Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.
The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.
There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:
P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2
In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.
To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.
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Please help! Show your work.
The value of the variable x in the equation 6 / -4.5 = 8 / 4x is - 3 / 2.
How to solve equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore, let's solve the equation.
The variable in the equation is x . A variable is a number represented with letter in an equation.
Therefore,
6 / -4.5 = 8 / 4x
cross multiply
6(4x) = -4.5(8)
24x = - 36
divide both sides of the equation by 24
Therefore,
x = -36 / 24
x = - 3 / 2
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Arrange the steps in order to simplify the expression
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
Given: a || b
Find the missing angle measures in the diagram. Explain how you find each angle measure. (explain please)
The missing angles measures in the diagram above when calculated is given below:
<1 = 42°
<2 = 76°
<3 = 62°
<4 = 76°
How to calculate the missing angle measures?For <1:
The total angle on a straight line = 180°
That is: angles <1+62°+<4 = 180
<1 = 180-62+76
= 180-138
= 42°
For <4: 180= 62+42+<4
<4 = 180-104
= 76°
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A car is driving on a road with a velocity of 20 − 10t miles per hour,
where t is the time in hours since the car started driving. What is the total distance
travelled by the car between times t = 0 and t = 3? Show work.
a. 5mi
b. 10mi
c. 15mi
d. 20mi
e. 25mi
The total distance traveled by the car between t = 0 and t = 3 is given as follows:
c. 15 mi.
How to obtain the total distance?The velocity function is given as follows:
v(t) = 20 - 10t.
The distance function is the integral of the velocity function, hence it is given as follows:
d(t) = 20t - 5t².
The distance at t = 0 is given as follows:
d(0) = 20(0) - 5(0)²
d(0) = 0.
The distance at t = 3 is given as follows:
d(3) = 20(3) - 5(3)²
d(3) = 15.
Hence the total distance is given as follows:
15 - 0 = 15 mi.
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question in the picture
1.) The average monthly income for Brianna would be = $1,850
2.) The average monthly expenses for Brianna would be =$3,145
3.) The total monthly cash flow = =$ −1,295
How to calculate the monthly income for Brianna?The monthly pay check after tax = $1600
The annual scholarship stipend = $3000
That is 3000/12 = $250
Therefore, the average monthly income = 1600+250 = $1,850.
The average monthly expenses = 700+120+75+140+25+110+100+300+250+(12000+1000+1500+800+600/12)
= 1820 + 15900/12
= 1820 + 1325
= $3,145
The monthly cash flow = 1850-3145 =$ −1,295
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in the diagram at the right, the length of a square is (3x+7) units. The dimensions of the cut-out rectangle are x by (2x+5) units. Which choice expresses the area of the shaded regions, in square units?
[tex] {(3x + 7)}^{2} - ((2x + 5) \times x) [/tex]
[tex] = 7 {x}^{2} - 5x + 49[/tex]
Use the model to estimate f(x) when
x
=
5
.
f(x) =
Use the model to estimate f(x) when
x
=
10
.
f(x) =
Using the model to estimate f(x) when x = 5 and x = 10, the vaues are 18.33 and 17.78
Using the model to estimate f(x) when x = 5 and x = 10From the question, we have the following function that can be used in our computation:
f(x) = -0.11x + 18.88
Also, we have
x = 5 and x = 10
Substitute the known values in the above equation, so, we have the following representation
f(5) = -0.11 * 5 + 18.88 = 18.33
f(10) = -0.11 * 10 + 18.88 = 17.78
Hence, the values are 18.33 and 17.78
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Complete question
Question: A statistician calculated the following linear model to describe the data: f(x) = – 0.11x + 18.88 Use the model to estimate f(x) when x = 5
If (2x, x + 17, x + 21, ....) is an arithmetic sequence find the value of x ?
Answer:
Since (2x, x + 17, x + 21, ...) is an arithmetic sequence, we know that the common difference between consecutive terms is constant.
