The total number of ways the study can be selected is: 637065
Given,
Total number of women in a group= 13
Total number of men in a group = 12
Number of women chosen = 8
Number of men chosen = 8
∴ the total number of ways the study group can be selected = 13C₈ and 12C₈.
This in the form of combination factor = nCr
∴ nCr = n!/(n₋r)! r!
13C₈ = 13!/(13 ₋ 8)! 8!
= 13!/5!.8!
= 1287
12C₈ = 12!/(12₋8)! 8!
= 12!/5! 8!
= 495
Now multiply both the combinations of men and women
= 1287 × 495
= 637065
Hence the total number of ways the study group is selected is 637065
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Raj and Priyanka are playing a game in which each person takes turns to snap open a book at a random page. The LAST TWO DIGITS OF THE PAGE NUMBER ON THE RIGHT SIDE is taken as the person's score.
A player's TOTAL score is calculated by adding each turn's score to the previous total. Which of the following could NOT be Priyanka's score after 4 rounds of the game?
A. 6
B. 88
D. 145
C. 250
After four rounds of the game, it is impossible that Prinyanka's score could be A. 6.
What is the lowest score Priyanka could get at round 4?The numbers of the right side are shown to be odd numbers. the lowest numbers that Priyanka can get are:
= 1, 3, 5, 7
Assuming Priyanka picks 1 and 3 which are the lowet number, the total Priyanka would get i:
= 1 + 1 + 3 + 3
= 8
it is therefore not possible to get 6 points after 4 rounds of the game.
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find the surface area of a cylinder with height of 8 feet and base diameter of 6 feet
Answer:
[tex]66\pi[/tex] ft²
Step-by-step explanation:
First find the area of the rectangle surrounding the cylinder.
Since the base diameter is 6 feet, the circumference [tex]=\pi d=6\pi[/tex].
Since the height is 8 feet, the area of the rectangle is [tex]6\pi\times8[/tex] or [tex]48\pi[/tex]
Now the area of the base circle [tex]=\pi r^2 = \pi\times\frac{1}{4}d^2=9\pi[/tex]
There are 2 base circles, so [tex]9\pi\times2=18\pi[/tex]
Surface area = [tex]18\pi+48\pi=66\pi[/tex] ft²
Question
If h (x) = 10x, then for what value of x does h (x) = 100,000 ?
Answer:
x=10000
Step-by-step explanation:
A jar contains 11 brown and 18 blue marbles. A marble is drawn at random. What is the theoretical probability of NOT drawing a blue marble?
Answer:
come omo-tzzf-ivc In meet I will tell
A bag has green and purple marbles. Two-fifths of the marbles are green, and the rest are purple.
a. Draw a bar model for this situation.
b. If there are 134 green marbles, how many are purple?
The number of purple marbles in the bag are; 201 purple marbles
How to work out fraction of bar model?We are told that Two-fifths of the marbles are green, and the rest are purple.
A) The image attached shows the bar model where the shaded parts denote the purple marble while the unshaded parts denote the green marbles.
B) We are told that there are 134 green marbles.
If the total number of marbles are x. Then;
(2/5)x = 134
x = 134 * 5/2
x = 335 marbles
Thus;
Purple Marbles = (3/5) * 335 = 201 purple marbles
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14 points
Choose the correct graph of the given system of equations.
y − 2x = −1
x + 3y = 4
graph of two lines, one with a positive slope and one with a negative slope, that intersect at the point negative 1, 1 with text on graph that reads One Solution negative 1, 1
graph of two lines that intersect at the point 1, 1 with text on graph that reads One Solution 1, 1
graph of two parallel lines with positive slopes with text on graph that reads No Solution
The graph of the given system of equations is shown below
Graph of simultaneous linear equations
From the question, we are to graph the given system of equations.
The given system of equations are
y − 2x = −1
x + 3y = 4
The graph of the given system of equations is shown below
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The graph plots four equations. Which pair of equations has (4, 8) as its solution?
