1. _____ is exchanging one good for another without using money.
Credit
Barter
Negotiating
Brokering
2. A _____ has to be paid in full on the due date. (1 point)
Charge card
Credit card
Debit card
Check card
3. The _____ is the original amount owed on a loan. (1 point)
Loan due
Interest
Available balance
Principal
4. APR is used to calculate the _____. (1 point)
Loan amount
Interest accrued
Principal
Future earnings,

Answers

Answer 1
Barter is exchanging one good for another without using money. .A Credit card has to be paid in full on the due date. The Principal is the original amount owed on a loan. APR is used to calculate the Interest accrued.
Answer 2

The answers are:

1. Barter

2. charge card

3. principal

4. interest accured


Related Questions

for the final answer do i add the 5 to (x+1) making it 5x+5 or do i leave it how it is? Also how do i find the domain

Answers

You don't "add the 5" in any event. Multiplication is very different from addition, and precision of vocabulary is important.

It depends on what your teacher or answer key expect. You can take a hint from the fact that the given polynomials are all multiplied out.

(5x^2 +5)/(x -1)

_____
The domain of polynomials in general is "all real numbers." However, you must exclude any specific numbers that make the rational expression be undefined. This includes numbers that make the denominator of the numerator zero, as well as those that make either the numerator or the denominator of the denominator zero. In other words, you must exclude from the domain
.. x ∈ {-5, 1, 2}

Write the equation of a line that includes the point (1, 5) and has a slope of 3 in standard form. 3x + y = 5 –3x + y = 5 3x + y = 2 –3x + y = 2

Answers

-10 is the answer lah bro . 

What is an equation stating that two ratios are equivalent.

Answers

the answer is a proportion 
Final answer:

A proportion is an equation that shows two ratios are equivalent, such as 1/2 = 3/6. It is commonly used with unit rates and unit scales in various fields including science, engineering, and everyday measurements.

Explanation:

An equation stating that two ratios are equivalent is known as a proportion. For example, the equation 1/2 = 3/6 is a proportion because it shows that the two ratios have the same value. Proportions are very useful in various aspects of mathematics and science. Notably, they are essential when dealing with unit rates and unit scales, where comparisons between two measurements are made.

A unit rate is a special kind of ratio where one of the quantities is one, such as 55 miles per hour (55/1 mph). It describes how many units of the first type of measurement corresponds to one unit of the second type of measurement. Similar in concept, a unit scale compares the dimensions of an actual object to a model or drawing. For instance, a map might have a unit scale that reads 1 inch = 100 feet, which would be written as 1 inch/100 feet.

When applying proportions in real-world scenarios, we can create conversion factors to switch from one measurement to another. This is directly applicable to cooking recipes, chemistry with mole ratios, or engineering with the transformer equation, where ratios of different quantities are kept consistent.

Learn more about Proportion here:

https://brainly.com/question/34018947

#SPJ6

A poker hand consist of 5 cards?
a.find the total number of possible five card poker card hands.
b.find the number of ways in which one can king can be selected? c)find the number of ways in which four aces can be selected .
d.find the number of ways of getting four aces and one king.

Answers

c) it is answer in four acres can be selected.

In poker probability calculations, there are 2,598,960 possible five-card hands, various specific hand combinations such as those containing a king or four aces have their own probability, which can be determined using the formulas for combinations.

Calculations for Poker Probabilities

The subject of probability in a poker hand involves various combinations and permutations. Here's how the calculations are made:

Total number of five-card poker hands: The total number is calculated using combinations, as the order in which cards are drawn does not matter. This is given by the combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of available cards (52), and r is the number of cards drawn (5). Thus, there are 52! / (5!(52-5)!)= 2,598,960 possible hands.

Number of ways one king can be selected: There are four kings in a deck, so there are C(52, 5) - C(48, 5) ways to choose a hand with at least one king, as you subtract the number of hands without any kings from the total number of hands.

Number of ways four aces can be selected: There is only one way to choose all four aces, and then there are 48 remaining cards to choose the fifth card from, which gives 48 combinations.

