Part(A),
The value of the mean is 27.1, the value of the mode is 12 and median is 27.5.
Part(B),
Tennis players should report the median value to show they are less prepared for the tournament.
Part A:
To calculate the mean, we need to find the sum of all the data values and divide by the total number of values:
Sum of the data = 12 + 12 + 29 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 271
Number of data values = 10
Mean = sum of the data/number of data values
Mean = 271 / 10
Mean = 27.1
Therefore, the mean time spent practicing is 27.1 minutes.
To find the median, we need to arrange the data in order from smallest to largest:
12, 12, 20, 22, 26, 29, 31, 31, 40, 68
There are 10 data values, so the median is the average of the two middle values:
Median = (26 + 29) / 2
Median = 27.5
Therefore, the median time spent practicing is 27.5 minutes.
To find the mode, we need to identify the data value that occurs most frequently. In this case, there are two modes:
Mode = 12 and 31
Therefore, the modes for the time spent practicing are 12 and 31 minutes.
To find the range, we need to subtract the smallest data value from the largest data value:
Range = largest data value - smallest data value
Range = 68 - 12
Range = 56
Therefore, the range of time spent practicing is 56 minutes.
Part B:
Based on the scenario, it is more appropriate for the tennis players to report the median value to show they are less prepared for the tournament. This is because there is one outlier value of 68, which is much larger than the other data values.
The mean is affected by outliers and may not represent the typical amount of time spent practicing for the tournament. On the other hand, the median is not affected by outliers and represents the middle value of the data set, which is a more accurate measure of the typical amount of time spent practicing.
Therefore, tennis players should report the median value to show they are less prepared for the tournament.
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A wild horse runs at a rate of 8 miles an hour for 6 hours. Let y be the distance, in miles, the horse
travels for a given amount of time, x, in hours. This situation can be modeled by a function.
Which of these describes the domain of the function?
A. 0≤x≤6
B. 0≤y≤6
C. 0≤x≤ 48
D. 0≤ y ≤ 48
0≤x≤6 best describes the domain of the function.
The domain of a function describes the set of all possible input values.
In this case, the input variable is x, which represents the time in hours.
Since the horse runs for 6 hours, it is not possible for x to be greater than 6.
Additionally, x cannot be negative or zero, since time cannot be negative or zero.
Therefore, the domain of the function is 0 ≤ x ≤ 6.
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Need help with these math problems , I know #2 is on the arrow looking on is original is A = 36 units^2 and scale drawing is A = 9 units^2, just don’t know how I got it.
The areas of the figures are 36 square units & 9 square units and the scale factor of dilation is 1/2
Estimating the areas of the figuresFrom the question, we have the following parameters that can be used in our computation:
The composite figures
The areas of the figure is calculated using the sum of the individual areas
So, we have
Figure 1 = Rectangle + Triangle
Using the area formulas, we have
Figure 1 = 5 * 4 + 1/2 * 8 * 4
Evaluate
Figure 1 = 36
The second figure is not clear
However, from the question text we have the area to be
Figure 2 = 9
So, the scale factor from figure 1 to 2 is
Scale factor = √[Figure 2/Figure 1]
This gives
Scale factor = √[9/36]
Evaluate
Scale factor = 1/2
Hence, the scale factor is 1/2
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NO LINKS!! URGENT HELP PLEASE!!!
Find the equation of a parabola with a vertex at (-2, 6) and that passes through the (-4, -5)
Answer:
[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]
Step-by-step explanation:
As we know that
The standard equation of a parabola with vertex at point (h,k) is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the vertex
and "a" is a coefficient that determines the direction and shape of the parabola.
We know that the vertex of our parabola is (-2, 6),
so we can substitute those values into the equation to get:
[tex]y = a(x + 2)^2 + 6[/tex]
Now finding a.
