Answer:
[tex]{m}^{2} +7m + 28 = 0[/tex]
Step-by-step explanation:
Given that,
[tex]m = {x}^{2} + 3[/tex]
We know that,
[tex] {x}^{2} = m- 3[/tex]
Now look at the sum
[tex]( {x}^{2} + 3) ^{2} + 7 {x}^{2} + 21 = - 10 \\ [/tex]
[tex]( {x}^{2} + 3) ^{2} + 7 {x}^{2} + 21 = - 10 \\ {m}^{2} + 7 \times m- 3 + 21 = - 10 \\ {m}^{2} +7m + 18= - 10 \\ {m}^{2} + 7m + 18+ 10 = 0 \\ {m}^{2} + 7m + 28 = 0[/tex]
What is total number of elements in 3 trials of rolling a 6-sided die?
Answer:
216 elements
Step-by-step explanation:
the total number of elements of a dice is :
6^n
6 stand for the 6 faces of the dice
n stands for the number trial
then total number of elements in 3 trials of rolling a 6-sided die is 6^3=216 elements
In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer: 16,384
Step-by-step explanation:
The seven marbles have different colours, so we can differentiate them.
Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.
For the first marble, we have 4 options ( we have 4 jars)
For the second marble, we have 4 options.
Same for the third, for the fourth, etc.
Now, the total number of combinations is equal to the product of the number of options for each selection.
We have 7 selections and 4 options for each selection, then the total number of combinations is:
C = 4^7 = 16,384
Answer:
the answer is 16384
Step-by-step explanation:
have a nice day.
What percent of 24 is 18? 60 is what percent of 48? Write 1.052 as a percent.
Answer:
24 of 18 is 75%
60 of 48 is 80%
1.052 is 105.2%
Step-by-step explanation:
Mr.lopez wrote the equation 32g+8g-10g=150
Answer:
g=5
Step-by-step explanation:
32g+8g-10g=150
30g=150
g=5
(Dividing polynomials ick!) Please help I'm failing summer class:)
Answer:
The answer is 9 (D).
Step-by-step explanation:
Hope this helps!
which of the following is equivalent to [ (x^ 2 y^ 3 )^ -2/ (x^ 6 y^ 3 z)^3]? worth 60 points!
Answer:
[tex]\dfrac{1}{x^{48}y^{36}z^{6}}[/tex]
Step-by-step explanation:
[tex] (\dfrac{(x^2y^3)^{-2}}{(x^6y^3z)^{2}})^3 = [/tex]
[tex] = (\dfrac{1}{(x^6y^3z)^{2}(x^2y^3)^{2}})^3 [/tex]
[tex] = (\dfrac{1}{x^{12}y^6z^{2}x^4y^6})^3 [/tex]
[tex]= (\dfrac{1}{x^{16}y^{12}z^{2}})^3[/tex]
[tex]= \dfrac{1}{x^{48}y^{36}z^{6}}[/tex]
Answer:
[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]
Step-by-step explanation:
[tex]\displaystyle[\frac{(x^2 y^3)^{-2}}{(x^6 y^3 z)^2 } ]^3[/tex]
[tex]\displaystyle \frac{(x^2 y^3)^{-6}}{(x^6 y^3 z)^6 }[/tex]
[tex]\displaystyle \frac{(x^{-12} y^{-18})}{(x^{36} y^{18}z^6 ) }[/tex]
[tex]\displaystyle \frac{x^{-48} y^{-36}}{z^6 }[/tex]
[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]
Does anyone know the answer
Solution: C
Explanation:
Use the cosine rule
A^2=B^2+C^2-2BCcos a
5^2=8^2+8^2-2×8×8cos a
cos a=(25-64-64)÷(-2×64)
a=36.419°
approx = 36
. What is half the next number in the pattern 1, 3, 9, 27, 81
A. 234
B. 67
D c. 468
0 0.76
Answer:
A. 243
Step-by-step explanation:
just multiply the next number by 3
81*3= 243
Answer:
[tex]\boxed{243}[/tex]
Step-by-step explanation:
The ratio can be found by dividing a term in the sequence by the previous term.
[tex]\frac{27}{9} =3[/tex]
Each term gets multiplied by 3 to get the next term.
