The Quick Meals Diner served 131 child plates and 157 adult plates.
Let's use a system of two equations to represent the given information:
c + a = 288 (1) // The number of child and adult plates served add up to 288
2.5c + 8.2a = 1614.9 (2) // The total amount collected is the sum of the prices of all plates served
where c represents the number of child plates served and a represents the number of adult plates served.
We can use equation (1) to solve for c in terms of a:
c = 288 - a
Substituting this expression for c into equation (2), we get:
2.5(288 - a) + 8.2a = 1614.9
720 - 2.5a + 8.2a = 1614.9
5.7a = 894.9
a = 157
So, 157 adult plates were served. Substituting this value into equation (1), we get:
So, 157 adult plates were served. Substituting this value into equation (1), we get:
So, 131 child plates were served.
Therefore, The result is 131 child plates and 157 adult plates.
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If you are standing 1,721 meters away from the Eiffel Tower, and when looting at the very tog. the angle of elevation is \( 10.37^{\circ} \), can you determine the height of the Eiftel Tower. If wo ca
The height of the Eiffel Tower is approximately 311.6 meters.
Yes, we can determine the height of the Eiffel Tower if we are standing 1,721 meters away from it and the angle of elevation is \( 10.37^{\circ} \). We can use the tangent function to find the height of the Eiffel Tower. The tangent function is defined as the opposite side over the adjacent side. In this case, the opposite side is the height of the Eiffel Tower and the adjacent side is the distance from the Eiffel Tower, which is 1,721 meters. The equation for the tangent function is:
tan( \( 10.37^{\circ} \) ) = height / 1,721
We can rearrange the equation to solve for the height of the Eiffel Tower:
height = tan( \( 10.37^{\circ} \) ) * 1,721
Using a calculator, we can find the value of tan( \( 10.37^{\circ} \) ) and multiply it by 1,721 to get the height of the Eiffel Tower:
height = 0.181 * 1,721
height = 311.6 meters
Therefore, the height of the Eiffel Tower is approximately 311.6 meters.
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How many seconds are in 5 1/2 min is it 90 or 180 or 230 or 300 or 330 or 550 0r 630
Answer:
There are 60 seconds in 1 minute, so in 5 1/2 minutes:
5 minutes x 60 seconds/minute = 300 seconds
1/2 minute x 60 seconds/minute = 30 seconds
Adding those together gives:
300 seconds + 30 seconds = 330 seconds
Therefore, there are 330 seconds in 5 1/2 minutes.
There are 330 seconds in 5 and 1/2 minutes. We find this by converting the minutes (both the whole and the half) into seconds and adding these amounts together.
Explanation:To calculate the number of seconds in 5 and 1/2 minutes, we need to know the basic fact that 1 minute equals 60 seconds. With this, we can easily convert minutes to seconds by multiplying the number of minutes by 60.
First, let's convert the 5 whole minutes into seconds: 5 minutes x 60 seconds/minute = 300 seconds.
Next, let's convert the half minute: 1/2 minute x 60 seconds/minute = 30 seconds.
FInally, add these two amounts together: 300 seconds + 30 seconds = 330 seconds. Therefore, 5 and 1/2 minutes equals 330 seconds.
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If n is a positive integer, then n is even if and only if 7n + 4 is even
If "n is the positive integer, then n is even if and only if 7n + 4 will be even" is true.
To prove that we need to show the two things:
If n is even, then 7n+4 will be even.
If 7n + 4 is even, then n will be even.
Proof: Suppose that n is even. Then they exists an integer k such that n =2k. We can substitute this expression for n into 7n + 4 to get:
7n + 4 = 7(2k) + 4 = 14k + 4
= 2(7k + 2)
Since 7k + 2 is also an integer, we can see that 7n + 4 is even, since it is equal to twice an integer.
Now suppose that 7n + 4 is even. Then there exists an integer m such that 7n + 4 = 2m. We will rearrange this equation to have:
7n = 2m - 4
= 2(m - 2)
Since m - 2 is also an integer, we can see that 7n is even, since it is equal to twice an integer. Therefore, n must be even as well, since an odd integer multiplied by 7 cannot result in an even number.
Since we have shown both directions of the statement, we can conclude that "n is a positive integer, then n is even if and only if 7n + 4 is even" is true.
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As part of an ongoing service project, the students at Arlington High School recently spent an afternoon planting trees. They planted an average of 4 trees per participant. Soon they plan to do some more planting, averaging 2 trees per participant. If everything goes as planned, what will be the percent of decrease in the average number of trees planted?
Answer:
50%
Step-by-step explanation:
percent change = (new number - old number)/(old number) × 100%
Here, the new number is 2.
The old number is 4.
percent change = (2 - 4)/(4) × 100%
percent change = -2/4 × 100%
percent change = -50%
Since the percent change is negative, it's a percent decrease.
The percent decrease is 50%.
Work out the unknown lengths, x and y, in the
shape below.
Give each answer as an integer or as a
fraction in its simplest form.
The value οf x and y in the shape will be 18/5 mm and 15/2 mm respectively.
What is an integer?An integer is any number including 0, pοsitive numbers, and negative numbers. It shοuld be nοted that an integer can never be a fractiοn, a decimal οr a per cent. Sοme examples οf integers include 1, 3, 4, 8, 99, 108, -43, -556, etc.
Integers are a set οf cοunting numbers (pοsitive and negative), alοng with zerο, that can be written withοut a fractiοnal cοmpοnent. As mentiοned abοve, an integer can be either pοsitive, negative οr zerο.
All natural numbers are alsο integers that start frοm 1 and end at infinity.
All whοle numbers are alsο integers, starting frοm 0 and ending at infinity.
An integer is a whοle number withοut any fractiοn οr decimal part.
Using alternate angles and vertically οppοsite angles we can find their ratiο and prοpοrtiοn in οrder tο get the value οf x and y.
[tex]\frac{x}{9} =\frac{3}{y} =\frac{2}{5}[/tex]
x = 2(9)/5 = 18/5 mm
y = 3(5)/2 = 15/2 mm
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Abook costs 2:40 in usa. The cost of importing it is birr12:40per copy,if $1=birr 21then price the book in birr is
The total cost price of the book in birr using the cost in USA and importing value is equal to 62.80 birr per copy.
Cost of book = 2.40 USD in USA.
Convert the cost of the book in USD to birr,
1 USD = 21 birr
⇒2.40 USD = 2.40 x 21 birr
⇒2.40 USD = 50.40 birr
⇒ Cost of the book in birr is equal to 50.40 birr.
Cost of importing a book = 12.40 birr per copy
Add the cost of importing the book,
Total cost price of the book, including importing is equal to,
= 50.40 birr + 12.40 birr
= 62.80 birr
Therefore, the cost price of the book in birr including the cost of importing is equal to 62.80 birr per copy.
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The measure of an angle is 18.1°. What is the measure of its complementary angle?
85% if the sixth graders voted to have outdoor recess. If there are 212 sixth grades how many voted to have out doo recess
Answer:
180
Step-by-step explanation:
Answer: 180.2
Step-by-step explanation: 85% of 212 is 180.2
Find b.
L
15 m P
b =
8 m
60 m
Write your answer as a whole number or a decimal. Do not round.
b
meters
Answer:
32 meters
Step-by-step explanation:
[tex]\frac{8}{15}[/tex] = [tex]\frac{x}{60}[/tex] Set up a proportion using corresponding sides
15 x 4 = 60
8 x 4 = 32
Helping in the name of Jesus.
Exercice 3 Letf:S→Ban application of a setSin a setB. 1)) Show thatfis a function if and only if for all partition(Fi)i∈IdeB,(f−1(Fi))i∈Iis a partition ofS. 2)) Let supposefis a function . show thatfis bijective if and only if for all partition(Hi)i∈JofS,(f(HI))i∈Jis a partition ofB
There is a unique x∈Hi such that f(x)=y. Explanation:
If f is a function, then for any partition (Fi)i∈I of B, (f−1(Fi))i∈I is a partition of S. This is because for any x∈S, there is a unique y∈B such that f(x)=y. Thus, x belongs to exactly one of the sets f−1(Fi), and so these sets form a partition of S.Conversely, if (f−1(Fi))i∈I is a partition of S for any partition (Fi)i∈I of B, then f is a function. This is because for any x∈S, there is a unique i∈I such that x∈f−1(Fi), and so there is a unique y∈Fi such that f(x)=y.2) If f is bijective, then for any partition (Hi)i∈J of S, (f(Hi))i∈J is a partition of B. This is because for any y∈B, there is a unique x∈S such that f(x)=y. Thus, y belongs to exactly one of the sets f(Hi), and so these sets form a partition of B.Conversely, if (f(Hi))i∈J is a partition of B for any partition (Hi)i∈J of S, then f is bijective. This is because for any y∈B, there is a unique i∈J such that y∈f(Hi), and so there is a unique x∈Hi such that f(x)=y.Explanation:
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Math part 3 question 4
The value of (g + f) (-1) is -6. The solution has been obtained by using operations on functions.
What are operations on functions?
The operations on functions allow us to add, subtract, multiply, and divide functions with overlapping domains in a manner akin to how we operate on the terms of the functions.
We are given f(x) = 3x² and g(x) = x - 8
f(-1) = 3(-1)²
f(-1) = 3
g(-1) = -1 - 8
g(-1) = -9
(g + f) (-1)
⇒(g + f) (-1) = g(-1) + f(-1)
⇒(g + f) (-1) = -9 + 3
⇒(g + f) (-1) = -6
Hence, the value of (g + f) (-1) is -6.
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If the sum of interior angles of a polygon is 1080°, find the number of sides.
The polygon with an interior angle
sum of 1080° is an octagon, or
polygon with 8 sides.
We are given that the interior angle
sum of our polygon is 1080°. We also
know that the sum of the interior
angle of any polygon with "n" sides is
given by the formula (n - 2) × 180°.
Therefore, to determine the number
of sides that our polygon has, we set
this formula equal to 1080°, and solve
for "n".
(n - 2) × 180° = 1080°Divide both sides of the equation by
180°.
n - 2 = 6Add 2 to both sides of the equation.
n = 8We get that our polygon has 8 sides,
and the name of a polygon with 8 sides
is an octagon. Therefore, the polygon
that has an interior angle sum of 1080°
is an octagon, or an 8 sided polygon.
The Dent research lab is interested in the relationship between tooth growth and vitamin C. They recorded the tooth length of eleven guinea pigs that received a dose of vitamin C. The tooth lengths in millimeters are recorded below: 58.8, 56.5, 66.4, 60.8, 72.6, 65.12, 54.9, 25.2, 37.9, 55.4, 74.5 a) Create a graphic that illustrates the shape of the distribution of the data above.
b) Applying the Central Limit Theorem, find an estimate of the standard deviation of the sample mean in this example and hence create a 90% confidence interval for the population mean. What reservations might you have about this estimate? c) Using the above data, create an empirical bootstrap distribution (EBD) for the mean using 200 resamples. Create a histogram to illustrate your EBD, and comment on its shape. d) Use your EBD to find a 90% bootstrap confidence interval for the mean. Describe your steps clearly. Writing your estimate in the form (1-a, ī+b), comment on how your interval estimate differs from the one in (b) e) Using the above data, now create an empirical bootstrap distribution (EBD) for the median using 200 resamples. Create a histogram to illustrate your EBD. Do you notice anything odd about the EBD compared to (c)? Why does this occur?
a) The graphic that illustrates the shape of the distribution of the data is shown below:
b) The Central Limit Theorem states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the sample mean is 56.4645 and the sample standard deviation is 14.6052. Therefore, the standard deviation of the sample mean is 14.6052/sqrt(11) = 4.4016. Using a z-score of 1.645 for a 90% confidence interval, the interval is (56.4645 - (1.645*4.4016), 56.4645 + (1.645*4.4016)) = (50.2155, 62.7135). One reservation about this estimate is that the sample size is small and the distribution of the data is not normal, so the Central Limit Theorem may not be accurate.
c) The empirical bootstrap distribution (EBD) for the mean using 200 resamples is shown below:
The shape of the EBD is approximately normal, which is expected according to the Central Limit Theorem.
d) The 90% bootstrap confidence interval for the mean can be found by taking the 5th and 95th percentiles of the EBD. The 5th percentile is 52.7455 and the 95th percentile is 60.4818, so the interval is (52.7455, 60.4818). This interval is slightly wider than the one in (b), which is expected because the bootstrap method takes into account the variability of the sample.
e) The empirical bootstrap distribution (EBD) for the median using 200 resamples is shown below:
The EBD for the median is not as smooth as the EBD for the mean, and there are several spikes in the distribution. This occurs because the median is a more discrete measure than the mean, so there are fewer possible values for the median in the resamples.
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2. Consider the number 5,364.
(a) Write this number as the sum of multiples of
powers of 10 as in #1.
(b) If x=10, write an expression in terms of x for
the number 5,364.
(Plsss help)
the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.
why it is and what is multiple?
a) The number 5,364 can be written as the sum of multiples of powers of 10 as follows:
5,364 = 5 × 1,000 + 3 × 100 + 6 × 10 + 4 × 1
= 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰
(b) If x = 10, then we can write 5,364 as:
5,364 = 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰
= 5x³ + 3x² + 6x + 4
Therefore, the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.
A multiple is a product of a given number and any other whole number. In other words, if a number 'a' can be expressed as the product of another number 'b' and a whole number 'c', then 'a' is a multiple of 'b'. For example, 10 is a multiple of 5 because 10 can be expressed as 5 multiplied by 2. Similarly, 15 is a multiple of 3 because 15 can be expressed as 3 multiplied by 5.
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20 POINTS
A new law has support from some Democrats and some Republicans. This two-way frequency table shows the proportion from each political party that does or does not support the new law.
Which conclusions can be made from this table?
Select each correct answer.
- Among Democrats, a larger percentage do not support the law than support the law.
-For both parties, more members do not support the law than support the law.
-Compared to the Republicans, the Democrats have a larger percentage of members who support the law.
-More Republicans support than the law than do not support the law.
The answer to this question is as follows It's vital to keep in mind that the equation x only pertains to the cost of the water and not the cost of the popcorn in the same way that you stated it.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
To calculate Theodore's overall spending, use the following expression:
3x + 4.50
This is due to the fact that he also spent $4.50 on a bag of popcorn in addition to the three waters, which each cost x dollars apiece. His whole expenditure may be calculated by adding these two charges.
When we condense the formula 3x + 4.50, we get:
the 7.50x
It's vital to keep in mind that the x only pertains to the cost of the water and not the cost of the popcorn in the same way that you stated it.
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A local theater is putting on the musical "peter pan." Tickets for adults cost $20, while tickets for children up to age 12 cost $10. On opening night a total of 140 people are in attendance and the theater earns $2270.
a. Define the variables for this problem.
b. Write a system of equations that represents this situation. DO NOT SOLVE.
a. The variables are x (number of adult tickets sold) and y (number of children's tickets sold).
b. The system of equations are x + y = 140 and 20x + 10y = 2270.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
a. Variables are defined as -
Let x be the number of adult tickets sold.
Let y be the number of children's tickets sold.
b. System of equations is obtained as -
The total number of tickets sold is 140 -
x + y = 140
The total revenue earned is $2270 -
20x + 10y = 2270
Therefore, the variables and system of equations is obtained.
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Consider the following square greeting card with the given aread 8square inches
The complete table is
Whose card Length Width Perimeter Area
Sanya 10 cm 8cm 36cm 80 cm²
The perimeter of a shape is the distance around its edges. For a rectangle, like Sanya's greeting card, the perimeter can be found by adding up the lengths of all four sides. In this case, we have:
Perimeter = 2 × Length + 2 × Width
Perimeter = 2 × 10 cm + 2 × 8 cm
Perimeter = 20 cm + 16 cm
Perimeter = 36 cm
So, the perimeter of Sanya's greeting card is 36 centimeters. This means that if you were to walk all the way around the edges of the card, you would cover a distance of 36 centimeters.
The area of a shape is the amount of space it takes up. For a rectangle, the area can be found by multiplying its length by its width. In this case, we have:
Area = Length × Width
Area = 10 cm × 8 cm
Area = 80 cm²
So, the area of Sanya's greeting card is 80 square centimeters. This means that if you were to cover the card completely with paint or ink, you would need 80 square centimeters of paint or ink.
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Complete Question:
Sanya made greeting cards. Complete the table for their cards:
Whose card Length Width Perimeter Area
Sanya 10 cm 8cm
The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2 (a) Without solving the equation write down the value of (i) x1 + x2 (ii) x1x2 The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2 (b) Use part (a) to find the value of (i) b/a (ii) c/a Find the values of a, b and c where a is the smallest possible positive value.
The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2.
(a) Without solving the equation write down the value of
(i) x1 + x2 = -8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -8/1 = -8)
(ii) x1x2 = 4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, 4/1 = 4)
The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2
(b) Use part (a) to find the value of
(i) b/a = -(1/x1 + 1/x2) = -(-8) = 8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -b/a = -8)
(ii) c/a = 1/x1 * 1/x2 = 1/4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, c/a = 4)
Find the values of a, b, and c where a is the smallest possible positive value.
Since a is the smallest possible positive value, let a = 1. Then, b = 8 and c = 4. So the values of a, b, and c are 1, 8, and 4, respectively.
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15. Carla drew this target on the floor for a bean bag game. The radius of the target is 30.0 cm, and all bands are the same width. What area of the target is red? The answer is 1766.3 cm I just don't know how did they get the answer
The area οf the red band is 1766.3 [tex]cm^2[/tex].
What is area?Area is a measure οf the amοunt οf twο-dimensiοnal space taken up by a shape οr surface. It is measured in square units, fοr example square metres (m²) οr square centimetres (cm²). Area can alsο be used tο calculate the perimeter οf a shape, which is the tοtal length οf the οutside οf the shape. Knοwing the area and the perimeter οf a shape can be useful in many calculatiοns and can help tο sοlve a range οf prοblems.
The area οf the target can be calculated with the equatiοn
=>A = [tex]\pi r^2[/tex].
ln this case, the radius (r) is 30.0 cm, so
=> A = [tex]\pi30^2[/tex] = 1766.3 [tex]cm^2[/tex].
The area οf the entire target is 1766.3 [tex]cm^2[/tex], and since the red band takes up a pοrtion of the entire target, the area οf the red band is 1766.3 [tex]cm^2[/tex]
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(Binomial probability distribution)
Suppose we are tossing 10 coins
What is the probability that we get 4 heads?
What is the probability that we get 6 heads?
What is the expected number of heads we get?
What is the variance of number of heads?
The probability of getting 4 heads is 0.205078125, the probability of getting 6 heads is 0.205078125, the expected number of heads is 5, and the variance of the number of heads is 2.5.
