Exercise 12.1.1: Coin flips and events. About A coin is flipped four times. For each of the events described below, express the event as a set in roster notation. Each outcome is written as a string of length 4 from {H, T}, such as HHTH. Assuming the coin is a fair coin, give the probability of each event. (a) The first and last flips come up heads. (b) There are at least two consecutive flips that come up heads. (c) The first flip comes up tails and there are at least two consecutive flips that come up heads.
Answer:
a [tex]Pr = 0.25[/tex]
b [tex]Pr = 0.50[/tex]
c [tex]Pr = 0.1875[/tex]
Step-by-step explanation:
Given
[tex]n = 4[/tex] --- number of times
[tex]r = 2[/tex] --- faces of a coin
First, is to determine the sample size.
This is calculated as:
[tex]Size =r^n[/tex]
[tex]Size =2^4[/tex]
[tex]Size =16[/tex]
Solving (a): First and last slip is head
This event is represented as:
[tex]E=\{HHHH, HHTH, HTHH, HTTH\}[/tex]
The probability is calculated as:
[tex]Pr = \frac{n(E)}{Size}[/tex]
[tex]Pr = \frac{4}{16}[/tex]
[tex]Pr = 0.25[/tex]
b) At least 2 consecutive flips that is heads.
This event is represented as:
[tex]E=\{HHHH,HHHT,HHTH,HHTT,THHH,THHT,HTHH,TTHH\}[/tex]
The probability is calculated as:
[tex]Pr = \frac{n(E)}{Size}[/tex]
[tex]Pr = \frac{8}{16}[/tex]
[tex]Pr = 0.50[/tex]
c) First is tail and at least 2 consecutive flips is head.
This event is represented as:
[tex]E=\{THHH,THHT,TTHH\}[/tex]
The probability is calculated as:
[tex]Pr = \frac{n(E)}{Size}[/tex]
[tex]Pr = \frac{3}{16}[/tex]
[tex]Pr = 0.1875[/tex]
Solve for X and Y
20x 25x 7x 5y 20x
9514 1404 393
Answer:
(x, y) = (5, 9)
Step-by-step explanation:
We must find the value of x before we can find the value of y. Fortunately, simply adding the arcs around the circle will give an equation for x.
25x +20x +7x +20x = 360 . . . . angles in degrees
72x = 360 . . . simplify
x = 5 . . . . . . divide by 72
__
The value of the external angle at J is half the difference of arcs GL and HK. That is, ...
5y = (25x -7x)/2 = 9x = 9(5) . . . . simplify, fill in for x
y = 9 . . . . . . divide by 5
__
(x, y) = (5, 9)
An item sells for $40. The sales tax on
the item is 8%. What is the sales tax and
total cost?
Answer:
$43.20 total
$3.20 sales tax
Explication:
40*1.08=43.2
Answer:
sales tax = $3.20
total cost = $43.20
Step-by-step explanation:
To calculate the sales tax on an item, multiply the price of the item by the tax percent in decimal form. To convert a percent to decimal form, divide the percent by (100).
Sales tax percent: 8%
In decimal form: 0.08
Multiply the sales tax in decimal form by the price of the item to find out the sales tax amount,
(item_price) * (sales_tax)
= (40) * (0.08)
= 3.2
Sales tax amount: $3.20
To find the total cost of the product, add the sales tax amount to the item price,
(item_price) + (sales_tax_amount)
= 40 + 3.20
= 43.20
Solve for x:
1.1.1
x² - 6x=0
Answer:
zoom in
mark me as brainliest
10 points
question 5: a, b, and c.
Answer:
the First One By Adding Four
The Second One Add Five And Two
The Third Add Two And Substract Four
Select all correct conversions.
0.6 km = 6,000 m
46 m = 4,600 cm
457 mm = 4.57 cm
7.5 m = 0.0075 km
0.31 m = 310 mm
Which ones are it?
Answer:
310 mm 0.6 km = 6,000 m 457 mm = 4.57 cmStep-by-step explanation:
The statements 46 m = 4,600 cm, 0.31 m = 310 mm, 7.5 m = 0.0075 km and 0.31 m = 310 mm are correct conversations
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that conversations 1km = 1000 m
1 cm = 10 mm
1 m = 100 cm
0.6 km = 6,000 m is not correct, as 0.6 km is 600m
46 m = 4,600 cm is correct.
