Landon had 56 playing cards. He kept 12 for himself and
dealt the rest evenly to his 4 friends. Which expression best
represents the number of cards each friend received?
We need to use simple division to solve the problem. The number of cards each friend received is 11.
It is said that Landon has 56 cards, he kept 12 cards for himself, so we can subtract 12 cards from the whole lot to get the total number of cards he distributes among his friends.
56-12=44
There are 44 cards that he will distribute among his friends equally, we can get that by simply dividing the total number of cards by the number of friends which is 4.
number of cards for each friend=44/4=11
Therefore the number of cards each friend received is 11.
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the cost per hour for fuel to run a train is v2 15 dollars, where v is the speed of the train in miles per hour. (note that the cost goes up as the square of the speed.) other costs, including labor, are $300 per hour. how fast should the train travel on a 300-mile trip to minimize the total cost for the trip?
The train should travel at a speed of 30√5 miles/hour on a 300-mile trip to minimize the total cost for the trip?
Given the cost per hour for fuel to run is v^2/15 dollars:
Labor cost=$300 per hour
Calculate the velocity to travel on a 300-miles trip:
Total time t=Distance/speed
=300/v
t=300/v
Total cost=(fixed cost*time)+(variable cost*time), where fixed cost is $300 per hour and variable cost is v^2/15 dollars , and time t=300/v
Total cost=(300*300/v)+((v^2/15)*(300/v))
=(90000/v)+(300v/15)
Now, to minimize the total cost on a 300-mile trip, we differentiate the total cost with respect to the velocity:
Let the d/dv of total cost be C(v):
C(v) =(-90000/v^2+300/15=0
(-90000/v^2+300/15)=0
90000/v^2=300/15
90000/v^2=20
v^2=90000/20
v^2=4500
v=√4500
v=30√5 miles/hour
Hence, the speed is 30√5 miles/hour
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Write the domain for the following piecewise-defined function using intervalnotation,2 if x < 1f(x) =1 2 – x2 if x > 1
The domain of a function are the values for which the function is defined or in the other words, it is the set of all possile values that the function accepts.
Therefore:
[tex](-\infty,1)U(1,\infty)[/tex]Jamie thinks that 1 is neither prime
nor composite.
Show why you agree or disagree with him.
Yes, I do agree with Jamie.
1 is NEITHER a prime number NOR a composite number.
Reason for agreeing:-
We know that a PRIME NUMBER is any given number that has only one as a factor. I.e it is only divisible by 1 AND ITSELF.
And, a COMPOSITE NUMBER is any number that is divisible by a number other than one and itself.
Here in the case of 1, we see that it is divisible by 1 and itself, and since it cannot have any other factor we can't put in either of the two categories
how many apples does john eat
Answer:
you gave no context....so ill just guess 3.
Determine the approximate value of d.
4.29 cm
5.32 cm
6.24 cm
7.16 cm
Approximate value of d = 4.29 cm.
What is cosine rule?The Cosine Rule states in trigonometry that the square of the length of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of angle contained between them. Cosine rule is also known as the law of cosines or the Cosine Formula.
In Δ ADR , AR = d, DR = 8 cm. AD = 5 cm. ∠D = 28°
By using cosine rule,
AR² = AD² + DR² - 2 AD ×DR CosD
AR² = 5² + 8² - 2×(5)×(8) × Cos 28°
AR² = 25 + 64 - 80 Cos 28°
AR² = 89 - 80 Cos 28°
AR² = 89 - 80 × (0.8829)
AR² = 89 - 70.6358
AR² = 18.3641
AR = 4.29 cm. = d
Thus, approximate value of d = 4.29 cm.