[tex]81 \times 3 = 243[/tex]
Music CD's cost $9 each, and movies cost $10 each. If you
spend $78 and buy 8 items, how many of each did you buy?
Answer:
2 CDs and 6 movies
Step-by-step explanation:
Let the number of CD you bought be x, and the number of movies you bought be y.
Since you bought 8 items in total,
x + y = 8 ______(1)
The sum of money spent is 78, so
9x + 10y = 78 ________(2)
From equation (1),
x = 8 - y ________(3)
Substitute (3) into (2),
9 (8-y) + 10y = 78
72 - 9y + 10y = 78
- 9y + 10y = 78-72
y = 6
Now substitute y=6 into (3).
x = 8 - y
x = 8-6
x = 2
Therefore, you bought 2 CDs and 6 movies.
Use cubic regression to find a function that fits the following points.
Answer:
Step-by-step explanation:
To use the regression function on your calculator, first hit STAT then choose 1:Edit by pressing ENTER. Then a table pops up. If it's not clear, arrow up to L1, hit CLEAR then ENTER and the table empties. Do the same with L2. Arrow left and right as needed to get from one column to the other. Then in L1 enter the x values one at a time, hitting ENTER after each. When all the x values are in, arrow over to L2 and enter the y values in the same way.
Next, hit STAT again, then right arrow over to CALC. Choose 6:CubicReg by either arrowing down to it or by pressing 6. If you have a TI 83+, the equation comes right up for you; if you have a TI 84+ or 84+CE, you have to arrow down to CALCULATE and hit ENTER to get your equation. The equation is
[tex]-2x^3+2x^2-4x+3[/tex] with a coefficient correlation (r-squared) value of 1 which means this is a perfect equation for this data and all the points you entered into the table fall perfectly on this curve.
2. Susan wants to use blue, yellow, green, and pink paint to decorate her house. She needs 3 times as much blue paint as yellow paint and ½ much yellow paint as green paint. She needs 3 ¼ gallons of pink paint, which is ¾ of a gallon more than the green paint she needs. How much paint does Susan need in all?
Answer:
B = Blue
Y = Yellow
G = Green
P = Pink
The info that we have is:
3*B = Y
(1/2)Y = G
P = (3 + 1/4) gal
P = G + 3/4 gal.
So we have 4 equations. The first step is replacing the third equation into the fourth equation, and get:
G + 3/4 gal = (3 + 1/4) gal
G = (3 + 1/4) gal - 3/4 gal = (2 + 2/4) gal
Now we can replace this into the second equation ((1/2)*Y = G) to find the value of Y.
(1/2)Y = (2 + 2/4) gal
Y = 2*(2 + 2/4) gal = (4 + 1)gal = 5 gal.
Now we can replace this into the first equation and get:
3*B = 5gal
B = 5/3 gal = (1 + 2/3)gal
So the total amount of paint used is:
T = P + G + Y + B = (3 + 1/4) gal + (2 + 2/4) gal + 5gal + (1 + 2/3)gal
T = (11 + 3/4 + 2/3)gal
T = (11 + 9/12 + 8/12)gal = (11 + 17/12)gal = (11 + 1 + 5/12)gal = (12 + 5/12) gal.
Write these series with summation notation. 1,4,9,16...
Answer: [tex]\sum\limits_{i=1}^{n} n^2[/tex] , where n is a natural number.
Step-by-step explanation:
A series can be represented in a summation or sigma notation.
Greek capital letter, ∑ (sigma), is used to represent the sum.
For example: [tex]\sum\limits_{n=1}^{\infty} n=1+2+3+4+5+...[/tex], where n is a natural number.
The given series : 1,4,9,16 which can be written as [tex]1^2, 2^2, 3^2,...[/tex] .
So , we can write it as
[tex]\sum\limits_{n=1}^{\infty} n^2[/tex] , where n is a natural number.
Answer:
B=6
C=n^2
Just did the test
Step-by-step explanation:
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
y=-*x+9
y=-*x+5
y=-3x – 1ly
y=-3x + 25
Answer:
y = -3x - 11
Step-by-step explanation:
(y - y1)/(x - x1) = (x2 - x1)/(y2 - y1)
(y - 7)/(x + 6) = (-3 + 6)/(6 - 7)
(y - 7)/(x + 6) = 3/-1 = -3
y - 7 = -3(x + 6)
y - 7 = -3x - 18
y = -3x -18 - 7
y = -3x - 11
what is this expression in rational exponent form cuberoot√5xy^2
Answer:
[tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{5xy^2}[/tex]
We need to find the expression in rational exponent form.
It can be written as
[tex](5xy^2)^{\frac{1}{3}}[/tex] [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]
[tex]=(5)^{\frac{1}{3}}(x)^{\frac{1}{3}}(y^2)^{\frac{1}{3}}[/tex] [tex][\because (ab)^m=a^mb^m][/tex]
[tex]=5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
Therefore, the required expression is [tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].
A box of 15 cookies costs $ 9 What is the cost for 1 cookie?
Answer:
60 cents or $0.60
Step-by-step explanation:
9.00/15 = 0.6
Answer:
$.60
Step-by-step explanation:
This is just 9 divided by 15 which is $.60
This is hard for me, can someone please help? Loren solved the equation 10 = StartFraction 19 Over 9 EndFraction (149) + b for b as part of her work to find the equation of a trend line that passes through the points (1, 130) and (10, 149). What error did Loren make? She should have solved 10 = StartFraction 9 Over 19 EndFraction (149) + b for b. She should have solved 1 = StartFraction 19 Over 9 EndFraction (130) + b for b. She should have solved 149 = StartFraction 19 Over 9 EndFraction (10) + b for b. She should have solved 130 = StartFraction 9 Over 19 EndFraction (1) + b for b.
Answer:
149=19/9 (10) +b
130=19/9(1)+b
Step-by-step explanation:
for Loren to find a line passes through two points:(1,130), (10.149)
1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9
m=19/9
to find b in the equation y=mx+b for point (1,130)
y=130, x=1, m=19/9
130=19/9(1)+b
for point (10,149)
149=19/9 (10) +b
you have two options
The solution is, the equations of line passes through two points:(1,130), (10.149) is:
149=19/9 (10) +b
130=19/9(1)+b
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
for Loren to find a line passes through two points:(1,130), (10.149)
1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9
m=19/9
to find b in the equation y=mx+b for point (1,130)
y=130, x=1, m=19/9
130=19/9(1)+b
for point (10,149)
149=19/9 (10) +b
you have two options
Hence, The solution is, the equations of line passes through two points:(1,130), (10.149) is:
149=19/9 (10) +b
130=19/9(1)+b
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
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can u help me spot the sequence
Answer:
Hey mate... I don't know the first three... But mayb I can help u in last one.
Step-by-step explanation:
The answer is : 2: 6: 18: 54: 162: 426
I can see the pattern by multiplying.. As from 3
2x3=6 :6x3=18 :18x3= 54 :54x3=162 :162x3=426
So I guess this is the ans
Hope it helped u!
To work out the area in m² of material required for a pair of curtains, a seamstress squares the height of the window in m and adds 0.5.
a) What area of material is required for a window of height 1.2meters?
b) What area of material is required for a window of height p meters?
c) if the area of material required is 2.75m²,what is the height of the window?
Answer:
a. Area = 1.94m²
b. Area = (p² + 0.5)m²
c. Height = 1.5m
Step-by-step explanation:
Given
Let H represents Height and A represents Area
From the first and second statements, we have that:
[tex]A = H^2 + 0.5[/tex]
a. Calculating Area When Height = 1.2
[tex]A = H^2 + 0.5[/tex]
Substitute 1.2 for H
[tex]A = 1.2^2 + 0.5[/tex]
[tex]A = 1.44 + 0.5[/tex]
[tex]A = 1.94[/tex]
Hence, the area is 1.94m²
b. Calculating Area When Height = p
[tex]A = H^2 + 0.5[/tex]
Substitute p for H
[tex]A = p^2 + 0.5[/tex]
Hence, the area is (p² + 0.5)m²
c. Calculating Height When Area = 2.75m²
[tex]A = H^2 + 0.5[/tex]
Substitute 2.75 for A
[tex]2.75 = H^2 + 0.5[/tex]
Subtract 0.5 from both sides
[tex]2.75 - 0.5 = H^2 + 0.5 - 0.5[/tex]
[tex]2.75 - 0.5 = H^2[/tex]
[tex]2.25 = H^2[/tex]
Take Square Root of both sides
[tex]\sqrt{2.25} = \sqrt{H^2}[/tex]
[tex]\sqrt{2.25} = H[/tex]
[tex]1.5 = H[/tex]
[tex]H = 1.5[/tex]
Hence, the height is 1.5m
ASAP The tee for the fourth hole on a golf course is 300 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
C. 97.5 yd
Step-by-step explanation:
The distance between Marsha, the ball and the tee for the fourth hole, forms a triangle.