The common difference can be found by subtracting any two consecutive terms in the sequence. Let's subtract the second term (x + 17) from the first term (2x):
2x - (x + 17) = x - 17
Now let's subtract the third term (x + 21) from the second term (x + 17):
(x + 17) - (x + 21) = -4
Since the common difference is constant, we can set the two expressions for the common difference equal to each other:
x - 17 = -4
Solving for x, we get:
x = 13
Therefore, the value of x that makes the sequence (2x, x + 17, x + 21, ...) an arithmetic sequence is x = 13.
after the school carnival there were 20 apples left over eight students shared these apples equally how many apples did each student receive
Answer:
They would have gotten 2 full apples each. There would be 4 left over. If they decided to split those 4 apples, they would have gotten 2 1/2 apples each.
Step-by-step explanation:
20 ÷ 8 = 16 R 4
16 ÷ 8 = 2 (the full apples they got each_)
4 x 2 = 8 (split the 4 apples in half to make 8)
Therefore, each student would have gotten 2 full apples and 1/2 of an apple.
Which triangle could be drawn as it is described?
The triangle which can be drawn as per the condition described is only option 2. an isosceles triangle with measure 20° and 80°.
Triangle which can be drawn as per the measurements are,
An acute triangle with sides measuring 7, 4, 2.
In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.
According to the Pythagorean theorem.
7²< 4² + 2²
49 < 16 + 4
49 < 20
This is a contradiction, since 49 cannot be less than 20.
It is not possible to draw triangle.
An isosceles triangle with measures of angle 20° and 80°.
Sum of interior angles of a triangle is 180°
Here, third angle = 180° - ( 20° + 80° )
⇒Third angle = 80°
Two angles are congruent ⇒ opposite sides to congruent angles are also congruent.
It forms a isosceles triangle.
An obtuse triangle with sides measuring 5, 10 and 15.
Side lengths 5, 10, and 15 do not form a triangle at all.
Since the sum of the two shorter sides is less than the longest side.
5 + 10 = 15
It is not possible to have an obtuse triangle with sides measuring 5, 10, and 15.
An scalene triangle with angle measuring 110° and 35°.
Sum of the interior angles is always 180°.
Measure of the third angle ,
180° - 110° - 35° = 35°
Three angles of the triangle measure 110°, 35°, and 35°.
It represents isosceles triangle.
Therefore, the possible triangle as per the given condition is only option 2. isosceles triangle with measure 20° and 80°.
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An automobile purchased for use by the manager of a firm at a price of $32,500 is to be depreciated by using the straight-line method over 5 years. What will be the book value of the automobile at the end of 3 years? (Assume that the scrap value is $0.) $
The book value of the automobile at the end of 3 years is $13,000.
What is the book value?The straight-line method is method of depreciation that allocates the same depreciation expense each year.
Straight line depreciation expense = (Cost of asset - Salvage value) / useful life
($32,500 - 0) / 5 = $6,500
Total depreciation in 3 years = $6,500 x 3 = $19,500
Book value = cost of the automobile - total depreciation
$32,500 - $19,500 = $13,000
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In 2016 , a clinical study in a small town of New Hampshire found that about 13 % of its population had the flu . The study also showed that 19 % of the people who had the flu tested negitive while 8% of of the people who did not have the flu tested positive . based on the given information construct a realative frequency table.
The relative frequency of a person having the flu and testing positive for the flu is 0.1053/0.901 = 0.117, or approximately 11.7%. The relative frequency table is given below.
To get the relative frequencies, we divide each cell value by the total frequency of the table.
This is how we construct relative frequency table.
To construct a relative frequency table, we need to determine the different possible outcomes and their corresponding frequencies based on the given information.
Let's define the following events:
A: a person has the flu
B: a person tests positive for the flu
Then, using the information given in the problem, we can construct the following relative frequency table:
A (has the flu) not A (does not have the flu) Total
B 0.13*0.81 = 0.1053 0.08*0.87 = 0.0696 0.1749
not B 0.19*0.81 = 0.1540 0.63*0.87 = 0.5471 0.7011
To 0.2843 0.6171 0.901
In this table, the values in the cells represent the product of the probability of the row event and the probability of the column event. For example, the value 0.1053 in the top left cell represents the probability of a person having the flu (event A) and testing positive for the flu (event B), which is calculated as 0.13 x 0.81.
The total frequency for each row and column is calculated by summing the values in that row or column. The total frequency for the entire table is the sum of all the values, which is 0.901 in this case.
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This is for the following two questions.