Number of ways of getting four aces and one king: There are four kings to choose from and one specific combination of aces, so there are 4 ways to have a hand with four aces and one king.

choose the answer that best completes the sentence. if you know a root of a function is -2 + sqrt3 , then __
A. 2 + sqrt3 is a possible root
B. 2 + sqrt3 is a known root.
C. -2 - sqrt3 is a possible root.
D. -2 - sqrt3 is a known root.

Answers

answer:

d. -2 - sqrt3 is a known root.

hope this helps! :o)


Answer:the answer is D

Step-by-step explanation:

Determine 10th term : 5,-25,125

Answers

Every time, the previous term is multiplied by -5. 
Keep doing this until you reach the tenth term. 
You will get -9,765,625. 
Hope this helps!

What number would you add to complete the square for the equation below?x2 + 10x = 0?

Answers

For a quadratic of the form [tex]x^2+bx=-c[/tex], we complete the square by first adding 
[tex](\dfrac{b}{2})^2[/tex]
to each side.

Here, the coefficient b is equal to 10. We take half of this—5—and square it to get 25. We add this to both sides of the equation.

FYI, this equation can easily be factored, so there's no need to complete the square.

Jenna's parents required her to put $10 of her $50 monthly allowance into a savings account for what percent of her monthly allowance did this represent?

Answers

$10 is 20% of $50 dollars therefore the answer is it represented 20% of her monthly allowance

Final answer:

To determine the initial amount needed in a bank account to reach $10,000 in ten years with 10% compound interest, use the compound interest formula.

Explanation:

To find out how much money you need to put in a bank account to have $10,000 in ten years with 10% interest compounded annually:

Use the formula for compound interest: A = P(1 + r/n)^(nt)

Plug in the values: $10,000 = P(1 + 0.10/1)^(1*10)

Solve for P: P = $10,000 / (1.10^10)

Calculation:

PV = FV / (1 + r/n)^(n*t)

Inserting the known values:

PV = $10,000 / (1 + 0.10/1)^(1*10)

PV = $10,000 / (1.10)^10

Calculating the exponent:

PV = $10,000 / 2.59374

Finally:

PV = $3,855.43 (approximately)

Therefore, you need to put approximately $3,855.53 into the bank account initially.

You and your friend are standing back-to-back. Your friend runs 10 feet forward and then 8 feet right. At the same time, you run 11 feet forward and then 12 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?

Answers

Approximately about (20.71 ft)

find the positive value of x in the geometric sequence 7x-2,4x+4,3x

Answers

Hello,


Let's assume k the ratio.

[tex] \left \{ {{3x=k*(4x+4)} \atop {4x+4=k*(7x-2)}} \right. \\\\ \left \{ {{3x-4kx=4k} \atop {4x-7kx=-2k-4}} \right. \\\\ \left \{ {{x(3-4k)=4k} \atop {x(4-7k)=-2k-4}} \right. \\\\ \left \{ {{x=\dfrac{4k}{3-4k} \atop {x=\dfrac{-2k-4}{4-7k} \right. \\\\ \dfrac{4k}{3-4k}=\dfrac{-2k-4}{4-7k}\\\\ 36k^2-6k-12=0\\ 6k^2-k-2=0\\ \boxed{k= \dfrac{2}{3} \ or\ k= -\dfrac{1}{2}}\\\\ x=\dfrac{4*\dfrac{2}{3} }{3-4*\dfrac{2}{3} }=8\\ x=\dfrac{4*\dfrac{-1}{2} }{3-4*\dfrac{-1}{2} }=-\dfrac{2}{5}\\ [/tex]

[tex] \boxed{x= 8 \ or\ x= -\dfrac{2}{5}}\\\\ [/tex]





The value of x = 8.

We have a geometric sequence.

We have to determine the positive value of x.

Define Geometric Sequence.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio.

According to the question -

The Geometric sequence is -

7x - 2, 4x + 4, 3x

According to the concept of Geometric sequence -

[tex]$\frac{a(2)}{a(1)} =\frac{a(3)}{a(2)}[/tex]

[tex]$\frac{4x+4}{7x-2} =\frac{3x}{4x +4}[/tex]

(4x + 4)(4x + 4) = 3x(7x - 2)

16[tex]x^{2}[/tex] + 16x + 16x + 16 = 21[tex]x^{2}[/tex] - 6x

16[tex]x^{2}[/tex] + 32x + 16 = 21[tex]x^{2}[/tex] - 6x

38x + 16 = 5[tex]x^{2}[/tex]

5[tex]x^{2}[/tex] - 38x - 16 = 0

Solve the above quadratic equation, you will get two roots -

x = 8    and     x = 0.4

Since, we need positive value, therefore -

x = 8.

