Using the binomial distribution, it is found that there is a 0.0108 = 1.08% probability of the coin landing tails up at least nine times.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
The coin is fair, hence p = 0.5.The coin is tossed 10 times, hence n = 10.The probability that is lands tails up at least nine times is given by:
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098[/tex]
[tex]P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.001[/tex]
Hence:
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0098 + 0.001 = 0.0108[/tex]
0.0108 = 1.08% probability of the coin landing tails up at least nine times.
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The circumference of a circle is approximately 43.96 centimeters. What is the radius of the circle? 3.14 for Pie
-7 Centimeters
-11 Centimeters
-14 Centimeters
-22 Centimeters
Answer:
7 Centimeters
Step-by-step explanation:
The first four terms of a sequence are shown on the graph below.
What can be concluded about the sequence?
The common ratio of the sequence is 2.
The common difference of the sequence is 2.
The next term of the sequence is represented by the point (5, 64).
The next term of the sequence is represented by the point (5, –64).
Answer:
The next term of the sequence is represented by the point (5, –64)
Step-by-step explanation:
From inspection of the graph, the first four terms of the sequence are:
(1, -4)(2, 8)(3, -16)(4, 32)Each x-value increases by 1 for each consecutive term.
Each y-value is the previous y-value multiplied by -2.
Therefore, it is a geometric sequence with a common ratio of -2.
Following the above rule, if the last term in the sequence is (4, 32), then the next term in the sequence will be:
x = 4 + 1 = 5y = 32 × -2 = -64So, the next term of the sequence is represented by the point (5, –64)
Is it possible to draw a triangle with side
lengths 6, 3, and 5?
Yes..
Add 2 sides together and if it’s larger than the 3rd side it’s possible
6 + 3 = 9, which is larger than 5
3 + 5 =8 which is larger than 6
6 + 5 = 11 which is larger than 3
Answer:
YESStep-by-step explanation:
The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
so
6+3=9
6+5=11
3+5=8
yes it is possible
in the figure, line segment AB, is tangent to the circle at point A
Answer:
AB = 12 in
Step-by-step explanation:
given a tangent and a secant from an external point to the circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant, that is
AB² = BC × BD = 8 × 18 = 144 ( take square root of both sides )
AB = [tex]\sqrt{144}[/tex] = 12
Answer:
AB = 12 in
Step-by-step explanation:
Theorem
When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Secant: a straight line that intersects a circle at two points.
Tangent: a straight line that touches a circle at only one point.
Given:
Secant segment = BDExternal secant segment = BCTangent segment = AB[tex]\sf AB^2=BD \cdot BC[/tex]
[tex]\implies \sf AB^2=(8+10) \cdot 8[/tex]
[tex]\implies \sf AB^2=18 \cdot 8[/tex]
[tex]\implies \sf AB^2=144[/tex]
[tex]\implies \sf AB=\pm\sqrt{144}[/tex]
[tex]\implies \sf AB=\pm 12[/tex]
As distance is positive, AB = 12 in
The figure is cut into 15 equal pieces. Shade 2/3 of the figure.
Answer:
Shade 10 of the pieces.
Step-by-step explanation:
Part 2: Approximately what value of will give her a box with the greatest volume? Explain your reasoning.
( only need part 2 already have part one thx)
The value of x that gives the box the greatest volume is approximately 2.08
How to determine the value that gives the greatest volume?The equation of the volume of the box is given as:
V(x) = x(12 - 2x)(13 - 2x)
Expand
V(x) = (12x - 2x^2)(13 - 2x)
V(x) = 156x - 24x^2 - 26x^2 + 4x^3
V(x) = 156x - 50x^2 + 4x^3
Differentiate the function
V'(x) = 156 - 100x + 12x^2
Set to 0
156 - 100x + 12x^2 = 0
Rewrite as:
12x^2 - 100x + 156 =0
Divide through by 4
3x^2 - 25x + 39 =0
Using a graphing calculator, the values of x are:
x = 2.08 and x = 6.26
Substitute these values of x in V(x)
V(2.08) = 2.08 * (12 - 2 * 2.08)(13 - 2 * 2.08) = 144.16
V(6.26) = 6.26 * (12 - 2 * 6.26)(13 - 2 * 6.26) = -1.56
The volume cannot be negative.
So, we have:
V(2.08) = 144.16
Hence, the value of x that gives the box the greatest volume is approximately 2.08
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Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
Answer:
[tex]29i[/tex]
Step-by-step explanation:
From this information, we can write the following equation: [tex](2-5i)(2 + 5i)(i)[/tex]
We can see that there is the factorization of the difference of squares, so we can first expand that. The equation will become the following: [tex](4+25)(i)[/tex]
= [tex]29i[/tex]
hope this helped! :)
Solve log (5x+7)=log(8x-2)
What is the midpoint of AB?
Answer:
[tex](-4, -\frac{1}{2} )[/tex]
Step-by-step explanation:
A (-5, -4)
B (-3, 3)
We can apply the midpoint formula: [tex](\frac{-5 + -3}{2} , \frac{-4 + 3}{2} )[/tex]
[tex]= (-4, -\frac{1}{2} )[/tex]
hope this helped! :)
A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?
I aded the graph
Answer:
D. 80
Step-by-step explanation:
The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.
200 × .375 = 75
75 rounded to the nearest tens value is 80
It takes 10 people 15 hours to prepare the gym for the school dance. How many hours would it take 12 people to prepare the gym?
Answer
18 hours
Step-by-step explanation:
if 10 people spend 15 hours
one person spend 15/10=1.5
so 1.5 × 12=18hours
solve this using pythagorean theorem please and give me the right answer and i will give YOU brainliest and a like in return.
Answer:
6.8 miles
Step-by-step explanation:
a^2+b^2=c^2
Please help me out! Need this done ASAP!
Answer:
a. power of a point
b. CE = 4.6
Step-by-step explanation:
a. the power of a point theorem states that BE*BC = BA*BD
b. using the equation above, find CE:
BE * 10 = 3 * 18
BE = 5.4
CE = BC - BE = 10-5.4 = 4.6
the number of ducks living at the pond increased by 40%
So I have a 90.8 in a class the final is 15% of the grade there is a final worth 3.75% of the final grade and a final worth 11.25% of the final grade. I know I have to get a 87% in total on the final grade but what grade would I have to get on each test separately. What would be the worst possible grade I could get on both finals to still end up with a A.
Answer: I know this answe won't be that helpful but I'm pretty sure worsth you can get on both is like a high B. Its pretty hard to tell since you'll be dealing with like formative summative precentages and total point precentages or something But in my honest opinion seems like a high B on one and maybe like a 83-84 on the other.
> 4
Ansley ate 12 of a bag of popcorn. Erica
ate 12 of the same bag of popcorn. What
fraction of the bag of popcorn did Ansley
and Erica eat in all?
The area of undeveloped land in a suburban town is decreasing at a rate of 17.3% annually. in 2016, there were 3,400 acres of undeveloped land. if t represents the number of years since 2016, which equation can be used to determine after how many years the town will have 900 acres of undeveloped land remaining?
Based on the rate of decrease and the acres of undeveloped land, the equation to determine the number of years till 900 acres is remaining is B)900 = 3,400(0.827)^t.
Which equation shows the number of years till 900 acres are remaining?As 900 acres is the target number of acres to remain, this will be on the left side of the equation as the y value.
The right side of the equation would be:
= Current number of acres remaining x ( 1 - rate of decrease) ^ number of years
= 3,400 x ( 1 - 17.3%) ^ number of years
Putting them together:
900 = 3,400(0.827)^t.
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Find the distance between the points (1,2) and (9,8)
Answer:
10
Step-by-step explanation:
✓(y1-y2)²+(x1-x2)²
✓(2-8)²+(1-9)²
✓(-6)²+(-8)²
✓36+64
✓100
=10
Answer:
10
Step-by-step explanation:
At a park, the logging trail is a circle with a radius of 200 meters. how far is it around the trail? use 3.14 or pi. show your work
Answer:
400π
Decimal Form:
1256.63706143
Explanation: To find the around the trail, you'll use the circumference formula.