0.31 m = 310 mm is correct
457 mm = 4.57 cm is incorrect, as 457 mm is 45.7 cm
7.5 m = 0.0075 km is correct
0.31 m = 310 mm is correct
Hence, the statements 46 m = 4,600 cm, 0.31 m = 310 mm, 7.5 m = 0.0075 km and 0.31 m = 310 mm are correct conversations
To learn more on Unit of Measurement click:
https://brainly.com/question/15402847
#SPJ2
The store sells 6 donuts for $15 Kim has $37.50 how many donuts can she buy?
Answer:
12 if the donuts are sold in boxes and not singular, 15 if you can buy a smaller sized box
Step-by-step explanation:
Hope this helps! have a great day!
EVERYBODY LOOK.
^^^^^^^^^^^^^^^^^^^
40 FREEPOINTS
Answer:
Oh ok add me abelthegoat8
Step-by-step explanation:
Answer:
I don't have sc, but thx for the points! :)
Step-by-step explanation:
have a good day!
Newton yayınları anahtar kodu
Answer:
What does this even say maybe I can try and help.
Answer this I’ll give brainalist + points, please help!
Answer:
B
Step-by-step explanation:
the mean of A
= (84 + 84 + 85 + 86) ÷ 4
= 339 ÷ 4
= 84.75
the median of A
= (84 + 85) ÷2
= 169 ÷ 2
= 84.5
84.75 > 84.5
the mean of B
= (74 + 79 + 82 + 87) ÷ 4
= 332 ÷ 4
= 80.5
the median of B
= (79 + 82) ÷2
= 161 ÷ 2
= 80.5
80.5 = 80.5
the mean = the median
the mean of C
= (63 + 66 + 67 + 68) ÷ 4
= 264 ÷ 4
= 66
the median of C
= (66 + 67) ÷2
= 133 ÷ 2
= 66.5
66 < 66.5
the mean of D
= (14 + 16 + 18 + 19) ÷ 4
= 67 ÷ 4
= 16.75
the median of D
= (16 + 18) ÷2
= 34 ÷ 2
= 17
16.75 > 17
Tan x= sin x/cos X. Therefore tan (90-A) =
Answer:
tan (90° - A) = cot A
Step-by-step explanation:
tan (90° - A) = sin (90° - A) / cos (90° - A) = cos A / sin A = cot A
literally a goat if someone gives me an answer for this please
Answer: D, 100
Step-by-step explanation:
Answer: 100 (D)
Step-by-step explanation:
cuz
NEED HELP PLEASE ASAP! BRAINLIEST TO RIGHT ANSWER! Two similar rectangles have areas of 6 in.2 and 24 in.2. What is the scale factor of the smaller rectangle to the larger rectangle?
A. 2 : 1
B. 4 : 1
C. 6 : 1
about travels in the following path. How far north did it travel? Round your answer to the nearest 10th of a mile
Answer:
19.1 miles
Step-by-step explanation:
The situation given represents a right triangle.
Thus, we would use trigonometric function to find how far north the boat travelled.
Let's represent how far the boat travelled north with "x".
Thus:
Reference angle = 23°
Opposite = x
Adjacent = 45 miles
Apply TOA:
Tan 23° = Opp/Adj
Tan 23° = x/45
Multiply both sides by 45
45 × Tan 23° = x
x = 45 × Tan 23°
x = 19.1013667
x = 19.1 miles (nearest tenth of a mile)
During a fundraiser, students in Math Club make a $0.50 profit for every candy bar they sell. Let n represent the number of candy bars the club sells. Let t represent the total profit earned, in dollars. What is the total profit earned for selling 10 candy bars?
Answer:
$5
Step-by-step explanation:
If every candy bar is $0.50 and they sell 10 just do
0.50 x 10 = 5
4 × 1 + 3 × 1/10 + 9 x 1/1,000 in word form
Plsss 15 points :)
Answer:
four multipled by one plus three multiplied by one tenth plus 9 multiple by one one thousandth
When is subtraction always the first operation done in an expression?
Never
When it follows addition in an expression.
When it is the first operation in an expression, from left to right.
When it is in parentheses in an expression.
Answer:
When it is the first operation in an expression, from left to right.
12 = 0.005 X W
Solve the equation
Answer: look at the picture
Step-by-step explanation: Hope this help :D
Directions: Find the perimeter and area of each figure below.
