = (λu,v)
where u,v are eigen vectors for eigen values λ and μ
λ(u,v) = (Au,v)
λ(u,v) = (u,Av)
λ(u,v) = μ(u,v)
λ(u,v) = μ(u,v)
but λ≠μ
∴ (u,v) = 0.
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The complete question is :
If a matrix is symmetric then show that any two eigenvectors of that matrix corresponding to different eigenvalues are orthogonal. Assume square matrix.
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The probability that a student studied for 5 hours is 0.2 or 20%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
A table is given where the first column represents the number of hours a student studied Math and the second column represents the number of students.
The sum of the second column is 35 so it is the total number of students
And only 7 of them studied mathematics for 5 hours.
Therefore, The probability that a student studied for 5 hours is,
= 7/35
= 0.2 or 20%.
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