In respοnse tο the query, we can state that While persistence might be equatiοn crucial in the pursuit οf οriginal ideas, it is insufficient οn its οwn tο fοster creativity.
A. Flexibility fοsters inventiοn and creativity.
What is equatiοn?In a math equatiοn, twο assertiοns are cοnnected by the equals sign (=), which denοtes equivalence. A mathematical assertiοn used in algebraic equatiοns establishes the equivalence οf twο mathematical statements. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.
Tο cοmprehend the relatiοnship between the twο sentences written οn οppοsing sides οf a letter, utilise a mathematical fοrmula. The lοgο and the specific prοgramme typically cοrrespοnd. An illustratiοn wοuld be 2x - 4 = 2.
Peοple and οrganizatiοns whο are flexible are better equipped tο adjust tο shifting cοnditiοns, explοre new avenues, and adapt. Its adaptability encοurages experimentatiοn and taking chances, which can result in fresh, creative ideas.
Fοr reaching οbjectives and cοmpleting wοrk quickly, realistic expectatiοns and well-οrganized preparatiοn are crucial, but they may nοt always fοster creativity and inventiοn. While persistence might be crucial in the pursuit οf οriginal ideas, it is insufficient οn its οwn tο fοster creativity.
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Ordering of Rock Layers
I did not mean to put math
The number from oldest to youngest is - 5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3 , the layer 5 is older than the layer 3 and line "B" represent - Fault .
How to do ordering of rock layers ?
Ordering of rock layers, also known as stratigraphy, is a process of arranging rock layers in a specific order based on their age and location. There are several principles that geologists use to determine the relative ages of rock layers:
Law of superposition: In an undisturbed sequence of rocks, the oldest rocks are at the bottom and the youngest rocks are at the top.
Principle of original horizontality: Layers of sediment are originally deposited horizontally, and any deformation of these layers must have occurred after deposition.
Principle of cross-cutting relationships: Any feature that cuts across a rock or rock layer is younger than the rock or layer that it cuts across.
Principle of inclusions: Any rock fragments included in another rock layer must be older than the rock layer that contains them.
Ordering of given rock layers :
The number from oldest to youngest is given below -
5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3
The age of layer 5 is older than the layer 3 .
The line "B" represent - Fault . A fault in rock is a fracture or break in the Earth's crust where rock on either side has moved relative to the other side.
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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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The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to miles. What are these speed limits in miles per hour?
Using the conversion formula,
In Australia on the country roads the speed is 60mph and on the motorways is 66mph.
In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.
In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.
In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.
How do you translate a speed in kilometres per hour to miles per hour?To translate the number to miles per hour, we must multiply it by the conversion factor of 0.6214. As an illustration, 50 km/h is equivalent to 31.07 mph.
In the question,
By multiplying each speed limits with the conversion factor = 0.6214,
we can get the speed limits in miles per hour.
Therefore,
In Australia on the country roads the speed is 60mph and on the motorways is 66mph.
In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.
In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.
In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.
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The complete question is:
The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to miles. What are these speed limits in miles per hour?
Suppose that the augmented matrix of a system of linear eq [[1,0,5,-(11)/(3)],[-4,1,-23,(68)/(3)],[5,0,25,-(43)/(3)]]
The solution to this system of linear equations is x = 11/3, y = -3/13, and z = 1/12.
The augmented matrix of a system of linear equations is [[1,0,5,-(11)/(3)],[-4,1,-23,(68)/(3)],[5,0,25,-(43)/(3)]]. To solve this system, we can use the process of elimination.
Step 1: Add 4 times row 1 to row 2.
[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[5,0,25,-(43)/(3)]]
Step 2: Subtract 5 times row 1 from row 3.
[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[0,0,15,-(32)/(3)]]
Step 3: Divide row 2 by -13.
[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,15,-(32)/(3)]]
Step 4: Add 3 times row 2 to row 3.
[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,12,-(1)/(13)]]
Step 5: Divide row 3 by 12.
