The probability of getting exactly 1 head when a fair coin is tossed 9 times is approximately 0.017, to the nearest thousandth.
To find the probability of getting exactly 1 head when a fair coin is tossed 9 times, we can use the concept of binomial probability. The probability of getting a head on a single coin toss is 1/2, and the probability of getting a tail is also 1/2.
In this case, we want to calculate the probability of getting exactly 1 head out of 9 tosses. This can be represented as a binomial probability with parameters n (number of trials) and p (probability of success).
Using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where n is the number of trials, k is the number of successful outcomes, and p is the probability of success.
In our case, n = 9, k = 1, and p = 1/2.
Plugging these values into the formula:
P(X = 1) = (9 choose 1) * (1/2)^1 * (1 - 1/2)^(9 - 1)
P(X = 1) = 9 * (1/2) * (1/2)^8
P(X = 1) = 9 * (1/2)^9
P(X = 1) = 9/2^9
P(X = 1) ≈ 0.017
Therefore, the probability of getting exactly 1 head when a fair coin is tossed 9 times is approximately 0.017, to the nearest thousandth.
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The number of hours, t, it takes a boat to travel 15 miles upstream is represented
by the given equation.
15
t=
r-c
Which equation represents the rate of the current, c, in terms of r, the rate of the
boat, and t?
A.
15 - rt
CE
15-16
BC=
rt - 15
c = - 7
C. C= -15+r+t
D. C = 15 -r-t
The equation of c is an illustration of subject of formula
The equation of c in terms of r and t is c = r - 15/t
How to determine the equation?The equation is given as:
t = 15/(r - c)
Cross multiply
t(r - c) = 15
Divide both sides by t
r - c = 15/t
Subtract r from both sides
-c = -r + 15/t
Multiply both sides by -1
c = r - 15/t
Take LCM
[tex]c = \frac{rt - 15}{t}[/tex]
Hence, the equation of c in terms of r and t is [tex]c = \frac{rt - 15}{t}[/tex]
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Six different names were put into a hat. A name is chosen 125 times and the name Grace is chosen 17 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Question content area bottom
The experimental probability of choosing the name Grace is __
(Type an integer or a simplified fraction.)
Answer:
Step-by-step explanation:
The experimental probability of choosing Grace is 13.6% (17/125*100)
The theoretical probability of choosing Grace is 16.67% (1/6)
Each probability would change because they depend on the data set so if the data set changes, that means the probability will also change depending on the amount it changes.
f(x) = sinx - 3 cosx is a sinusoid.
True or false
===========================================================
Explanation:
The function can be broken down into the form
f(x) = g(x) - 3*h(x)
where,
g(x) = sin(x)
h(x) = cos(x)
Both g and h are sinusoidal with the same period of 2pi. Therefore, the linear combination of these functions is also sinusoidal with the same period of 2pi. If the periods didn't match up, then it's likely the function isn't sinusoidal and instead some other complicated crazy curve.
Extra notes:
A sinusoidal curve is one that has a steady up and down smooth sine curve to it. Think of a simple ocean wave. A cosine curve is really a sine curve in disguise. It's been phase shifted 90 degrees or pi/2 radians. It's not a coincidence that the word "sine" is found in "cosine".When I say "period of 2pi", I mean the curve repeats itself every 2pi radians. This is equivalent to 360 degrees. The repeating pattern goes on forever.Can someone please help me?
Answer:
24
Step-by-step explanation:
area = wl (6×4 = 24)
w width l length
Find the Surface Area.
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Surface areas and volumes.
Here we will find surface areas by adding individual parts.
Surface area ==> Small rectangle + big rectangle + base rectangle + 2* right angled triangles.
so we get as,
area of shape = 721.1 yards.
option D.) is correct.
Find the area using the given image.
Answer:
4.
Step-by-step explanation:
Area = 1/2 * base + height
= 1/2 * 2 * 4
= 4 unit^2.
What is the center of a circle whose equation is x2 y2 – 12x – 2y 12 = 0? (–12, –2) (–6, –1) (6, 1) (12, 2)
The center of a circle whose equation is x^2 +y^2 – 12x – 2y +12 = 0 is (6,1)
Equation of a circleThe standard equation of a circle is expressed as:
x^2 + y^2 + 2gx + 2fy + c = 0
where:
(-g, -f) is the centre of the circle
Given the equations
x^2 +y^2 – 12x – 2y +12 = 0
Compare
2gx = -12x
g = -6
Similarly
-2y = 2fy
f = -1
Centre = (6, 1)
Hence the center of a circle whose equation is x^2 +y^2 – 12x – 2y +12 = 0 is (6,1)
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Patty has a checking account at a local bank. The monthly checking fee is $10, including any checks she writes. Nonbank ATM withdrawals cost $2. At the beginning of the month, Patty’s checking account balance is $700. She deposited $300 from her job and withdrew $20 in cash from a nonbank ATM. She wrote a check for $100 to a local charity. What is her checking account balance at the end of the month?
