When you flip a coin, there are only two possible outcomes, heads (H) or tail (T).
If you consider the coin to be fair, then both outcomes have the exact same probability which can be calculated as the number of favorable outcomes divided by the total number of outcomes.
For the event "flip a coin" the probability of obtaining tail is:
[tex]\begin{gathered} P(T)=\frac{nº\text{favorable outcomes}}{total\text{ outcomes}} \\ P(T)=\frac{1}{2} \end{gathered}[/tex]The experiment consists on flipping the coin 8 times:
The coin is flipped 8 times, so the number of trials of the experiment is fixed (n=8).
Each trial has only two possible outcomes "Head"(failure) or "Tail" (success)
The probability of the result being tail is the same for each time the coin is flipped, this represents the probability of success of the experiment (p=0.5).
Each trial of the experiment (flipping the coin) is independent.
This experiment meets the binomial criteria, which means that it is a binomial experiment.
To calculate the probability you can apply the formula for the binomial probability:
[tex]P(X)=\frac{n!}{(n-X)!X!}\cdot(p)^X\cdot(q)^{n-X}[/tex]Where
n is the number of trials
X is the number of successes
p is the probability of success
q is the probability of failure and is complementary to p
For this experiment:
The number of trials is n=8
The number of successes is X=7
The probability of success is p=0.5
The probability of success is q=1-p=1-0.5=0.5
Use these values to calculate the probability of obtaining 7 tails:
[tex]\begin{gathered} P(X=7)=\frac{8!}{(8-7)!7!}\cdot(0.5)^7\cdot(0.5)^{(8-7)} \\ P(X=7)=\frac{8!}{1!\cdot7!}\cdot(0.5)^7\cdot(0.5)^1 \\ P(X=7)=\frac{40320}{1\cdot5040}\cdot\frac{1}{128}\cdot\frac{1}{2} \\ P(X=7)=8\cdot\frac{1}{128}\cdot\frac{1}{2} \\ P(X=7)=\frac{1}{32}\cong0.03125 \end{gathered}[/tex]The probability of getting 7 tails when flipping the coin 8 times is
P(X=7)= 0.03125
1. (08.01 LC)Describe the process for calculating the volume of a cone. Use complete sentences.
The volume of cone is calculated using this formula:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ r\colon\text{radius} \\ h\colon\text{height} \\ \pi\colon\text{ a constant with a value of }\frac{22}{7} \end{gathered}[/tex]So, to obtain the volume of a cone, the radius and the height must be known.
We then multiply the value of the constant pi by the square of the radius and the height, and then divide the final result by 3.
The unit is cubic unit.
If angle YWV is 48 degrees, what is the measure of angle Y?Required to answer. Single choice. 52429048
According to the image given there is a right triangle formed in which we are missing one of the angles, for that we know that the sum of thr interior angles of every triangle has to be equal to 180°.
Using this information
[tex]90+48+Y=180[/tex]we clear the equation for Y
[tex]\begin{gathered} Y=180-90-48 \\ Y=42 \end{gathered}[/tex]The measure of angle Y is 42°.
QUESTION Bgraph the line with the given slope and point 2 stepsthere are two steps with in 1 question
By definition, the slope of a line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]You can observe that it is the change in "y" divided by the change in "x".
In this case, you have the following slope:
[tex]m=\frac{2}{3}[/tex]Then the change in "y" in 2 and the change is "x" is 3.
Given the point (-4,1), you can follow these steps to graph the line:
1. Plot the given point on the coordinate plane.
2. Knowing that the slope is
[tex]m=\frac{2}{3}[/tex]You must move 3 units to the right and then 2 units up. This will give you a new point.
3. Graph the line. It must pass through those points.
The graph is:
I do not understand how to do these two questions below.
Question 5:
Step 1
From the figure, we can say that vertically opposite angles are equal.
Step 2:
From the diagram,
which of the following number lines represents the inequality x> 1.5?
Answer:
The answer would be D
Step-by-step explanation:
The inequality x>1.5, or x is greater than 1.5, has to have a line going to the right because x has to be greater than 1.5, so answers B and C can't be it. Because the symbol is greater than instead of greater than or equal to, the circle will be open, and the circle for option A is closed, so the answer is D
Melissa is choosing between two exercise routines,In Routine #1, she burns 42 calories walking. She then runs at a rate that burns 14.25 calories per minute.In Routine #2, she burns 25 calories walking. She then runs at a rate that burns 18.5 calories per minute.For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #27Use t for the number of minutes spent running, and solve your inequality for t.