[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,1,(1)/(12)]]
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How can you use place value to find the quotient of a multiple of Value 10 and a number?
By following the 6 steps explained, you can find the quotient of a multiple of 10 and any number.
How to use place value to find quotient?
To use place value to find the quotient of a multiple of 10 and a number, you can use the following steps:
Write down the multiple of 10 and the number being divided.Determine how many times the number being divided goes into the first digit of the multiple of 10.Write down that digit as the first digit of the quotient.Subtract the product of that digit and the number being divided from the first digit of the multiple of 10 to get the remainder.Bring down the next digit of the multiple of 10 to the remainder to form a new dividend.Repeat steps 2-5 until all digits of the multiple of 10 have been used.Learn more about place value here: https://brainly.com/question/25137147
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Three partners luc, Deborah and Melanie R176 496,R29 416 and R102 956
Among Luc, Deborah, and Melanie, the ratio in which the profit was shared is 2:3:7.
Let us assume that the ratio in which the profit shared among the three partners is L:D:M,
We know that the total profit for the year is = R176496,
We also know that Luc received R29416 and
Melanie received R102956.
So, Deborah profit share is calculated as;
⇒ Deborah's share = Total profit - Luc's share - Melanie's share
⇒ Deborah's share = R176496 - R29416 - R102956
⇒ Deborah's share = R44124,
So, now we know that the ratio of the profit shared among the three partners is:
⇒ L:D:M = R29416 : R44124: R102956
To simplify this ratio, we can divide all the amounts by R14708,
We get,
⇒ L:D:M = 2:3:7
Therefore, the profit was shared in the ratio of 8:1:28 among Luc, Deborah, and Melanie.
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The given question is incomplete, the complete question is
Three partners Luc, Deborah and Melanie, share the profits of a business. The profit for the year is R176496. If Luc receives R29416 and Melanie receives R102956, determine the ratio in which the profit was shared.
Perform long division, please clearly show work of remainders
and arrows, where numbers pass down.
Thanks
1. 32.156 / 100
2. 174.787 / 0.01
There are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.
To perform long division, we need to follow these steps:
Set up the long division problem with the dividend on the inside and the divisor on the outside of the division symbol.
Determine how many times the divisor can go into the first digit or group of digits of the dividend.
Write the result above the division symbol and multiply it by the divisor.
Subtract the result from the first digit or group of digits of the dividend.
Bring down the next digit or group of digits from the dividend and repeat the process until there are no more digits to bring down.
The final result is the quotient with any remainders.
For the first problem, 32.156 / 100, we can set it up like this:
```
100 | 32.156
```
Since 100 cannot go into 32, we need to bring down the next group of digits, which is 156. Now we have:
```
100 | 3215.6
```
100 can go into 3215 a total of 32 times, so we write 32 above the division symbol and multiply it by 100:
```
32
100 | 3215.6
-3200
-----
15.6
```
Now we bring down the next group of digits, which is 6:
```
32.1
100 | 3215.6
-3200
-----
156
```
100 can go into 156 a total of 1 time, so we write 1 above the division symbol and multiply it by 100:
```
32.16
100 | 3215.6
-3200
-----
156
-100
-----
56
```
Since there are no more digits to bring down, we are left with a remainder of 56. So the final result is 32.156 with a remainder of 56.
For the second problem, 174.787 / 0.01, we can set it up like this:
```
0.01 | 174.787
```
Since 0.01 cannot go into 174, we need to bring down the next group of digits, which is 787. Now we have:
```
0.01 | 17478.7
```
0.01 can go into 17478 a total of 1747800 times, so we write 1747800 above the division symbol and multiply it by 0.01:
```
1747800
0.01 | 17478.7
-17478
-----
0.7
```
Since there are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.
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Perform the multiplication or division and simplify
x2 + 2xy + y2
x2 − y2
·
3x2 − xy −
2y2
2x2 − xy −
3y2
After performing multiplication or division and simplify we get 2x2 − xy − 3y2 as the answer of this question.