Since the parabola passes through point (-4, -5). Substituting these coordinates into the equation, we get:
-5 = a(-4 + 2)^2 + 6
-5 =a(-2)^2+6
-5=4a +6
-5-6=4a
4a=-11
a =- 11/4
Substituting the value of an equation second, we get
[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]
Therefore, the equation of the parabola with a vertex at (-2, 6) and passing through (-4, -5) is y =
[tex] \frac{-11}{4} (x + 2)^2 + 6[/tex]
Answer:
[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]
Step-by-step explanation:
The vertex form of a parabola is:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex."a" is the leading coefficient.Given the vertex is at (-2, 6), substitute h = -2 and k = 6 into the equation:
[tex]y=a(x-(-2))^2+6[/tex]
[tex]y=a(x+2)^2+6[/tex]
To find the value of a, substitute the point (-4, -5) into the equation and solve for a:
[tex]\begin{aligned}-5&=a(-4+2)^2+6\\-5&=a(-2)^2+6\\-5&=4a+6\\-5-6&=4a+6-6\\-11&=4a\\\dfrac{-11}{4}&=\dfrac{4a}{4}\\-\dfrac{11}{4}&=a\\a&=-\dfrac{11}{4}\end{aligned}[/tex]
Substitute the found value of a back into the equation:
[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]
Therefore, the equation of a parabola with a vertex at (-2, 6) and that passes through the point (-4, -5) is:
[tex]\boxed{y=-\dfrac{11}{4}(x+2)^2+6}[/tex]
Quadrilateral ABCD is inscribed in a circle such that:
Answer:
∠ C = 84°
Step-by-step explanation:
A quadrilateral inscribed in a circle is a cyclic quadrilateral.
the opposite angles sum to 180° , that is
∠ A + ∠ C = 180 , then
x² + 60 + 8x + 36 = 180
x² + 8x + 96 = 180 ( subtract 180 from both sides )
x² + 8x - 84 = 0 ← in standard form
(x + 14)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x + 14 = 0 ⇒ x = - 14
x - 6 = 0 ⇒ x = 6
x > 0 , then x = 6 , so
∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°
The letters in the word HORSES are arranged in a row.How many unique arrangements are there of the letters?
Enter your answer in the box.
_____ arrangements
Answer:
180
Step-by-step explanation:
The word HORSES has 6 distinct letters, so we can arrange them in 6! = 720 ways if all the letters were unique.
However, in this case, the letters E and S are repeated twice. Therefore, we must divide by the number of arrangements of the repeated letters to avoid counting the same arrangement more than once.
The letter E appears twice, so there are 2! = 2 ways to arrange the E's within the word. Similarly, the letter S appears twice, so there are 2! = 2 ways to arrange the S's within the word.
Thus, the total number of unique arrangements of the letters in the word HORSES is:
6! / (2! × 2!) = 720 / 4 = 180
Therefore, there are 180 unique arrangements of the letters in the word HORSES.
This graph represents the flight path of a model rocket launched in a park.
What do the key features of the curve represent in terms of the flight path of the rocket?
Chose from the drop-down to match each situation.
ill give brainlyest to the first to correctly answer this
The drop down menu is used to match each situation as below.
1. The rocket reached its maximum the x-value of the vertex
height in 5 s.
2. ground level the y-intercept
3. The rocket launcher was the y-value of the point containing
on the ground. the x-intercept on the right
4. The rocket was in the air 10 the x-intercept on the right
5. The maximum height of the the y-value of the vertex
rocket is 50 ft.
6. the time the rocket was the x-value of the point containing the
launched y-intercept
What is the key feature of the curveThe key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.
The vertex is the point the rocket had the maximum and height.
Generally, the curve traces a parabolic path
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Ms. Garcia bought 3 packs of red notepads,
5 packs of yellow notepads, and 8 packs of
green notepads. There were 3 notepads in each
package. How many notepads did Ms. Garcia
buy in all?
Answer: red = 9, yellow = 15 green = 24, total = 48 notepads were bought.
Step-by-step explanation:
3 x 3 = 9, so 9 red. 3 x 5 = 15, so 15 yellow. 3 x 8 = 24, so 24 green. In total this is equal to 48 notepads. 9 + 15 + 24 = 48.
HELP ASAP ASAP PLS PLS I NEED DONE NOW AND BRAINLIEST
Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
6 4
12 8
24 16
45 30
At this rate, how many papers will Mr. Harris grade in 60 minutes?
34 papers
40 papers
44 papers
75 papers Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
6 4
12 8
24 16
45 30
At this rate, how many papers will Mr. Harris grade in 60 minutes?
34 papers
40 papers
44 papers
75 papers
Answer:
40
Step-by-step explanation:
6:4 = 1,5 which means he grades 1 paper per 1,5 minute. 60:1,5 = 40 papers
Philip finances a new refrigerator.
The function y = 600 - 75x
represents the remaining balance, y,
of the refrigerator purchase after
x months.