2πr
2 x 3.14 x 200
I need help with part 2 on this question (Screenshot)
6a-2y>4
Solve inequality for y
Determine the period.
Acellus
Explanation:
One root (aka x intercept) is at x = 0
The next root over isn't clear, but luckily we can skip over it and see the next root after that is x = 5
After this point, the curve repeats itself. This means the period is 5 units.
The graph repeats itself every 5 units, aka the cycle is 5 time units long.
A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation 23 + 6,2 - 27x= 140 can be used to find x. Height: (x+9) in. Width: (2 - 3) in Length: xin. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer. O The length is 7 inches, the width is 4 inches, and the height is 16 inches. O The length is 5 inches, the width is 2 inches, and the height is 14 inches. O The length is 4 inches, the width is 1 inch, and the height is 13 inches. O The length is 3 inches, the width is O inches, and the height is 12 inches.
For this case we have the following equation for the volume:
[tex]x^3+6x^2-27x=140 < br/ >[/tex]
Rewriting the equation we have:
[tex]x^3+6x^2-27x=140=0 < br/ >[/tex]
We factor the equation to find the roots of the polynomial.
We have then:
[tex](x-5)(x+4)(x+7)=0 < br/ >[/tex]
Then, we discard the negative roots, because the dimensions of the figure must be positive.
We have then that the length is:
[tex]x=5 < br/ >[/tex]
The height is:
[tex]x+9=5+9=14 < br/ >[/tex]
The width is:
[tex]x-3=5-3=2 < br/ >[/tex]
Thus, the dimensions are:
[tex]5*14*2 < br/ >[/tex]
Answer:
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
A shirt that was selling for $80 is reduced to $60. Find the percent decrease in price.
Answer:
25% decrease
Step-by-step explanation:
Percentage Decrease = [(Start Value - Final Value) / |Start Value|]×100
80 - 60 = 20
20 / 80 = 0.25
0.25(100)= 25%
NEED HELP ASAP
Question A.) k=5
Question B.) ????
Answer:
b) [tex]f^{-1}(x) = \frac{4x+5}{3}[/tex]
Step-by-step explanation:
b) To find the inverse function, switch the [tex]x[/tex] and [tex]y[/tex] variables and solve for [tex]y[/tex]:
[tex]f(x) = \frac{3x-5}{4}\\y = \frac{3x-5}{4}\\x = \frac{3y-5}{4}\\4x = 3y-5\\4x+5 = 3y\\\frac{4x+5}{3} = y\\f^{-1}(x) = \frac{4x+5}{3}[/tex]
Verify Answer:
[tex]f(1) = \frac{3(1)-5}{4} = -0.5\\f^{-1}(-0.5) = \frac{4(-0.5)+5}{3} = 1[/tex]
A hot air balloon holds 1,592 cubic meters of helium. the density of helium is 0.1785 kilograms per cubic meter. how many kilograms of helium does the balloon contain, rounded to the nearest tenth of a kilogram? 432.3 kg 284.2 kg 2,043.7 kg 5,435.3 kg
By taking the product between density and volume we will see that the mass is 284.2 kg
How to find the mass of helium?Remember that density is the quotient between mass and volume, then:
mass = density*volume.
Here we know that:
volume = 1,592 m³density = 0.1785 kg/m³Taking the product of these two we get:
mass = (1,592 m³)*(0.1785 kg/m³) = 284.2 kg
So the correct option is the second one.
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Answer:
284.2 kg my good sir
Step-by-step explanation:
Big brain
What change in government did the British demand of Massachusetts?
needs help
Answer:
They were no longer able to trade with England. They were no longer able to elect their own governor.The triangles are similar by the AA Similarity Postulate. Find the value of x.
Write a problem that can be
solved using a line plot. Draw and label the
line plot and solve the problem.
Answer:
0/5 1/5 2/5 3/5 4/5 5/5 hope this helps
Please I'm serious no time for nonsense
Draw (3) Convex Polygons & (3) Non- polygons .
Answer & step-by-step explanation:
Convex: Triangle, Square, Pentagon. (Has to be equal sided and angled)
Non-Convex: Draw a weird shape, such as a deformed star, a 5 sided shape with no equal sides, such as these listed below:
