Answer:
a) 0.27 = 27% probability that a randomly chosen card holder has annual income $20,000 or less.
b) 0.778 = 77.8% probability that (s)he carries a balance
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a) What is the probability that a randomly chosen card holder has annual income $20,000 or less?
20% of 30%(carry no balance).
30% of 70%(carry balance). So
[tex]P = 0.2*0.3 + 0.3*0.7 = 0.06 + 0.21 = 0.27[/tex]
0.27 = 27% probability that a randomly chosen card holder has annual income $20,000 or less.
b) If this card holder has an annual income that is $20,000 or less, what is the probability that (s)he carries a balance?
Conditional probability.
Event A: Annual income of $20,000 or less.
Event B: Carries a balance.
0.27 = 27% probability that a randomly chosen card holder has annual income $20,000 or less
This means that [tex]P(A) = 0.27[/tex]
Probability of a income of $20,000 or less and balance.
30% of 70%, so:
[tex]P(A \cap B) = 0.3*0.7 = 0.21[/tex]
The probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.21}{0.27} = 0.778[/tex]
0.778 = 77.8% probability that (s)he carries a balance
PLEASE HELP PLEASE
A girls' choir is choosing a uniform for their concert. They can pick red, green or
purple sweaters, and they can pick tan, white or black skirts. The shoes they need
come in gold and black. Assuming all combinations are acceptable, how many
different combinations can the choir pick?
Answer:
18
Step-by-step explanation:
=============================================================
Explanation:
There are 3 colors to pick for the sweaters (red, green, purple).There are 3 colors for the skirts (tan, white, black)There are 2 colors for the shoes (gold, black)Multiply out those values mentioned to get the final answer: 3*3*2 = 9*2 = 18.
There are 18 different outfit combos.
---------------
Further explanation (optional section):
Let's say we only worried about the sweaters and shoes, and for now there's only one color for the skirt. We have 3 colors for the sweaters and 2 for the shoes. Imagine a table with 3 rows and 2 columns. Each row is a different color for the sweater and each column is a different color for the shoe. There are 3*2 = 6 cells inside the table. Each cell is a different outfit.
For instance, we could have R = red sweater and G = gold shoe. Then that means RG = red sweater + gold shoe outfit. So we'd have RG as one of the cells of this 6 cell table.
Now imagine that we laid out a table that is 6 by 3. The 6 is from the 6 outfits calculated earlier, and the 3 is now accounting for the colors of the skirts. We'd then have 6*3 = 18 combos total. Again, each cell inside the table represents a different outfit combo.
Let's say you have a 4 gallon and a 10 gallon pailHow can you measure exactly 2 gallons of water?
You can fill the 10 gallon pail all the way up. After that, you can pour the water from the 10 gallon pail, into the 4 gallon pail 2 times. That will leave you with 2 gallons in the 10 gallon pail.
A bowl has 2 gold marbles, 3 blue marbles and 5 white marbles. A marble is randomly selected and then placed back in the bowl. You do this 5 times. What is the probability of choosing 1 gold marble, 1 blue marble and 3 white marbles?
Answer:
2/10 or 1/5 gold, 3/10 blue and 5/10 or 2/5 white
Step-by-step explanation:
2+3+5=10
since you do this 5 times and get 5 marbles it can be:
2/10 or 1/5 gold, 3/10 blue and 5/10 or 2/5 white
The probability of choosing 1 gold marble, 1 blue marble and 3 white marbles is 2/5
Probability is the likelihood or chance that an event will occur.
If there are 2 gold marbles, 3 blue marbles and 5 white marble in the bowl, the total number of marbles will be 10 marbles.
Pr(1 gold marble) = 2/10 = 1/5
Pr(1 blue marble) = 3/10
Pr(3 white marble) = [tex]\frac{3}{5C_3} = \frac{3}{10}[/tex]
Add all the probability;
Pr(hoosing 1 gold marble, 1 blue marble and 3 white marbles) = 1/5 +3/10 + 3/10 = 8/10 = 2/5
Hence the probability of choosing 1 gold marble, 1 blue marble and 3 white marbles is 2/5
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A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $115 (without tax) and that the calculator cost $20 more than four times the cost of the textbook. What was the cost of each item? Let x= the cost of a calculator and y= the cost of the textbook. The corresponding modeling system is {x+y=115x=4y+20. Solve the system by using the method of substitution.
Answer:
X=$96
Y=$19
Step-by-step explanation:
x=4y+20
X+Y=$115
4Y+20+Y=$115
5Y+20=$115
-20 -20
5Y=$95
/5 /5
Y=$19
X=4 x $19 + $20
X=$76+$20
X=$96
In linear equation, cost of calculator = $96 , cost of textbook = $19 is the cost of each item .