Thus, the distance between Marsha's ball and the hole can be calculated using the Cosine formula below:
c² = a² + b² - 2abcos(C)
Where,
c = distance between Marsha's ball and the hole = ?
a = distance between the tee for the fourth hole and the tee = 300 yd
b = distance between tee and the hole = 255 yd
C = 18°
c² = 300² + 255² - 2(300)(255)cos(18)
c² = 90000 + 65025 - 153000 × 0.951
c² = 155025 - 145503
c² = 9522
c = √9522 ≈ 97.5
c = distance between Marsha’s ball and the hole = 97.5 yd (nearest tenth)
I need help ASAP thank you!!
Answer:
Step-by-step explanation:
Hello!
a)
You have three triangles and you have to find the ratio of the adjacent sides to the angle 23.1º
Remember, considering a specific angle ∠, "the adjacent sides" are those that make contact with the angle and the "opponent side" is the one that is in the opposite side of the angle and the hypotenuse is the longest side of the right triangle, always opposed to the right angle.
First triangle, the adjacent sides, are
JL= 20.17m (hypotenuse)
JK= 18.55m
Ratio: [tex]\frac{JK}{JL}= \frac{18.55}{20.17}= 0.9196= 0.92[/tex]
Second triangle, adjacent sides:
PR= 141.19m (hypotenuse)
PQ= 129.85m
Ratio: [tex]\frac{PQ}{PR} = \frac{129.85}{141.19}= 0.9196= 0.92[/tex]
Third triangle, adjacent sides:
XZ= 181.53m (hypotenuse)
XY= 166.95m
Ratio: [tex]\frac{XY}{XZ} = \frac{166.95}{181.53} = 0.9196= 0.92[/tex]
b)
Using the calculator you have to calculate the trigonometric ratios of 23.1º:
sin(23.1º)= 0.392= 0.39
cos(23.1º)= 0.9198= 0.92
tan(23.1º)= 0.426= 0.43
c)
To calculate the trigonometrical ratios manually you have to do as follows:
Consider the angle A
[tex]sinA= \frac{opposite}{hypotenuse}[/tex]
[tex]cosA= \frac{adjacent}{hypotenuse}[/tex]
[tex]tanA= \frac{opposite}{adjacent}[/tex]
In item a) you calculated the ratios of the adjacent sides of the angle by the hypotenuse, this is equal to the cosine of the given angle.
I hope this helps!
A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender?
Answer: 120
Step-by-step explanation:
Given: A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles.
The total number of marbles in the bag : 2+2+1+5+6=16
Now, the number of ways of selecting sets of four marbles include one of each color other than lavender is
[tex]\( C(2,1) \times C(2,1) \times C(5,1) \times C(6,1)=2 \times 2 \times 5 \times 6\)=120[/tex] [[tex]\because\ C(n,1)=n[/tex]]
Hence, the number of sets of four marbles include one of each color other than lavender = 120
Suppose that a bacterial culture was known to double every 2 days. After 46 days, it covered the entire surface area in the petri dish. When did it cover half the area? Explain.
Answer:
in day 44 it covered half the area.
Step-by-step explanation:
A bacterial culture doubles every two days, so if today it covers [tex]3 cm^2[/tex], in two days it will cover [tex]6cm^2[/tex]. In other words, if today it covered x space, two days ago it covered half the space [tex](\frac{x}{2})[/tex].
Now, following that reasoning, we have that after 46 days the bacterial culture covered the entire surface area in the Petri dish, therefore, two days ago it covered half the area and we can conclude that in day 44 it covered half the area.
Julio’s rotation maps point K(–6, 9) to K’(9, 6). Which describes the rotation? 90 degrees clockwise rotation 180 degrees rotation 90 degrees counterclockwise rotation 270 degrees clockwise rotation
Answer: 90 degrees clockwise rotation
Step-by-step explanation:
Common rotations about Origin :
90° clockwise (x,y)→(y,-x)
90° counterclockwise (x,y)→(-y,x)
180° (x,y)→ (-x,-y)
270° clockwise (x,y)→(-y,x)
Given: Julio’s rotation maps point K(–6, 9) to K’(9, 6).
Rotation corresponding to this is (x,y) → (y,-x) since K(–6, 9) → K’(9, -(-6)) = K(9,6).
Therefore, Julio’s rotates 90° clockwise to map point K(–6, 9) to K’(9, 6).
so , correct answer is "90 degrees clockwise rotation".
Answer:
90 degrees clockwise
Step-by-step explanation:
EDGE2020
Point K is rotated 90°. The coordinate of the pre-image point K was (2, –6) and its image K’ is at the coordinate (−6, −2). Find the direction of the rotation. The direction of rotation was .
Answer:
Hello! The answer to your question will be below.
Step-by-step explanation:
The answer would be clockwise.
So point k was rotated 90 degrees clockwise.....
Review.....
Question:
Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.
THE DIRECTION OF THE ROTATION WAS CLOCKWISE.
Hope this helps! :)
⭐️Have a wonderful day!⭐️
Answer:
clockwise.
So point k was rotated 90 degrees clockwise.....
Review.....
Question:
Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.
Step-by-step explanation:
dentify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. To determine her air qualityair quality, MirandaMiranda divides up her day into three parts: morning, afternoon, and evening. She then measures her air qualityair quality at 33 randomly selected times during each part of the day. What type of sampling is used?
Answer:
The sampling method used is a stratified sampling method
Step-by-step explanation:
sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.
Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.
What is the diameter of the circle whose center is at (6, 0) and that passes through the point (2, -3)?
Answer:
10
Step-by-step explanation:
[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^2[/tex]
[tex]\left(x-6\right)^{2}+\left(y-0\right)^{2}=r^2\\[/tex]
We used (2,-3)
[tex]\left(2-6\right)^{2}+\left(-3-0\right)^{2}=25[/tex]
[tex]r^2=25\\[/tex] , so [tex]r = 5[/tex]
But this one is asking for the diameter, and to find it. It's simply 2r.
2*5 = 10
What is the explicit formula for this sequence?
Greetings from Brasil...
With the recursive formula, lets build the sequence:
A1 = 4
A2 = A1 - 7
A3 = A2 - 7
A4 = A3 - 7
A5 = A4 - 7
(...)
But pay attention to A3....
A3 = A2 - 7 but A2 = A1 - 7 , so rewriting A3
A3 = (A1 - 7) - 7 ⇒ A3 = A1 + 2.(- 7)
A4 = A3 - 7 ⇒ A4 = [(A1 - 7) - 7] - 7 = A1 + 3.(- 7)
A5 = {[(A1 - 7) - 7] - 7} - 7 = A5 + 4.(- 7)
so
An = A1 + (n - 1).(- 7)Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.) 40
Answer:
Probability of selecting none of the correct six integers:
a) 0.350
b) 0.427
c) 0.489
d) 0.540
Step-by-step explanation:
a) 40
Given:
Number of integers in a lottery 6
Order in which these integers are selected does not matter
To find:
Probability of selecting none of the correct six integers
Solution:
When the order of selection does not matter then we use Combinations.
Given integers = 40
Number of ways to choose 6 from 40.
Let A be the sample space of choosing digits 6 from 40.
Then using Combinations:
(n,k) = n! / r! (n-r)!
n = 40
r = 6
40C6
=(40,6) = 40! / 6! ( 40 - 6)!
= 40! / 6!34!
= 40*39*38*37*36*35*34! / 6!34!
= 2763633600 / 720
= 3838380
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 40
n = 40 - 6 = 34
r = 6
34C6
=(34,6) = 34! / 6! ( 34 - 6)!
