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3 years ago

For the following, work each by hand showing all steps. (4 points each)

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

8 0

Answer:

0.0358

Step-by-step explanation:

In a 52 deck, 13 cards are Clubs, and 26 cards are red.

There are ₁₃C₃ ways to choose 3 Clubs from 13.

There are ₂₆C₂ ways to choose 2 red cards from 26.

There are ₅₂C₅ ways to choose 5 cards from 52.

P = (₁₃C₃ ₂₆C₂) / ₅₂C₅

P = (286 × 325) / 2598960

P = 0.0358

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Anthony has been saving nickels dimes quarters over the last year he knows that he has twice as many nickels as quarters. change

OLga [1]

Answer:

The number of nickel's coin is 150

The number of dime's coin is 35

The number of quarter's coin is 75

Step-by-step explanation:

Let

x ----> the number of nickel's coin

y ---> the number of dime's coin

z ---> the number of quarter's coin

Remember that

$1\ nickel=\$0.05$

$1\ dime=\$0.10$

$1\ quarter=\$0.25$

we know that

$x+y+z=260$ ----> equation A

$0.05x+0.10y+0.25z=29.75$ ----> equation B

$x=2z$ ----> equation C

substitute equation C in equation A and equation B

$2z+y+z=260$

$3z+y=260$ ---> equation A1

$0.05(2z)+0.10y+0.25z=29.75$

$0.35z+0.10y=29.75$ -----> equation B1

Solve the system of equations A1 and B1 by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (75,35)

see the attached figure

z=75, y=35

<em>Find the value of x</em>

$x=2(75)=150$

therefore

The number of nickel's coin is 150

The number of dime's coin is 35

The number of quarter's coin is 75

8 0

3 years ago

A random sample of museum visitors were asked whether they will purchase tickets to an upcoming exhibit. The resulting confidenc

Vladimir [108]

Answer:

the margin of error is 0.05

Step-by-step explanation:

Margin of error = confidence interval ÷ 2

MOE = CI ÷ 2

Confidence interval CI = 0.2 - 0.1 = 0.1

MOE = CI ÷ 2 = 0.1 ÷ 2 = 0.05

the margin of error is 0.05

3 0

3 years ago

What is 5r-3/2???????

Andrej [43]

3.5r.....................

8 0

3 years ago

Complete the square to write the quadratic expression in vertex form.

Anvisha [2.4K]

Answer:

1. (x - 3)² = 8

2. (x + 2)² = 3

3. (x + 6)² = $\frac{101}{2}$

4. (x + 3)² = 27

5. (x + 4)² = 13

6. $\bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9}$

Step-by-step explanation:

Completion of Square: $(x - a) ^2 = x^2 - 2ax + a^2$

In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.

1. x² - 6x + 1 = 0

Taking the constant term to the other side, we get:

x² - 6x = - 1

⇒ x² - 2(3)x = -1

⇒ x² -2(3)x + 9 = - 1 + 9 [Adding 9 to both the sides]

⇒ x² -2(3)x + 3² = 8

⇒ (x - 3)² = 8 is the answer.

2. 3x² + 12x + 3 = 0

Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.

3x² + 12x = -3

Dividing by 3 through out, x² + 4x = - 1

⇒ x² + 2(2) + 4 = -1 + 4

⇒ x² +2(2) + 2² = 3

⇒ (x + 2)² = 3 is the answer.

3. 2x² + 24x = 29

x² + 12x = $\frac{29}{2}$

⇒ x² + 2(6)x + 36 = $\frac{29}{2}$ + 36

⇒ x² + 2(6)x + 6² = $\frac{29 + 72}{2}$

⇒ (x + 6)² = $\frac{101}{2}$ is the answer.

4. x² + 6x - 18 = 0

x² + 6x = 18

⇒ x² + 2(3)x = 18

⇒ x² + 2(3)x + 9 = 18 + 9

⇒ x² + 2(3)x + 3² = 27

⇒ (x + 3)² = 27 is the answer.

5. x² + 8x + 3 = 0

x² + 8x = -3

⇒ x² + 2(4)x = -3

⇒ x² + 2(4)x + 16 = - 3 + 16

⇒ x² + 2(4)x + 16 = 13

⇒ (x + 4)² = 13 is the answer.

6. 9x² - 30x + 6 = 0

9x² - 30x = - 6

⇒ x² $- \frac{30}{9}$ x = - 6

$\implies x^2 -2 \bigg( \frac{15}{9} \bigg )x + \frac{225}{81} = - 6 + \frac{225}{81}$

$\implies x^2 - 2\bigg( \frac{15}{9} \bigg ) x + \bigg ( \frac{15}{9} \bigg ) ^2 = \frac{261}{81}$

$\bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9}$ is the answer.

6 0

4 years ago

. If f(x) = 3x - x, what is the value of f(7 - 2)?

kifflom [539]

Answer:

Step-by-step explanation:

f(x) =3x-x=2x,

f(7-2)=f(5)= 2*5=10

4 0

3 years ago