Suppose in routine 1 and 2, Melissa rune for t minutes.
She burns 42 calories walking and then she runs at a rate that burns 14.25 calories per minute in rouitne 1.
So, total calories she burns in routine 1 is
[tex]42+14.25t[/tex]Again, in routine 2, she burns 25 calories walking and she runs at a rate that burns 18.5 calories per minute in rouitne 2.
So, total calories she burns in routine 2 is
[tex]25+18.5t[/tex]Accordingly,
[tex]\begin{gathered} 42+14.25t\leq25+18.5t \\ 18.5t-14.25t\ge42-25 \\ 4.25t\ge17 \\ t\ge4 \end{gathered}[/tex]So, Melissa should run for minimum 4 minutes
what is the linear equation of (0,10) (-10,-7)
Consider that the general form of a linear equation can be writen as follow:
y = mx + b
where m is the slope of the line and b the y-intercept
use the following formula for the calculation of m:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) = (-10,-7) and (x2,y2) = (0,10). Replace these values of the coordinates into the formula for m:
m = (10 - (-7))/(0-(-10))
m = (17)/(10)
m = 1.7
The y-intercept of the line is the value of the y coordinate when x=0, from the point (0,10) you can notice that y=10 when x=0. Then, the y-interceot is b =10
FInally, replace the values of m and b into the general expression for y:
y = mx + b
y = 1.7x + 10
Identify the the coefficients of variable terms of the expression -2x^2+8x
Cofficient of variable terms is :
[tex]-2x^2+8x[/tex][tex]\begin{gathered} -2x^2+8x \\ x(-2x+8) \end{gathered}[/tex]So the first variable
[tex]-2x^2[/tex]so the cofficent is -2
and the cofficent of second variable is:
[tex]8x[/tex]So the cofficent of second term is 8.
Mr.Cumme has 5 bags of jelly beans for his classroom. Each bag is 7/8 full. Which expression can be used to represent the total amount of full bags of jelly beans?- A. 7 divided by (8x5)- B. (5X7) divided by 8- C. 8 divided by (7X5)- D. 6x ( 7 divided by 5)
Consider that the coefficient for the number of full bags is 7/8 and the number of bags is 5. By divinding these numbers you get the total amount of full bags:
[tex]\frac{\frac{7}{8}}{\frac{5}{1}}=\frac{7}{5\times8}[/tex]when we have used division between fractions (Notice what we added a 1 denominator to 5).
Hence, the answer:
A. 7 divided by (8 x 5)
JUST NEED HELP ON THE LAST ONE AND A VERIFICATION ON EVERYTHING ELSE !!!!!!!!!
In any right triangle with acute angles x and y, then
The sum of x and y is 90 degrees
[tex]\begin{gathered} \sin x=\cos y \\ \cos x=\sin y \\ x+y=90^{\circ} \end{gathered}[/tex]Then for part (1)
Since triangle XYZ is a right angle at Z
Then
[tex]X+Y=90^{\circ}[/tex]Then X and Y are complementary angles
Part (2)
sin X = opposite/hypotenuse
[tex]\sin X=\frac{x}{z}[/tex]sin Y = opposite/hypotenuse
[tex]\sin Y=\frac{y}{z}[/tex]cos X = adjacent/hypotenuse
[tex]\cos X=\frac{y}{z}[/tex]cos Y = adjacent/hypotenuse
[tex]\cos Y=\frac{x}{z}[/tex]Part (3)
[tex]\begin{gathered} \sin X=\cos Y \\ \cos X=\sin Y \end{gathered}[/tex]Part (4)
Since sin = cos, then
The sum of the 2 angles must be 90
One of them is 23 degrees, then the other must be
[tex]90-23=67[/tex]The answer is
[tex]\cos (23)=\sin (67)[/tex]Hi! May you please help me complete question 4. I'm kinda confused
Given:
The coordinates of the figure ABC are,
A(-2,0)
B(-3,-4)
C(-1,-4)
To find the correct statement:
Let us find the coordinates after rotating the figure 90 degree clockwise direction.
As we know,
In a rotation of 90 degrees clockwise, every point (x,y) will be changed to (y, -x).
So, we get,
D(0,2)
E(-4, 3)
F(-4,1)
It perfectly matches with given graph.