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-27 = -w/5 solve for w simplify your answer as much as possible
Answer:
w = 135
Step-by-step explanation:
-27 = -w/5
multiply both sides by 5:
5(-27) = 5(-w/5)
- 135 = -w
divide both sides by -1:
- 135/-1 = -w/-1
w = 135
pls help
im grade 6
Math plsss help me ill give you 10 points
Answer:
7.25
Step-by-step explanation:
Barangay Maligaya is 28.5km
Since Ricardo traveled 12.75km by Jeep and 8.5km by tricycle and rest by hiking
Jeep = 12.75
Tricycle = 8.5
Hiking = 12.75 + 8.5
=21.25
Total= 28.5
=28.5 -21.25
= 7.25
Identify which of the twelve basic functions listed below fit the description.
The four functions with a local minima are:
y = x², y = |x|, y = sin x, y = cos x
A function f(x) has a local minima if its second derivative, f''(x) > 0 at the point where f'(x) = 0.
We use this to find which among the functions y = x, y = x², y = x³, y = |x|, y = 1/x, y = eˣ, y = √x, y = ln x, y = sin x, y = cos x, y = int(x), y = 1/(1+e⁻ˣ) has a local minima.
y = xy' = 1. There is no point x such that y' = 0. So it has no local minima.
y = x²y' = 2x
y' = 0
⇒ 2x = 0
⇒ x = 0
y'' = 2 > 0
So y = x² has a local minima at x = 0
y = x³y' = 3x²
y' = 0
⇒ 3x² = 0
⇒ x = 0
y'' = 6x = 0 at x = 0
So y = x³ has no local minima.
y = |x|i.e., y = x, when x ≥ 0 and y = -x , when x < 0
So y ' = 1, when x ≥ 0 and y' = -1, when x < 0
But at x = 0, y = 0 and y' = 0.
Now y'' = 0 everywhere. But the graph of y = |x| clearly shows that y = |x| has a local minimum at x = 0.
y = 1/xy' = -1/x²
Here, y' is nowhere zero and hence doesn't has a local minima.
y = eˣy' = eˣ
eˣ is nowhere zero and hence it does not has a local minima.
y = √xy' = 1/2√x
Here also y' is nowhere zero and hence it does not has a local minima.
y = ln xy' = 1/x
Here also y' is nowhere zero and hence it does not has a local minima.
y = sin xy' = cos x
y' = 0
⇒ cos x = 0
⇒ x = (2n+1)π/2, n = 0,1,2,....
y'' = -sin x
-sin ((2n+1)π/2) = -1, when n = 0,2,4,... and -sin ((2n+1)π/2) = 1, when n = 1,3,5,....
So y = sin x has local minima at x = (2n+1)π/2, where n = 1,3,5,....
y = cos xy' = -sin x
y' = 0
⇒ -sin x = 0
⇒ x = nπ
y'' = -cos x
-cos(nπ) = (-1)ⁿ⁺¹
So, -cos(nπ) = 1, when n = 1,3,5,.... and -cos(nπ) = -1, when n = 0,2,4,...
Hence y = cos x has local minima at x = nπ with n = 1,3,5,....
y = int(x)y' = x
y' = 0
⇒ x = 0
y'' = 1 >0
So y = int (x) has local minima at x = 0
y = 1/(1+e⁻ˣ)y' = e⁻ˣ/(1+e⁻ˣ)²
y' = 0
⇒ e⁻ˣ/(1+e⁻ˣ)² = 0
⇒ e⁻ˣ = 0
⇒ 1/eˣ = 0 which is not possible anywhere.
Hence y = 1/1+e⁻ˣ has no local minima.
Finally the four functions with local minima are:
y = x², y = |x|, y = sin x, y = cos x
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Determine if √64 is rational or irrational and give a reason for your answer.
For one journey from London to Marseille, the ratio number of adults: number of children = 11: 2. There were 220 adults in total on this journey. All of the children and 70% of the adults paid the standard fare. The remaining adults paid the premier fare. Calculate the total of the fares paid by the adults and the children.