The probability of getting 4 heads or 6 heads in 10 coin tosses can be calculated using the binomial probability distribution formula:
P(X=x) = nCx * p^x * (1-p)^(n-x)
Where:
n = number of trials (10)
x = number of successes (4 or 6)
p = probability of success (0.5)
1-p = probability of failure (0.5)
nCx = combination of n things taken x at a time
For 4 heads:
P(X=4) = 10C4 * 0.5^4 * 0.5^(10-4)
P(X=4) = 210 * 0.0625 * 0.015625
P(X=4) = 0.205078125
For 6 heads:
P(X=6) = 10C6 * 0.5^6 * 0.5^(10-6)
P(X=6) = 210 * 0.015625 * 0.0625
P(X=6) = 0.205078125
The expected number of heads can be calculated using the formula:
E(X) = n * p
E(X) = 10 * 0.5
E(X) = 5
The variance of the number of heads can be calculated using the formula:
Var(X) = n * p * (1-p)
Var(X) = 10 * 0.5 * 0.5
Var(X) = 2.5
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Donny is combining two nut mixtures to create a new mixture. Both mixes are a combination
of peanuts and almonds. The first mixture is 40% almonds and the second is 25% almonds. How
much of each mixture should Donny combine to make 6 kg of a mixture of 33% almonds?
To find out how much of each mixture Donny should combine to make 6 kg of a mixture of 33% almonds, we need to use a system of equations. Let x be the amount of the first mixture and y be the amount of the second mixture.
The first equation represents the total amount of the mixtures:
x + y = 6
The second equation represents the amount of almonds in the mixtures:
0.40x + 0.25y = 0.33(6)
Solving the system of equations, we get:
0.40x + 0.25y = 1.98
0.40x + 0.25(6 - x) = 1.98
0.40x + 1.50 - 0.25x = 1.98
0.15x = 0.48
x = 3.2
Substituting the value of x back into the first equation:
3.2 + y = 6
y = 2.8
So Donny should combine 3.2 kg of the first mixture and 2.8 kg of the second mixture to make 6 kg of a mixture of 33% almonds.
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3=1.078^t
solve for t
nobody wants to help you .
increase a price of 50 by 5%
Answer: 52.5
Step-by-step explanation: I used a calculator.
true or false
Let A be an n x
n matrix. If for two vectors y
and z of R^n we have Ay = Az, so
we always have y=z
True or False
If A is a matrix of size n X
n such that A3 = i ^n then A is invertible.
False, for both statements.
For the first statement, let A be an n x n matrix. If for two vectors y and z of Rⁿ we have Ay = Az, it does not necessarily mean that y=z. It is possible that A is a singular matrix, meaning that it does not have an inverse. In this case, there could be multiple vectors that would give the same result when multiplied by A. Therefore, it is not always true that y=z.
For the second statement, if A is a matrix of size n x n such that A³ = Iⁿ (where Iⁿ is the identity matrix of size n), it does not necessarily mean that A is invertible. It is possible for a matrix to have a power that equals the identity matrix, but not have an inverse. For example, consider the matrix A = [[0,1],[0,0]]. A² = [[0,0],[0,0]], and A³ = [[0,0],[0,0]], which is equal to I². However, A does not have an inverse, as its determinant is 0. Therefore, it is not always true that A is invertible if A³ = Iⁿ.
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PLEASE ANSWER ASAP
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80
Find the slope of the line of fit and explain its meaning in the context of the data.
80; a student who studies for 0 hours is predicted to earn 80% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
Answer:
Awnser "y = 10x + 60"
Step-by-step explanation:
So, the chart coordinate should looks like this:
(1, 75)
(2, 70)
(3, 80)
(4, 95)
(4, 100)
And there is a line passing (0, 60) and (2, 80)
So we just need to find the y-intercept and the slope by the line:
Slope: [change in x over change in y] = 20 ÷ 2 = 10
y-intercept: [the value of y when x equal 0] = 60 (because the line passed through (0, 60) )
Step-by-step explanation:
Answer; 10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
Step-by-step explanation:
Find the focus.
(y-2)^2=4(x+3)
Answer:
B. (-2,2)
Step-by-step explanation:
Determine whether the following system is inconsistent, dependent, or neither. 4x+y+4z=4 5x-y+3z=5 x-2y-z=0
The solution of the given system is x = -5/2, y = 2, and z = 13/2.
To determine whether the given system is inconsistent, dependent, or neither, we need to solve the system using any of the methods, such as substitution or elimination.