Hence, the value of x = 8.

To solve more questions on Geometric sequence, visit the link below -

https://brainly.com/question/19201330

#SPJ2

Will mark brainliest!!

The histogram shows the ages of cars sold at a car auction.

What percent of the cars was less than 20 years old or more than 40 years old?

Answers

.96% (?)

I know not the correctness of my answer due to:
The Total was 8 to fit the criteria, the others older than 20 but younger than 40 are 12
(However I do not know how to calculate percentage, went to Google and got a percentage calculator to find what percentage 8 is to 12)
40% I hoped me helped

How do you do this? It's so confusing! Please help!

Answers

check the picture below.

notice AB ⟂ BC , whilst ∡B = 30°.

now, if we run a perpendicular line from C to AB, it'll be a 90° angle at M, however ∡AMC has to be 105°, so it has to be slanted more towards A, like in the picture, and surely you already know which one is the shortest.

Can someone please help me solve this problem????

Weston is buying a house for $215,000. He is financing $185,000 and obtained a 30-year, fixed-rate mortgage with a 6.525% interest rate. How much are his monthly payments?

$1,005.94

$1,362.48

$1,614.09

$1,172.37,

Answers

$1,172.37 The formula for calculating the payment on a loan is P = r(PV)/(1 - (1 + r)^(-n)) where P = Payment PV = Present value r = interest per period n = number of periods Since there's 12 months per year and the loan is for 30 years, there will be 12 * 30 = 360 periods. The interest rate per month will be 0.06525 / 12 = 0.0054375, and finally, the present value is the size of the loan at 185000. Now let's substitute and solve. P = r(PV)/(1 - (1 + r)^(-n)) P = 0.0054375(185000)/(1 - (1 + 0.0054375)^(-360)) P = 1005.9375/(1 - (1.0054375)^(-360)) P = 1005.9375/(1 - 0.141961802) P = 1005.9375/0.858038198 P = 1172.369134 P = 1172.37 So the monthly interest and principle payments are $1,172.37 Note: The actual payments will be higher since the above figure doesn't include insurance and taxes.
For this problem, we will be using the formula for loan:

PMT=P[(r/n)/1-(1+r/n)^-ny]
where: 
P=Principal Value
r=rate
n=number of compoundings/year
y=year

To solve:
*Weston is only financing $185,000.

P=$185,000
r=6.525% or 0.06525
n=12 (monthly)
year=30

PMT=185000[(0.06525/12)/1-(1+0.6525/12)^-12*30
        = 185000[(.0054375)/1-(1+.0054375)^-360
        = 185000[(.0054375)/1-(1.0054375)^-360
        = 185000[(.0054375)/1-(0.142)
        = 185000[(.0054375)/(.858)
        = 185000(0.00634)
        = 1,172.37

Answer: $1,172.37

Luis strength trains two times per week. He uses 12-pound weights and performs three sets of eight repetitions. He wants to improve his frequency. What should he do?

Increase to 10 repetitions.
Increase to 15-pound weights.
Increase to four sets.
Increase to three times per week.

Answers

Increase to 10 repetitions. Increasing repetitions increases the frequency of each period (or set). It will be increased by 2 for every set Luis does. The other choices may increase resistance, or amount of sets done but do not affect frequency.

To improve his frequency in strength training, Luis should increase his strength training days to three times per week. Hence, the correct option is fourth.

Luis wants to improve his frequency in strength training. Since he is already training twice a week, to enhance frequency, he should consider increasing the number of days he strength trains. Therefore, the best option for Luis would be to increase to three times per week. This aligns with the muscle-strengthening activities recommendation which suggests activities should be performed on 2 or more days a week, and this can be increased over time. Luis can also regularly increase the intensity of his workouts by adding more weight or sets, to ensure continuous muscle overload and growth.

NEED HELP ASAP AND WILL GIVE A MEDAL ***
Tammy is using a treadmill, and when she puts her hands on the bar, sensors read her heart rate. Today, the sensors are telling Tammy that she is reaching 183, which is the highest rate in her target zone. What should she do to get the most effective workout?