A couple plans to retire in 35 years. At that time, they would like to have enough money in an account so that they can receive a $6,000 every month end for the next 25 years. The account earns 8% APR compounded monthly and will continue to do so until there is a zero balance in the account.
To achieve this goal, how much money does the couple need to have in this account by the time they retire?
If they have not saved any money yet, how much does the couple need to deposit each month end until they retire?
The couple needs to deposit about $554.49 each month end until they retire to reach their goal.
How to solveTo find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:
FV = PMT * [((1 + r)^n - 1) / r]
We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:
PMT = FV / [((1 + r)^n - 1) / r]
We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:
PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]
PMT ≈ 554.49
Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.
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1. Lana completed 22 of the puzzles in
her puzzle book. There are 10 puzzles
remaining. What percent of the puzzle
has she completed?
Answer:
Lana has completed 22 out of 32 puzzles in her book. To find the percentage of the puzzle she has completed, divide the number of puzzles she has completed by the total number of puzzles in the book and multiply by 100.
22/32 x 100 = 68.75%
Lana has completed 68.75% of the puzzles in her book.
Answer:
Lana has completed 68.75% of the puzzles in her puzzle book.
Step-by-step explanation:
Lana has completed a total of 22 puzzles and there are 10 puzzles remaining, so the total number of puzzles in the book is:22 + 10 = 32To find the percentage of puzzles Lana has completed, we can use the following formula:percentage = (completed puzzles / total puzzles) x 100%Substituting the values, we get:percentage = (22 / 32) x 100%
percentage = 0.6875 x 100%
percentage = 68.75%Therefore, Lana has completed 68.75% of the puzzles in her puzzle book.
Find the polar coordinates of a point with Cartesian coordinates (x,y)=(−√2,−√2).
Answer: The correct answer is (2,5π/4).
Step-by-step explanation:
The correct polar coordinates of the point (-√2, -√2) are (r, θ) = (2, 5π/4).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((-√2)^2 + (-√2)^2)
= √(2 + 2)
= √4
= 2
θ = atan2(-√2, -√2)
= 5π/4 radians
So, the correct polar coordinates of the point (-√2, -√2) are (r, θ) = (2, 5π/4).
Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
Snow flake
A.
No
B.
Yes; 3 lines of symmetry
C.
Yes; 6 lines of symmetry
D.
Yes; 12 lines of symmetry
The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.
How many lines of symmetry does a snowflake have ?Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.
So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided
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Need help don’t get it
Answer:
[tex] \frac{210}{360} = \frac{7}{12} [/tex]
This figure represents 7/12 of the circle.
Find a quadratic equation which has solutions x=7 and x=-9. Write the quadratic form in the simplest standard form x^2+bx+c=0
Answer: x^2+2x-63
Step-by-step explanation:
Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)
=x^2-(7-9)+(7*(-9))
=x^2+2x-63
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Which one of these tables are proportional? Show your work.
Answer:
Table B is proportional since y = 1.5x:
4.5 ÷ 3 = 1.5
7.5 ÷ 5 = 1.5
10.5 ÷ 7 = 1.5
You are going on a long trip and want to calculate your fuel efficiency. When you start your trip your odometer read 106069 miles. At the end of your trip your odometer reads 106485 miles.
You started your trip with a full tank of gas. After the trip, you refill the tank with 13 gallons of gas.
What was your fuel efficiency for this trip, in miles per gallon?
Answer:32mi/gal
Step-by-step explanation:
106485 - 106069 = 416mi (the distance that you traveled)
416/13 = 32
32mi/gal
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it.
If there’s a red mark on the bottom of the duck, the person wins a small prize.
If there’s a blue mark on the bottom of the duck, the person wins a large prize.
Many ducks do not have a mark.
After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize.
Estimate the number of the 160 ducks that you think have red marks on the bottom.
Answer:
We can use the information provided to estimate the number of ducks that have red marks on the bottom.
If only 3 out of 50 people have won a small prize, then we can estimate that the probability of winning a small prize is 3/50 or 0.06. Since the person wins a small prize if there’s a red mark on the bottom of the duck, we can estimate that the proportion of ducks with red marks is also 0.06.
So, we can estimate the number of ducks with red marks as follows:
Number of ducks with red marks = 0.06 x 160
Number of ducks with red marks = 9.6
We can estimate that there are about 9 or 10 ducks with red marks on the bottom.
