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3 years ago

If f(x) = 7x^2 - 3x +1 and g(x) = 3x - 2, find the following by matching.

Mathematics

1 answer:

Cloud [144]3 years ago

4 0

f(x) = 7x² - 3x + 1

g(x) = 3x - 2

1. g(0) This means that x is 0, so you can plug in 0 for x in the equation:

g(x) = 3x - 2

g(0) = 3(0) - 2

g(0) = -2

2. g(1) x is 1

g(x) = 3x - 2

g(1) = 3(1) - 2

g(1) = 3 - 2

g(1) = 1

3. f(1) x is 1

f(x) = 7x²- 3x + 1

f(1) = 7(1)² - 3(1) + 1

f(1) = 7 - 3 + 1

f(1) = 5

4. f(x) = 7x²- 3x + 1

f(-2) = 7(-2)²- 3(-2) + 1

f(-2) = 7(4) + 6 + 1

f(-2) = 28 + 7

f(-2) = 35

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A drawer contains 3 white shirts, 2 blue shirts, and 5 gray shirts. A shirt is randomly

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Answer:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}$

$P(First\ White) = \dfrac{3}{10}$

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

$P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }$

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

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3 years ago

Mr. O'Donnell goes to the store to buy a shirt. The shirt is $20, but he also has to pay a 9% tax. What is the total price he ha

mart [117]

Answer:

The total price that he has to pay is $21.8.

Step-by-step explanation:

Mr. O'Donnell goes to the store to buy a shirt. The shirt is $20, but he also has to pay a 9% tax.

First you convert the sales tax percentage to its decimal form: in this case 9% becomes 0.09.

To calculate the cost of the tax, the following multiplication must be performed:

cost of product or service* sales tax (in decimal form) = total sales tax

In this case:

$20*0.09= $1.8

Finally, you must add the value of the total sales tax to the cost of the product or service to obtain the total cost. In this case:

$20 + $1.8= $21.8

So, <u><em>the total price that he has to pay is $21.8.</em></u>

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3 years ago

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

I=(a,d,f)

Reptile [31]

Answer:

Step-by-step explanation:

I = {a,d,f}

H = {bcc,g}

Intersection of I & H contains elements present in both I and H.

Since there are no common elements, the intersection is a null set, or

I intersect H = { }

The union of I and H contains elements present in either I or H, without repetitions (order is not important in the roster form of set notation)

I union H = {a,d,f,bcc,g}

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3 years ago