what is -3 exponent 2 in expanded form?
Answers
Answer:
-3 times -3 that is -4 exponent two in expanded form
Step-by-step explanation:
-3²
= -3 • -3
eg. Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression. 5,325 in expanded notation form is 5,000 + 300 + 20 + 5 = 5,325.
Related Questions
What is a Regression equation
Answers
Answer:
Regression equations can help you figure out if your data can be fit to an equation.This is extremely useful if you want to make predictions from your data- either future predictions or indications of past behavior.For example,you might want to know what your savings are going to be worth in the future.There are several types of regression equations,some of the more common include exponential and simoke linear regression.In elementary statistics,the regression equation you are most likely to come across is the linear form.
PLS I REALLY NEED HELP WITH THIS. THANK YOU SO MUCH!!
Cedric earned $50 doing yard work. Cedric spent d dollars on a gift for his family and had X dollars left over.
Explain whether this equation is correct or not:
50 – X = d
Answers
Cedric starts with $50, and takes away x many dollars. His remaining total would be D many dollars. Variables are just letters representing an unknown amount. :)
if a car travels at a constant speed of 45km/hr how long will a journey of 270km take?
Answers
Answer:
I think the answer is "6" but I could be wrong.
Find the quotient of 3/5 3/7. Write your answer in the simplest form.
Answers
\(\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}\)
A dolphin dives down into the ocean and resurfaces along a path that is modeled by x2 – 16x – 8y = 0, where the distances are in feet. How many feet is the dolphin from its starting point along the water's surface? (5 points)
Answers
Answer:
approx 17 ft
Step-by-step explanation:
You need to find the 'zeroes' of this equation......where the depth is zero
x^2 - 16x - 8 = 0 You will need to use the Quadratic Formula
with a = 1 b= -16 c = -8
to find x = 8 +- 6 sqrt 2
the distance between these zeroes is 12 sqrt2 = 16.97 = ~ 17 feet
The following value 1.23456789 x 10-6
what is a answer?
Answers
Answer 1:
1.23456789 × (10-6) = 4.93827156
Answer 2:
(1.23456789 × 10) - 6 = 6.3456789
Answer 3:
1.23456789 × \(10^{-6}\) = 0.000000123456789
Hope this helped! :)
A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
120
86.4
Answers
The number of the students that prefer documentaries is 120.
What is the number that prefer documentaries?We know that in this case, we are dealing with the pie chart and that it is a representation of the preferences of each of the students that we have in the data set that is given.
We can see that;
Number that prefer documentaries = 22 %
Total number of the students = 500
We then have;
Number that prefer documentaries = 22/100 * 500
= 120
Hence, we have 120 students that prefer documentaries.
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Covert 11/4 into a percent
Answers
Answer: Should be 275%
Step-by-step explanation:
Write an algebraic
expression for 9
less than the quo-
tient of 6 and a num-
ber x.
Answers
Answer:
The answer is 9<6/x
Step-by-step explanation:
.....
What are the vertex and x-intercepts of the graph of y = x2 – 4x – 21? Select one answer for the vertex and one for the x-intercepts. A. x-intercepts: (–3, 0), (7, 0) B. x-intercepts: (3, 0), (7, 0) C. x-intercepts: (3, 0), (–7, 0) D. Vertex: (2, 13) E. Vertex: (2, –25) F. Vertex: (–2, –9)
Answers
Answer:
To find x-intercept ,let y=0
0=x²-4x-21
(x+3)(x-7)=0
x=-3 or x=7
(-3;0) or (7;0)
To find vertex
x=
\( \frac{ - b}{2a} = x\)
x=4/2=2
y=(2)²-4(2)-21=-25
(2;-25)
choose A and E
write the following numerals in words
\(3 \frac{4}{5} \)
Answers
Everyone in the population must have an of being selected in order for a sample to be an
Answers
Answer: Everyone in your population must have an equal, non-zero chance of being selected. (In other words, everyone has an equal chance of receiving a survey.) You must know, specifically, what that chance of being selected is for each person.
find the exact value of tan(165°) using a difference of two angles
Answers
Answer: \(-2+\sqrt{3}\)
=========================================================
Work Shown:
Apply the following trig identity
\(\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\)
Now let's rationalize the denominator
\(\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\\)
----------------------
As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.
Or you can note how
\(\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949\)
which helps us see that they are the same thing.
Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as \(\sqrt{3}-2\) but it's the same as above.
Hannah jumped from the side of the pool and Dove under the water 4 ft from the pool side. She came out of the water 12 ft away from the poolside. Her path under the water was in the shape of a parabola. If the X intercepts are the points where she entered and exited the water, finally access of the Symmetry by looking at the graph of the x-intercepts. How far from where she entered the water was Hannah when she reached her lowest point in the pool? What is the axis of symmetry? What is the distance?
Answers
The distance from where she entered the water to when she reached her lowest point in the pool is 16 ft
The axis of symmetry is x = 8 ft
How to find the Vertex of a Parabola?We are told that she jumped from the side of the pool and the point at which she made contact with the water to dive under was a distance of 4 ft horizontal from the pool side. Secondly, the point at which she came out of the pool was 12 ft from the pool side.
Thus, since the points where she came out and where she dove into the pool are the x-intercepts, then it means that the factors of the parabola formed are; (x - 4) and (x - 12)
Thus, the quadratic equation formed by the parabola is;
y = (x - 4) * (x - 12)
y = x² - 16x + 48
Now, the coordinates for the vertex will be (h, k).
h = -b/2a
h = -(-16)/(2 * 1)
h = 8
k = 8² - 16(8) + 48
k = -16
Thus, the distance from where she entered the water to when she reached her lowest point in the pool is 16 ft
The axis of symmetry is x = 8 ft
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Find the slope of the line passing through the points (6, 4) and (6, -3).
Answers
Answer:
undefined
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 x_1)
slope = (-3 - 4)/(6 - 6)
slope = -7/0
Since division by zero is undefined, this line has undefined slope.
prove that 3^(2n+2) -8n-9 is divisible by 8
Answers
3−22−1=(3−1)−22…(1)
3
n
−
2
n
2
−
1
=
(
3
n
−
1
)
−
2
n
2
…
(
1
)
Now, if
n
is even, we observe that:
3≡1(8)=>3−1≡0(8)…(2)
3
n
≡
1
(
m
o
d
8
)
=>
3
n
−
1
≡
0
(
m
o
d
8
)
…
(
2
)
and of course:
22≡0(8)…(3)
2
n
2
≡
0
(
m
o
d
8
)
…
(
3
)
Hence, by (1)
(
1
)
, (2)
(
2
)
and (3)
(
3
)
when
n
is even, we are done.
In case at which
n
is odd, we see that:
3≡3(8)=>3−1≡2(8)…(4)
3
n
≡
3
(
m
o
d
8
)
=>
3
n
−
1
≡
2
(
m
o
d
8
)
…
(
4
)
Moreover, when
n
is odd there exists integer
m
, such that =2+1
n
=
2
m
+
1
and we easily observe that:
22=2(2+1)2=82+8+2…(5)
2
n
2
=
2
(
2
m
+
1
)
2
=
8
m
2
+
8
m
+
2
…
(
5
)
Hence by (5)
(
5
)
, we conclude that:
22≡2(8)...(6)
2
n
2
≡
2
(
m
o
d
8
)
.
.
.
(
6
)
Finally, by (1)
(
1
)
, (4)
(
4
)
and (6)
(
6
)
when
n
is even, we are done and hence the proof follows.