(see picture)
Answer:
B and D
Step-by-step explanation:
Both B and D cross over the point (4, 8) therefore they share the solution (4, 8)
Deepak is choosing a password for his phone using letters from the alphabet, A-Z. The password must be four letters long, and he can repeat letters. How many different passwords can he create?
Answer: 26 × 4
Step-by-step explanation: There are 26 letters in the alphabet lettered A through Z.
Deepak is given the choice of picking a four letter password of his liking, using any four letters. Since the letters he uses can be repeated, it is 26 * 4 possibilities, since there are 26 different possibilities of letters from the alphabet he could choose, for 4 times. Also, since letters can be repeated, 26 stays the same. If letters could not be repeated, it would be 26 * 25 * 24 * 23.
Answer:
B. 26⁴
Step-by-step explanation:
If the password is 4 letters long and he can repeat letters then:
1st letter: any one of the 26 letters from the alphabet2nd letter: any one of the 26 letters from the alphabet3rd letter: any one of the 26 letters from the alphabet4th letter: any one of the 26 letters from the alphabetTherefore, to find the total number of passwords he can create, simply multiply the number of permutations for each letter of his password:
⇒ 26 × 26 × 26 × 26 = 26⁴
The graph that correctly represents the given system of equations is graph , and the solution to the system is ( ,
what graph would it be, doing this on plato rn.
The question was incomplete. Below you will find the missing content.
Use the system of equations and graphs below to complete the sentence.
x - 2y = 5
3x + 15y = -6
The graph that correctly represents the given system of equations is a graph ( ), and the solution to the system is ( , ).
The correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).
Given the first equation is x-2y=5
in this equation of line, the x-coordinate is:
x-(2.0)=5
⇒ x=5
The x-coordinate will be (5,0).
in this equation of line, the y-coordinate is:
0- 2y=5
⇒y= -5/2
The y-coordinate will be (0,-5/2).
So the first line equation has x-coordinate (5,0) and y-coordinate (0,-5/2).
Similarly,
Given the second equation is 3x+15y=-6
in this equation of line, the x-coordinate is:
3x+(15.0)=-6
⇒ x=6/3=2
The x-coordinate will be (2,0).
in this equation of line, the y-coordinate is:
(3.0)+15y=-6
⇒y= -6/15= -2/5
The y-coordinate will be (0,-2/5).
So the second line equation has x-coordinate (2,0) and y-coordinate (0,-2/5).
Equation-1: x - 2y = 5
⇒x =2y+5
putting the value of x in equation-2
3x + 15y = -6
⇒ 3(2y+5)+15y=-6
⇒6y+15+15y=-6
⇒21y=-6-15=-21
⇒y=-21/21=-1
putting the value of y in equation of x
x= 2(-1)+5= -2+5= 3
The solution of system of equations will be (3,-1)
Checking all the options
In option B one line has x-coordinate (5,0) and y-coordinate (0,-5/2) and another line has x-coordinate (2,0) and y-coordinate (0,-2/5).
And the point of intersection of two lines is (3,-1).
Therefore the correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).
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Which equation can be used to calculate the surface area of the triangular prism net show below?
The net of a rectangular prism. The rectangular sides are 10 centimeters by 13 centimeters, 10 centimeters by 12 centimeters, and 10 centimeters by 5 centimeters. The triangular sides have a base of 5 centimeters and height of 12 centimeters.
[Not drawn to scale]
Surface Area = (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)
Surface Area = (one-half) (5) (13) + (one-half) (5) (13) + (13) (10) + (12) (10)
Surface Area = (2) (5) (13) + (5) (10) + (13) (10) + (12) (10)
Surface Area = (one-half) (5) (12) + (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)
The equation that can be used to calculate the surface area of the triangular prism net shown below is mathematically given as
SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)
Which equation can be used to calculate the surface area of the triangular prism net shown?Generally, The region or area that is occupied by the surface of any particular item is referred to as that object's surface area.
In conclusion, the equation surface area of the triangular prism will be one that accommodates all parameters
SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)
SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)
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What is the slope of the line that contains these points?
x: -7| -4 | -1 | 2
y: -7| 14 | 35 | 56
slope:?
