MATHEMATICS COLLEGE

Solve for x.
7x = 42

Answers

Answer 1

Answer:

Answer:

x = 6

Step-by-step explanation:

Answer 2

Answer:

Answer:

x=6

Step-by-step explanation:

7x=42

X divided by 7 and 42 divided by 7 gives you

x=6

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Given the digits 2,5,7,9, 4, and 1, how many 4-digit codes can be made if 4 pointsthe first digit must be even and the last digit must be greater than 6?8012048144
Can someone help me translate this into a mathematical notation One fourth of three times a number is five

Jessica is playing a game where there are 4 blue markers and 6 red markers in a box. She is going to pick 3markers without replacement.
If she picks all 3 red markers, she will win a total of $500. If the first marker she picks is red but not all 3 markers
are red, she will win a total of $100. Under any other outcome, she will win $0.
What is the expected value of Jessica's winnings?
Round your answer to the nearest cent.

Answers

Answer:

The probability of Jessica picking 3 consecutive red markers is: (1/6)

The probability of Jessica's first marker being red, but not picking 3 consecutive red markers is:

(3/5)−(1/6)=(13/30)

So i am bit stuck here

what i think is it shouldn't be that complex it should be as simple as chance of Jessica's first marker being red=chance of getting red 1 time i.e P(First marker being red)=(6/10) can any explain me the probability of Jessica's first marker being red=(13/30)?

Step-by-step explanation:

Answer:

$126.67

Step-by-step explanation:

Help please I don’t get this

Answers

Answer: 62.5 (assuming it flies straight up, because we don't know the speed of the bird going straight, left, right, or back.)

Step-by-step explanation:

They want to know how far the bird flies in a minute. What you do is you use the char to help you figure it out, by dividing the first row both by 2, so it would give the answer under the altitude column.

Kalvin sells bottles of water at baseball games he pays 0.75 per bottle and 3.78 for the ice to keep cold let b represent the number of bottles of water he buys c represent his total cost

Answers

Answer:

3.78+.75b=c

Step-by-step explanation:

Find the indicated probability. a bag contains four chips of different colors, including red, blue, green, and yellow. a chip is selected at random from the bag and then replaced in the bag. a second chip is then selected at random. make a list of the possible outcomes (for example rb represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. (hint: there are 16 possible outcomes.)

Answers

Answer:

0.25

Step-by-step explanation:

Let

r = red

b = blue

g = green

y = yellow

If the first chip is r, the second can be r, b, g or y. The 4 possibilities are rr, rb, rg, ry.
If the first chip is b, the second can be r, b, g or y. The 4 possibilities are br, bb, bg, by.

If the first chip is g, the second can be r, b, g or y. The 4 possibilities are gr, gb, gg, gy.

If the first chip is y, the second can be r, b, g or y. The 4 possibilities are yr, yb, yg, yy.

From the 4 + 4 + 4 + 4 = 16 possible outcomes, there are 4 in which the chips are of the same color (rr, bb, gg, yy). The probability that the two chips selected are the same color is

4/16 = 0.25 = 25%

Which words in the salutation should be capitalized? dear aunt mary,

Choose all answers that are correct.

A.
Mary

B.
Dear

C.
Aunt

Answers

All A B and C because Dear is the start of a sentence and Aunt Mary is a title.

All of the words should be capitalized.

Set up and evaluate the optimization problems. (Enter your answers as comma-separated lists.) Find two positive integers such that their sum is 14, and the sum of their squares is minimized. Find two positive integers such that their sum is 14, and the sum of their squares is maximized.

Answers

Answer and Step-by-step explanation:

Let x and y be two positive integers and their sum is 14:

X + y = 14

And the sum of square of this number is:

f = x2 + y2

= x2+ (14 – x)2

Differentiate with respect to x, we get:

F’(x) = [ x2 + (14 – x)2]’ = 0

2x + 2(14-x)(-1) = 0

2x +( 28 – 2x)(-1) = 0

2x – 28 +2x = 0

2x + 2x = 28

4x = 28

X = 7

Hence, y = 14 – x = 14 -7 = 7

Now taking second derivative test:

F”(x) > 0

For x = y = 7,f reaches its maximum value:

(7)2 + (7)2 = 49 + 49

= 98

F at endpoints x Є [ 0, 14]

F(0) = 02 + (14 – 0)2

= 196

F(14) = (14)2 + (14 – 14)2

= 196

Hence the sum of squares of these numbers is minimum when x = y = 7

And maximum when numbers are 0 and 14.

Final answer:

To find two positive integers such that their sum is 14, and the sum of their squares is minimized, we need to consider all possible pairs of positive integers and calculate their sums of squares. The pair (6, 8) has the minimum sum of squares of 100. To find two positive integers such that their sum is 14, and the sum of their squares is maximized, the pairs (1, 13) and (2, 12) both have the maximum sum of squares of 170. Since we need to find two positive integers, the pair (1, 13) is the answer.

Explanation:

To find two positive integers such that their sum is 14 and the sum of their squares is minimized, we need to consider all possible pairs of positive integers that add up to 14 and calculate their sums of squares. Let's list all the pairs:

1 and 13: 1^2 + 13^2 = 170
2 and 12: 2^2 + 12^2 = 148
3 and 11: 3^2 + 11^2 = 130
4 and 10: 4^2 + 10^2 = 116
5 and 9: 5^2 + 9^2 = 106
6 and 8: 6^2 + 8^2 = 100
7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (6, 8) has the minimum sum of squares, which is 100.

Similarly, to find two positive integers such that their sum is 14 and the sum of their squares is maximized, we need to again consider all possible pairs and calculate their sums of squares. Let's list the pairs:

1 and 13: 1^2 + 13^2 = 170
2 and 12: 2^2 + 12^2 = 148
3 and 11: 3^2 + 11^2 = 130
4 and 10: 4^2 + 10^2 = 116
5 and 9: 5^2 + 9^2 = 106
6 and 8: 6^2 + 8^2 = 100
7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (1, 13) and the pair (2, 12) both have the maximum sum of squares, which is 170. Since we need to find two positive integers, the pair (1, 13) is the answer.