Answer: 174
Step-by-step explanation: ok so we divide 220 by 11 to get 20 and times that by two to get 20 children on this journey then see that all children paid and 70 percent of adults so 70 percent of 220 is 154 and then 154 + 20 is 174 so thats the number of fares paid
write a pair of fractions whose sum is 7/11and difference is 3/11
If;
[tex]\frac{x}{11}=a[/tex] and[tex]\frac{y}{11} =b[/tex]then these variables must meet the following conditions below;
[tex]a+b=\frac{7}{11}[/tex][tex]a-b=\frac{3}{11}[/tex]In rational expressions (fractional numbers), if the denominators are equal, arithmetic operations are performed with the numerators. Therefore;
[tex]x+y=7[/tex][tex]x-y=3[/tex]If we add both equations at the same time, we get the following result;
[tex]x+y+x-y=7+3[/tex][tex]2x=10[/tex][tex]x=5[/tex]Now that we have found the unknown x, we can find the unknown y.
[tex]x+y=7[/tex][tex]5+y=7[/tex][tex]y=2[/tex]Now let's write our fraction pairs.
[tex](\frac{5}{11},\frac{2}{11} )[/tex]Answer:
[tex]\frac{5}{11}[/tex] and [tex]\frac{2}{11}[/tex]
Step-by-step explanation:
let the 2 fractions be x and y , x > y , then
x + y = [tex]\frac{7}{11}[/tex] → (1)
x - y = [tex]\frac{3}{11}[/tex] → (2)
add the 2 equations term by term to eliminate y
2x + 0 = [tex]\frac{10}{11}[/tex]
2x = [tex]\frac{10}{11}[/tex] ( divide both sides by 2 )
x = [tex]\frac{5}{11}[/tex]
substitute x = [tex]\frac{5}{11}[/tex] into (1) and solve for y
[tex]\frac{5}{11}[/tex] + y = [tex]\frac{7}{11}[/tex] ( subtract [tex]\frac{5}{11}[/tex] from both sides )
y = [tex]\frac{2}{11}[/tex]
the pair of fractions are [tex]\frac{5}{11}[/tex] and [tex]\frac{2}{11}[/tex]
Marta does 30 minutes of exercise a day. greg des 40 minutes of exercise a day. how many more minutes does marta exercise greg in one month of 31 days? answers
Answer:
Martha exercises 310 minutes more than Greg in a 31-day month!
Step-by-step explanation:
30x
40x
Where x equals the number of days.
Let's plug it in:
30(31) = 930
40(31) = 1240
Let's subtract:
1240 - 930 = 310
MEANING Marta exercises 310 minutes more than Greg in a 31-day month!
x-2=4(x+1) divided by 2
33 1/3 of 66 is i will give points if help
Answer: 2200
Step-by-step explanation:
33 1/3 of 66
Marilyn purchased 2,000 shares of stock for $25.43 per share. She sold them for $44.10 per share. Express her capitol gain to the nearest tenth of a percent.
Marilyn's capital gain is 73%.
How to find her capital gain?
Marilyn purchased 2,000 shares
$25.43 per share
She sold them for $44.10 per share
Solution:
Capital gain per share = 44.10 - 25.43 = $18.67
Capital gain for 2,000 shares = 2000*18.67
= $37,340
Her capital gain is $37,340.
The price of 2000 shares she bought initially = 2,000*25.43
= $50,860
Her capital gain in percentage = 37,340/50,860*100
= 73.41
That is,
73%
Her capital gain is 73%.
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2 $ 11 OA 1 2 3 4 5 -2 4 4 2 OB $ 4 5 2 1 C. 1 2 3 4 5 3 2 D.
C is the correct option
Here, we want to selct which of the plotted points in the graphs correctly represent the given points
The given points are (2,21/2) and (-1 1/2,-4)
As we can see on the graphs, there are four different marked points
We just need to select the graph that contains the points
What the point (2, 2 1/2) means is that we have point 2 on the x-axis and trace point 2 1/2 on the y-axis
This point is missing in the first two options
However, on the third option C, we can see this option
We can check if the second option is there too
(-1 1/2 , -4)
We have -1 1/2 on the x-axis and -4 on the y-axis
We can see this on the third option too
So option C is our correct answer
Margie’s work for adding linear expressions is shown below. After checking her answer key, she solved it incorrectly.