The slope of the given line containing the given points is; 7.
How to Calculate the slope of a Line?
The formula for slope of a line between two coordinates is;
Slope(m) = (y2 - y1)/(x2 - x1)
Now, let us take the last 2 coordinates which are;
(-1, 35) and (2, 56).
Thus, the slope is;
m = (56 - 35)/(2 - (-1))
m = 21/3
m = 7
Thus, the slope of the given line containing the given points is 7.
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A company in its first year of business produced 150 training manuals for a total cost of $2.350. The following
year, the company produced 50 more manuals at a cost of $ 1,450. Use this information to find a linear equation
that gives the total cost of producing training manuals from the number of manuals produced.
Answer:
y = 9x +1000
Step-by-step explanation:
The relation for the total cost of manuals based on the number produced will be the sum of a base cost and a variable cost. The variable cost is the product of the cost per manual and the number of manuals.
Cost per manualThe cost per manual can be found by looking at the increase in cost relative to the increase in the number of manuals produced:
cost per manual = (increase in cost)/(increase in production)
= ($2350 -1450)/(150 -50) = $900/100 = $9
Base costThe base cost will be added to the product of the cost per manual and the number of manuals. For the 2nd year purchase, this is ...
$1450 = base cost + (50 manuals)×($9/manual)
$1450 = base cost + $450
base cost = $1450 -450 = $1000
EquationThe equation for the cost in dollars (y) of producing x manuals can now be described by ...
y = (cost per manual)x +(base cost)
y = 9x +1000
look at the picture
Answer:
i can't see the picture.
Hernandez Company issued $380,000, 7%, 10-year bonds on January 1, 2022, for $407,968. This price resulted in an effective-interest rate of 6% on the bonds. Interest is payable annually on January 1. Hernandez uses the effective-interest method to amortize bond premium or discount.
For calculation of the following entries, the bond interest expense will gotten by multiplying the carrying bond value by the market interest rate.
Journal entry to record issuance of the bonds
Date Account titles Debit Credit
Jan. 1. Cash $407,968
Bonds payable $380,000
Premium on bonds payable $27,968
($407,968 - $380,000)
Journal entry to record accrual of interest and the premium amortizationDate Account titles Debit Credit
Dec. 31. Bond interest expense $24,478
Premium bond payable $2,122
Bond interest payable $26,600
Journal entry to record payment of interestDate Account titles Debit Credit
Jan. 1. Bond interest payable $26,600
($380000 * 7%)
Cash $26,600
Missing words "Prepare journal entries to record (a) The issuance of the bonds, (b) The accrual of interest and the premium amortization on December 31, 2022 and (c) The payment of interest on January 1, 2022"
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You want to buy a $33,000 car. The company is offering a 3% interest rate for 36 months (3 years). What will your monthly payments be?
Answer:
$959.68
Step-by-step explanation:
The loan amortization formula can be used to find the payment amount.
FormulaA = P(r/n)/(1 -(1 +r/n)^(-nt))
A = payment amount; P = principal borrowed; r = annual interest rate; t = number of years; n = payments per year (and number of times interest is compounded per year).
ApplicationFor a principal amount of $33,000 at an interest rate of 3%, the 36 monthly payments will be ...
A = $33000(0.03/12)/(1 -(1 +0.03/12)^(-12·3)) ≈ $959.68
The monthly payments will be $959.68.
Use the table to the right to answer the following question.
Compare the energy released by fission of 1 kilogram of element B to that released by burning 1 kilogram of element A.
Fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A
How to compare the energy released?The given parameters are:
Energy A = 5.1 * 10^7
Energy B = 1.5 * 10^11
The amount of energy B in proportion to energy A is calculated as
Proportion = Energy B/Energy A
So, we have:
Proportion = (1.5 * 10^11)/(5.1 * 10^7)
Divide 1.5 by 5.1
Proportion = 0.2941 * 10^11/10^7
Divide 10^11 by 10^7
Proportion = 0.2941 * 10^4
Evaluate
Proportion = 2941
Hence, fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A
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Find the y-intercept of the line on the
graph.
Answer:
The y intercept is the point where the line crosses the y axis.
Step-by-step explanation:
A runner can run 3miles in minutes. At this rate, how many 15miles can he run in 45minutes?
15
Answer:
9
Step-by-step explanation:
I believe the question is stating he can run 3 miles in 1 minute? Though it does make sense, here's the breakdown. :)
3 x 45 = 135 Miles total
135 / 15 = 9 "15" miles ran after 45 minutes.
If this is not what you meant to ask, let me know!
You want to place stone pavers around the edge of your concrete patio. The patio is 12 ft wide by 14 ft long and each stone paver is 14 inches long . How many stone pavers will you need to go around the patio (not counting the side against the house which is 14 ft long)? (round to the nearest whole number )
33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
12 inch = 1 ft
Total perimeter of patio not counting the side against the house = 12 + 12 + 14 = 38 feet
38 feet = 38 feet * 12 inch per feet = 456 in
Number of stone pavers needed = 456 in / 14 in = 32.57 ≅ 33
33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long
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Pls help! Geometry
Find the area
Answer:
197.9
Step-by-step explanation:
find the area of the large circle and subtract the area of the small circle
area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
area of large circle = 144[tex]\pi[/tex]
area of small circle = 81[tex]\pi[/tex]
area of shaded region = 63[tex]\pi[/tex]
which is equal to about 197.9
A table blueprint uses the scale 3 inches :2 feet.If the model is 15 inches long how long is the table!!!!!HURRY
Answer:
I am pretty positive it is thirty if you need work shown just let me know if it is wrong for some reason then I apologize.
Step-by-step explanation:
If the model is 15 inches. Then the length of the table will be 10 feet.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
A table blueprint uses the scale 3 inches :2 feet.
The scale factor will be 2 feet: 3 inches.
If the model is 15 inches.
Then the length of the table will be
⇒ (2 feet/ 3 inches) x 15 inches
⇒ 2 x 5
⇒ 10 feet
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how high up a vertical wall will a 26-foot-long extension ladder reach if its base is placed 10 feet away from the wall
Answer:
24ft high
Step-by-step explanation:
Assuming the wall is perpendicular to the ground (so that it forms a right angle, and that when the ladder is placed on the ground and leaned up against the wall that it forms a right triangle), we can use the Pythagorean Theorem to describe the situation mathematically.
The Pythagorean TheoremFor any right triangle (a triangle that has a right angle) the Pythagorean Theorem applies. The Pythagorean Theorem describes the relationship between side lengths as [tex]a^2+b^2=c^2[/tex], where "c" is the length of the "hypotenuse" (the side across from the right angle), and "a" and "b" are the lengths of the "legs" (the other two sides that are touching the right angle). Since addition is commutative, it doesn't matter which leg you pick for side "a" or side "b", it only matters that the hypotenuse must be "c".
Given that the ladder is across from the right angle (the angle formed by the wall and the ground... the two "legs"), the ladder represents the hypotenuse in this situation.
Substituting known values, and solving the equation[tex]a^2+b^2=c^2[/tex]Substitute known values, and simplify...
[tex]a^2+(10)^2=(26)^2[/tex]
[tex]a^2+100=676[/tex]
Subtract 100 from both sides...
[tex](a^2+100)-100=(676)-100[/tex]
[tex]a^2=576[/tex]
Apply the square root property...
[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]
[tex]a=\pm 24[/tex]
[tex]a=24[/tex] or [tex]a=- 24[/tex]
Since the distance height the ladder will reach is not a negative number, we reject the negative solution. Hence, the ladder will reach 24ft high, if placed 10ft from the base of the wall.