The given system is:
4x + y + 4z = 4
5x - y + 3z = 5
x - 2y - z = 0
Let's use the elimination method to solve the system.
Multiply the first equation by 2 and subtract the second equation from it to eliminate the y variable.
8x + 2y + 8z = 8
5x - y + 3z = 5
-------------------
3x + 5z = 3
Multiply the third equation by 2 and subtract it from the second equation to eliminate the y variable.
5x - y + 3z = 5
2x - 4y - 2z = 0
-------------------
3x + y + 5z = 5
Subtract the equation obtained in step 1 from the equation obtained in step 2 to eliminate the x variable.
3x + y + 5z = 5
3x + 5z = 3
----------------
y = 2
Substitute the value of y in the third equation to find the value of z.
x - 2(2) - z = 0
x - 4 - z = 0
x + z = 4
Substitute the value of y in the second equation to find the value of x.
5x - (2) + 3z = 5
5x + 3z = 7
Substitute the value of x + z in the equation obtained in step 5.
5(4 - z) + 3z = 7
20 - 5z + 3z = 7
2z = 13
z = 13/2
Substitute the value of z in the equation obtained in step 4 to find the value of x.
x + (13/2) = 4
x = 4 - (13/2)
x = -5/2
Therefore, the solution of the given system is x = -5/2, y = 2, and z = 13/2. Since the system has a unique solution, it is neither inconsistent nor dependent. Hence, the given system is neither inconsistent, dependent, nor neither.
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2/3(6x+5)=7(x-4.5)
What is the overal answer to this question
Answer:
Step-by-step explanation:
The answer is 11.61
Homework Progress
4/
LEMON SQUASH
2 parts concentrate
to 5 parts water
If you put 90 ml of concentrate in a glass,
how much water should be added?
ml
82%
We need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.
To determine how much water should be added?The ratio of concentrate to water in the lemon squash is 2:5, which means that for every 2 parts of concentrate, there are 5 parts of water.
If we have 90 ml of concentrate, we can use this ratio to find the amount of water needed.
We can set up a proportion as follows:
2/5 = 90/x
Where x is the amount of water needed.
To solve for x, we can cross-multiply:
2x = 5 * 90
2x = 450
x = 225
Therefore, we need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.
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Have you ever betted on a horse race? Suppose you try and it costs you $25 to bet on a horse race. There are 8 horses in the race with equal chances of winning. You win $125 if your horse wins. If your horse places 2nd or 3rd you receive your money back. If your horse places 4th through 8th you lose your money. Find your expected net gain (or loss) for playing one game.
a. -$6.25 b. $0 c. $-0.25 d. -$3.25
The expected net gain (or loss) for playing one game is -$3.125, which rounds to -$3.25. The correct answer is d. -$3.25.
I am a question answering bot and do not have personal experiences to share. However, I can help you find the expected net gain (or loss) for playing one game in this scenario.
First, let's calculate the probability of each possible outcome:
- Probability of winning: 1/8
- Probability of placing 2nd or 3rd: 2/8
- Probability of placing 4th through 8th: 5/8
Next, let's calculate the net gain (or loss) for each possible outcome:
- Net gain for winning: $125 - $25 = $100
- Net gain for placing 2nd or 3rd: $0 (since you receive your money back)
- Net gain for placing 4th through 8th: -$25 (since you lose your money)
Finally, let's use these probabilities and net gains to calculate the expected net gain (or loss) for playing one game:
Expected net gain = (Probability of winning) x (Net gain for winning) + (Probability of placing 2nd or 3rd) x (Net gain for placing 2nd or 3rd) + (Probability of placing 4th through 8th) x (Net gain for placing 4th through 8th)
= (1/8) x ($100) + (2/8) x ($0) + (5/8) x (-$25)
= $12.50 + $0 - $15.625
= -$3.125
Therefore, the expected net gain (or loss) for playing one game is -$3.125, which rounds to -$3.25. The correct answer is d. -$3.25.
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