Complete the equation that represents the relationship between p and a.
The equation that represents the relationship between p and a is a = p - 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 0)/(7 - 6)
Slope (m) = 1/1
Slope (m) = 1.
At data point (6, 0) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 1(x - 6)
y = x - 6 ≡ a = p - 6
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Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of three fifths to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(5.8, −3), B′(1.6, −1.5), C′(−1.6, 3), D′(2.5, 3)
A′(−12, 18), B′(−6, 6), C′(12, −6), D′(12, 12)
A′(2.4, −3.6), B′(1.2, −1.2), C′(−2.4, 1.26), D′(−2.4, −2.4)
A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4)
If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:
Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).
Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).
Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).
Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).
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A rectangular prism shaped display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall. What is the volume of the display case in cubic inches?
A. 73 1/4 in
B. 320 1/4 in
C. 10, 328 1/16 in
D. 28,372 5/8 in
Answer:
The volume of the display case in cubic inches is 10,328 1/16 in.
Karissa wants to use the data to determine which brand is most absorbent. Based on the data collected at the beginning of the contest, enter the approximate number of paper towels needed to clean each square foot of the spill. Enter the number of Brand A paper towels needed per square foot in the first box. Enter the number of Brand B paper towels needed per square foot in the second box. Enter the number of Brand C paper towels needed per square foot in the third box.
Therefore, we need 17 towels of brand C to clean a single sq ft
How to solveBrand A:
we add up all the sq ft cleaned by brand a
0.75+1.50+2.25=4.5
and we add up all paper towels used in total
6+13+20=39
now
to clean 4.5 square ft, we need 39 towels. how many we need to clean a single square foot?
4.5 sq ft ___________39 towels
1 sq ft_____________A
and A= 1 sq ft * 39 towels / 4.5 sq ft
and that gives us 8.6 towels, so we need 9 towels to clan a square foot with the brand A
now we repeat this with bran b and c
brand B:
0.75+1.75+2=4.5 sq ft
9+22+25= 56 towels
4.5 sq ft________56 towels
1 sq ft__________B
B= 1 sq ft * 56 towels / 4.5 sq ft = 12.4
so we need 13 towels of brand B
at last
brand C:
1+1.75+2.5=5.25 sq ft
17+29+41= 87 towels
5.25 sq ft________87 towels
1 sq ft__________C
C= 1 sq ft * 87 towels / 5.25 sq ft = 16.57 towels
Therefore, we need 17 towels of brand C to clean a single sq ft
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What is a square of a binomial?
A square of a binomial is a polynomial expression that results from multiplying a binomial by itself. The result is a trinomial expression with three terms.
Write a recursive sequence that represents the sequence defined by the following explicit formula:
The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:
[tex]a_1 = -32[/tex][tex]a_{n + 1} = -\frac{1}{4}a_n[/tex]What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The explicit formula of the sequence is given as follows:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The first term and the common ratio for this problem is given as follows:
[tex]a_1 = -32, q = -\frac{1}{4}[/tex]
The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:
[tex]a_{n + 1} = -\frac{1}{4}a_n[/tex]
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Fill the blank with either E or to make the statement true.
- 13 {8, 13, 22, 36}
***
fill in the answer box to complete your choice
We can see here that the statements that are true are:
B. The symbol should be used because (8, 13, 22, 36) is a set and none of the elements in - 13 is a set.
C. The ∉ symbol should be used because ∉ is not an element of the set.
F. The ∈ symbol should be used because ∉ is not an element of the set.
What is a set?A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.
Numbers, letters, words, forms, persons, and other mathematical things can all be included in a set.
We can see here that -13 ∉ (8, 13, 22, 36).
These statements are true because -13 is not actually an element of (8, 13, 22, 36). Thus, in the given set of data, -13 is not seen in the given set.
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The dimensions of a cylinder are shown in the diagram
Round to the nearest whole number , what is the total surface area of the cylinder in cubic centimeters
Answer:
S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3
what is the volume of the cube shown
[tex] {( \frac{9}{4} )}^{3} [/tex]
=
[tex] \frac{729}{64} [/tex]
Answer: 11 25/64
Step-by-step explanation: 2 1/4 x 2 1/4= 5 1/16 x 2 1/4 = 11 25/64