The domain and the range of the function are given as follows:
Domain: 0 ≤ x ≤ 8.Range: 0 ≤ y ≤ 600.What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.The function in this problem is given as follows:
y = 600 - 75x.
The input variable x represents the number of months, which cannot be negative, hence the lower bound of the domain is given as follows:
x = 0.
Meaning that the upper bound of the range is of y = 600.
The balance remaining cannot be negative, hence:
The lower bound of the range is of y = 0.The upper bound of the domain is: 600 - 75x = 0 -> x = 600/75 -> x = 8.Missing InformationThe problem asks for the domain and the range of the function.
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Who recommended that artists paint scenes of modern life?
Charles Baudelaire
John Ruskin
Louis Leroy
Sir Joshua Reynolds
Answer:
Charles Baudelaire recommended that artists paint scenes of modern life.
Charles Baudelaire was the one who recommended that artists paint scenes of modern life.
the sum of a numberator and a denominator of a fraction is 4140. when reduced fraction, it is 7/13
Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials.
Answer:
Kenneth's average stacking time is less than 8.2 seconds.
Brainly wouldn't allow me to give an explanation because apparently, it contains inappropriate words..? How odd.
Answer:
The data does not provide sufficient evidence to conclude that Kenneth's mean stacking time is is less than 8.2 seconds
Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level.
Step-by-step explanation:
Null hypothesis (H0): mu = 8.2 seconds
Alternate hypothesis (Ha): mu < 8.2 seconds
Significance level = 0.04
p-value = 0.0401
Using the p-value approach for testing hypothesis, do not reject H0 because the p-value 0.0401 is greater than the significance level 0.04.
There is not sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds.
In school need some help
Answer:
1.
a) 3 cubes
b) 5 cubes
c) 15 cubes
d) 45 cubes
2.
a) 2 cubes
b) 4 cubes
c) 8 cubes
d) 8 , 1/8
Step-by-step explanation:
1.
a) 3 cubes because 1.5/0.5=3
b) 5 cubes because 2.5/0.5=5
c) 15 cubes because 5x3=15
d) 45 cubes because the height 1.5/0.5=3 so 3x15=45
2.
a) 2 cubes beacuse 1/0.5=2
b) 4 cubes because the lenght is 1/0.5=2
c) 8 cubes because the height is 1/0.5=2 4x2=8
d) 8 , 1/8
Given P( A) =0.12 P (B) = 0.12 P(A)=0.12, = 0.3 P(B)=0.3 and P(A ∪ B) = 0.334 P(A∪B)=0.334, find the value of P(A∩B), rounding to the nearest thousandth, if necessary.
The value of P(A∩B) rounding to the nearest thousandth, if necessary is: 0.086
How to solve probability problems?The parameters given are:
P(A) = 0.12
P(B) = 0.3
P(A ∪ B) = 0.334
We want to find the probability P(A∩B)
The P(A∪B) probability formula is given as:
P(A∪B) = P(A) + P(B) - P(A∩B)
where:
P(A) is Probability of event A happening
P(B) is Probability of event B happening
P(A∩B) is Probability of happening of both A and B.
Thus:
0.334 = 0.12 + 0.3 - P(A∩B)
P(A∩B) = 0.12 + 0.3 - 0.334
P(A∩B) = 0.086
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Let f (x) = log2(x) + 2 and g(x) = log2(x3) – 6. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)
The simplified expression for h(x) is h(x) = 4 log₂(x) - 4.
Given information:
f(x) = (log₂(x) + 2) and g(x) = (log₂(x³) - 6)
h(x) = f(x) + g(x) = (log₂(x) + 2) + (log₂(x³) - 6)
Using the rules of logarithms, we can simplify g(x) as follows:
g(x) = log₂(x³) - 6
= 3 log₂(x) - 6.
Now we can substitute this into the expression for h(x):
h(x) = (log₂(x) + 2) + 3 log₂(x) - 6
= 4 log₂(x) - 4
Therefore, the simplified expression for h(x) is h(x) = 4 log₂(x) - 4.
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The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written. The store manager then deposited $956.60. Find the checkbook balance
The checkbook balance is $5703.25.
To find the checkbook balance, we need to start with the original balance and then subtract the amounts of the checks written and add the amount of the deposit.
Original balance: $7349.44
Checks written: $1349.67 + $344.12 = $1693.79
Deposit: $956.60
To find the checkbook balance, we can subtract the total amount of the checks written from the original balance and then add the deposit:
Checkbook balance = Original balance - Checks written + Deposit
Checkbook balance = $7349.44 - $1693.79 + $956.60
Checkbook balance = $5703.25
Therefore, the checkbook balance after store manager deposited $956.60 is $5703.25.
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Graph the system below and write its solution.
x+3y=-6
Note that you can also answer "No solution" or "Infinitely many" solutions.
Solution:
0
solution
The number of solutions of the system of equations in this problem is given as follows:
Infinitely many solutions.
How to obtain the solution of the system of equations?The system of equations for this problem is defined as follows:
x + 3y = -6.y = -x/3 - 2.Writing the second equation in standard format like the second, we have that:
x/3 + y = -2.
Multiplying by 3:
x + 3y = -6.
The two equations are equal, meaning that the system has an infinite number of solutions, and the two equations are the same on the graph.
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Pamela paid $8.95 for 5 pounds of bananas. How much will it cost to buy 2 pounds of bananas at the same rate?
Answer:
$3.58
Step-by-step explanation:
Because we know that the 2 lbs of bananas will be purchased at the same rate, the price per pound for 5 lbs of bananas is proportional to the price per pound for 2 lbs of bananas.
Thus, we can solve for price, p of 2 lbs of bananas by setting up a proportion:
[tex]\frac{8.95}{5}=\frac{p}{2}\\ \\ 17.90=5p\\\\3.58=p[/tex]
HELPPPPPPPPPPP
Nathaniel has 132 DVDs in his collection.
Each DVD case has the dimensions shown.
He plans to buy shelves for the collection
that are 31.5 inches wide and cost $15.75
each. How much will it cost Nathaniel to
shelve his DVD collection? Explain how you
found your answer.
The dimensions are 7.5in, 5.3in, 0.6in
The cost of shelving Nathaniel’s DVD collection is 15.75×27=$425.25.
We are given that;
Dimensions =7.5in, 5.3in, 0.6in
To find the cost of shelving Nathaniel’s DVD collection, we need to find how many shelves he needs and multiply that by the price of each shelf. To find how many shelves he needs, we need to find how many DVDs can fit on one shelf and divide that by the total number of DVDs.
Since the shelves are 31.5 inches wide and the DVDs are 5.3 inches wide, we can fit 5.331.5≈5.94 DVDs on one shelf. We round this down to 5 DVDs per shelf because we cannot fit a partial DVD on a shelf.
Since Nathaniel has 132 DVDs in his collection, he needs 5132=26.4 shelves. We round this up to 27 shelves because we cannot use a partial shelf.
Therefore, by algebra the answer will be 15.75×27=$425.25.
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The US Fish and Wildlife Service reported that the mean length of a 6 year old trout in the Arolik River in Alaska is 480 and standard deviation of 40 mm. Assume length of trout is normally distributed,
a) Find the 58th percentile of the lengths
The 58th percentile of the lengths is 489.4 mm.
What is the 58th percentile of the lengths?The 58th percentile of the lengths is calculated from normal distribution curve as shown below.
The mean of the distribution is at the 50th percentile.
The 58th percentile is between the mean and 1 standard deviation above the mean.
Mean (50%) = 480 mm
58% = ?
1 standard deviation above the mean (84%)= M + S.D = 480 mm + 40 mm = 520 mm
We are going to interpolate, to find the approximate value of the length.
50 ----- 480 mm
58 ----- ?
84 ------- 520 mm
(58 - 50)/(84 - 50) = (x - 480)/(520 - 480)
0.235(40) = x - 480
9.4 = x - 480
x = 489.4 mm
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URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!
If you know what question this is please answer I couldn’t fit everything in the picture :(
Restaurant
No commute 3
0-1 Hr Commute 10
> 1 Hr Commute 28
Sum 41
The correct groupings for each probability are given below as follows:
The probability that you have more than a 1 hour commute: Marginal-57/134 = 42.5% chanceThe probability that you make a home-cooked meal and you have more than a 1-hour commute: Joint-7/134 = 5% chanceThe probability that you eat at a restaurant given that you have no commute: Conditional-3/37 = 8% chanceThe probability that you get takeout food: Marginal-50/134 = 37% chanceThe probability that you eat at the restaurant and have no commute: Joint probability 3/134 = 2% chanceThe probability that you commute 0-1 hour given that you get take-out food: Conditional-18/50 = 36% chanceWhat is joint probability?The possibility of two events occurring simultaneously and at the same time is known as joint probability.
Joint probability is the likelihood that event Y will take place at the same time as event X.
An example of a joint probability is the probability that you eat at the restaurant and have no commute
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Consider the derivation of an alternate form of the cosine double angle identity. A 2-column table with 4 rows. Column 1 has entries 1, 2, 3, 4. Column 2 is labeled Step with entries cosine (2 x) = cosine squared (x) minus sine squared (x), = cosine squared (x) minus (1 minus cosine squared (x)), = cosine squared (x) minus 1 minus cosine squared (x), = 2 cosine squared (x) minus 1. What is the error in this derivation? In step 1, cos(2x) is equal to cos2(x) + sin2(x). In step 2, sin2(x) should have been replaced with 1 + cos2(x). In step 3, cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x). In step 4, 2cos2(x) – 1 should be 1 – 2cos2(x).
The error in this derivation in step 3 will be cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).
The trigonometric identities are given as,
sin²x + cos²x = 1
cos 2x = cos²x - sin²x
A 2-column table with 4 rows.
Column 1 Column 2
1 cos 2x = cos²x – sin²x
2 = cos²x – (1 – cos²x)
3 = cos²x – 1 – cos²x
4 = 2 cos²x – 1
The error in this derivation in step 3 will be cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).
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Identify the parts of the expression. Then write a word expression for the numerical or algebraic expression 1.5×6+8.3
The numerical value of the algebraic expression 1.5 × 6 + 8.3 is 17.3; The factors are 1.5 and 6 & the terms: 1.5 * 6 and 8.3
Identifying and solving the parts of the expressionFrom the question, we have the following parameters that can be used in our computation:
1.5 × 6 + 8.3
The above expression is an algebraic expression and as such the parts of the expressions are
Factors: 1.5 and 6Terms: 1.5 * 6 and 8.3When the expression is evaluated, we have
1.5 × 6 + 8.3 = 17.3
This means that the result of evaluating the expression 1.5 × 6 + 8.3 is 17.3
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Which comparison is true? (Homework)
A) 8 x 2 5/6 < 8
B) 2 x 1 2/5 > 2
C) 5 x 1 1/3 < 5
D) 7 x 3/7 > 7
B.
B, is the true comparison
Working her way through school, Liz works two part-time jobs for a total of 28 hours a week. Job A pays $6.00 per hour, and Job B pays $6.60 per hour. How many hours did she work at each job the week that she made $175.80? (Round to two decimal places if necessary.)
Answer:
A: 15 hoursB: 13 hoursStep-by-step explanation:
You want to know the number of hours Liz worked at each job, when the total pay for a total of 28 hours work was $175.80. Job A paid $6 per hour, and job B paid $6.60 per hour.
SetupWe can let 'b' represent the number of hours worked at job B. Then (28-b) is the number of hours worked at job A. Liz's total pay was ...
6(28 -b) +6.60(b) = 175.80
SolutionSimplifying the equation gives ...
0.60b +168.00 = 175.80
0.60b = 7.80 . . . . . . . . . . . subtract 168
b = 13 . . . . . . . . . . . . . . divide by 0.6
28-b = 28-13 = 15 . . . hours at Job A
Liz worked 15 hours at Job A, and 13 hours at Job B.
__
Additional comment
Here, we used one equation. If you use two equations, you can get this same equation by substituting for the variable representing hours at Job A. Letting the variable represent hours at the higher-paying job generally results in arithmetic using positive numbers. If you write the equation for the hours at Job A, negative numbers will usually be involved. Though it shouldn't, sometimes that causes confusion.
A graphing calculator may offer two or three ways (or more) you use to can solve the equations. One of them is illustrated in the attachment. It solves the equations ...
a + b = 28 . . . . . . . . . . . . equation for total hours6a + 6.6b = 175.8 . . . . . . equation for total payConsider the quadratic equation 4x² - 11x-3-0. Which of the following shows
this equation rewritten and ready to solve using factoring by grouping?