What are instances of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.let cost of calculator = x
cost of textbook = y
x=4y+20 .................(1)
X+Y= 115 .................(2)
put value of equation 1 in 2
4Y+20+Y= 115
5Y+20= 115
5Y = 115 - 20
5Y = 95
Y = 95/5
Y = 19
Put value of y in equation 1
X=4 x 19 + 20
X= 76+ 20
X= 96
cost of calculator = 96
cost of textbook = 19
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Which expression is a sixth root of -1+i sqrt3?
(Look at photo for options)
Answer:
D
6sqrt2(cos(20)+I sin (20))
Answer:
The answer is D: 6sqrt2(cos(20)+isin(20))
Step-by-step explanation:
I’ve honestly been trying to figure out why this is the answer but I have no idea I just happened to get it right.
Due today...
Explain how to use the area of a parallelogram to find the area of a triangle
!NO LINKS, NO FILES!
please :)
Answer:
If you draw a diagonal across the parallelogram from one vertex to the opposite vertex, you divide the parallelogram into two congruent triangles. Each triangle thus has 1/2 of the area of the parallelogram.
5. What is the distance between two points with coordinates at (17, 21) and (28, 13)?
A 11.4
C 18.5
B 13.6
D 20
Answer:
this is the answer A
Step-by-step explanation:
Please please help me please please I really need help please please help me please please
Answer:
1d674hh
Step-by-step explanation:
drrx+mub
Josephine has a rectangular garden with an area of 2x2 + x – 6 square feet.
Which expressions can represent the length and width of the garden?
length = x2 – 3 feet; width = 2 feet
length = 2x + 3 feet; width = x – 2 feet
length = 2x + 2 feet; width = x – 3 feet
length = 2x – 3 feet; width = x + 2 feet
Answer:
D
Step-by-step explanation:
One coin is flipped six times. What is the probability of flipping two heads and four tails?
Answer:
1/6 x 1/6 = 1/36
1/36 is our probability of getting two heads and four tails.
Help me please with this thank you
Find area using law of sines
Answer:
4
Step-by-step explanation:
HOPE THIS HELPED!!! I TRIED AND REMEMBERED
Find the measure of an arc formed by 1 slice of pizza
Divide £104 in the ratio 3:5
Answer:
39:65
Step-by-step explanation:
104/(3+5) = 104/8 = 13 13(3):13(5) = 39:65
Mark buys a wooden board that is 7 1/2 feet long. The cost of the wooden board is $0.50 per foot, including tax. Enter the total cost, in dollars, of the wooden board.
Answer:
$3.75
Step-by-step explanation:
The board is 7 and a half feet long. It costs 0.5 per foot.
Therefore we can just multiply the two to find the total cost:
0.5 x 7.5 = $3.75
Hope this helped!
oliver wants a hat that original price is $25, the store is having a 20% off sale, with this sale what is the final cost?
Answer:
$20
Step-by-step explanation:
25 x 0.2=5
25-5= 20
Which expression is equivalent to j(j)(j)(j)(j)(j)(j)(j)(j)(j)(j)(j)(j)?
o 13'
o 13j
o j13
oj + 13
need help fast pls!
College Math! Pls help
Answer:
right: 11.15
left: 17.15
Step-by-step explanation:
right formula: [tex]\int _a^bf\left(x\right)dx\:\approx \Delta \:x\left(f\left(x_1\right)+f\left(x_2\right)+...+f\left(x_n\right)\right)[/tex]
left formula: [tex]\int _a^bf\left(x\right)dx\:\approx \Delta \:x\left(f\left(x_0\right)+f\left(x_1\right)+...+f\left(x_{n-1}\right)\right),[/tex]
[tex]\Delta \:x\:=\:\frac{b-a}{n}[/tex]
estimating : [tex]\int _1^7\left(\frac{7}{x}\right)dx[/tex] , with n = 6 (number of sub-intervals in Riemann sum)
right: 1 [tex]\left(f\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)+f\left(x_4\right)+f\left(x_5\right)+f\left(x_6\right)\right)[/tex] =[tex]1\cdot \left(\frac{7}{2}+\frac{7}{3}+\frac{7}{4}+\frac{7}{5}+\frac{7}{6}+1\right)[/tex] = 11.5
left: [tex]1\cdot \left(f\left(x_0\right)+f\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)+f\left(x_4\right)+f\left(x_5\right)\right)[/tex] =
[tex]1\cdot \left(7+\frac{7}{2}+\frac{7}{3}+\frac{7}{4}+\frac{7}{5}+\frac{7}{6}\right)[/tex] = 17.15
NEED ANWSERS FAST
33-38
Find the value of x
Answer:
33. 18
34. 50
35. 50
36. 5
37. 1
38. 24
Step-by-step explanation:
Explanation found on photo! Hope it helped and my apologies for my messy work
25 points and brainliest for correct answer!!
