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erma4kov [3.2K]
2 years ago
13

Eve plays basketball. She makes 5 free throws for every 3 free throws that she misses. If she missed 36 free throws at her last

practice, how many free throws did she make?
Mathematics
1 answer:
jenyasd209 [6]2 years ago
4 0

Answer:

60

Step-by-step explanation:

We can write a proportion to solve

5 made        x made

------------   = -----------

3 missed      36 missed

Using cross products

5 * 36 = 3x

Divide each side by 3

5 * 36/3 = 3x/3

50 = x

She made 60

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Which of the following statements is true?
SIZIF [17.4K]

1. is true

2. is true

3. true because the sign is greater than or equal to.

4. true

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4 0
3 years ago
Determine the minimum value of f(x, y, z) = 2x 2 + y 2 + 2z 2 + 5 subject to the constraint 3x + 2y + 3z = 4. +
vlada-n [284]
<span>We want to optimize f(x,y,z)=x^2 y^2 z^2, subject to g(x,y,z) = x^2 + y^2 + z^2 = 289. 

Then, ∇f = λ∇g ==> <2xy^2 z^2, 2x^2 yz^2, 2x^2 y^2 z> = λ<2x, 2y, 2z>. 

Equating like entries: 
xy^2 z^2 = λx 
x^2 yz^2 = λy 
x^2 y^2 z = λz. 

Hence, x^2 y^2 z^2 = λx^2 = λy^2 = λz^2. 

(i) If λ = 0, then at least one of x, y, z is 0, and thus f(x,y,z) = 0 <---Minimum 
(Note that there are infinitely many such points.) 
(f being a perfect square implies that this has to be the minimum.) 

(ii) Otherwise, we have x^2 = y^2 = z^2. 
Substituting this into g yields 3x^2 = 289 ==> x = ±17/√3. 

This yields eight critical points (all signage possibilities) 
(x, y, z) = (±17/√3, ±17/√3, ±17/√3), and  
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I hope this helps! </span><span>
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8 0
3 years ago
4
VLD [36.1K]
Answer is D. 81

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4 0
3 years ago
19. Marianna wants to buy a new tennis racket that
Tema [17]

Answer:

11 weeks

Step-by-step explanation:

30-8=22

22/2= 11

7 0
3 years ago
An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the
lora16 [44]

Answer:

Expected benefit under this policy = $ 2694

Step-by-step explanation:

Given - An insurance policy on an electrical device pays a benefit of

            4000 if the device fails during the first year. The amount of the

            benefit decreases by 1000 each successive year until it reaches 0.

            If the device has not failed by the beginning of any given year, the

            probability of failure during that year is 0.4.

To find - What is the expected benefit under this policy ?

Proof -

Let us suppose that,

The benefit = y

Given that, the probability of failure during that year is 0.4

⇒Probability of non-failure = 1 - 0.4 = 0.6

Now,

If the device fail in second year , then

Probability = 0.6×0.4

If the device fail in third year, then

Probability = 0.6×0.6×0.4 = 0.6² × 0.4

Going on like this , we get

If the device is failed in n year, then

Probability = 0.6ⁿ⁻¹ × 0.4

Now,

The probability distribution is-

Benefit , x       4000       3000             2000            1000              0

P(x)                 0.4         0.6×0.4         0.6² × 0.4     0.6³ × 0.4     1 - 0.8704

                      (0.4)       (0.24)            (0.144)         (0.0864)       (0.1296)

At last year, the probability = 1 - (0.4+ 0.24+ 0.144+ 0.0864) = 1 - 0.8704

Now,

We know that,

Expected value ,

E(x) = ∑x p(x)

       = 4000(0.4) + 3000(0.24) + 2000(0.144) + 1000(0.0864) + 0(0.1296)

       = 1600 + 720 + 288 + 86.4 + 0

       = 2694.4

⇒E(x) = 2694.4 ≈ 2694

∴ we get

Expected benefit under this policy = $ 2694

5 0
2 years ago
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