The factorized form of the quadratic equation is:
4(x - 3)*(x + 0.25) = 0
Which is the factorized form of the quadratic?The quadratic equation is 4x² - 11x -3 = 0
To do that, we need to find the zeros, so let's use the quadratic formula:
[tex]x = \frac{11 \pm \sqrt{(-11)^2 - 4*4*-3} }{2*4} \\\\x = \frac{11 \pm 13 }{8}[/tex]
Then the two roots are:
x = (11 + 13)/8 = 3
x = (11 - 13)/8 = -2/8 = -0.25
Then the factorized form is:
4(x - 3)*(x + 0.25) = 0
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Una versión muy simplificada de una tabla de insumo-producto para la economía de Israel en 1958 divide dicha economía en tres sectores agricultura, manufactura y energía con los si-guientes resultados.
a) ¿Cuántas unidades de producción agrícola se requieren para obtener una unidad de produc-to agrícola?
b) ¿Cuántas unidades de producción agrícola se requieren para obtener 200 000 unidades de productos de esta naturaleza?
c) ¿Cuántas unidades de producción agrícola se requieren para obtener 50 000 unidades de energía?
d) ¿Cuántas unidades de energía se requieren para obtener 50 000 unidades de productos agrí-colas?
Note that:
a) 1 unit of agricultural production required to obtain 1 agricultural product.
b) 200,000 units of agricultural production are required to obtain 1 of agricultural product.
c) 22,727 units of agricultural production are required to obtain 50,000 units of energy.
d) we need 27,825 units of energy to produce 50,000 units of agricultural products.
How did we get the aabove answer?a) According to the table, the coefficient of production for agriculture is 0.293, that is
0.293 units of agricultural production = a unit of agricultural product.
b) To obtain 200,000 units of agricultural products we say
0.293 x 200,000,= 58,600 units of agricultural production.
c) the coefficient of production for energy with respect to agriculture is 0.044,
that is ,
0.044 units of agricultural production = a unit of energy.
So
50,000 units of energy,=
0.044 by 50,000,
= 2,200 units of agricultural production.
d) To obtain 50,000 units of agricultural products
use the Leontief inverse of the input-output table, which is simply the inverse of the coefficient matrix.
[ 3.4175 -0.2345 -0.5565 ]
[-0.1894 4.8264 -0.2114 ]
[-0.3074 0.1772 4.8324 ]
[ (3.4175 x0) + (-0.2345 x 0) + (-0.5565 x 50,000) ]
[ (-0.1894 x0) + (4.8264x 0) + (-0.2114 x50,000) ]
[ (-0.3074 x0) + (0.1772 x0) + (4.8324 x50,000) ]
[ -27,825 ]
[ -10,570 ]
[ 241,620 ]
Thus, we need 27,825 units of energy to produce 50,000 units of agricultural products.
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Can u please solve the problem
The complete proof to show that ∠HIJ ≅ ∠EFG is:
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
∠HIJ ≅ ∠EFG Substitution property
Proof of congruent anglesFrom the question, we to prove that the given angles are congruent.
The given angles are ∠HIJ and ∠EFG
To prove that angle HIJ is congruent to angle EFG we will complete the given table.
The given table is
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
Now, we will complete the proof by adding the last statement and its reason
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
∠HIJ ≅ ∠EFG Substitution property
Hence,
We have completed the proof by using the substitution property
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Autumn's Pumpkin Patch started the day with 432 pumpkins, each priced at $5. Most of
the pumpkins sold. At the end of the day, there were only 129 pumpkins left. How much
money did the pumpkin patch make today?
Answer:
It's very simple you just subtract 432 and 129. And you get 303. Then you just multiple 303 by 5 and you get 1515.
1515
maria and joan went shopping. maria bought 3 pair of jeans that each cost the same amount and 4 t-shirts that each cost the same amount. joan bought 2 pair of jeans that each cost the same amount, and 1 t-shirts that each cost the same amount. what is the cost of the jeans and shirts
Result:
The total cost of the jeans and shirts = 5(x + y)
How do we determine the cost?Let's use variables (x and y) to show the total cost of one pair of jeans and one T-shirt, respectively.
Let x = the cost of one pair of jeans.
Let y = e the cost of one T-shirt.
Given:
Maria bought 3 pairs of jeans and 4 T-shirts, all at the same price. That is:
3x = cost of Maria's jeans
4y = cost of Maria's T-shirts
Joan bought 2 pairs of jeans and 1 T-shirt, all at the same price. That is:
2x = cost of Joan's jeans
y = cost of Joan's T-shirt
To find the total cost of all they bought, add up the costs:
Total cost = Maria's cost + Joan's cost
Total cost = 3x + 4y + 2x + y
Total cost = 5x + 5y
So the total cost is 5 times the sum of the cost of one pair of jeans and one T-shirt.
Simplify the expression by factoring out a common factor of 5, and we get:
Therefore, total cost = 5(x + y)
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