Increase her running speed without adjusting the incline
Use the machine to maintain or decrease her intensity
Do additional aerobic exercises immediately after the treadmill
Use the machine to increase the incline and intensity,

Answers

Tammy should use the machine to maintain or decrease her intensity. 183 is a very high heart rate and indicates that she is working at, or near, a maximal effort. She should not increase the intensity (speed or incline).

What is the lateral area of this regular octagonal pyramid?(PICTURE ONE)




114.8 cm²

162.4 cm²

229.7 cm²

281.3 cm²

2.What is the slant height x of the square pyramid?(PICTURE 2)

The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge and is labeled as x. The length of the lateral edge is 8 meters. The lateral edge makes a 60 degree angle with the base edge

Express your answer in radical form.

3.What is the surface area of this square pyramid? (pICTURE 3)

Round your answer to the nearest tenth, if necessary.


43.8 yd²

66.6 yd²

105 yd²

171.6 yd²

Answers

Q1)
the lateral area of the pyramid is the total area of all the lateral faces excluding the base.
In this regular octagonal pyramid, the lateral sides are triangles. As there are 8 triangles we need to find the area of all 8 sides.
Area of one lateral triangle face = 1/2 * base * slant height 
slant height is the hypotenuse of the right angled triangle formed from the base of the pyramid with the perpendicular height.
slant height - l
l² = 7² + 7² = 49 *2
 l²  = 98 
l = √98
l = 9.9
Area = 1/2 * 5.8 cm * 9.9 cm 
         = 28.71 cm²
There are 8 sides 
total lateral area = 8 * 28.71 = 229.68 rounded off is 229.7 cm²
third option is correct - 229.7 cm²

Q2)
in the triangular face, the lateral edge makes a 60° angle with the base edge. Therefore 2 of the angles are 60° each, since the sum of the interior angles of a triangle is 180°, the third angle too is 60°. this makes the triangle an equilateral triangle with equal angles, hence equal sides. 
since lateral edge is 8 cm,base edge too is 8 cm. 
since this is an equilateral triangle, the perpendicular line cuts the base edge at its midpoint, bisecting the line forming 2 right angled triangles.
in the right angled triangle, height of triangle is x slant height ,
base = 8 /2 = 4 cm
hypotenuse = 8 cm
We need to find x, use Pythogoras' theorem 
4² + x² = 8²
16 + x² = 64
x² = 62 - 16
x = √48
x = √4x√4x√3
  = 2x2√3
  = 4√3 cm

Q3)
surface area of the square pyramid 
surface area of the base + surface area of triangular faces 
square area = length x length 
                    = 6.2 x 6.2 
                    = 38.44 yd²
triangular face area = 1/2 * length * height 
since the angle between lateral edge and base edge is 60°, its an equilateral triangle where all sides are equal. in this case each side is 6.2 yd. 
to find the perpendicular height, use pythogoras' theorem
the perpendicular line(slant height ) cuts the base edge at its midpoint, therefore length of the right angled triangle is = 6.2/2 = 3.1 yd

slant height - l
l² + 3.1² = 6.2²
l² = 38.44 -9.61
l²  = 28.83 
l = 5.37
area = 1/2 *length *height 
        = 1/2 * 6.2 * 5.37
        = 16.64 yd²
there are 4 triangles = 4 * 16.64 = 66.58 yd²
total area = 38.44 + 66.58 = 105 yd²
correct answer is 3rd option - 105 yd²

Answer:

1.  229.7cm^2

2.  4 (square root) 3 cm

3.  16.64yd^2

Step-by-step explanation:

I just took th test, and came to confirm the other guys' answers ;)

what is the 8th term in the following sequence 28,33,38,43.....

Answers

To solve this, you have to figure out how they created the sequence, i.e., how did they get from 28 to 33 and then from 33 to 38 (etc.). If you subtract 28 from 33 the answer is 5, and the same is true for all the consecutive numbers in the sequence, so you have to add five to 43 to figure out the next term. You already have four terms, so we only need 4 more:
28, 33, 38, 43, 48, 53, 58, 63   63 is the 8th term. 










































You and your friend are standing back-to-back. Your friend runs 16 feet forward and then 12 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?