So, Betty's statement is correct.
If we translate the figure two units up and two units right, the given point B (-3,-4) will be changed to (-1,-2) and its reflected point over the y-axis will be (1,-2).
But, this does not match with E(-4,3).
So, Veronica's statement is wrong.
Hence, Betty's statement alone is the correct one.
What are the possible values for p in the equation below? Check all that apply. Ipl = 12 -12 -6 0 1 6 12 24
Explanation:
The absolute value of any number is always positive it doesn't matter if the number is positive or negative.
In this case we have that the absolute value of p is 12, therefore p could be 12 or -12
Answers:
• -12
,• 12
Answer:
Step-by-step explanation:
12 and -12 is the answer
A and F
a factory makes 4.8 kilograms of pumpkin pie filling per minute. how many kilograms of pie filling will the factory make in 10 minutes?
ANSWER
48kg
EXPLANATION
In 1 minute, the factory makes 4.8kg of pumpkin pie filling, so in 10 minutes it will make,
[tex]10\min \cdot\frac{4.8\operatorname{kg}}{1\min}=48\operatorname{kg}[/tex]In 10 minutes, the factory makes 48 kilograms of pumpkin pie filling.
5) Kendall is making a cone shaped party hats for his birthday. Then, each hatwill be filled with candy. The height on each cone is 7.5 inches and theradius is 1.5 inches. If she has 12 friends coming, how many cubic incheswill he need to fill all 12 hats with candy?
Explanation
In the question, we are given that,
[tex]\begin{gathered} height\text{ of cone = 7.5 inches} \\ radius\text{ of cone = 1.5 inches} \end{gathered}[/tex]We will need to find the volume of the cone.
[tex]volume\text{ of a cone =}\pi r^2h[/tex]Therefore, we will have;
[tex]V=\pi\times1.5^2\times7.5=53.0144[/tex]So for 12 hats with candy, we will have;
[tex]12\times V=12\times53.0144=636.1728[/tex]Answer: 636.1728 cubic inches
Solve the quadratic equation using the quadratic formula or by completing the square. Show exact answers in simplified radical form; no rounded decimals. x^2-6x+1=0
By using Quadratic formula, the solutions are
[tex]x = {3 + 2\sqrt{2}}[/tex] or [tex]x = {3 - 2\sqrt{2}}[/tex]
What is Quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
If [tex]ax^2+bx + c = 0 (a\neq 0)[/tex] be a quadratic equation,
[tex]x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
This is the quadratic formula
Here,
The given quadratic equation is
[tex]3x^2 = 7x - 3\\3x^2 - 7x + 3 = 0\\[/tex]
a = 1, b = -6, c = 1
x =
[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4\times 1 \times 1}}{2\times 1}\\\frac{6 \pm \sqrt{36 - 4}}{2}\\\frac{6 \pm \sqrt{32}}{2}\\\frac{6 \pm 4\sqrt{2}}{2}\\\frac{2(3 \pm 2\sqrt{2})}{2}\\{3 \pm 2\sqrt{2}}[/tex]
[tex]x = {3 + 2\sqrt{2}}[/tex] or [tex]x = {3 - 2\sqrt{2}}[/tex]
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AHow many degrees mustFigure A be rotatedcounterclockwise aroundthe origin in order toline up with Figure B?BA. 90B. 180C. 270D. 360
The figure A when rotated through 180 degrees counterclockwis, figure B will be obtained
correct answer is OPTION B
If you translate the triangle below 5 units down and 5 units to the left, what quadrant(s) would it be in?
The traslated triangle would be:
We can conclude that it would be in the 3rd quadrant.
Answer: Option 3
I’m not sure on how to do it right as I keep getting this wrong. Please help!
Given the function:
[tex]A(t)=40(0.83)^t[/tex]Where A(t) shows the amount of drug in a body after t hours.
Let's solve for the following:
• (a). Initial dosage:
Apply the exponential functions:
[tex]f(x)=a(b)^x[/tex]Where:
a is the initial value
b is the change factor.
Thus, we have the following:
a = 40
b = 0.83
Therefore, the initial dose is 40 mg.
• (b). What percent leaves the body each hour?
Apply the function:
[tex]f(x)=a(1-r)^x[/tex]Where:
r is the decay rate.
Thus, we have:
b = 1 - r
r = 1 - b
r = 1 - 0.83
r = 0.17
The percent that leaves the body each hour will be:
0.17 x 100 = 17%
Therefore, 17 percent of the drug leaves the body each hour.
• (c). What amount of drug is left after 12 hours?
Substitute 12 for t and solve for A(12):
[tex]\begin{gathered} A(12)=40(0.83)^{12} \\ \\ A(12)=40(0.1068900077) \\ \\ A(12)=4.28 \end{gathered}[/tex]The amount left after 12 hours is 4.28 mg.
• (d). The first whole number of hours at which there is less than 6 mg left.
Plug in 5.9 for A(t) and solve for t.
[tex]5.9=40(0.83)^t[/tex]Divide both sides by 40:
[tex]\begin{gathered} \frac{5.9}{40}=\frac{40(0.83)^t}{40} \\ \\ 0.1475=(0.83)^t \end{gathered}[/tex]Take the natural logarithm of both sides:
[tex]\begin{gathered} ln(0.1475)=tln(0.83) \\ \\ t=\frac{ln(0.1475)}{ln(0.83)} \\ \\ t=10.2 \end{gathered}[/tex]Therefore, the first whole number of hours where there is less than 6 mg left is 10 hours.
ANSWER:
• (a) 40 mg
,• (b) 17%
,• (c). 4.28 mg
,• (d). 10 hours
Suppose you and a friend are playing a game that involves flipping a fair coin 3 times. Let X = the number of times
that the coin shows heads. You have previously shown that all conditions have been met and that this scenario
describes a binomial setting.
Determine the value of n and p and calculate the mean and standard deviation of X. Round the standard deviation to
three decimal places.
■ n=
■
■
p=
Hx=
0x =
h
Done
Using the normal distribution, it is found that, the standard deviation is 0.86
What does "normal" describe in statistics?Normal usually refers to the word "normal" in a normal distribution.
The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.
In a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is;
σ = √np(1- p)
After finding the z-score, we need the p-value associated with this z-score, which is the percentile of X.
The given parameters are:
n = 3 ---- the number of flips
p = 0.5 --- the probability
The standard deviation is calculated as:
σ = √np(1- p)
σ = √3 (0.5) (0.5)
σ = 0.86
Hence, the standard deviation is 0.86
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Calculate the volume of a triangular pyramid 12cm tall and with a base 12cm long and 10cm wide
Remember that the volume of a triangular pyramid can be calculated using the formula:
[tex]V=\frac{A_{base}\cdot height}{3}[/tex]So first, let's calculate the area of the base:
[tex]A_{base}=\frac{10\cdot12}{2}=60[/tex]Using this in the formula,
[tex]V=\frac{60\cdot12}{3}=240[/tex]Thereby, the volume of the pyramid is 240 cubic centimiters
Find limit as x approaches three from the right of f of x. .
EXPLANATION
The expression means that we need to compute the limit as the function f(x) approaches 3 from the right.
We need to use the lines that comes from the right of 3 and gets as close as we want to x=3.
That is the line that has the open circle around y=3
Therefore, the limit is equal to 3
simplify the expression 5x + 6 (x-2) -8 (x-3)A. 19x + 36 B. 19x + 12 C. 3x - 36 D. 3x + 12
Given the expression:
5x + 6 (x-2) -8 (x-3)
Let's simplify the exression using the following steps:
Step 1.
Apply distributive property:
5x + 6x + 6(-2) - 8x - 8(-3)
5x + 6x - 12 - 8x + 24
Step 2.
Combine like terms:
5x + 6x - 8x - 12 + 24
3x + 12
Therefore, the simplified expression is:
3x + 12
ANSWER:
D. 3x + 12
A sine function has an amplitude of 3, a period of π, and a phase shift of pi over 2 period What is the y-intercept of the function?
The sine fuction we have is
[tex]f(x)=3\sin \mleft(2x+\frac{\pi}{2}\mright)[/tex]If we want the y-intercept, we must put x = 0, then
[tex]\begin{gathered} f(x)=3\sin (2x+\frac{\pi}{2}) \\ \\ f(0)=3\sin (\frac{\pi}{2}) \\ \\ f(0)=3\cdot1 \\ \\ f(0)=3 \end{gathered}[/tex]Therefore the y-intercept is 3.
