Given data:
The diagonals of rhombus d1 = 15 in and d2 = 20 in
The area of the rhombus,
[tex]\begin{gathered} A=\frac{1}{2}\times d1\times d2 \\ A=\frac{1}{2}\times15\times20 \\ A=150\text{ inches sq.} \end{gathered}[/tex]Now, to find the perimeter of rhombus we first find the side of rhombus.
The diagonal of the rhombus is considered as diameter, so the radius will be
d1 = r1 = 7.5
d2 = r2 = 10
So, by using the pythagorean theorem we find the side of the rhombus
[tex]\begin{gathered} h^2=(7.5)^2+(10)^2 \\ h^2=56.25+100 \\ h^2=156.25 \\ h=12.5 \end{gathered}[/tex]The perimeter of the rhombus is,
[tex]\begin{gathered} P=4\times side \\ P=4\times12.5 \\ P=50\text{ inches} \end{gathered}[/tex]Thus, the area is 150 in. sq. and perimeter is 50 in.
Evaluate and simplify the expression
when a = 2 and b = 4.
4a - 2(a + b) + 1 = [?]
Answer:
-3
Step-by-step explanation:
4(a) - 2(a + b) + 1 = [?]
4(2) - 2(2+4) + 1
8 - 4 - 8 + 1
appilcation of bodmas
4 - 8 + 1
- 4 + 1
-
3
please help! I do not understand and it is due tonight!!!!!!!
Consider that there are, generally, the following types of angles pairs,
1. Adjacent Angles: Angles that share a common side and are formed on the same vertex.
2. Complementary Angles: Angles that are adjacent and together form a right angle.
3. Supplementary Angles: Angles that are adjacent and whose sum of degree measures is 180 degrees.
a.
The adjacent angles to angle 4 are angles 1 and 3.
There are no complementary angles associated with angle 4.
The supplementary angles to angle 4, are angles 1 and 3.
Thus, the angle pairs that include angle 4 are,
[tex](\angle4\text{ and }\angle1),\text{ }(\angle4\text{ and }\angle3)[/tex]b.
The adjacent angles to angle 5 are angles 6 and 7.
There are no complementary angles associated with angle 5.
The supplementary angles to angle 5, are angles 6 and 7.
Thus, the angle pairs involving angle 5 are,
[tex](\angle5\text{ and }\angle6),\text{ }(\angle5\text{ and }\angle7)[/tex]Which equation is true when A.n = 1.2 B.
1.2n=10 n+1=1.2 C. 5+n=6.2 D. 10n=1.2
The true equation is 5 + n = 6.2.
Here we have to find the equation for which n = 1.2.
So the first equation is
10n = 1.2
So for this, we get the value of n as:
n = 1.2/10
= 0.12
which is not equal to 1.2.
So it is not correct
The second equation is:
n + 1 = 1.2
n = 0.2
which is not equal to 1.2
So it is also not correct.
The third equation is:
5 + n = 6.2
n = 6.2 - 5
= 1.2
So it is correct.
The fourth equation is:
1.2n = 10
n = 10/1.2
= 8.33
Here n is not equal to 1.2
So it is also correct.
Therefore the correct equation is 5 + n = 6.2.
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The equation for a line that has a y-intercept of -8 and passes through (-4,2) is y=-5/2x-8 True False
1) Let's verify whether that's true or not, plugging in that point into the equa
(-4,2)
[tex]\begin{gathered} 2=\frac{-5}{2}(-4)\text{ -8} \\ 2=10-8 \\ 2=2 \end{gathered}[/tex]Since this is an identity, in other words, the left side is equal to the right side then we can say that's true.
So that's true y=-5/2x-8 is the equation of the line that has in one of its points the y-coordinate y=-8
If the events have the same theoretical probability of happening, then they are called
Answer:7937
Step-by-step explanation:7596
There is a 5% chance that the mean reading speed of a random sample of 21
second grade students will exceed what value?
There is a 5% chance that second graders will be faster than 94.597 wpm.
Sample size = 21
standard deviation = 10 wpm
SE = 10/sqrt(21) = 2.18 as a consequence.
Let X be the average reading speed of 21 second-grade students. z = (X - 91)/2.18 Normal(91,2.18) (91,2.18).
If the 95th percentile of a standard normal variable z is 1.65 [5% probability], the outcome is 91 + 1.65 x 2.18 = 94.597.
So there's a 5% chance that the average reading speed of a random sample of 21 second-graders will be faster than 94.597 wpm.
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Hello! Please take a look at the picture to see the questions, thank you!
In the question, we are asked to find the degree and the leading coefficient of the polynomial below
[tex]f(x)=3x^4+2x^3+5x^2+7[/tex]Explanation
The degree of the polynomial is the highest of all the degrees that make up the polynomial. Since each term in the polynomial has a degree we will pick the largest one.
Also, the leading coefficient is the coefficient of the term with the largest degree. Using these concepts, we can derive our answer as.
Answer:
[tex]4,3[/tex]Option A
A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area? Explain or show your reasoning
If a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
The length of the rectangular prism = 2 cm
The width of the rectangular prism = 2 cm
The height of the rectangular prism = 5 cm
The surface area of the rectangular prism = 2(lw+lh+hw)
Where l is the length
w is the width
h is the height
Substitute the values in the equation
The surface area of the rectangular prism = 2(2×2+2×5+2×5)
= 2(4+10+10)
= 2×24
= 48 centimeter square
Hence, if a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
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Given the definitions of f(x) and g(x) below, find the value of (gof)(9). f(x) = -x + 11 g(x) = 3x2 - x + 14
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = -x + 11
g(x) = 3x² - x + 14
(gof)(9) = ?
Step 02:
(gof)(x) = 3(-x+11)² - (-x+11) + 14
= 3(x² + 2(-x)(11) + 121) + x - 11 + 14
= 3(x² - 22x + 121) + x - 11 + 14
= 3x² - 66x + 363 + x - 11 + 14
= 3x² - 65x + 366
(gof)(9) = 3(9)² - 65(9) + 366
= 3(81) - 585 + 366
= 243 - 585 + 366
= 24
The answer is:
(gof)(9) = 24
O GRAPHS AND FUNCTIONSFinding values and intervals where the graph of a functioning is..
a.
From the graph we notice that when x=-1 the value of the function is zero; therefore:
[tex]f(-1)=0[/tex]and it is not negative.
b.
The function is positive when its graph is above the x-axis. We notice that this happens in two regions of the graph:
From -4 to -3
From -1 to 4
Therefore, the function is positive in:
[tex]\lbrack-4,-3)\cup(-1,4)[/tex]c.
The function is zero when the graph intersect the x-axis; from the graph we have that the function is zero for:
[tex]\begin{gathered} x=-3 \\ x=-1 \\ x=4 \end{gathered}[/tex]Garcia Co. owns equipment that cost $81,600, with accumulated depreciation of $43,200.
Record the sale of the equipment under the following three separate cases assuming Garcia sells the equipment for (1) $50,600 cash, (2) $38,400 cash, and (3) $33,300 cash.
(1) $50,600 cash implies that $50,600 - $38,400 = $12,200
Hence gets gain of $12,200.
(2) $38,400 cash implies that $38,400 - $38,400 = $0
Hence No profit no loss.
(3) $33,300 cash implies that $33,300 - $38,400 = - $5,100
Hence loss of $5,100.
Depreciation :-Depreciation is the gross reduction in the book value of an asset due to regular use or wear and tear.
A capital gain occurs when Garcia Co. receives an amount in excess of the book value of the equipment.
If Garcia Co. receives an amount equal to the book value of the equipment, no profit or loss will result from the disposal.
If Garcia Co. receives an amount below the book value of the equipment, it will experience a capital loss.
In the given question cost of equipment is $81,600 with accumulated depreciation of $43,200 so that the book value will be
$81,600 - $43,200 = $38,400.
Now (1) $50,600 cash implies that $50,600 - $38,400 = $12,200
Hence gets gain of $12,200.
For (2) $38,400 cash implies that $38,400 - $38,400 = $0
Hence No profit no loss.
For(3) $33,300 cash implies that $33,300 - $38,400 = - $5,100
Hence loss of $5,100.
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If XD = 2X – 6 and XV = 3x – 6 and WY and XV bisect at D, what is XV?
The diagonal WY bisects the diagonal XV at point D, which means that XV is divided into two equal line segments XD and XV.
[tex]XD=XV[/tex]Replace the equation above with the given expressions for both line segments:
XD= 2x-6
XV= 3x-6
[tex]2x-6=3x-6[/tex][tex]undefined[/tex]I'll give brainliest!
Answer:
x equals to 11!!!
Answer:
11.
Step-by-step explanation:
1.02 x 10^11 = 102,000,000,000
Hope this helps!
Brainliest please, thanks!
The radius, R, of a sphere is 4.8 cm. Calculate the sphere's volume, V. Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.) --0- V = 3 em Х 5 ?
The formula to calculate the volume of a sphere is given to be:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius.
From the question, we have the following parameters:
[tex]\begin{gathered} \pi=3.14 \\ r=4.8 \end{gathered}[/tex]Therefore, the volume is calculated to be:
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times4.8^3 \\ V=463.0 \end{gathered}[/tex]The volume is 463.0 cm³.
1. The data set represents the number of cars in a town given a speeding ticketeach day for 10 days.2 4 5 5 7 7 8 8 8 121. What is the median? Interpret this value in the situation.*
ANSWER:
7
STEP-BY-STEP EXPLANATION:
We have the following data:
[tex]2,4,5,5,7,7,8,8,8,12[/tex]The median is the data value that separates the upper half of a data set from the lower half. Therefore:
In this case, being even, the two data are half, but since the value is the same, that is, 7, the median is equal to 7.
The interpretation of this value is in the middle of the 10 days (days 5 and 6), 7 would be the number of cars in a town given a a speeding ticket.
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.042 for the estimation of a population
proportion? Assume that past data are not available for developing a planning value for p*. Round up to the next whole number.
The sample size should be taken as 545.6 to obtain a margin of error of 0.042 for the estimation of a population proportion.
What is sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component. The sample size chosen for a study is typically influenced by the cost, convenience, or ease of data collection as well as the requirement that the sample size have adequate statistical power.
As given in the question,
Confidence level is 95% and the margin of error is 0.042
So,
1 - α = 0.95,
α = 0.05,
E = 0.042
planning value (p) = 0.5
To calculate Sample size the formula is:
[tex]n = \frac{p(1-p)(Z_{a/2})^2}{E^2}[/tex]
From the table we can find that:
[tex]Z_{a/2} = 1.96[/tex]
Putting the values given in the question in formula:
[tex]n = \frac{0.5(0.5)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(3.841)}{0.00176}[/tex]
n = 545.6
Hence the sample size is 545.6
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Find the value of x that will make A||B5x + 20A-В.3x + 60x= [?]Enter
ANSWER:
The value of x is 20
STEP-BY-STEP EXPLANATION:
By properties of the angles we know that these angles are equal, since they are alternative external angles. Thanks to that we can do the following equality to calculate the value of x:
[tex]5x+20=3x+60[/tex]Solving for x:
[tex]\begin{gathered} 5x-3x=60-20 \\ 2x=40 \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]Given the equation 5X-10=50 which properties will be used to solve for XA. Adition and subtractionB. Subtraction and divisionC. Adition and division D. Subtraction and Multiplication
Let's solve for x and see what properties are used
First, add 10 to both sides of the equation
[tex]\begin{gathered} 5x-10=50 \\ 5x-10+10=50+10 \\ 5x=60 \end{gathered}[/tex]Now, divide by 5 on both sides of the equation
[tex]\begin{gathered} \frac{5x}{5}=\frac{60}{5} \\ x=12 \end{gathered}[/tex]Therefore, the correct answer is C. Adition and division
What is the answer to 2(7x-3)+9
Answer:
14x+3 is the answer I think
The solution to the given equation would be [tex]14x+3[/tex].
Hope this helps!
Edgar drew a scale drawing of the town library. The scale of the drawing was 5
centimeters: 2 meters. The parking lot is 34 meters wide in real life. How wide
is the parking lot in the drawing?
Answer:
85 cmStep-by-step explanation:
The scale factor is:
5 cm ÷ 2 mFind the width of the parking lot in the drawing:
5 cm ÷ 2 mx cm ÷ 34 mCross multiply and find the value of x:
x = 5*34/2x = 85 cmA composite figure is created using asquare and a semicircle. What is the area ofthe figure?12 in200.52202.52204.52206.52
The area of the composite figure will be the sum of the area of the square and the area of the semicircle. The formula for determining the area of a square is expressed as
Area = length^2
From the diagram,
length = 12
Area of square = 12^2 = 144
The formula for determining the area of a semicircle is expressed as
Area = 1/2 * pi * radius^2
Radius = diameter/2
The diameter of the semicircle is 12. Thus,
radius = 12/2 = 6
pi = 3.14
Area of semicircle = 1/2 * 3.14 * 6^2 = 56.52
Area of composite figure = 144 + 56.52 = 200.52 in^2
The first option is the correct answer
A football team was able to run the ball for 8 yards on their first play. On the second play they lost 12 yards. The third play they lost another 11 yards. What was their total yards they gained?
The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Subtraction = Minus of any two or more numbers.
Summation = addition of two or more numbers or variable
Let's consider all gained yards by positive (+) and all lost yards by negative (-).
Given that,
In the first play = +8 yards (gain)
In second play = -12 yards (lost)
In the third play = 11 yards (Lost)
So total yards = +8 - 12 - 11 = -15 (Lost)
Therefore, the football team lost 15 yards.
Hence "The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards".
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Can someone please explain to me where I did my math wrong and correct me. The answer is supposed to be $1065.00
The problem says: Lonnie Flanagan's weekly gross pay is $1250. Each week she has $64.37 in deductions, plus state tax of 2% of her gross pay, social security taxes of 6.2%, and Medicare taxes of 1.45%. What is her net pay?
I did 1250 - 64.37 = 1185.63
1185.63 (2%) = $23.71 State income Tax
1185.63 (6.2%) = $73.51 Social Security Tax
1185.63 (1.45%) = $17.19 Medicare tax
Then I added the 3 together.
$23.71 + $73.51 + $17.19 = $114.41
Then I subtracted $113.41 from $1250.
1250 - 113.41 = $135.59 net pay.
What did I do wrong?
The net pay for Lonnie Flanagan is $1065.
How to calculate the net pay?From the information, Lonnie weekly gross pay is $1250 and each week she has $64.37 in deductions, plus state tax of 2% of her gross pay, social security taxes of 6.2%, and Medicare taxes of 1.45%.
Her net pay will be:
= Gross pay - Deduction - Tax - Social security - Medicare
= $1250 - $64.37 - (2% × $1250) - (6.2% × $1250) - (1.45% × $1250)
= $1250 - $64.37 - $25 - $$77.50 - $18.125
= $1065
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rThe number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs012.34P(x)0.640.250.060.03.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?
N = Number of data
x1...xn = Samples
[tex]s=\sqrt[]{\frac{\sum ^n_{n\mathop=1}(y-\mu)^2}{n-1}}[/tex]Let's calculate first:
[tex]\sum ^n_{n\mathop=1}yn=0.64+0.25+0.06+0.03+0.02=1[/tex]Now:
[tex]\sum ^n_{n\mathop=1}yn^2=(0.64)^2+(0.25)^2+(0.06)^2+(0.03)^2+(0.02)^2=0.477[/tex]So:
[tex]s=\sqrt[]{\frac{0.477-\frac{(1)^2}{5}}{5-1}}=0.2631539473\approx0.3[/tex]Artrigerator contains 5 cans of diet soda and 8 cans of regular soda. If three cans of soda are randomly selected without replacement, determine the probability that all can selected are diet soda. Use combinations to determine theprobabilityThe probability that all can selected are diet soda is(Type an integer or a simplified fraction)
The total number of cans in the refrigerator is 5 + 8 = 13
The number of diet soda cans is 5 while the number of regular soda cans is 8
If three cans are selected, the probability that the can is a diet soda can is
5/13
Since it was not replaced, the number of diet soda cans left would be 4 and the total number of cans left would be 12. The probability that the next selected can is a diet can is
4/12 = 1/3
Since it was not replaced, the number of diet soda cans left would be 3 and the total number of cans left would be 11. The probability that the next selected can is a diet can is
3/11
Thus, the probability that the three selected cans are diet soda cans is
5/13 * 1/3 * 3/11 = 5/143
= 0.035
the probability that the three selected cans are diet soda cans is 0.035
da can
r
need help due tommorow
Finding the ratio of
a)1:9
b)2 : 7
c) 2 : 5
What is Ratio?
A ratio indicates how often one number contains another number. For example, if a fruit bowl contains 8 oranges and 6 lemons, the ratio of oranges to lemons is 8 to 6. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to whole fruit is 8:14.
Given,
Total no. of students = 42
a) Students who prefer punk to students who prefer hip-hop
No. of students in punk = 2
No. of students in hip-hop = 18
The Ratio will be,
punk : hip-hop = 2:18
= 1:9
b) Students who prefer rock to total no. of students that are surveyed
No. of students in rock = 12
Total no. of students = 42
The Ratio will be,
rock : total students = 12 : 42
= 2 : 7
c) Students who prefer rock or classic rock to students who prefer all music
No. of students in rock = 12
Total no. of students who likes other music = 42 - 12
= 30
The Ratio will be,
rock : total students with different music = 12 : 30
= 2 : 5
Hence, The ratio comparison in three different way
a)1:9
b)2 : 7
c) 2 : 5
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please di it quickly I just need to confirm answer
The Solution:
Given:
[tex]\begin{gathered} V=(-5,3) \\ \\ W=(\frac{3}{2},-\frac{1}{2}) \end{gathered}[/tex]Required:
To find the value of V - W
[tex]V-W=\lbrace(-5-\frac{3}{2}),(3--\frac{1}{2})\rbrace=(-6\frac{1}{2},3\frac{1}{2})=(-\frac{13}{2},\frac{7}{2})[/tex]
Therefore, the correct answer is [option 3]
16. The height, h, in feet of an object above the ground is given by h = -16t² +64t+190, t≥0, where t is the time in seconds. a) b) c) d) When will the object be 218 feet above the ground? When will it strike the ground? Will the object reach a height of 300 feet above the ground? Find the maximum height of the object and the time it will take.
the maximum height is 254 feet.
Answer:
a) 0.5 seconds and 3.5 seconds.
b) 5.98 seconds (2 d.p.)
c) No.
d) 254 feet at 2 seconds.
Step-by-step explanation:
Given equation:
[tex]h=-16t^2+64t+190, \quad t \geq 0[/tex]
where:
h is the height (in feet).t is the time (in seconds).Part aTo calculate when the object will be 218 feet above the ground, substitute h = 218 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 218\\-16t^2+64t+190-218& = 0\\-16t^2+64t-28 & = 0\\-4(4t^2-16t+7) & = 0\\4t^2-16t+7 & = 0\\4t^2-14t-2t+7 &=0\\2t(2t-7)-1(2t-7)&=0\\(2t-1)(2t-7)&=0\\\implies 2t-1&=0\implies t=\dfrac{1}{2}\\\implies 2t-7&=0 \implies t=\dfrac{7}{2}\end{aligned}[/tex]
Therefore, the object will be 218 feet about the ground at 0.5 seconds and 3.5 seconds.
Part bThe object strikes the ground when h is zero. Therefore, substitute h = 0 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 0\\-2(8t^2-32t-95) & = 0\\8t^2-32t-95 & = 0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(-95)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024+3040} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{4064} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot 254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4 \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{254} }{4}[/tex]
As t ≥ 0,
[tex]\implies t=\dfrac{8+ \sqrt{254} }{4}\quad \sf only.[/tex]
[tex]\implies t=5.98 \sf \; s \; (2 d.p.)[/tex]
Therefore, the object strikes the ground at 5.98 seconds (2 d.p.).
Part c
To find if the object will reach a height of 300 feet above the ground, substitute h = 300 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 300\\-16t^2+64t+190-300 & =0\\-16t^2+64t-110 & =0\\-2(8t^2-32t+55) & =0\\8t^2-32t+55& =0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(55)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024-1760} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{-736} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot -1 \cdot 46} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{-1} \sqrt{ 46}}{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4i\sqrt{ 46} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{ 46} \;i}{4}[/tex]
Therefore, as t is a complex number, the object will not reach a height of 300 feet.
Part dThe maximum height the object can reach is the y-coordinate of the vertex.
Find the x-coordinate of the vertex and substitute this into the equation to find the maximum height.
[tex]\textsf{$x$-coordinate of the vertex}: \quad x=-\dfrac{b}{2a}[/tex]
[tex]\implies \textsf{$x$-coordinate of the vertex}=-\dfrac{64}{2(-16)}=-\dfrac{64}{-32}=2[/tex]
Substitute t = 2 into the equation:
[tex]\begin{aligned}t=2 \implies h(2)&=-16(2)^2+64(2)+190\\&=-16(4)+128+190\\&=-64+128+190\\&=64+190\\&=254\end{aligned}[/tex]
Therefore, the maximum height of the object is 254 feet.
It takes 2 seconds for the object to reach its maximum height.
Figure out how many offspring there would be for the fifth and sixth generations using the equation
Explanation
We are given the following:
The table above models the function:
[tex]\begin{gathered} f(x)=a(4)^x \\ where \\ a=initial\text{ }value\text{ }(when\text{ }the\text{ }generation)=0 \\ x=generation \end{gathered}[/tex]We are required to determine how many offspring there would be for the fifth and sixth generations using the equation.
This is achieved thus:
[tex]\begin{gathered} \text{ Offspring:} \\ Fifth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=5 \\ F\imaginaryI fth\text{ }generat\imaginaryI on\to6(4)^5=6144 \end{gathered}[/tex][tex]\begin{gathered} Sixth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=6 \\ S\imaginaryI xth\text{ }generat\imaginaryI on\to6(4)^6=24576 \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} 5th\text{ }generation=6144 \\ 6th\text{ }generation=24576 \end{gathered}[/tex]
Cuál es la probabilidad de obtener exactamente 5 caras en 10 lanzamientos de una moneda?
The probability of getting exactly 5 heads in 10 tosses of a coin 24.6%
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Ten times are spent flipping coins.
Total number of results = 2¹⁰ = 1024
C(10, 5) = 252 is the total number of favorable outcomes.
Probability is
252/1024,
which equals :
=0.24, or
=24.6%.
Therefore, the chance of getting exactly 5 "heads" out of a possible 10 is 0.246, or 24.6%.
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