Answers

You would throw a baseball 9 feet and your friend would catch the baseball. Hope this helps!
Let's assume that you stared at the origin.  So your friend moved 16 units along the x-axis and 12 down the y-axis landing him at (16, -12), while you on the other hand run 12 feet forward along the x-axis, and 9 units into the negative y area.  This makes you at (-12, -9).  So solve graph these points.  Use the graph to count the difference between the 2 x coordinates, you should get 28, the solution for the y distance (ignore the negatives) is 3.  So we can use the Palagorien Theorem to solve.  (28)2 + (3)2 = x2.  Solve for x.

784+9=x2
793=x2
28.1602556807=x

John says the transformation rule (x, y) es002-1.jpg (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?

Answers

John didn't check his work.

The appropriate transformation rule is (x -4, y-7).

_____
John's signs were in error.

Sample Response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.


A rectangle is 1/2 feet long and 3/4 wide what is the area of rectangle

Answers

The rectangle is 1/2 ft long.
I assume you left out "ft" from the width, so the width is 3/4 ft.

A = LW = 1/2 ft * 3/4 ft = 3/8 ft^2


The area of rectangle is L×W.

A = 1/2 × 3/4
A = 0.375 or 3/8

Determine the equation for the parabola graphed below.

Answers

The general equation for a parabola is: y = a(x - b)^2 + c
So given the vertex is at (-1, 7), this means that b = -1 and c = 7:
y = a(x + 1)^2 + 7
Then we substitute a point from the graph (aside from the vertex). The easiest is the y-intercept of (0, 5):
5 = a(1)^2 + 7
a = -2
Therefore the equation is: y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5

The equation for the parabola graphed below is  [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]

A parabola's general equation is: y = a(x - b)2 + c

Given that the vertex is located at (-1, 7), this means that b = -1 and c = 7:

y = a(x + 1)^2 + 7

Then, instead of the vertex, we replace a point from the graph. The y-intercept of (0, 5) is the simplest:

5 = a(1)^2 + 7

a = -2

As a result, the equation is as follows: [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]

A serving of a certain cereal has 8 grams of sugar in 1 portion. Which equation shows how the amount of sugar and the number of portions are related? The s stands for the grams of sugar and the p stands for the portions of cereal.

Answers

I love this kind of problems 
it would be p=1 and s=8 
it helps to keep on going like a chart 
ex: 1/8 2/16 3/24 etc


your gamer unstopableboy21

The equation relating sugar amount and portions in a cereal serving is s = 8p. To find how many servings of cereal are needed to consume a specific amount of sugar, moles are converted to grams, then related to the sugar content per serving.

The equation relating the amount of sugar (s) and number of portions (p) in a serving of cereal is:

s = 8p

To answer the given problem, let's relate moles of sugar to grams and servings. First, we convert moles to grams, then use the sugar content in grams per serving to find the number of servings needed to consume the specified amount of sugar.

hElP!
A carpenter designs two cabinets: one in the shape of an oblique rectangular prism and one in the shape of a right rectangular prism. The volume of each cabinet is 4,608 cubic inches. The oblique rectangular prism is 48 inches tall and has an edge length of 64 inches. The right rectangular prism has a height of 48 inches. Which statements about the cabinets are true? CHECK ALL THAT APPLY
a. The cabinets have the same base area.
b.The base area of the oblique prism is smaller than the base area of the right prism.
c.The cabinets may have the same base dimensions.
(MORE DOWN BELOW),

Answers

Answer:

A- The cabinets have the same base area.

C- The cabinets may have the same base dimensions.

D- The cabinets may have different base dimensions

Step-by-step explanation:

Answer:

A. C. D.

Step-by-step explanation:

Please Help!!!

The figure shows a line graph and two shaded triangles that are similar:



Which statement about the slope of the line is true? (5 points)
Select one:
a. It is fraction 1 over 2 throughout the line.

b. It is 2 throughout the line.

c. The slope from point O to point A is fraction 1 over 2 time the slope of the line from
point A to point B.

d. The slope from point O to point A is two times the slope of the line from point A to point B.

Answers

The slope is 1/2 throughout the entire line.

Looking at the first triangle, the rise is 2 and the run is 4.  That gives us a slope of 2/4 = 1/2.

For the second triangle, the rise is 1 and the slope is 2.  This gives us a slope of 1/2.

Any linear function will have the same slope throughout the entire line.

What does -3.4 E + 38 mean? (In normal number terms).

Answers

"E" stands for exponent, specifically 10. If something says "E+38" (like in Microsoft Excel), that means 10^38 in scientific notation.  
Therefore, "-3.4 E + 38" means -3.4x10^38.  
The "+38" means there are 38 zeros following a 1 as the exponent. It also works with negative numbers. For example, E-3 equals 10^-3

Exponential Growth/Decay Function

Hint/Tip:

Remember, the basic general exponential function form is: y = Abx In detail, b is written as (1-r) where r is the rate of growth or decay, so our detailed formula is: y = A(1-r)x

Always work with the rate as a decimal number, not as percentage. If the rate is given as percent (%), you will need to divide it by 100 to have the decimal form.

The value of a car is $21,500. It loses 12% of its value every year.

(a) Write a function that represents the value y (in dollars) of the car after x years.

(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)

Answers

(a) Write a function that represents the value and (in dollars) of the car after x years.
 For this case what we should do is write the equation of exponential type.
 We have then:
 y = A (b) ^ x
 Substituting the values:
 y = 21500 (0.88) ^ x
 Answer:
 y = 21500 (0.88) ^ x

 (b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
 We use the function found in part (a) and evaluate for x = 6.
 We have then:
 y = 21500 (0.88) ^ 6
 y = 9985 $
 Answer: 
 the value of the car after 6 years is: 
 y = 9985 $

In triangle XYZ, the length of side XY is 24 mm and the length of side YZ is 34 mm. Which of the following could be the length side XZ?

A. 8 mm
B. 63 mm
C. 42 mm
D. 60 mm

Answers

In a triangle, the length of any side is greater than the difference of the lengths of the other two sides and less than the sum of the lengths of the other two sides.

34 mm - 24 mm = 10 mm

The length of side XZ must be greater than 10 mm.

24 mm + 34 mm = 58 mm

The length of side XZ must be less than 58 mm.

The only choice between 10 mm and 58 mm is 42 mm.

Kail Ryans 10 laps around the track each day each lap around the track is 400 m meters how many times around the track will she need to run a total of 12 kilometers

Answers

hello

1 km = 1000 m

12 km = 12,000 m

Each day, she runs 10 * 400 m = 4000 m

12,000 m / 4000 m = 3

It will take 3 days.

Have a nice day

Set operations including cardinality of power sets and listing the elements of a power set and finding the number of subsets of a given size. let u = {-1, 0, 1, 2, 3, 4, 6} , a = {-1, 1, 2, 3, 4} and b = {0, 2, 4, 6}. find
a.a u b,
b.a ∩ b,
c.b – a,
d.the power set of b and its cardinality

Answers

a. a [tex]\cup[/tex] b
a [tex]\cup[/tex] b means the resulting set when a and b are merged, less duplicates.
a [tex]\cup[/tex] b={-1, 1, 2, 3, 4} [tex]\cup[/tex]  {0, 2, 4, 6}
={-1,0,1,2,3,4,6}

b. a [tex]\cap[/tex] b
a [tex]\cap[/tex] b means the set of members which are common to both a and b.
a [tex]\cap[/tex] b={-1, 1, 2, 3, 4} [tex]\cap[/tex]  {0, 2, 4, 6}
={2,4}

c. b-a
b-a is the set of members present in b but not in a.
{0, 2, 4, 6}-{-1, 1, 2, 3, 4}
={0,6}

d. Power set of b, its cardinality
Power set is the set of all possible combinations of elements.
There are 2^n members in the power set of x where n is the number of elements in the set x.
For example, power set of S={1,2} is {[tex]\phi[/tex],{1},{2},{1,2}}
The cardinality of S above is the number of elements in the set, therefore 2^2=4.

For b={0,2,4,6}
The power set is
{[tex]\phi[/tex],{0},{2},{4},{6},{0,2},{0,4},{0,6},{2,4},{2,6},{4,6},{0,2,4},{0,2,6},{0,4,6},{2,4,6},{0,2,4,6}}
for a total of 2^4=16 members in the power set.
Therefore the cardinality of the power set is 16.

 

The union of A and B is {-1, 0, 1, 2, 3, 4, 6}, the intersection is {2, 4}, and the difference B - A is {0, 6}. The power set of B contains 16 subsets.

Set Operations: Union, Intersection, Difference, and Power Sets

Let's solve the given problems step by step:

a. The union of sets A and B (A ∪ B)

A ∪ B represents all unique elements that are in either set A or set B.

Given: A = {-1, 1, 2, 3, 4} and B = {0, 2, 4, 6}

A ∪ B = {-1, 0, 1, 2, 3, 4, 6}

b. The intersection of sets A and B (A ∩ B)

A ∩ B represents all elements that are present in both sets A and B.

A ∩ B = {2, 4}

c. The difference of sets B and A (B - A)

B - A represents all elements that are in set B but not in set A.

B - A = {0, 6}

d. The power set of B and its cardinality

The power set of a set is the set of all its subsets, including the empty set and the set itself. If a set has n elements, its power set will contain 2^n subsets.

B = {0, 2, 4, 6}

The power set of B is: { {}, {0}, {2}, {4}, {6}, {0, 2}, {0, 4}, {0, 6}, {2, 4}, {2, 6}, {4, 6}, {0, 2, 4}, {0, 2, 6}, {0, 4, 6}, {2, 4, 6}, {0, 2, 4, 6} }

The cardinality of the power set of B is 2^4 = 16.

In summary:

A ∪ B = {-1, 0, 1, 2, 3, 4, 6}

A ∩ B = {2, 4}

B - A = {0, 6}

The power set of B has 16 elements.

What is the volume of a square pyramid with a base length of 6 cm and a height of 9 cm?



Enter your answer in the box.


cm³

Answers

Just took the test, it’s 108

Answer:

1/3 x base squared x  height

Step-by-step explanation:

so yes 108 is correct.

Other Questions
How to find the equation of a circle If you have been waking up too early for several weeks, you are probably suffering from Which of the following is not a psychological adaptation Use the information below to find EF such that triangle ABC is congruent to triangle DEFAB=36 BC=24 DE=48 m Which of these is defined by population, territory, government, and sovereignty?nation-statecivilizationparliamentdistrictfederation Ms. Romero is buying a scrapbook and sheets of designer paper. She has $30 and needs at least $15.75 to buy the scrapbook. Each sheet of paper costs $0.29. 300.29x15.75 to find the number of sheets of paper, x, she can buy. How many sheets of paper can she buy? How many 1/100 are in 3/10 Based on what you have read, explain the advantages of digital signals over analog signals. Mercutio and benvolio are concerned because tybalt has challenged romeo to a duel. mercutio then makes a joke and says that romeo is already dead. how has romeo died' according to him? how many moles are there in 78.3g of CO2? n the 1960s, new evidence helped support the theory of continental drift and change it into the theory of plate tectonics. What was this new evidence? Nolan bought 26 yards of rope, the rope costs 2 dollars per foot, how much did Nolan play for the rope? what is the volume of the rectangular pyramidA.360B.540C.720D.1080 Why does the monster see himself as different from Adam? A.Adam is placed in charge of nature, whereas the monster is a victim of the natural world. B.Adam has generational links to other people on Earth, whereas the monster has no link to any human. C.Adam's body was filled with strength and health, whereas the monster's body was physically weak and unhealthy. D.Adam came into the world happy and protected, whereas the monster entered the world confused and alone. Find the value of x so that line m is parallel to line n.A. 57B. 51C. 50D. 49 Who was the chinese reformer who became president of china in 1911? Someone please help?? :(Julie started with Newton's second law of motion. She drew a free-body diagram of an inclined plane experiment. She derived an equation for the acceleration down the inclined plane and determined how it would change if she changed the angle of the incline. From there she was able to derive an equation to find the coefficient of friction of any material on the inclined plane.In the scenario, how did Julie determine her findings on the coefficient of friction?a. inductive reasoningb. deductive reasoning from a valid principlec. deductive reasoning from an invalid principle, what was the climate in ancient greece what is the analogie for wasp the city is planning to build a new park by enlarging the current park by a scale factor of 4. The current park has an area of 37,625 yd squared. what is the area of the new park