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shtirl [24]
1 year ago
15

If the range of the function y = f(x) is {y | y ≥ 11, y ∈ R}, then the range of the new function g(x) = f(x + 2) - 3 is

Mathematics
1 answer:
mafiozo [28]1 year ago
3 0

Answer:

y ≥ 8

Explanation:

Note that if f(x) is transformed into f(x + a) - b

The original functions is shifted a units to the left and b units downward.

Horizontal shifting will not affect the range of the function, only vertical shifting will change its range.

From the given, g(x) is the transformation of f(x) with

g(x)=f(x+2)-3_{}

f(x) is shifted 2 units to the left and 3 units downward, we will disregard the horizontal shifting.

Since f(x) has a range of y ≥ 11, and g(x) is 3 units downward, the range will also move 3 units downward.

y ≥ 11 - 3

The answer is y ≥ 8

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Mercury is a naturally occurring metal that can be harmful to humans. The current recommendation is for humans to take in no mor
kirill [66]

Answer:

A.) A person weights 80 kg can consume Haddock fish = 149 grams

B.) A person weights 80 kg can consume Swordfish fish = 8 grams

C.) A person weights 80 kg can consume Tuna fish = 23 grams

D.) A person weights 80 kg can consume Snapper fish = 50 grams

Step-by-step explanation:

Given - Mercury is a naturally occurring metal that can be harmful to humans. The current recommendation is for humans to take in no more than 0.1 microgram for every kilogram of their weight per day. Fish generally carry high levels of mercury, although certain fish have higher mercury content than others. Fish, however, are healthy sources of many other nutrients, so nutritionists recommend keeping them in the human diet. The figure below shows the average mercury content of several types of fish.

To find - If a person weighs 82 kg, how much of each fish can they safely consume? round to the nearest gram.

A.Haddock

B.Swordfish

C.Tuna

D.Snapper​

Proof -

Firstly, determine how many micro grams of mercury a person can consume who weighs 82 kilograms.

⇒82 × 0.1 =  8.2 micro grams.

Now,

a.)

For Haddock fish-

It consumes 0.055 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.055

                                              = 149.09 ≈ 149 grams

So,

A person weights 80 kg can consume Haddock fish = 149 grams

b.)

For Swordfish fish-

It consumes 0.995 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.995

                                              = 8.24 ≈ 8 grams

So,

A person weights 80 kg can consume Swordfish fish = 8 grams

c.)

For Tuna fish-

It consumes 0.350 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.350

                                              = 23.43 ≈ 23 grams

So,

A person weights 80 kg can consume Tuna fish = 23 grams

d.)

For Snapper fish-

It consumes 0.165 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.165

                                              = 49.697 ≈ 50 grams

So,

A person weights 80 kg can consume Snapper fish = 50 grams

6 0
3 years ago
The explicit formula for an arithmetic sequence is an = 20 + (n − 1)(2). What is the 200th term?
Andrews [41]

Answer:

a_{200}=418

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given by :

a_n=20+(n-1)2 ...(1)

We need to find the 200th term of the sequence.

Put n = 200 in equation (1)

a_{200}=20+(200-1)2\\\\=20+199\times 2\\\\=418

So, the 200th term of the sequence is 418.

7 0
3 years ago
TRUE OF FALSE
Keith_Richards [23]

Answer:

false it does not change the shape but it does change the size

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
-3(-x+4)=5+3(x+1) please help​
Lostsunrise [7]

Answer:

No solution.

Step-by-step explanation:

Step 1: Write equation

-3(-x + 4) = 5 + 3(x + 1)

Step 2: Solve for <em>x</em>

  1. Distribute: 3x - 12 = 5 + 3x + 3
  2. Combine like terms: 3x - 12 = 3x + 8
  3. Subtract 3x on both sides: -12 ≠ 8

Here, we see that <em>x</em> has to equal no solution. No value of <em>x</em> would make the equation true.

3 0
3 years ago
Read 2 more answers
A study investigated whether price affects people's judgment. Twenty people each tasted six cabernet sauvignon wines and rated h
patriot [66]

Answer:

t=5.5080( to 3 d.p)

Step-by-step explanation:

From the data given,

n =20

Deviation= 34/20= 1.7

Standard deviation (sd)= 1.3803(√Deviation)

Standard Error = sd/√n

= 1.3803/V20 = 0.3086

Test statistic is:

t = deviation /SE

= 1.7/0.3086 = 5.5080

ndf = 20 - 1 = 19

alpha = 0.01

One Tailed - Right Side Test

From Table, critical value of t =2.5395

Since the calculated value of t = 5.5080 is greater than critical value of t = 2.5395, the difference is significant. Reject null hypothesis.

t score = 5.5080

ndf = 19

One Tail - Right side Test

By Technology, p - value = 0.000

Since p - value is less than alpha , reject null hypothesis.

Conclusion:

From the result obtained it can be concluded that ,the data support the claim that the mean rating assigned to the wine when the cost is described as $90 is greater than the mean rating assigned to the wine when the cost is described as $10.

5 0
3 years ago
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