Given: (-3.78b + 12) - (4.82b - 16)
Step 1: -3.78b + 12 + -4.82b - 16
Step 2: -3.78b + -4.82b + 12 - 16
Step 3: (-3.78b + 4.82b) + (12 - 16)
Step 4: -8.6b + (-4)
Part A: Identify and explain the first step where Margie made an error
Part B: Explain how to correctly write the expression in the fewest terms by correcting the error in Part A.
There is a mistake in the first step. The correct way to add the linear expression is (−3.78b + 12) − (4.82b − 16) = -8.6b + 18
How to correctly write adding linear expression?An expression is used to show the relationship between the variables.
The linear expression to add is as follows: (−3.78b + 12) − (4.82b − 16)
Firstly we open the bracket on the right side by multiplying the negative sign by the numbers in the brackets.
(−3.78b + 12) − (4.82b − 16)
−3.78b + 12 - 4.82b + 16
Combine like terms
−3.78b + 12 - 4.82b + 16
-3.78b - 4.82b + 12 + 16
Add the like terms
-3.78b - 4.82b + 12 + 16
-8.6b + 18
Therefore, she made the mistake in the first step.
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Simplify before multiplying 15/20 x 2/5
Thanks!
Answer:
3/10 hope this helps you answer your question!
Simplify the expression. Show your work.
[tex]\sqrt{\frac{4x^2}{3y} }[/tex]
[tex]\sqrt{\cfrac{4x^2}{3y}}\implies \cfrac{\sqrt{4x^2}}{\sqrt{3y}}\implies \cfrac{\sqrt{2^2x^2}}{\sqrt{3y}}\implies \cfrac{2x}{\sqrt{3y}}[/tex]
Answer:
[tex]\frac{2x}{\sqrt{3y} }[/tex]
Step-by-step explanation:
Hope that's helps.
12] Will's salary is three times Nathan's salary. Together they earn $192 per week. Find the salary of each boy.
Nathan's salary is $48 and Will's salary which three times of Nathan's salary is $144.
What is salary?
An employment contract may include a salary clause as a type of recurring payment from an employer to an employee. In contrast, piece wages are paid separately for each job, hour, or other unit rather than on a regular schedule. Salary can also be seen from the perspective of operating a corporation as the expense of obtaining and keeping employees to carry out operations; this is known as a personnel expense or salary expense. Payroll accounts are used in accounting to record salaries.
It is given in the question that Will's salary is three times Nathan's salary.
So, lets assume that Nathan's salary is X it implies that Will's salary will be 3 times X = 3X
Together they earn $ 192.
So,
X + 3X = 192
4X = 192
X = 192/4
X = 48
Therefore, Nathan's Salary is $48
Since, Will's salary is 3 times of Nathan's salary,
So,
Will's salary = 3 (48) = 144
Therefore, Will's Salary is $144
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Walter pays 2.53 to ship a package that weighs 5.5 onces. which is the cost to ship 1 ounce
To determine the price per ounce walter paid to ship the package you can use cross multiplication.
If 5.5 ounces ______$2.53
Then 1 ounce______$x
[tex]\begin{gathered} \frac{2.53}{5.5}=\frac{x}{1} \\ x=0.46 \end{gathered}[/tex]He will pay $0.46 per ounce
1080 sec: 6 min: 1080 sec simplified
Answer: 18 mins
Step-by-step explanation
there is 3600 secs in an hour so do the same for this.
6 mins is 360 secs and times 360 by 3 is 1080 and then double it they figure out how many mins is 2160 im sorry if thats confusing.