= 34! / 6! 28!
= 34 * 33 * 32 * 31 * 30 * 29 * 28! / 6! 28!
=968330880 / 720
= 1344904
Probability of selecting none of the correct six integers:
P(E) = E / A
= 1344904 / 3838380
= 0.350
Probability of selecting none of the correct six integers is 0.350
b) 48
Following the method used in part a)
(n,k) = n! / r! (n-r)!
n = 48
r = 6
48C6
=(48,6) = 48! / 6! ( 48 - 6)!
= 48! / 6! ( 42 )!
= 48*47*46*45*44*43*42! / 6!42!
= 8835488640 / 720
= 12271512
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 48
n = 48 - 6 = 42
r = 6
42C6
= (42,6) = 42! / 6! ( 42 - 6)!
= 42! / 6! 36!
= 3776965920
= 5245786
P(E) = E / A
= 5245786/12271512
= 0.427
c) 56
(n,k) = n! / r! (n-r)!
n = 56
r = 6
56C6
=(56,6) = 56! / 6! ( 56- 6)!
= 56! / 6! ( 50 )!
= 56*55*54*53*52*51*50! / 6! 50!
= 23377273920/6
= 32468436
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 56
n = 56 - 6 = 50
(50,6) = 50! / 6! ( 50- 6)!
= 50*49*48*47*46*45*44! / 44! 6!
= 11441304000 / 6
= 15890700
P(E) = E / A
= 15890700 / 32468436
= 0.489
d) 64
(n,k) = n! / r! (n-r)!
n = 64
r = 6
64C6
=(64,6) = 64! / 6! ( 64 - 6)!
= 64! / 6! ( 58 )!
= 64*63*62*61*60*59*58! / 6! 58!
= 53981544960 / 720
= 74974368
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 64
n = 64 - 6 = 58
(58,6) = 58! / 6! ( 58- 6)!
= 58*57*56*55*54*53*52! / 52! 6!
= 29142257760/ 6
= 40475358
P(E) = E / A
= 40475358/ 74974368
= 0.540
The probability of selecting none of the correct six integers in a lottery is, 0.350.
Number of integers given = 40
So, Total outcomes for choosing 6 from 40 integers.
Number of arrangements [tex]=_{6}^{40}\textrm{C}[/tex]
[tex]=\frac{40!}{6!*34!} =3838380[/tex]
Since, we have to find probability of selecting none of the correct six integers in a lottery.
Remaining integer = 40 - 6 =34
Let favourable outcomes is selecting none of the correct six integers.
So, number of arrangements, = [tex]=_{6}^{34}\textrm{C}[/tex]
= [tex]\frac{34!}{6!*28!}=1344904[/tex]
Probability is defined as, divide favourable outcomes by total outcomes.
So, The probability of selecting none of the correct six integers in a lottery,
[tex]P=\frac{1344904}{3838380}=0.35[/tex]
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Suppose you deposit $5,000 in a savings account where the interest earned is compounded continuously
at a rate of 12.5%. How many years will it take the balance in the account to triple (round your answer to
the nearest year)?
0 9 years
O 8 years
Answer:
9 years i think
Step-by-step explanation:
A spherical mirror gives an image magnified 5 times at a distance 5 m. determine whether the mirror is convex or concave? How much will be the focal length of the mirror?
Answer:
a) The mirror is concave
b) The focal length of the mirror = -1.25m or -5/4 m
Step-by-step explanation:
a) Determine whether the mirror is convex or concave?
A concave mirror is a spherical mirror that it's magnification is equal to, less than or more than 1 while a convex mirror is a mirror whereby it magnification is always less than one.
From the above question we are told that the spherical mirror is magnified 5 times.
Hence, because the spherical mirror is magnified 5, it is a concave mirror.
b) Magnification = - image distance/ object distance
Magnification = 5
Image distance = 5m
Object distance = ???
5 = -5/Object distance
Object distance = -5/5
= -1m
Formula for focal length =
1/f = 1/v + 1/u
v = image distance = 5
u = object distance = -1
1/f = 1/5 +1/-1
1/f = 1/5 - 1
1/f = -4/5
f = -5/4
f = -1.25m
The focal length of the mirror = -1.25m