What is A ∩ B? Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}.

Answers

Answer 1

Answer: $A=\{1;\ 3;\ 5;\ 7;\ 9;...;\ 99\}\n\nB=\{50;\ 55;\ 60;\ 55;\ 70;...;\ 150\}\n\nA\ \cap\ B=\{55;\ 65;\ 75;\ 85;\ 95\}$

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-3/7, -8/3 and -5/2,-2 slope

Answers

so the points are (-3/7,-8/3) and (-5/2,-2)
to find the slope do
(y2-y1)/(x2-x1)
(x,y)
x1=-3/7
y1=-8/3
x2=-5/2
y2=-2

subsitute
$(-2-( (-8)/(3) ))/( (-5)/(2) - (-3)/(7) )$
simplify by finding similar denomenators
$((-6)/(3)-( (-8)/(3) ))/( (-35)/(14) - (-6)/(14) )$
$((-6)/(3)( (8)/(3) ))/( (-35)/(14) + (6)/(14) )$
add
$((2)/(3))/( (-29)/(14))$
multiply top and bottom by $\frac{-14}{29$
$((-28)/(87))/(1)$
$(-28)/(87)$
answer is
slope= $(-28)/(87)$

You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes. a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:

b. how long does it take you to jog around the park? it takes you minutes to jog around the park.

Answers

Answer:

Part a) The system of equations is

$2x+y=10$

$2x+3y=22$

Part b) The number of minutes it takes you to jog around the park is $6\ min$

Step-by-step explanation:

Part a) Write a system of linear equations

Let

x-----> the number of minutes it takes you to jog around your block

y---> the number of minutes it takes you to jog around the park

we know that

$2x+y=10$ ----> equation A

$2x+3y=22$ ----> equation B

Part b) How long does it take you to jog around the park?

Multiply equation A by -1 both sides

$-1(*2x+y)=-10$ ------> $-2x-y=-10$ ----> equation C

Adds equation B and equation C

$2x+3y=22\n-2x-y=-10\n-------\n 3y-y=22-10\n2y=12\ny=6\ minutes$

Find the value of x

$2x+(6)=10$

$2x=10-6$

$x=4/2=2\ minutes$

Final answer:

Write the information as a system of linear equations: 2x + y = 10 and 2x + 3y = 22. Solving these equations, we find that it takes 6 minutes to jog around the park.

Explanation:

Given the information provided in the question, we first need to represent the given information through a system of linear equations. Following the instructions in the question, let x represent the time in minutes to jog around the block, and y represent the time in minutes to jog around the park.

From the given problem, we know:

2x + y = 10
2x + 3y = 22

To find how long it takes you to jog around the park (the value of y), we can use the method of substitution or elimination. In this case, let's use the method of substitution: we can start by solving the first equation for 2x, giving us 2x = 10 - y.

Substituting that into the second equation gives us 10 - y + 3y = 22, simplifying which leads to 2y = 12, and further simplification yields y = 6. Therefore, it takes you 6 minutes to jog around the park.

Learn more about system of linear equations here:

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What is the next value 1 I 2 L 3 F 4

Answers

Based on the pattern, 1 I 2 L 3 F ... the number corresponds to the number of lines of the letter. 1 refers to the vertical line in I. 2 refers to the vertical and horizontal lines that form L. 3 refers to the vertical and 2 horizontal lines that form F. So, 4 will most likely refer to E, one vertical line and 3 horizontal lines.

Final answer:

The sequence provided isn't clear in its pattern between numbers and letters. The pattern doesn't match recognizable numerical patterns and may require additional context or information to decode. Therefore, the next value in this sequence is unclear.

Explanation:

The pattern in the sequence 1 I 2 L 3 F 4 seems to be pairing a number with a corresponding alphabetical character. However, the association between the numbers and characters is not directly clear from the given sequence. Applying a numerical pattern might provide a logical solution, but the provided information doesn't seem to align with common numerical patterns.

For example, if we map the alphabetical sequence to numbers (where A=1, B=2, C=3, etc.), we don't get a recognizable pattern. It appears the sequence might involve a more complex pattern or it's possible there could be a typo or error in the question. If this is a question related to cryptography or coding, additional information may be required to decode the sequence.

Unfortunately, without more context or information, it's challenging to definitively determine the next value in the sequence. Regardless, always ensure to look out for patterns in terms of the positions and values of the numbers or letters in a sequence.

Learn more about Pattern Analysis here:

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WIll reward with high brainly points if these questions are aswered correctlyCarnival Wilson gets a flu shot that breaks apart over time. On the day of the vaccination, he has 500 mL of the solution. AFTER ONE DAY, he has 400 mL in his system. After two days, there was 320 mL. After three, there was 256 mL.

What is the exponential equation for this problem?
What is the decay FACTOR?
What is the decay RATE?

Answers

A = Ao(x)^t

Ao = 500

A = 500(x)^t

400 = 500 (x)^1

x = 4/5

A = 500(4/5)^t << The exp eqn

Approximate the value of 44 to the nearest hundredth

Answers

I dont really understand the question. But from how u asked it then it would be 44.00

A bank pays 5% interest compounded annually. What principal will grow to $12,000 in 10 years.

Answers

Answer: 7366.96 dollars

========================================================

Use the compound interest formula:

A = P(1+r/n)^(n*t)

where in this case,

A = 12000 = amount after t years

P = unknown = deposited amount we want to solve for

r = 0.05 = the decimal form of 5% interest

n = 1 = refers to the compounding frequency (annual)

t = 10 = number of years

-------

Plug all these values into the equation, then solve for P

A = P(1+r/n)^(n*t)

12000 = P(1+0.05/1)^(1*10)

12000 = P(1.05)^(10)

12000 = P(1.62889462677744)

12000 = 1.62889462677744P

1.62889462677744P = 12000

P = 12000/1.62889462677744

P = 7366.95904248911

P = 7366.96

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