Answer: 0
Step-by-step explanation: trust me
it's already graded and I got it wrong can you tell me the answer
The slope is given by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \text{let:} \\ (x1,y1)=(1,-17) \\ (x2,y2)=(5,-1) \\ m=\frac{-1-(-17)}{5-1}=\frac{-1+17}{4}=\frac{16}{4}=4 \end{gathered}[/tex]I need help with this question please. This is non-graded.
The standard form of a quadratic equation is the following:
[tex]y=ax^2+bx+c[/tex]Where a, b and c are numbers. In this case we are given a quadratic equation in vertex form:
[tex]y=(x-4)^2-16[/tex]We can expand the squared binomial:
[tex]\begin{gathered} y=x^2-2\cdot4\cdot x+(-4)^2-16 \\ y=x^2-8x+16-16 \\ y=x^2-8x \end{gathered}[/tex]AnswerThen the answer is the second option.
I know that the equation is 5/9 (x-1) squared -3 What is the y-coordinate for the point where the parabola intersects the x-axis?
Answer:
-22/9
Explanation:
If the equation of the parabola is
y = 5/9 (x - 1)² - 3
The y-coordinate for the point where the parabola intersects the x-axis can be calculated by replacing x = 0, so
y = 5/9 (0 - 1)² - 3
y = 5/9 (-1)² - 3
y = 5/9 (1) - 3
y = 5/9 - 3
y = -22/9
Therefore, the y-coordinate is -22/9
Please assist me in knowing how to figure these out.
we have the equation
[tex]H(t)=180-a(108)^{-t}[/tex]A) since H is an exponential function 180 represents the maximum posible value of H or the maximum temperature that the center of the cake can reach
b)
we have
H(t)= 22° C
when placed in the oven or t=0
[tex]22=180-a(108)^0[/tex][tex]22=180-a(1)[/tex][tex]a=180-22=158[/tex]the value of a is 158
C)
H(t)=150°C
we already know a=158
let's solve for t
[tex]150=180-(158)(1.08)^{-t}[/tex][tex]-30=-(158)(1.08)^{-t}[/tex][tex]\frac{30}{158}=1.08^{-t}[/tex][tex]ln(\frac{30}{158})=ln(1.08^{-t)}[/tex][tex]ln(\frac{30}{158})=-t*ln(1.08)[/tex][tex]-t=\frac{ln(\frac{30}{158})}{ln(1.08)}[/tex][tex]t=-\frac{ln(\frac{30}{158})}{ln(1.08)}=21.587[/tex]now this is the time 29 minutes before taking the cake out of the oven
so the total time is 29+21.587
then the total time the baking thin was in the oven
is 50.587 minutes
The following is the graph of the function f. Determine the domain and range of f. Assume the entire function is shown.Domain:Range:
Given:
Required:
We need to find the domain and range of the given function.
Explanation:
Recall that the domain of a graph consists of all the input values shown on the x-axis.
[tex]Domain\text{ =\lbrack-5,5\rbrack}[/tex]Recall that the range is the set of possible output values, which are shown on the y-axis.
[tex]Range=[-25,25][/tex]Final answer:
[tex]Domain\text{ =\lbrack-5,5\rbrack}[/tex][tex]Range=[-25,25][/tex]Is 3.0 equal to 3.0000000
Answer:
Yes
Explanation:
Yes, 3.0 is equal to 3.0000 because in Mathematics, once we have only zeros after the decimal point, we can discard them and write only the whole number part. So 3.0 and 3.0000 can both be written as 3.
Ruth has a piece of wood that measures 2 2/9 feet. She cut off 1 1/3 feet of
wood for a project. How much wood does she have remaining?
After finding the difference between total measure of wood and cut off wood, she have remaining 8/9 wood.
In the given we have to find the remaining wood.
Ruth has a piece of wood that measures 2 2/9 feet.
Now converting the mixed fraction in improper fraction by multiplying the 2 and 9 then add 2 in the multiplication of 2 and 9.
So the improper fraction is 20/9.
So The measure of wood = 20/9 feet
She cut off 1 1/3 feet of wood for a project.
Now converting the mixed fraction in improper fraction by multiplying the 1 and 3 then add 1 in the multiplication of 1 and 3.
So the improper fraction is 4/3.
So, she cut the wood = 4/3 feet
Now the remaining wood = Total measure of wood−cut the wood
Remaining wood =20/9−4/3
Now equal the denominator of both values.
Remaining wood =20/9 −4/3 ×3/3
Remaining wood =20/9 −12/9
Remaining wood =(20−12)/9
Remaining wood =8/9
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