The question is asking you to perform the multiplication or division and simplify:
x2 + 2xy + y2 ÷ x2 − y2 =
(x2 + 2xy + y2)(3x2 − xy − 2y2) ÷ (x2 − y2) =
3x4 − x3y − 2x2y2 − 3xy2 + 2xy3 + 2y4 ÷ (x2 − y2) =
3x4 − x3y − 2x2y2 − 2y4 ÷ (x2 − y2)
= 2x2 − xy − 3y2
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the equation of L is y=5x+1
the equation of L is 2y-10x+3=0
show that these two lines are parallel
The two lines are parallel because both have equal slope.
What area parallel lines?
If two lines do not cross one another anywhere on the plane, they are considered to be parallel. All parallel lines are spaced equally apart from one another.
Numerous forms have parallel lines running along their edges. In the rectangle below, the single and double arrow lines, as well as their junction points, are parallel to one another. Additionally, it is possible to create both horizontal and vertical shapes.
Given : line 1 : y=5x+1
line 2 : 2y-10x+3=0
2y = 10x - 3
We know that, parallel lines always have equal slope.
The slope can be found by using formula :
coefficient of y / coefficient of x
So, here, line 1 has slope = 2/10 = 1/5
and, line 2 has slope = 1/5
So, both have same slopes hence, both are parallel lines.
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I WILL GIVE BRAINLIEST TO WHOEVER ANSWER ALL 3 QUESTIONS RIGHT AND MANY POINTS I BEG PLEASE
In theory think about how many sides are on a dice and the numbers that are shown on each side.
it is a six sided dice
In an experiment the dice is rolled 20 times and lands on 1 two times and on 5 four times.
Find each experimental and theoretical probability.
a) landing on 5
Experimental:
Theoretical
b) not landing on 1
Experimental:
Theoretical:
c) landing on 1
Experimental:
Theoretical:
(please help)
Answer:
a) experimental : 4 ÷ 20 = 1/5 or 20%
Theoretical : 1/6
b) experimental: 18÷20= 9/10 or 90%
Theoretical : 5/6 or 83%
c) experimental: 2÷20 = 1/10 or 10%
Theoretical : 1/6
a farmer can exchange 72 pigs for 54 sheep at a price of 560 each. what is the price of 1 pig
Answer:
72*price of pig= 54*560
price of pig=54*560/72
= 420
When solving with radical exponents, what has to be true in order for you to solve them?
The radical expressions' exponents should match, or you should be able to modify the expressions to make the exponents match.
what is radical ?A radical is a symbol used in mathematics to symbolise the root of a number or mathematical expression. The square root, denoted by the sign, is the most prevalent variety of radical. The result of multiplying the square root of a number by itself is the initial value. For instance, 3 is the square root of 9, as 3 3 Equals 9. Additional values for radicals include cube roots, fourth roots, and so forth. A value that, when raised to the power of n, yields the initial number is known as the nth root of a number.
given
You usually need an equation with a single radical expression or multiple radical expressions that can be combined into a single expression when solving with radical exponents.
The radical expressions' exponents should match, or you should be able to modify the expressions to make the exponents match.
As soon as you have one radical expression, you can separate the radical word and then raise both sides of the equation to the proper power to get rid of the radical.
The resulting solution for the variable can then be solved.
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For what values of a will the quadratic y=ax^(2)-6x+3 have no real zeroes? (1) a=1 (3) a=-5 (2) a=-2 (4) a=7
For a=7 the quadratic equation have no real roots. (4)
For a quadratic equation y=ax^(2)-6x+3 to have no real zeroes, the discriminant of the equation must be less than zero. The discriminant of a quadratic equation is given by the formula b^(2)-4ac, where a, b, and c are the coefficients of the equation. In this case, a=a, b=-6, and c=3.
Plugging these values into the formula for the discriminant, we get:
(-6)^(2)-4(a)(3)<0
36-12a<0
12a>36
a>3
Therefore, the values of a that will make the quadratic equation have no real zeroes are those that are greater than 3. This means that the correct answer is (4) a=7, since this is the only value of a that is greater than 3.
