The probability of flipping tails at least two times in three flips is 1/2.
When flipping a coin, there are two possible outcomes: heads or tails. Each flip is independent of the previous flips, so the probability of getting tails on any given flip is always 1/2 (assuming the coin is fair).
To find the theoretical probability of flipping tails at least two times in three flips, we can use the binomial probability formula:
P(x ≥ k) = 1 - P(x < k)
where P(x < k) is the probability of getting tails fewer than k times in three flips.
To find P(x < k), we can add up the probabilities of getting tails 0 times and getting tails 1 time:
P(x < 2) = P(0 tails) + P(1 tail)
P(0 tails) = (1/2)⁰ x (1/2)³ = 1/8
P(1 tail) = 3 x (1/2) (1/2)² = 3/8 (since there are three ways to get exactly one tail: TTH, THT, HTT)
P(x < 2) = 1/8 + 3/8 = 1/2
Therefore, the probability of flipping tails at least two times in three flips is:
P(x ≥ 2) = 1 - P(x < 2) = 1 - 1/2 = 1/2
So the theoretical probability of flipping tails at least two times in three flips is 1/2 or 0.5 as a decimal.
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The equation y=464-8x describes the altitude y in feet of a plane x seconds after it begins its descent how many seconds will it take the plane to land
In 58 seconds after starting its descent, the aircraft will touch down.
The plane will land when its altitude y is zero.
So we can set y = 0 in the equation:
0 = 464 - 8x
Solving for x:
8x = 464
x = 58
Therefore, the plane will land 58 seconds after it begins its descent.
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Find the extrema of the function f(x,y)=x^2+y^2
Answer:
The function f(x,y) = x^2 + y^2 represents the equation of a paraboloid with its vertex at the origin. Since the function increases as we move away from the origin, there are no maximum points, but there is a minimum point at the origin.
To find this minimum point, we can take the partial derivatives of f(x,y) with respect to x and y, and set them equal to zero:
df/dx = 2x = 0
df/dy = 2y = 0
Solving these equations simultaneously gives us x = 0 and y = 0, which is the only critical point of the function. To determine whether this point is a minimum or maximum, we can use the second partial derivative test.
Taking the second partial derivatives, we have:
d^2f/dx^2 = 2
d^2f/dy^2 = 2
d^2f/dxdy = 0
At the point (0,0), both second partial derivatives are positive, which indicates that the point is a minimum. Therefore, the function f(x,y) = x^2 + y^2 has a minimum value of 0 at the point (0,0).
please help. maths trigonometry
The value of 5cos(tetha) + 4/sin(beta) is 9
What are complementary angles?Complementary angles are two angles that sum up to 90°. This means that in a right angled triangle sin( beta) is thesame as cos(90-tetha) and cos (beta) is sin(90-tetha).
Examples of complementary angles include: 30 and 60, 50 and 40 e.t.c
Therefore if tan ( tetha ) = 3/4, and tan(tetha) = opp/adj. This means opp is 3 and adj is 4
therefore hyp = √3²+4²
= √9+16 = √25
= 5
therefore cos(tetha) = 4/5
and sin beta = 4/5
therefore 5cos(tetha) + 4/sin(beta) = 5 × 4/5 +(4÷4/5)
= 4+5 = 9
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Exercise 1: Identify each triangle based on sides. (Equilateral, Isosceles or Scalene).
The triangles are classified according to their sides as:
1. equilateral 2. Scalene 3. and 4. Isosceles 5. equilateral 6. and 7. scalene triangle. 8. Isosceles 9. and 10. Equilateral
How to Identify Triangles based on their Sides?Recall the following:
A triangle is equilateral if all three sides are equal.
It is isosceles if it has two equal sides.
A triangle is scalene if all three sides are of different lengths.
1. The triangle is equilateral because all sides are equal.
2. Scalene
3. and 4. Isosceles (two sides are equal)
5. All sides are equal, so it is an equilateral triangle.
6. and 7. The three sides have different lengths, therefore, it is a scalene triangle.
8. Isosceles
9. and 10. Equilateral
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A pair of shoes usually sells for $67. If the shoes are 20% off, and sales tax is 5%, what is the total price of the shoes, including tax?
Answer:
If the shoes are 20% off, then the sale price of the shoes will be:
67 - 0.20 * 67 = 67 - 13.40 = 53.60
So the sale price of the shoes is $53.60.
If the sales tax is 5%, then the tax on the shoes will be:
0.05 * 53.60 = 2.68
So the tax on the shoes is $2.68.
To find the total price of the shoes including tax, we need to add the sale price of the shoes and the tax:
53.60 + 2.68 = 56.28
Therefore, the total price of the shoes, including tax, is $56.28.
Answer:
$56.28
Step-by-step explanation:
1. Find the shoes' sale price.
The shoes are 20% off. We will find the new price by first finding 20% of $67.
An easy way to do it:
10% of 67 = 6.7
20% of 67 = 13.4
to double the percentage of the first equation, double the answer.
Now that we know 20% of 67 we can take away 20% from it:
67 - 13.4 =53.6
Money uses 2 decimal points so we will add a 0 at the end of the result.
The price of the shoes with only the sale is $53.60.
2. Add sales tax
First find out 5% of $53.60.
An easy way to do it:
10% of 53.60 = 5.360
5% of 53.60 = 2.68
to half the percentage of the first equation, half the answer.
Now that we know the price of the tax we can add it to our shoe price. With the sale the shoe costs $53.60 and we will add our tax:
53.60 + 2.68 = 56.28
Add your units:
$56.28Find the equation of the line perpendicular to y=1/2x-1 and passes through the point (5,6)
The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.
To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.
The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.
Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:
y - 6 = -2(x - 5)
y - 6 = -2x + 10
y = -2x + 16
Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.
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URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!!!!!
Match the given information with the equation for the line
-5x + 3y = -12
y = 3/2 x - 8
2y-x = -4
Y= -3/4x-2
What is the length of the hypotenuse of the triangle when x=9 now!!!
The concept Pythagoras theorem is used here to determine the length of the hypotenuse. It is an important theorem which explains the relation between the sides of a right angled triangle. The length of hypotenuse is
According to Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. The sides of this triangle have been named perpendicular base and hypotenuse.
Hypotenuse² = Perpendicular² + Base²
9² + 4² = 97
√97 = 9.84 cm
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Your question is incomplete most probably your full question was:
What is the length of the hypotenuse of the triangle when x=9 now and other side y = 4.
A rectangular prism is 38 centimeters long, 18 centimeters wide, and 13 centimeters high. What is the surface area of the rectangular prism?'
Answer:
53,352 cm
Step-by-step explanation:
1. The first step is to draw the rectangle draw one rectangle over the other and start labeling the sides.
2. After labeling use the rectangle prism formula: L times W times H in this case it would be 38 times 18 times 13 this is equal to 8,892.
3. From there, we know that there are six sides so we can multiply this value by 6 so it would be 8,892 times 6 = 53,352 cm.
If I made a mistake or if have any questions feel free to tell me!
-Mathematics and Science Major for Middle School Students at Harvard University
HOW GIAND
4. The circle graph shows the results of a middle
school survey about favorite states to visit on
vacation. If 400 students were surveyed, how
many more students favor visiting Florida than
Colorado? (Example 2)
New York
7%
Favorite State to Visit
Other
16%
North
Carolina
Colorado
Florida
38%
15% California
13%
92 more students favor visiting Florida than Colorado
How many more students favor visiting Florida than Colorado?From the question, we have the following parameters that can be used in our computation:
Students = 400
Florida = 38%
Colorado = 15%
The percentage difference is
Difference = 38% - 15%
So, we have
Difference = 23%
This means that
Students = 23% * 400
Evaluate
Students = 92
Hence, the number of students is 92
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4. Solve for x ONLY *
Find the value of each variable.
Check the picture below.
9. Max's monthly electricity budget only allows him to use 250,50 kWh (kilowatt-hours). The cost for 1 kWh is R2,20. Calculate the cost of his electricity bill.
Using the given information, the cost of Max's electricity bill is R551.10
Calculating the cost of electricity billFrom the question, we are to calculate the cost of Max's monthly electricity bill
From the given information,
"Max's monthly electricity budget only allows him to use 250.50 kWh"
and
"The cost for 1 kWh is R2.20"
To determine the cost of Max's monthly electricity bill, we will multiply his monthly electricity budget by the cost for 1 KWh
That is,
Max's monthly electricity bill = 250.50 × R2.20
Max's monthly electricity bill = R551.10
Hence,
The cost of Max's monthly electricity bill is R551.10
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13.2.7 Check Your Understanding A savings account earns an Interest rate of 3.75% compounded semi-annually for an account with an initial deposit of $895. How much money will be in the account after 10 years? Round your answer to the nearest hundredth.
