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timofeeve [1]
3 years ago
5

At a local store, kelly and martin bought some notebooks and pencils. Kelly bought 4 notebooks and 25 pencils for 16.71. Martin

bought 6 notebooks and 20 pencils for 21.74 what is the cost of 1 notebook and 5 pencils
Mathematics
1 answer:
Nat2105 [25]3 years ago
6 0
Let n = cost of 1 notebook
Let p = cost of 1 pencil

Then,

3n + 4p = 8.5
5n + 8p = 14.5

You can solve for one variable in terms of the other and then substitute into the remaining equation.

3n + 4p = 8.5
+ 5n + 8p = 14.5

Multiply the top equation by -2 so that the p-containing terms cancel each other out:

-2(3n + 4p = 8.5)
+ 5n + 8p = 14.5
-n + 0 = -2.5

So after dividing both sides by -1, we see that n = $2.5. Plugging into the first equation gives p = $0.25.


3n + 4p = 8.5
5n + 8p = 14.5
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8m +7=8m+5<br> PLEAE HELP ASAP
bixtya [17]

Answer: 0 = − 2, Is the answer I think. Sorry if it's wrong.

5 0
2 years ago
If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of
seropon [69]

Answer:

0.347

Step-by-step explanation:

n = 3

p = 1/6

r = 1

Use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

P = ₃C₁ (1/6)¹ (5/6)³⁻¹

P = 0.347

Or, using a calculator:

P = binompdf(n, p, r)

P = binompdf(3, 1/6, 1)

P = 0.347

7 0
3 years ago
one batch of cookies makes 24 cookies. the recipe calls for 1 3/4 cups of flour. if Sarah needs to make 60 cookies how much flou
Svetllana [295]

Answer:

4 3/8 cups of flour needed for 60 cookies

Explanation:

You can multiply 24 by 2.5 to get 60 so you'd multiply the cups of flour by 2.5 as well. You multiply both of them by the same number because it's a ratio. You'd multiply then simplify to get the answer 4 3/8 cups of flour.

7 0
3 years ago
What is the value of z?
VashaNatasha [74]

Answer:

z = 61

Step-by-step explanation:

The exterior angle is congruent (equal to) the sum of the 2 farthest angles from it, so you can set the equation like this:

z + z - 11 = z + 50

Add like terms, which would be the 2 "z's" on the left side:

2z - 11 = z + 50

Then subtract the z on the right side from both sides:

2z - 11 = z + 50

-z          -z

___________

z - 11 = 50

Add 11 to both sides:

z - 11 = 50

  + 11    +11

________

z = 61

6 0
3 years ago
Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer
agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming:  the function is f(x)=x^{2} in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if  both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

g'(0)=g'(1)

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0

g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]

This is what the Bilateral Theorem says:

\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L

4 0
3 years ago
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