HELPPPP ASPPP
Answer:
17) [tex]6a^{3}b^{2}[/tex]
18) [tex]40m^{4} n^{10}[/tex]
19) 14x³y²
20) [tex]9x^{2} y^{6}[/tex]π
Step-by-step explanation:
17)
Area of triangle = 1/2*b*h
A = 1/2(4a²b)(3ab)
A = 6(a³b²)
18)
A = 1/2(4mn⁵)(20m³n⁵)
A = (40)(m⁴n¹⁰)
19)
A = 2 (1/2)(2xy)(3x²y)
A = (6x³y²) + (4x²y*2xy)
A = 6x³y² + 8x³y²
A = 14x³y²
20)
A = (3xy³)²
A = 3² x² (y³)²
Someone please help me answer this!! Show me all steps you used please!!!
Answer:
144
Step-by-step explanation:
20²-16²
pythagorean theorem
a²=b²-c²
Choose all of the shapes that are used to create the net of a cylinder. circle triangle wedge rectangle
Answer:
trianglw
Step-by-step explanation:
Answer:
Two circles and a rectangle will make up a cylander.
Step-by-step explanation:
Have a good day! :)
Which of the following is equivalent to the expression below?
4x + 2(3-x)
6x + 6
3x+6
5x + 6
2x +6
Answer:
2x + 6
Step-by-step explanation:
you have to factorize the above equation first and you'll get the answer
The 98 percent confidence interval (−0.248,−0.134) was constructed to estimate the slope of a regression model for a bivariate data set with 20 values. Alice claims that a sample size of 25 will produce a narrower interval, all other things remaining the same. Desmond claims that a sample size of 15 will produce a narrower interval. Which statement is true about the claims made by Alice and Desmond?
a. Alice’s claim is correct.
b. Desmond’s claim is correct.
c. Both Alice’s claim and Desmond’s claim are correct.
d. Neither Alice’s claim nor Desmond’s claim is correct.
e. There is not enough information to determine whether the claims are correct.
Answer:
a. Alice’s claim is correct.
Step-by-step explanation:
Margin of error of a confidence interval:
The margin of error of a confidence interval is inversely proportional to the sample size. This means that a smaller sample size leads to a smaller margin of error and a narrower interval, while a larger sample size leads to a larger margin of error and a wider interval.
Alice claims that a sample size of 25 will produce a narrower interval
25 > 20, so smaller margin of error and narrower interval, which means that Alice is correct.
Desmond claims that a sample size of 15 will produce a narrower interval.
15 < 20, so larger margin of error and wider interval, which means that Desmond is wrong.
So the correct answer is given by option a.
What is the measure of m?
12
4
n
m
m
[?]
Enter
will give brainliest
Answer:
8 I think
Step-by-step explanation:
if I'm wrong don't get offended
Express 1/3 as a repeating decimal and round to the nearest hundredth.
Answer:
1/3 is .333... so you can write .33.... or .33 with a line on top of the 3's
Step-by-step explanation:
.3 is in the tenths and .33 is in the hundredths place
help please triangles and trig
Given:
A figure of a right angle.
To find:
The value of x.
Solution:
We know that the measure of the altitude on the hypotenuse of a right right triangle is the geometric mean of the segments of the hypotenuse.
If the altitude "h", divides the hypotenuse in two segments "a" and "b", then
[tex]h=\sqrt{ab}[/tex]
In the given figure, the measure of the altitude is x and it divides the hypotenuse in two segments 3 units and 24 units.
Using the above theorem, we get
[tex]x=\sqrt{3\times 24}[/tex]
[tex]x=\sqrt{72}[/tex]
[tex]x=6\sqrt{2}[/tex]
Therefore, the required solutions for the given blanks are:
Blank 1: 72
Blank 2: 6
Blank 3: 2
Jed is building a roof for his shed. The highest point of the roof will be 3 ft higher than the top of the shed. The slanted roof will be 7 ft long. What is the measure of the angle formed by the top of the shed and the slanted roof?
Answer:
90 degrees
Step-by-step explanation:
Answer:
It’s 100% 25..
Step-by-step explanation:
someone help me please like mega pleaseee help a girl out
Answer:
B.
Step-by-step explanation:
Could someone pls help me
What is the value of x in the equation (2x + 1)1/3 + 3 = 6
Answer:
x = 4
Step-by-step explanation: