MATHEMATICS HIGH SCHOOL

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

{50, 55, 60, 65, 70, 75, 70, 85, 90, 95}
{55, 65, 75, 85, 95}
{all odd numbers between 1 and 99}
{numbers between 1 and 150 that are evenly divisible by 5}

Answers

Answer 1

Answer:

Answer: {55, 65, 75, 85, 95}

Step-by-step explanation:

Given: A = {odd numbers between 0 and 100}

B= {numbers between 50 and 150 that are evenly divisible by 5}

Thus, A={1,2,3,4,5,6,7,8,.......99}

and B={55,60,65,70,75,80,85,90,95......145}

The notation A ∩ B means A intersection B which is the set of elements that are common in set A and in set B.

Now, $A\bigcap B=\left \{ 55,65,75,85,95 \right \}$

Answer 2

Answer:

The elements of set A ∩ B are {55, 65, 75, 85, 95}

The sets are given as:

A = {odd numbers between 0 and 100}

B= {numbers between 50 and 150 that are evenly divisible by 5}

The above means that:

A = {1,2,3,4,5,6,7,8,.......99}

B = {55,60,65,70,75,80,85,90,95......145}

To calculate set A ∩ B, we list the common elements in both sets, without repetition.

So, we have:

A ∩ B = {55, 65, 75, 85, 95}

Hence, the elements of set A ∩ B are {55, 65, 75, 85, 95}

$(x-5)/(x^(2) +3x-40)$

What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to $x-5$ later):

$x^(2) +3x-40$

Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.

Let's begin building our expressions. We know that $x^(2)$ has an exponent of 2. When variables are multiplied, the exponents are added, meaning that $x*x=x^(2)$ . (Or $x^(1) + x^(1) =x^(2)$ , the 1s just don't show)

We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.

$x^(2) +3x-40 = (x+)(x-)$

Next, let's look at the factors of 40:

1 and 40 2 and 20 4 and 10 5 and 8

Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!

$8-5=3$

In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in $3x$ . Therefore, $8(-5)=-40$ .

$x^(2) +3x-40 = (x+8)(x-5)$

Now let's go back to our original equation and substitute our old expression with the new one:

$(x-5)/((x+8)(x-5))$

Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a $(1)/(1)$ .

$(x-5)/((x+8)(x-5))$ = $(1)/(x+8)$

Therefore, your simplified answer is $(1)/(x+8)$ !

Here's the whole process:

$(x-5)/(x^(2) +3x-40) \n\n(x+?)(x-?)\n\n40:\n1, 40\n2, 20\n4, 10\n5, 8\n\n8-5=3 \n(8x-5x=3x)\n\n(x+8)(x-5)\n\n(x-5)/((x+8)(x-5))=(1)/(x+8) \n\n(1)/(x+8)$

To check your answer, confirm your expressions using the box method attached.

I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!

Please help me!! 1. In the equation y = 25x, what is the constant of variation?

A. 25
B. 1/25
C. Zero
D. Undefined

2. In the equation of y = 25x, the number 25 also represents what?

A Rate of change
B the y - intercept
C the x-intercept

In the equation y = -4x, what is the constant of variation?

A. 4
B. zero
C. -4
D. undefined

4. The value of y varies directly with x and the constant of variation is 5. What is the value of x when y = 100? *
25
95
4
20

5. The value of y varies directly with x and the constant of variation is 13. What is the value of y when x = 6? *
A. 78
B. 2.16
C. 0.46
D. zero

The height of a stack of boxes varies directly with the number of boxes. A stack of 10 boxes is the 20 feet high. How tall is a stack of 18 boxes? *
9 feet
5 feet
36 feet
40 feet

Perry's pay is in direct variation to the hours she works. Perry earns $84 for 14 hours. How much will she earn for 24 hours? *
A. $ 144
B. $120
C. $2, 016
D. $336
Submit

Answers

Answer:

1. 25

2. Rate of Change

3. zero

4. 20

5. 2.16

6. 36ft

7. $144

Hope this helps

I dont know if all of these are right if not let me know

Answer:

1. Since the equation can be written in the form y=kx y = k x , y varies directly with x and k . The constant of variation, y , is 5 .

Step-by-step explanation:

A car salesperson sells cars at prices ranging from $5,000 to $45,000. the histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years. the median of the car is ___.

- $20,000
- $25,000
- $30,000
- $40,000

the distribution exhibits ___.

- a negative skew
- a positive skew
- symmetry
- uniformity throughout

Answers

Answer :

Given that : a car salesperson sells cars at prices ranging from $5,000 to $45,000.

So, The least price = $5000

The largest price = $45000

$\implies Median=(5000+45000)/(2)\n\n\implies Median = \$25000$

Therefore, The correct option is B. $25000

Now, we need to state what the distribution exhibits

From the graph we can see at the both sides of the median the graph is similar on the either side.

⇒ The graph is symmetrical about the median.

Hence, The distribution exhibits symmetry.

Therefore, The correct option is C. Symmetry

Answer: the correct answer is $25,000 (b)

The Second answer is symmetry (c)

Step-by-step explanation:

Suppose that a family wants to start a college fund for their child. If they can get a rate of 5.5% , compounded monthly, and want the fund to have a value of $35,450 after 20 years, how much should they deposit monthly? Assume an ordinary annuity and round to the nearest cent.

Answers

Answer:

They should deposit $81.38 monthly.

Step-by-step explanation:

We know that,

$\text{FV of annuity}=P\left(((1+r)^n-1)/(r)\right )$

where,

FV of annuity = $35,450

P = monthly payment,

r = rate of interest = 5.5% annually = $(5.5)/(12)\%$

n = number period = 20 years = 240 months

Putting all the values,

$\Rightarrow 35450=P\left(((1+(0.055)/(12))^(240)-1)/((0.055)/(12))\right )$

$\Rightarrow P(35450)/(\left(((1+(0.055)/(12))^(240)-1)/((0.055)/(12))\right ))$

$\Rightarrow P=\$81.38$

Therefore, they should deposit $81.38 monthly.

In 20 years a family will be able to earn 35 450 dollars. The interest that they earned is 5.5% compounded monthly. Now, let's find out how much will they need to save monthly to get this amount in 20 year:
=> 12 * 20 = 240 months
=> 35 450 / 240 months = 147.7 dollars per month is the money with interest
Let's subtract the interest
=> 147.7 * 0.055 = 8.1 dollars.
=> 147.7 - 8.1 = 139.6 dollars per month.

Pleaseee helppp I’m struggling