A group of friends go to the store buy some fruit. marcus buys 5 pounds of apples for $13.75 at this rate ,how many pounds of apples can marcus buy with $22
Answer:
He can buy 8 pounds
Step-by-step explanation:
13.75/5=2.75
22/2.75=8 or 8 pounds the to check your answer 2.75x8=22
a manufacturer produces a metal box with a square base, no top, and a volume of h w w 50 cm3 what dimensions minimize the amount of metal used to make the box.
the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm
Let the side of the square base be x
h be the height of the box
Volume V = x²h
50 = x²h
h = 50/x² ..... 1
Surface area = x² + 2xh + 2xh
Surface area S = x² + 4xh ...... 2
Substitute 1 into 2;
From 2; S = x² + 4xh
S = x² + 4x(50/x²)
S = x² + 200/x
To minimize the amount of material used; dS/dx = 0
dS/dx = 2x - 200/x²
0 = 2x - 200/x²
0 = 2x³ - 200
2x³ = 200
x³ = 100
x = ∛100
x = 4.6416cm
Since V = x²h
50 = 4.642²h
h = 50/21.548
h = 2.32cm
Hence the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm
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how do you Graph the line y=4x-1
Answer: Look at photo. Your y intercept is -1 and the line goes up 4 and right 1.
Step-by-step explanation: Look at your last number, the -1. That should be on the y axis. Put that number there and then take 4x which can also be read as 4/1x and from the point of -1, go up 4 and right 1.
the graph of a function f is shown above. at which value of x is f continuous, but not differentiable?
a) a
b) b
c) c
d) d
e) e
Answer:
d
Step-by-step explanation: d
Dennis's curtain company is making curtains for a local hotel. He wants each curtain to be 48 inches long. At the fabric store, fabric is sold by the foot. If Dennis's curtain company wants to make 63 curtains, how many feet of fabric will he need?
Dennis's curtain company needs 252 feet long fabric to make 63 curtains.
Given,
The length of a curtain = 43 inches
Number of curtains they want to make = 63
We have to find the length of fabric in foot needed to make 63 curtains.
1 foot = 1/12 inches
Now,
The total length of fabric needed in inches = Number of curtains × Length of 1 curtain = 63 × 48 = 3024 inches
Convert this into feet.
That is,
3024 × 1/12 = 252 feet.
Therefore,
Dennis's curtain company needs 252 feet long fabric to make 63 curtains.
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Heston is thinking of a fraction equivalent to 6/7.
The numerator is greater than 20 and the denominator is less than 30.
What fraction is Heston thinking of?
i need help with this. it’s just geometry
Answer:
27. 48°, 132°
28. The expressions resolve to both angles being 0°, a contradiction to the lines being distinct.
Step-by-step explanation:
Given a figure showing parallel lines crossed by a transversal with marked angles, you want to know (27) the measures of consecutive interior angles that have a ratio of 4:11, and (28) the contradiction in corresponding angles being marked (60-2x)° and (2x-60)°.
27. Algebra.The two marked angles are consecutive interior angles, so are supplementary. Using x for the smaller angle value, we can write the equation ...
x/(180-x) = 4/11 . . . . . the given ratio of the two angles
Multiplying by 11(180-x) gives ...
11x = 4(180-x)
15x = 4(180) . . . . add 4x and simplify
x = 48 . . . . . . . . divide by 15
Then the obtuse angle is ...
180 -48 = 132
The measures of the angles are ∠1 = 48°, ∠2 = 132°.
2. Error Analysis.The two marked corresponding angles are congruent, so ...
(60 -2x)° = (2x -60)°
4x = 120 . . . . . . . . . . . divide by °, add 2x+60
x = 30 . . . . . . . . . . divide by 4
60 -2x = 60 -2(30) = 0
2x -60 = 2(30) -60 = 0
The marked values require the angles to be 0°, which means the transversal is coincident with each of the "parallel" lines.
The given angle values require the lines not to be distinct, as the diagram shows they are.