A) $958
B) $868
C) $728
D) $658
Answer:
B) 868
Step-by-step explanation:
1. You add 700+300 which is 1000
2. You subtract the amount wasted or withdrawn which will get you 880
3. You subtract the fees which will then get you 868 as your answer
What is the value of the given expression when a=3 and b=5?
12a+12b
Answer:
see explanation
Step-by-step explanation:
12(3)+12(5)=use a calculator.
Type it in a calculator.
whats 4 x 4 x 4 divided by 2
Answer:
32
Step-by-step explanation:
4×4×4=64 then you divide 2 will be 32
Answer:
32
Step-by-step explanation:
4x4=16
16x4=64
64/2=32
[tex]Hence,TheAnswerTo...\\\frac{4^{3} }{2} =32[/tex]
y is inversely proportional to a cubed
when a = 2 and y = 10
a is directly proportional to x
when x = 4 and a = 20
find a formula for y in terms of x
Answer:
[tex]y = kx \\ formula \: connecting \: y \: and \: x[/tex]
Solve u^2= -25, where u is a real number.
Simplify your answer as much as possible.
If there is more than one colution
the answer is ±5i :)
vertex (-3, -3), point (2,97) find equation of parabola in vertex form
Answer:
y = 4(x+3)^2 - 3
Step-by-step explanation:
Vertex form y = a(x+3)^2 -3 sub in 2,97 to calculate a
97 = a(2+3)^2 - 3
a = 4
What is the multiplication problem that means the same thing as the division problem 1/3 ÷ 7?
Answer:
1/21 * 7 = 1/3
Step-by-step explanation:
The numbers in 1/3 divided by 7 are labeled below:
1 = numerator3 = denominator7 = whole numberTo make it a fraction form answer, you keep the numerator and multiply the denominator by the whole number to make a new denominator:
1
-------
3 x 7
=
1
-----
21
Thus, the answer to 1/3 divided by 7 in fraction form is:
1/21
To make the answer to 1/3 divided by 7 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
1/21 = 0.04761904761
1/21 * 7 = 0.3333333333.... ( 1/3 )
Jason's summer job allowed him to save $1200
to use as spending money throughout the
upcoming school year. To make sure he has
enough money, Jason plans to spend the same
amount each month and not run out of money
until the end of the school year in 10 months.
120x + y = 1200
Answer:Slope=-240.000/2.000=-120.000
Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
120*x+y-(1200)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve 120x+y-1200 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
which set of side lengths would form a right triangle
What is the slope of a line that is parallel to the line represented by the equation : y = 5x - 3?
Answer:
5
Step-by-step explanation:
This line equation is in y = mx + b form m will be the slope
m = 5 parallel line will have same slope = 5
here are two column vectors
Answer:
[tex] a = ( \frac{ - 6}{2} )[/tex]
Step-by-step explanation:
-2g=?
[tex] - 2( \frac{3 }{ - 1} ) \\ \\ ( \frac{ - 6}{2} )[/tex]
What is the rate of change and y intercept
Answer:
5
Step-by-step explanation:
If you were graphing y < -3x + 5, would you need a solid or broken line?
solid
broken
Answer:
broken
Step-by-step explanation:
when there isn’t an equals sign the line will always be broken
Below is the table of values of a function. Write the output when the input is n
input 3 5 9 n
output 1 3 7 ?
what is the last output number?
Answer:
N=17
?=15
Explanation;
Check out my attached work
Hope it helps, let me know if you have any questions
The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $65,000 10-year term policy for a 20-year-old female. Round your answer to the nearest cent
Answer:
273.00
Step-by-step explanation:
Find the value of tan(A+B)
Answer:
[tex]\tan (A+B) =-\frac{680}{111}[/tex]
Step-by-step explanation:
[tex]\tan A=\frac{12}{5}[/tex]
[tex]\cos B=\frac{45}{53}\implies \sec B=\frac{53}{45}[/tex]
Now, by trigonometric identity:
[tex]\tan^2 B =\sec^2B-1[/tex]
[tex]\implies \tan^2 B =\bigg(\frac{53}{45}\bigg)^2-1[/tex]
[tex]\implies \tan^2 B =\frac{(53)^2-(45)^2}{(45)^2}[/tex]
[tex]\implies \tan^2 B =\frac{(28)^2}{(45)^2}[/tex]
[tex]\implies \tan B =\pm\sqrt{\frac{(28)^2}{(45)^2}}[/tex]
[tex]\implies \tan B =\pm\frac{28}{45}[/tex]
It is given that: Angles A and B are in quadrant I.
---------------------> Angles A and B would be positive.
[tex]\implies \tan B =\frac{28}{45}[/tex]
Next,
[tex]\tan (A+B) =\frac{\tan A +\tan B}{1-\tan A \tan B}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{12}{5} +\frac{28}{45}}{1-\bigg(\frac{12}{5}\bigg) \bigg(\frac{28}{45}\bigg)}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{108}{45} +\frac{28}{45}}{1-\bigg(\frac{336}{225}\bigg)}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{136}{45}}{\bigg(\frac{225-336}{225}\bigg)}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{136}{45}}{\frac{-111}{225}}[/tex]
[tex]\implies \tan (A+B) =-\frac{680}{111}[/tex]
Matt has a box that measures 23 feet long and 16 feet wide. The volume of the box is 4,416 cubic feet. What is the height of the box in yards?
Answer:
ok
Step-by-step explanation:
The base of a solid is a circle centered at the origin with a radius r, and every plane section perpendicular to a diameter is a square. What is the volume of the solid
The volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.
The equation of the circle can be given as,
[tex]x^2+y^2=r^2[/tex]
Here, (r) is the radius of the circle.
Rewrite this equation as,
[tex]y^2=r^2-x^2\\y=\sqrt{r^2-x^2}[/tex]
This will give you the half the length of the side. Thus, the length of the side of the square is,
[tex]s=2y=2\sqrt{r^2-x^2}[/tex]
The area of the square it square of its side. Thus, the area of the square is,
[tex]A(x)=s^2\\A(x)=(2\sqrt{r^2-x^2})^2\\A(x)=4(r^2-x^2})[/tex]
The volume of the solid can be got by integrating the area of the cross-section.
[tex]V=\int\limits {A(x)} \, dx[/tex]
Here, A(x), provides the area of the square at the point x. Thus,
[tex]V=\int\limits {A(x)} \, dx\\V=\int\limits_{-r}^r {4(r^2-x^2)} \, dx\\V=[ {4(r^2x-\dfrac{x^3}{3})}]^r_{-r}\\V= {4(r^2(r)-\dfrac{(r)^3}{3})}- {4(r^2(-r)-\dfrac{(-r)^3}{3})}\\V=4[r^3-\dfrac{r^3}{3}}+ {r^3-\dfrac{r^3}{3}]\\V=\dfrac{16r^3}{3}[/tex]
Thus, the volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.
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In PQR, P = 90°, Q = 40° and PR =9cm. Find the length of QR .
Answer:
QR = 14.00 cm to the neatest hundredth.
Step-by-step explanation:
This is a right triangle with < P = 90.
So QR is the hypotenuse.
< Q is the angle opposite to the line PR.
sin Q = opposite/hypotenuse = PR/QR
sin 40 = 9/QR
QR = 9/sin40
= 14.002 cm.
Does Anyone know #19?
[tex]\text{Endpoints of diameter,}~~ A(4,6)~ \text{and}~ B(-3,-1)\\\\\text{Diameter,}~AB = \sqrt{(4+3)^2+(6+1)^2}\\\\~~~~~~~~~~~~~~~~~~~=\sqrt{7^2+7^2}\\\\~~~~~~~~~~~~~~~~~~~=7\sqrt2\\\\\text{So , radius}~ = \dfrac{AB}2 = \dfrac{7\sqrt 2}2 =4.9~\text{units.}\\\\\text{Hence the answer is B.}[/tex]
I think it’s b but I’m not sure
please help !!! im so lost with this
Answer:
hj means has a job
nj means no job
Step-by-step explanation:
Provide an example of a treatment and a control group.
Answer:
let's say you wanted to know if Gatorade increased athletic performance. Your experimental group would be given the Gatorade and your control group would be given regular water. or an experiment in which the researcher tests whether or not a new fertilizer has an effect on plant growth.
Step-by-step explanation:
Answer:an example of a treatment and a control group a human experimental group could receive a new medication, a different form of counseling, or some vitamin supplements. A plant treatment group could receive a new plant fertilizer, more sunlight, or distilled water. The group that does not receive the treatment is called the control group
Step-by-step explanation: