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3 years ago

Help me solve this please

Mathematics

1 answer:

Phoenix [80]3 years ago

7 0

Step-by-step explanation:

8x + 4y <= 136

2x + y <= 34

trying (15, 9) :

2x + 7y <= 70

2×15 + 7×9 <= 70

30 + 63 <= 70

93 <= 70

that does not work. so, (15, 9) is not a valid point of f(x, y) and therefore also no maximum.

trying (0, 10) :

2×0 + 7×10 <= 70

70 <= 70

that is true.

2×0 + 10 <= 34

10 <= 34

also true.

so, (0, 10) is the correct answer option.

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Determine whether each of these functions from {a, b, c, d} to itself is one-to-one, onto, bijective. (a) f(a)=b, f(b)=a, f(c)=c

Monica [59]

Answer:

See below

Step-by-step explanation:

Let S={a,b,c,d}. f : S→S is 1-1, if different elements of S have different images respect to f. f is onto if f(S)={f(x)|x∈S}=S. f is bijective if f is 1-1 and onto.

a) f is 1-1. Indeed, each element of S has a different image respect to f, thus no different elements of S have the same image (f(x)≠f(y) if x≠y).

f is onto, because f(S)={f(a),f(b),f(c),f(d)}={b,a,c,d}={a,b,c,d}=S. Then the direct image of f is equal to the codomain S, hence f is onto.

f is 1-1 and onto, hence f is bijective.

b) f is not 1-1. a≠b but f(a)=b=f(b).

f is not onto. a∈S, but there is not element x such that f(x)=a. In other words, the direct image f(S)={f(a),f(b),f(c),f(d)}={b,b,c,d}={b,c,d} is not equal to S.

f is not bijective, since f is not 1-1.

c) f is not 1-1. a≠d but f(a)=d=f(d).

f is not onto. a∈S, but there is not element x such that f(x)=a. In other words, the direct image f(S)={f(a),f(b),f(c),f(d)}={d,b,c,d}={b,c,d} is not equal to S.

f is not bijective, since f is not onto.

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3 years ago

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Step-by-step explanation:

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3 years ago

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3 years ago

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tresset_1 [31]

Answer:

h=1/2fg

Step-by-step explanation:

Solve for x, h=1/2fg

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h=1/2fg

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3 years ago

Which of the following statements about the percentiles for the standard normal distribution are correct? A. The 90th percentile

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Answer:

Correct option: (C) The 75th percentile is approximately 0.67

Step-by-step explanation:

The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.

If x is the pth percentile of a data set then,

P (X < x) = p/100

If $X\sim N(\mu, \sigma^{2})$ then $Z=\frac{X-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, $Z \sim N (0, 1)$ .

The 90th percentile of a standard normal distribution is:

P (Z < z) = 0.90, then z = 1.28

The 10th percentile of a standard normal distribution is:

P (Z < z) = 0.10, then z = -1.28

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P (Z < z) = 0.75, then z = 0.67

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P (Z < z) = 0.15, then z = -1.04

Thus, the correct statement is (C).

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