Convert to standard form equation. Quadratics
Only the y=1/3x^2+2 and the y=-1/7x^2+12
Answer:
For the y=1/3x^2+2 the answer is For the second one y=-1/7x^2+12 the answer is
Step-by-step explanation:
Evaluate the following equation for the given x value. Round your answer to
the nearest hundredth. *
у
600(0.732)"; x = 3
Answer:
585856859686
Step-by-step explanation:
546786676
please help meeeee i will give brainlyest
Answer:
answer is 63 min
Step-by-step explanation:
math+calculator like and subscribe to yourmom.com31
Fill in the boxes with values that make the statement true.
which sign makes the statement true? |6|? -8 greater than less than or equal to?
Answer:
|6| > -8
Step-by-step explanation:
The absolute value of |6| is 6. Because positives are greater than negatives, 6 is greater than -8.
Answer: greater than
Step-by-step explanation: Absolute value shows a number's distance from zero on a number line. 6's distance from 0 is still 6. 6 is greater than -8, therefore l6l>-8
Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch. She slipped and spilled 1/4 of the lemonade in the pitcher. What fraction of a gallon of lemonade did she spill?
Answer:
Susan spilled 1/6 of a gallon of lemonade.
Step-by-step explanation:
Since Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch, and she slipped and spilled 1/4 of the lemonade in the pitcher, to determine what fraction of a gallon of lemonade did she spill the following calculation must be performed:
2/3 = 0.6666
0.666666 x 1/4 = X
0.166666 = X
0.166666 = 1/6
Therefore, Susan spilled 1/6 of a gallon of lemonade.
A furniture manufacturing company manufactures dining-room tables and chairs. A table requires 8 labor-hour s for assembling and 2 labor-h ours for finishing. A chair requires 2 labor-hours for assembling and 1 labor-hour for finishing. The maximum labor-hours available p er day for assembly and finishing are 400 and 120, respectively. If x is the number of tables and y is the number of chairs produced per day, write a system of linear inequalities that indicates appropriate restraints on x and y.
Required:
Find the set of feasible solutions graphically for the number of tables and chairs that can be produced.
Answer:
See Annex In blue feasible region ( using Geogebra)
Step-by-step explanation:
Table 1.-
Assembling hours finishing hours
Product (tables) x 8 2
Product ( chairs) y 2 1
Availability 400 120
Constrains:
1.-Availability of assembling hours 400
8*x + 2* y ≤ 400
2.-Availability of Finishing hours
2*x + 1*y ≤ 120
3.-General constraints
x ≥ 0 y ≥ 0 integers
Factor the expression shown below completely.
18.12
603 + 50
OA. 2(31 – 5)2
OB. 2(6.1 – 5)2
OC. 3(2x - 5)
OD. 6(3.1 – 5)
RIGHT ANSWERS ONLY
A. 2(3x-5)²
Step-by-step explanation:
18x² - 60x + 50
= 2 (9x² - 30x + 25 ) ⇒⇒⇒ take 2 as common from all terms
note: 9x² = 3x * 3x and 25 = 5*5 and
3x * 5 *2 = 30x
so, this is a complete square
= 2(3x-5)(3x-5)
= 2(3x-5)²
Use the graph to write a linear function that relates y to x
y=
Answer:
y = [tex]\frac{4}{3}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (6, 10) ← 2 points on the line
m = [tex]\frac{10-2}{6-0}[/tex] = [tex]\frac{8}{6}[/tex] = [tex]\frac{4}{3}[/tex]
The line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = [tex]\frac{4}{3}[/tex] x + 2 ← equation of line
Consider this chart, which details a store’s sales revenue by department. A pie chart titled Sales by Department. Blue is pharmacy, red is clothing, green is hardware, and yellow is gardening. Which of the following statements indicate ways in which this graph is misleading? I. The sections are not numerically labeled. II. The time frame is not mentioned. III. It is unclear which color corresponds to which section. a. I and II b. II only c. I and III d. I, II, and III Please select the best answer from the choices provided A B C D
Answer:
Answer is A l and ll
Step-by-step explanation:
Hannah has been researching sales of garden supplies. She wants to show the pattern that sales follow over the course of a year. The line graph is most effective for the sales. The correct option is (D).
What is the line graph?An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.
here, we have,
Line graphs have two axes that are graphically represented as x and y, respectively (x,y).
There are three types of line graph which are as follows:
Multiple line graph.
Simple line graph.
Compound line graph.
Hence, Hannah has been researching sales of garden supplies. She wants to show the pattern that sales follow over the course of a year. The line graph is most effective for the sales.
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Complete question:
Hannah has been researching sales of garden supplies. She wants to show the pattern that sales follow over the course of a year. Which type of graphic would be most effective?
A. Bar chart
B. Pie chart
C. Flow chart
D. Line graph
MATHEMATICS
PLANE if it is a plane figure and write SOLID if it is a solid
1. shoebox
2. tiles 3.ball
4.wheel 5.playing card 6.wall sticker 7.basket ball court 8.kite 9.dringking glass 10.tv screenshot
Answer:
P=plane
S=solid
1.s
2.p
3.s
4.s
5.p
6.p
7.s
8.p
9.s
10.p
If you are helped with my answer pls tag me brianliest
THANK YOU...