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A certain disease has an incidence rate of 0.8%. If the false negative rate is 8% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.
The probability that a person who tests positive actually has the
the disease is, 10%.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, A certain disease has an incidence rate of 0.8%.
Therefore, The probability that a person who tests positive actually has the disease is,
= (8/0.8)%.
= 10%.
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x^3+x^2y-4y-4x write as a product
Answer: x^3+x^2y–4y–4x = (x-2)(x+2)(x+y)
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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read the ss
PLS HELP
Answer:
(0,4)
Step-by-step explanation:
Your coordinates of your Y-intercept is where the line crosses over the Y line (the vertical line). This means your x (x,y) is always going to be 0 and your y is going to be the number in which the line crosses over your Y-line.
Temperature during an illness: A person's temperature T in degrees Fahrenheit, during an illness is given by the function
T(t) = [4t / (t^(2)+1)] + 98.6
where tis the time since the onset of the illness, in hours. Find the interval on which the temperature was over 100∘F
The interval on which the temperature was over 100°F is (0.79, 1.26).
To find the interval on which the temperature was over 100°F, we need to solve the inequality T(t) > 100.
First, let's rearrange the equation to isolate t:
T(t) = [4t / (t²+1)] + 98.6 > 100
[4t / (t²+1)] > 1.4
4t > 1.4(t²+1)
0 > 1.4t² - 4t + 1.4
Now we can use the quadratic formula to find the values of t that make this inequality true:
t = [-(-4) ± √((-4)² - 4(1.4)(1.4))] / [2(1.4)]
t = (4 ± √(16 - 7.84)) / 2.8
t ≈ 1.26 or t ≈ 0.79
Therefore, the temperature was over 100°F between the interval (0.79, 1.26).
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(73) If you insert number of arithmetic means between - 65 and 125 and the twelveths mean = - 113 , then the number of means = .. (a) 12 (b) 13 (c) 14 (d) 15
The number of means is 13. Option B
How to find the number of meansWe can use the formula for the nth term of an arithmetic sequence to solve the problem. Let d be the common difference and n be the number of terms between -65 and 125.
Then we have:
a + (n-1)d = 125 (1)
a + nd = -113 (2)
Subtracting equation (2) from equation (1), we get:
(n-1)d + 238 = 0
Solving for d, we get:
d = -238/(n-1)
Using the formula for the twelfth term, we have:
a + 11d = -113
Substituting the expression for d, we get:
a - 11(238/(n-1)) = -113
Multiplying both sides by n-1, we get:
a(n-1) - 11(238) = -113(n-1)
Substituting a = -65 and simplifying, we get:
n = 13
Therefore, the number of means is 13
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James invests $5,980 in a retirement
account with a fixed annual interest rate of
5.61% compounded continuously. What
will the account balance be after 17 years?
Answer:
the account balance will be $15, 485.41
Step-by-step explanation:
Compound interest, can be calculated using the formula FV = P*(1+R/N)^(N*T), where FV is the future value of the loan or investment, P is the initial principal amount, R is the annual interest rate, N represents the number of times interest is compounded per year, and T represents time in years.
5890*(105.61/100)*17
=15485.41
Kimani can paddle her kayak 7 miles per hour in still water. It takes her as long to paddle 17.5 miles upstream as it takes her to travel 31.5 miles downstream. Determine the speed of the river's current. Enter an equation with the following properties: 1. It uses the variable c to represent the speed of the river's current in miles per hour. 2. It uses the information as it is given above. 3. It can be solved to answer the question. Equation: How fast is the river's current? σ* miles per hour
a)c = (31.5 - 17.5)/(31.5/7 + 17.5/7)
b)4 mph.
The equation to solve for the speed of the river's current is c = (31.5 - 17.5)/(31.5/7 + 17.5/7) = 4 mph. Therefore, the speed of the river's current is 4 miles per hour.
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A baker needs 15lb of cream cheese that contains 20% fat to fill a big order. But his supplier delivers one cream cheese that contains 10% fat, and another that contains 35% fat. How many pounds of each should a baker combine to fill the order?
Yolanda wants to rent a boat and spend at most $39. The boat costs $7 per hour, and Yolanda has a discount coupon for $3 off. What are the possible numbers of hours Yolanda could rent the boat? Can someone please help me!! ALKES IS A LOT! PLEASE HELP ME!!
The possible numbers of hours Yolanda could rent the boat is 6 hours.
What is inequality?The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().
Here the given boat cost per hour = $7.
Offer he gets = $3.
Now writing a inequality then, t represent number of hours,
=> 7t-3[tex]\le[/tex]39
Now solving this inequality for t then,
=> 7t[tex]\le[/tex]39+3
=> 7t[tex]\le[/tex]42
=> t[tex]\le[/tex]42/7
=>t[tex]\le[/tex]6
Hence the possible numbers of hours Yolanda could rent the boat is 6 hours.
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g in the axis of symmetry ng quadratic function by finding the key features. f(x)=x^(2)-2x-24 Axis of Symmetry:
The axis of symmetry of a quadratic function can be found by taking the negative of the coefficient of the x term, and then dividing it by 2. In this case, the coefficient of the x term is -2, so the axis of symmetry is located at x = -1.
The key features of the quadratic function are the vertex, the y-intercept, and the x-intercepts. To find the vertex, substitute the x-value for the axis of symmetry into the equation. In this case, the vertex is located at (x, y) = (-1, 27).
The y-intercept is found by setting x = 0 and solving for y. This gives us y = -24, so the y-intercept is located at (0, -24).
To find the x-intercepts, set y = 0 and solve for x. In this case, the x-intercepts are located at (2, 0) and (6, 0).
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Aidan and Godwin like saving money when grocery shopping by sharing the costs. Aidan buys 10 cans of soup for $8.69 and a case of (24 cans) of chili for $19.20. Godwin takes 4 cans of soup and 12 cans of chili. Not including sales tax, how much does Godwin owe Aidan?
Calculate the unit rate of the soup
What is the unit rate of the soup?
Calculate the unit rate of the chili
What is the unit rate of the chili?
How much does Godwin owe Aidan?
Answer: To find how much Godwin owes Aidan, we first need to calculate the total cost of the items Aidan purchased:
10 cans of soup for $8.69, so the cost per can of soup is $8.69/10 = $0.869 per can.
1 case of chili for $19.20, so the cost per can of chili is $19.20/24 = $0.80 per can.
Godwin takes 4 cans of soup at $0.869 per can, which is a total of 4 x $0.869 = $3.476 for the soup.
Godwin takes 12 cans of chili at $0.80 per can, which is a total of 12 x $0.80 = $9.60 for the chili.
Therefore, Godwin owes Aidan $3.476 + $9.60 = $13.076.
The unit rate of the soup is $0.869 per can.
The unit rate of the chili is $0.80 per can.
Step-by-step explanation:
Prove that {f € C°([0,1]) ||. f()dx = 0} is a vector space under the usual addition and scalar multiplica- tion of functions (recall that cº([0,1]) is the vector space of continuous real valued functions defined on the domain [0, 1]). For those that don't recall, the addition and scalar multiplication is defined "pointwise".
(f o g) (x) = f(x) + g(x) (r o f) (x) = rf(x)
To prove that {f € C°([0,1]) ||. f()dx = 0} is a vector space, we need to verify the following properties:
Closure under addition: Let f,g be two functions in {f € C°([0,1]) ||. f()dx = 0}. Then, for any x € [0,1], we have:
(f+g)(x) = f(x) + g(x)
Now, we can calculate the integral of (f+g)(x) from 0 to 1 as follows:
∫0^1 (f+g)(x) dx = ∫0^1 f(x) dx + ∫0^1 g(x) dx
Since f and g are in the set {f € C°([0,1]) ||. f()dx = 0}, we know that ∫0^1 f(x) dx = 0 and ∫0^1 g(x) dx = 0. Therefore, we have:
∫0^1 (f+g)(x) dx = 0
This means that f+g is also in the set {f € C°([0,1]) ||. f()dx = 0}, and thus the set is closed under addition.
Closure under scalar multiplication: Let f be a function in {f € C°([0,1]) ||. f()dx = 0} and let r be a scalar. Then, for any x € [0,1], we have:
(rf)(x) = r*f(x)
Now, we can calculate the integral of (rf)(x) from 0 to 1 as follows:
∫0^1 (rf)(x) dx = r*∫0^1 f(x) dx
Since f is in the set {f € C°([0,1]) ||. f()dx = 0}, we know that ∫0^1 f(x) dx = 0. Therefore, we have:
∫0^1 (rf)(x) dx = 0
This means that rf is also in the set {f € C°([0,1]) ||. f()dx = 0}, and thus the set is closed under scalar multiplication.
Existence of zero vector: The zero vector is the function f(x) = 0 for all x € [0,1]. This function clearly satisfies the condition that ∫0^1 f(x) dx = 0, and thus it is in the set {f € C°([0,1]) ||. f()dx = 0}.
Existence of additive inverse: Let f be a function in {f € C°([0,1]) ||. f()dx = 0}. Then, the additive inverse of f is -f(x) for all x € [0,1]. This function clearly satisfies the condition that ∫0^1 -f(x) dx = -∫0^1 f(x) dx = 0, and thus it is also in the set {f € C°([0,1]) ||. f()dx = 0}.
Since all the four properties are satisfied, we can conclude that {f € C°([0,1]) ||. f()dx = 0} is a vector space under the usual addition and scalar multiplication of functions.
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How many different two-digit numbers can be formed using the
digits 3,9,4,7,6,1,2 and 8 with repetition?
There are 64 different two-digit numbers that can be formed using the digits 3,9,4,7,6,1,2 and 8 with repetition.
To see why, note that there are 8 possible choices for the first digit (any of the 8 given digits can be used) and 8 possible choices for the second digit (again, any of the 8 given digits can be used). Therefore, by the multiplication principle of counting, there are 8x8=64 possible two-digit numbers that can be formed.
To find all possible two-digit numbers, simply list all possible combinations of the given digits, allowing repetition. One example would be: 11, 12, 13, ..., 98, 99.
Alternatively, you can use the formula for counting with repetition, which is n^k where n is the number of choices for each digit and k is the number of digits. In this case, n=8 (since there are 8 possible digits) and k=2 (since we want two-digit numbers). Therefore, the total number of possible two-digit numbers is 8^2=64.
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What is the first step in solving this system by elimination if we want to eliminate
the x variable first?
5x + y = 9
10x - 7y = -18
multiple choice
1. Add both equations together
2.Divide the bottom equation by 5
3.Subtract the bottom equation from the top
4.Multiply top equation by 2
The first step in solving by elimination is (4) Multiply top equation by 2
How to determine the first step in solving by eliminationFrom the question, we have the following parameters that can be used in our computation:
5x + y = 9
10x - 7y = -18
To eliminate x the coefficient of x in both equations muet be the same i.e 10
Using the above as a guide, we have the following:
Multiply (1) by 2
So, we have
10x + 2y = 18
10x - 7y = -18
Hence, the first step is (4)
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how many possible meals can be made by choosing a dinner from 6 main courses, 4 vegetables, 2 salads, and 3 beverages
Just multiplying the amount of possibilities in each category together will give us the total number of meals that can be made using the options provided.
This is known as the Fundamental Counting Principle. Using this principle, the total number of possible meals is:
6 main courses × 4 vegetables × 2 salads × 3 beverages = 144 possible meals
Therefore, there are 144 possible meals that can be made by choosing from the given options.
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Math is not my thing helpppppppppppppppppp
Answer: 3, 5, and 7
Step-by-step explanation:
Vertical angles, corresponding angles, and alt. ext. angles