The amount of money that will be in the account after 10 years is: $1297.70
How to solve Compound Interest Problems?The formula for solving compound interest is expressed as:
A = P(1 + r/n)^(nt)
where:
A is Accrued amount (equal to principal added to interest)
P is the Principal amount
r is the annual nominal interest rate expressed as a decimal
R is termed as the annual nominal interest rate which is expressed as a percentage
r is equal to R/100
n is the number of the compounding periods per unit of the time
t is the time which is expressed in decimal years
We are given:
r = 0.0375
n = 2 times per year
t = 10 years
P = $895
Thus:
A = 895(1 + 0.0375/2)^(2 * 10)
A = $1297.70
Thus, that is the money that will be in the account after a period of 10 years
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m ANGLE 1 = 3x-5 and m ANGLE 2 = 2x+7 find the values of angle 1 and 2
Answer: Angle one equals -15, and angle two equals 14, if the +7 equals a positive seven.
Step-by-step explanation:
There are more negatives than positives, so we make the ending answer negative, giving us -15. And the second one is simple multiplication, you double the 7 times two, or vice versa.
Hope this helps!
Is it an integer?
7/10 - yes or no
-6/1 - yes or no
-30.18 - yes or no
7 - yes or no
-76 - yes or no
The numbers as an integer or not are:
7/10 - no-6/1 - yes -30.18 - no7 - yes-76 - yesCategorizing the numbers as an integer or not?From the question, we have the following parameters that can be used in our computation:
7/10 - yes or no
-6/1 - yes or no
-30.18 - yes or no
7 - yes or no
-76 - yes or no
integers are numbers without decimal point (including 0)
Using the above as a guide, we have the following:
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
Which equations can be used to solve for y, the length of the room?From the question, we have the following parameters that can be used in our computation:
Area = 750
Length = y
Width = y - 5
The area is the product of the length and the width
So, we have
y * (y - 5) = 750
When expanded. we have
y^2 - 5y = 750
Lastly, we have
(y + 25)(y – 30) = 0 -- when factored
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16u-5u+18=3u-14???????
Answer:
u = -4
Step-by-step explanation:
You want the solution to the equation 16u -5u +18 = 3u -14.
SimplifyThe equation can be simplified by combining like terms:
11u +18 = 3u -14
SolutionAdding (-18-3u) to both sides, we have ...
8u = -32
u = -32/8 = -4 . . . . . . divide by the coefficient of u
The solution is u = -4.
really short question please help
Answer:2^4=4x-4 would be the answer
Step-by-step explanation: You would exponentiate both sides
Eloise bought 30 pounds of sand to refill 4 sandboxes at a local park. She is going to put the
same amount of sand in each sandbox. Which statement about this situation is true?
The amount of sand Eloise will put in each sandbox is 7.5 pounds (30 divided by 4).
HELP ME PLEASE ITS DUE TODAY!!! The following data shows the number of times a class of 7th graders ate breakfast over a 30-day period.
{4, 18, 22, 25, 15, 12, 22, 14, 19, 30, 24, 20, 21, 24, 29, 16, 20, 27, 24, 25}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (2 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (2 points)
Part A: Note that the best graphical representation to use for this kind of data is a Histogram.
Part B : Creating the historgram means you have to first chose the intervals for the data.
What is the reason for the choice above?When it comes to displaying the distribution of a set of continuous data, histograms offer an appropriate visualization method.
This display type divides the data into intervals and plots the number of observations that fall within each interval, hence providing frequency distribution information.
For instance, in creating a histogram for this particular dataset, one can choose intervals or bins with sizes e.g. 5 units covering a range between 0 and 30 before tabulating the count of observed variables in each bin and plotting these counts on the chart's vertical axis.
A histogram illustrates how often students ate breakfast within a 30-day timeframe. This frequency distribution features labeled axes, with the vertical axis representing "Frequency" and the horizontal axis depicting "Number of times students ate breakfast."
Each bar on the horizontal axis corresponds to an interval and shows its frequency on a scaled height basis.
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I need help with this question
The graph of the system of inequalities is on the image at the end.
How to graph the system of inequalities?Here we have the system of inequalities:
y > -2x + 9
y < 5x - 6
First we need to graph both of these lines with dashed lines (that is because the values on top of the lines are not solutions for the inequalities).
Then we need to shade the region above the first line, and the region below the second line.
Thenh the graph of the system is the one you can see in the image at the end.
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Which shapes have teo pairs of parallel side choose all that apply
Answer:
A parallelogram is a quadrilateral with 2 pairs of parallel sides.
Step-by-step explanation:
Mark brainliest, pls
What's the ordered pair so that's a solution for the given linear equation?
6x+4y=8
(-1, __ )
(__,-4)
Thanks!
The ordered pairs to a solution for the given linear equation are (-1, 3.5) and (4, -4).
To find the ordered pair that is a solution to the equation 6x + 4y = 8, we can substitute the given value of x or y and solve for the other variable.
For the first option, substituting x = -1, we get:
6(-1) + 4y = 8
-6 + 4y = 8
4y = 14
y = 3.5
So, the ordered pair (-1, 3.5) is a solution to the equation.
For the second option, substituting y = -4, we get:
6x + 4(-4) = 8
6x - 16 = 8
6x = 24
x = 4
So, the ordered pair (4, -4) is a solution to the equation.
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answer with explanation
a) Use the triangle below to answer questions a) and b). B 10 cm A 14 cm Determine which interior angle of the triangle is the largest,
The largest interior angle of the triangle is the angle A
Determining the largest interior angle of the triangleThe side lengths of the triangles are given as
b = 10 cm
a = 14 cm
The other side length is not given
So, we solve the question using the two side lengths
Having said that:
The general rule is that; the higher the side length, the larger the angle
14 cm is greater than 10 cm
This means that the angle A is greater than the angle B
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Help me please. !! Asap
Answer:
36cm
Step-by-step explanation:
The lightning bolt on the right is 3 times bigger than the one on the left. You can tell this because that leftside, vertical-ish piece (on both of them) is labelled. The small one is 25cm and the big one is 75cm.
25 × 3 = 75
The bottom right side is 12cm, so times by 3 to find the bigger one that matches.
12 × 3 = 36
If Matt's share is 20 % less than Kate's , how much is Kate's share more than Matt's ? A. 50 % B. 33.33 % C. 25 % D. 20 %
Answer:
20% (D)
Step-by-step explanation:
Consider the quadratic equation 4x² - 11x-3-0. Which of the following shows
this equation rewritten and ready to solve using factoring by grouping?
The factorized form of the quadratic equation is:
4(x - 3)*(x + 0.25) = 0
Which is the factorized form of the quadratic?The quadratic equation is 4x² - 11x -3 = 0
To do that, we need to find the zeros, so let's use the quadratic formula:
[tex]x = \frac{11 \pm \sqrt{(-11)^2 - 4*4*-3} }{2*4} \\\\x = \frac{11 \pm 13 }{8}[/tex]
Then the two roots are:
x = (11 + 13)/8 = 3
x = (11 - 13)/8 = -2/8 = -0.25
Then the factorized form is:
4(x - 3)*(x + 0.25) = 0
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Becky worked part-time at a restaurant. The amount of money she earned for each of six weeks is shown.
$50, $82, $39, $50, $31, $70
Becky earned $23 for working a seventh week. Which statement for these seven weeks is true?
OA. The median decreases and the mean remains the same.
OB. The mean and the median both decrease.
OC. The median and the mean both remain the same.
OD. The mean decreases and the median remains the same.
Answer:
Step-by-step explanation:
To answer this question, we need to calculate the mean and median of the given data set and then see how the additional earnings affect them.
First, let's calculate the mean of the original data set:
Mean = (50 + 82 + 39 + 50 + 31 + 70) / 6 = 322 / 6 = 53.67
Next, let's calculate the median of the original data set. To do this, we need to arrange the data set in order:
31, 39, 50, 50, 70, 82
The median is the middle value, which is 50.
Now, let's add Becky's earnings of $23 to the data set:
31, 39, 50, 50, 70, 82, 23
The new data set has 7 values. Let's calculate the new mean:
Mean = (50 + 82 + 39 + 50 + 31 + 70 + 23) / 7 = 365 / 7 = 52.14
The new mean is less than the original mean, so we can eliminate options A and C.
Now let's calculate the new median. We need to arrange the data set in order:
23, 31, 39, 50, 50, 70, 82
The median is still 50.
Therefore, the answer is option D: The mean decreases and the median remains the same.
$1500 is deposited in an account with 6%
interest rate, compounded continuously.
What is the balance after 5 years?
F = $[?]
Round to the nearest cent.
Enter
The balance after 5 years, if $1500 is deposited in an account with 6%
interest rate, compounded continuously is calculated as: $2,024.79.
How to Calculate Compound Interest?The formula for calculating the balance (F) in a continuously compounded account is:
[tex]F = Pe^{(rt)}[/tex]
where we have:
P is the principal amount,
e is the mathematical constant approximately equal to 2.71828, and
r is the interest rate, and t is the time in years.
In this case, P = $1500, r = 6%, and t = 5 years.
Plug these values into the formula and solve for F:
F = 1500e^(0.065)
F = 1500e^0.3
F = 15001.34985880758
F = $2,024.79 (rounded to the nearest cent)
Therefore, the balance after 5 years is $2,024.79.
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