Second proof:
3−22−1=(3−1)−22=
3
n
−
2
n
2
−
1
=
(
3
n
−
1
)
−
2
n
2
=
(3−1)(3−1+3−2+...+3+1)−22=
(
3
−
1
)
(
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
1
)
−
2
n
2
=
2[(3−1+3−2+...+3+1)−2]…(1)
2
[
(
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
1
)
−
n
2
]
…
(
1
)
Now, if we will prove that:
(3−1+3−2+...+3+1)−2≡0(4)
(
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
1
)
−
n
2
≡
0
(
m
o
d
4
)
we will be done. We easily observe that when
n
is even the number of powers of 3
3
from 3 1
1
to 3−1
3
n
−
1
is odd since −1
n
−
1
is odd. Moreove, since:
For =
n
=
odd =>3≡3(4)...(2)
=>
3
n
≡
3
(
m
o
d
4
)
.
.
.
(
2
)
For =
n
=
even =>3≡1(4)...(3)
=>
3
n
≡
1
(
m
o
d
4
)
.
.
.
(
3
)
we see that each consecutive pair of them is divisible by 4
4
. Hence, when
n
is even, we conclude that:
3−1+3−2+...+3+≡3(4)=>
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
≡
3
(
m
o
d
4
)
=>
3−1+3−2+...+3+1)≡0(4)...(4)
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
1
)
≡
0
(
m
o
d
4
)
.
.
.
(
4
)
and since
n
is even, it follows that:
2≡0(4)...(5)
n
2
≡
0
(
m
o
d
4
)
.
.
.
(
5
)
Hence, by (4)
(
4
)
and (5)
(
5
)
, we take:
(3−1+3−2+...+3+1)−2≡0(4)...(6)
(
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
1
)
−
n
2
≡
0
(
m
o
d
4
)
.
.
.
(
6
)
Now, when
n
is odd, we have an even number of consecutive powers of 3
3
and since each consecutive pair of them is divisible by 4
4
, we see that:
(3−1+3−2+...+3+1)≡1(4)...(7)
(
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
1
)
≡
1
(
m
o
d
4
)
.
.
.
(
7
)
and since
n
is odd, it follows that:
2≡1(4)...(8)
n
2
≡
1
(
m
o
d
4
)
.
.
.
(
8
)
Hence, by (7)
(
7
)
and (8)
(
8
)
, we take:
(3−1+3−2+...+3+1)−2≡0(4)...(9)
(
3
n
−
1
+
3
n
−
2
+
.
.
.
+
3
+
1
)
−
n
2
≡
0
(
m
o
d
4
)
.
.
.
(
9
)
Therefore, by (5)
(
5
)
and (9)
(
9
)
we complete the second proof.
Third proof (by induction):
For =1=>31−2(1)2−1=(0)(8)
n
=
1
=>
3
1
−
2
(
1
)
2
−
1
=
(
0
)
(
8
)
For =2=>32−2(2)2−1=(0)(8)
n
=
2
=>
3
2
−
2
(
2
)
2
−
1
=
(
0
)
(
8
)
For =3=>33−2(3)2−1=(1)(8)
n
=
3
=>
3
3
−
2
(
3
)
2
−
1
=
(
1
)
(
8
)
We assume that for =
n
=
k
:
3−2()2−1=8...(1)
3
k
−
2
(
k
)
2
−
1
=
8
m
.
.
.
(
1
)
where
m
is positive integer.
We will show that for =+1
n
=
k
+
1
:
3+1−2(+1)2−1=8...(2)
3
k
+
1
−
2
(
k
+
1
)
2
−
1
=
8
p
.
.
.
(
2
)
where
p
is positive integer.
By properly modifying (2)
(
2
)
, we have to show that:
3(3)−2(+1)2−1=8<=>
3
(
3
k
)
−
2
(
k
+
1
)
2
−
1
=
8
p
<=>
3(3)−22−4−2−1=8<=>
3
(
3
k
)
−
2
k
2
−
4
k
−
2
−
1
=
8
p
<=>
(3−22−1)+[2(3)−4−2]=8<=>
(
3
k
−
2
k
2
−
1
)
+
[
2
(
3
k
)
−
4
k
−
2
]
=
8
p
<=>
8+2[3−2−1]=8…(3)
8
m
+
2
[
3
k
−
2
k
−
1
]
=
8
p
…
(
3
)
Hence, by (3)
(
3
)
, if we will show that:
[3−2−1]≡04
[
3
k
−
2
k
−
1
]
≡
0
m
o
d
4
we will be done.
Case 1,
k
is odd:
3≡3(4)...(4)
3
k
≡
3
(
m
o
d
4
)
.
.
.
(
4
)
2≡2(4)...(5)
2
k
≡
2
(
m
o
d
4
)
.
.
.
(
5
)
Hence, by (4)
(
4
)
and (5)
(
5
)
, we take:
[3−2−1]≡04
[
3
k
−
2
k
−
1
]
≡
0
m
o
d
4
Case 2,
k
is even:
3≡1(4)...(6)
3
k
≡
1
(
m
o
d
4
)
.
.
.
(
6
)
2≡0(4)...(7)
2
k
≡
0
(
m
o
d
4
)
.
.
.
(
7
)
Hence, by (6)
(
6
)
and (7)
(
7
)
, we take:
[3−2−1]≡04
[
3
k
−
2
k
−
1
]
≡
0
m
o
d
4
and the third proof is now complete.
Omar recorded the number of hours he worked each week for a year. Below is a random sample that he took from
data.
13, 17, 9, 21
What is the standard deviation for the data?
Answers
Answer:
Approx. 4.47
Step-by-step explanation:
To calculate the standard deviation for the data, we need to follow these steps:
1. Calculate the mean (average) of the data:
mean = (13 + 17 + 9 + 21) / 4 = 15
2. Calculate the difference between each data point and the mean:
13 - 15 = -2
17 - 15 = 2
9 - 15 = -6
21 - 15 = 6
3. Square each difference:
(-2)^2 = 4
2^2 = 4
(-6)^2 = 36
6^2 = 36
4. Calculate the variance by taking the average of the squared differences:
variance = (4 + 4 + 36 + 36) / 4 = 20
5. Calculate the standard deviation by taking the square root of the variance:
standard deviation = sqrt(variance) = sqrt(20) ≈ 4.47
Therefore, the standard deviation for the data is approximately 4.47.
which mixed number is equivalent to the improper fraction of 41/10
Answers
Answer:
4 1/10 when u have a inproper fraction like that every 10 is one whole number
Dividing fractions word problem,
I need your help, yes you!
Answers
Answer: 2
Step-by-step explanation:
Answer:
I think it's 2kg
Step-by-step explanation:
13/5 ÷ 13/10
Reciprocate
13/5 × 10/13
= 26/13
=2kg
How would you round the number 9.9813 x 10-5 to two significant figures? Group of answer choices 10 1.0 x 10-4 10.0 x 10-5 9.9 x 10-5
Answers
Answer:
This Significant Figures Rounding Calculator rounds a given number to the amount of significant digits that you specify. This rounding number which you specify cannot be a negative number and it must be greater than 0. A number with 0 significant digits would be 0.
Step-by-step explanation:
How much would you need to deposit in an account now in order to have $5000 in the account in 10 years? Assume the account earns 4% simple interest. Round your answer to the nearest cent.
Answers
Answer:
$12500
Step-by-step explanation:
use si formula
SI=ptr/100
si=5000
t=10
r=4
Simple interest can be defined as the interest that accumulates on investment, savings, or a loan.
The amount you need to deposit in an account now in order to have $5000 to the nearest cent is $3,571.
From the question, we can see that we are to find the amount you need to deposit, this is also referred to as the Principal.
The formula to find the principal for simple interest is given as:
P = A / (1 + rt)
Where:
A = Final amount in the account = $5000
R = Interest rate = 4%
t = Time in years = 10 years
Calculation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year.
Solving our equation:
P = 5000 / ( 1 + (0.04 × 10)) = 3571.4285714286
P = $3,571.43
Approximately to the nearest cent is $3,571.
Therefore, the amount you need to deposit in an account now in order to have $5000 to the nearest cent is $3,571.
To learn more, visit the link below:
https://brainly.com/question/11412624
Is \(\sqrt{103}\) irrational or rational? What is your reasoning?
Answers
Answer: irrational
Step-by-step explanation:
\(\sqrt{103}\) is an irrational number because it is not a perfect square. Irrational numbers keep on terminating, so the answer to the question is irrational.
Hope this helps you!
The diagram shows a square-based cuboid. 4 cm by 10.Work out the volume of the cuboid. State the units of your answer.
Answers
Answer:
Step-by-step explanation:
The volume of a square-based cuboid is given by the formula:
V = l × w × h
where l is the length, w is the width, and h is the height of the cuboid.
If the length is 4 cm, the width is also 4 cm (since it is a square-based cuboid), and the height is 10 cm, we can substitute these values into the formula and calculate the volume:
V = 4 cm × 4 cm × 10 cm
V = 160 cubic centimeters (cm³)
Therefore, the volume of the square-based cuboid is 160 cubic centimeters.
Answer:
Step-by-step explanation:
Unfortunately, I cannot see the diagram you are referring to. However, I can provide you with the formula for calculating the volume of a square-based cuboid.
The volume of a square-based cuboid is calculated by multiplying the length, width, and height of the cuboid together. In other words:
Volume = length x width x height
So if the length of the cuboid is 4 cm, the width is also 4 cm (since it is a square-based cuboid), and the height is 10 cm, the volume can be calculated as:
Volume = 4 cm x 4 cm x 10 cm
Volume = 160 cubic centimeters
Therefore, the volume of the cuboid is 160 cubic centimeters (cc), or cm^3.
A camp counselor has 605 campers to divide into 11 teams. How many campers are on each team?
Answers
Answer: 55
Step-by-step explanation:
The answer fam is........ 55
HELP, ASAP PLEASE. 15 POINTS! ( Only 1 picture is attached)
Answers
The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million
How to find the input values of functions?
We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;
A(h) = -0.06h² + 2h + 4
where h is the time in number of hours after which the concentration is recorded.
Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;
A(4) = -0.06(4²) + 2(4) + 4
A(4) = -0.96 + 12
A(4) = 11.04 parts per million
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The company president thought that type of music listened to (country vs. classical) could predict production line output. For one week the entire plant listened to country music, then for the next week the entire plant listened to classical music. He then compared the production line output between the country and classical music production line outputs.
(a) What type of research hypothesis is tested in this study?
associative RH
causal RH
(b) What type of design is being used in this study?
true experiment
non-experiment
(c) What type of design is being used in this study (mark all that apply)
cross-sectional design
within-group design
between subjects design
repeated measures design
longitudinal design
within-subjects design
between groups design
(d) Will the design used in this study provide an appropriate test of the research hypothesis?
Yes, this design can be used to test this research hypothesis
No, this design can not be used to test this research hypothesis
Answers
a) Type of research hypothesis is tested in this study is causal RH
b) Type of design is being used in this study is non-experiment
c) Type of design is being used in this study is within-subjects design
d) No, the design used in this study cannot provide an appropriate test of the research hypothesis.
(a) The research hypothesis being tested in this study is a causal hypothesis. The company president believes that the type of music listened to can predict production line output.
(b) The type of design being used in this study is a non-experiment. The researcher is not manipulating the type of music listened to; instead, the plant is naturally exposed to either country or classical music.
(c) The design being used in this study is within-subjects design, as the same group of individuals is exposed to both types of music. It is also a repeated measures design, as the same individuals are measured twice (once under country music and once under classical music).
(d) No, the design used in this study cannot provide an appropriate test of the research hypothesis. Since the researcher is not manipulating the type of music listened to, it is possible that other variables could be affecting the production line output, such as different environmental conditions on each week, or different levels of motivation.
Therefore, it is difficult to determine if any differences in production line output are actually due to the type of music listened to. A true experiment with random assignment of workers to the two music conditions would provide a better test of the research hypothesis.
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I want a clear explanation please, i need to solve this
Answers
Answer:
(2,2)
Step-by-step explanation:
The slope is -2 so going from the point (1,4), the point would be (2,2)
In 1939, an earthquake measuring 8.3 occurred in Chillan, Chile, killing 28 000 people. In 1999, an earthquake in Taiwan measured 7.6 on the Richter scale and killed 2100 people. Compare the intensities of the two earthquakes. (THE ASNWER IS 5).
Answers
The Chillan earthquake had an intensity about 5 times greater than the Taiwan earthquake.
The Richter scale is logarithmic, meaning that a difference of 1 on the scale corresponds to a tenfold difference in the amplitude of the seismic waves. Therefore, we can calculate the difference in intensity between the two earthquakes using the formula:
difference in intensity
= 1\(0^{((magnitude of earthquake 1) - (magnitude of earthquake 2))\)
For the Chillan earthquake:
magnitude = 8.3
difference in magnitude = 8.3 - 7.6 = 0.7
For the Taiwan earthquake:
magnitude = 7.6
Plugging these values into the formula, we get:
difference in intensity = 10^(0.7) = 5.01187
This means that the Chillan earthquake had an intensity about 5 times greater than the Taiwan earthquake.
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For how many integers x is the equation 22x+1 = 3x - 3 true?
Answers
REmember that
the speed is equal to divide the distance by the time
so
speed=d/t
in this problem we have
speed=3.6x10^4 miles/hour
d=7.2x10^8 miles
substitute in the formula
\(3.6\cdot10^4=\frac{7.2\cdot10^8}{t}\)solve for t
\(\begin{gathered} 3.6\cdot10^4=\frac{7.2\cdot10^8}{t} \\ t=\frac{7.2\cdot10^8}{3.6\cdot10^4} \\ t=2.0\cdot10^4\text{ hours} \end{gathered}\)therefore
answer is option DIn a lottery game, a player picks 6 numbers from 1 to 48. if 4 of those 6 numbers match those drawn, the player wins third prize. let's walk through the steps to determine the probability of winning third prize.In how many ways can 4 winning numbers be chosen from the possible 6 numbers?In how many ways can 2 non-winning numbers be chosen from the pool of all non-winning numbers? The number of favorable outcomes would be to multiply the above two answers together, since we want 4 winning numbers and 2 non-winning numbers. What is the number of favorable outcomes? In how many ways can you pick any 6 numbers from the pool of 50 numbers? This is your total outcomes. What is the probability of winning third prize?
Answers
The probability of winning third prize in the lottery game is 0.0011 or about 0.11%.
In the given lottery game, the player picks 6 numbers from 1 to 48.
The number of ways 4 winning numbers can be chosen from the possible 6 numbers is calculated using the combination formula: C(6,4) = 15.The number of ways 2 non-winning numbers can be chosen from the pool of 42 non-winning numbers (total numbers - possible winning numbers) is calculated using the combination formula: C(42,2) = 861.The number of favorable outcomes is the product of the above two answers: 15 x 861 = 12,915.The total number of ways you can pick any 6 numbers from the pool of 48 numbers is calculated using the combination formula: C(48,6) = 12,271,512.The probability of winning third prize is the number of favorable outcomes divided by the total number of outcomes: 12,915 / 12,271,512 ≈ 0.0011 or about 0.11%. Therefore, the probability of winning third prize in this lottery game is relatively low.Learn more about probability:
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