Choose the function whose graph is given by:
5
OA. y= cos(x-1)
OB. y= sin(x+2)
OC. y=sin(x-2)
OD. y = sinx-2
Answer:
C.y=sin(x-2)
Step-by-step explanation:
Using the topic of transformation of functions(rules shown in picture above)
the the (x-2) moves the graph to places to the right
and as the sine graph goes through 0 and so you add 2 to the right (but there is a problem in the graph should in the picture as it should me labeled 0,90,180,270,360 not these small numbers)
hope it helps!! :)
I have two gold rings weighing 7.534g and 5,300 mg. Which is the heavier ring? By how much?
Answer:
7.534g ring is heavier, by 2.234g
Step-by-step explanation:
Note: mg =
[tex] {10}^{ - 3} grams[/tex]
[tex]5300mg = ( \frac{5300}{ {10}^{3} } )g \\ = ( \frac{5300}{1000} )g \\ = 5.3g[/tex]
From here we can see Ring A (7.534g) is heavier than Ring B(5,300mg)
Difference in Mass = 7.534g - 5.3g
= 2.234g
When flipping a fair coin 4 times in a row, which outcome is more likely: HTHT or HHHH.
Justify your answer
Answer:
See below
Step-by-step explanation:
equal probability each occurs 1 time out of 16 possibilities
tttt
ttth
ttht
tthh
thtt
thth
thhh
httt
htth
thth
htht
hthh
hhtt
hhth
hhht
hhhh
cual es el proceso de estas operaciones de :<, > o = ... porfavor
El uso de las dadas operaciones es:
a < b significa "a es menor que b"a > b significa "a es mayor que b"a = b significa "a es igual que b".¿Como utilizar las operaciones?Para las operaciones "<", ">", y "=" uso es:
a < b significa "a es menor que b"a > b significa "a es mayor que b"a = b significa "a es igual que b".Entonces simplemente debemos comparar los dos números, si vemos al primer problema, por ejemplo:
3 ___ 17/2
Sabemos que 17/2 = 8.5
8.5 es más grande que 3, entonces el signo que debe ir ahi es:
3 < 17/2.
Todas las operaciones que estan colocados en la hoja ya son correctos.
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what do both of these functions have in common? f(x)=3/2 (x-7) -2 g(x) = 1.5ln(x-2)+7
(x-7) should be absolute value of that.
Both the function have same vertical stretch of 1.5 , Option B is the correct answer.
What is a Function ?A function is a law that relates a dependent and an independent variable.
The functions given in the question is
f(x) = 3/2 |(x -7)| -2
g(x) = 1.5 ln(x-2)+7
For a function f(x)
f'(x) = a f(x) represents the stretching of a function if a> 1
here the value of a = 1.5 for both the functions , so they have same vertical stretch of 1.5 .
Therefore from the options given , Option B is the correct answer.
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Consider the following frequency table representing the scores on a test.
Scores on a Test
Class Frequency
20–29 9
30–39 4
40–49 3
50–59 2
60–69 10
Determine the number of scores between 19.5 and 49.5.
The number of scores between 19.5 and 49.5 using the cumulative frequency is 16.
What is the cumulative frequency?The cumulative frequency is the running total of frequencies over some class intervals.
The frequency refers to the number of elements in the set or class.
Therefore, the cumulative frequency is the sum of all previous frequencies up to the required point.
Data and Calculations:Scores on a Test
Class Frequency Cumulative Frequency
20–29 9 9 (0 + 9)
30–39 4 13 (9 + 4)
40–49 3 16 (13 + 3)
50–59 2 18 (16 + 2)
60–69 10 28 (18 + 10)
Thus, the number of scores between 19.5 and 49.5 using the cumulative frequency is 16.
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Exact volume:
Approximate volume:
Answer: Multiplying these factors gives the approximate volume of the original body
Step-by-step explanation:
The given convex body can be approximated by a sequence of nested bodies, eventually reaching one of known volume (a hypersphere), with this approach used to estimate the factor by which the volume changes at each step of this sequence.
Purdue has 1320 employees and plans to increase the number of employees by 20% each year. Is this linear or exponential? Which equation describes this situation?
Please Help!!!
Answer Quickly!!
The exponential function that describes the situation is:
[tex]A(t) = 1320(1.2)^t[/tex]
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.The parameters for this problem are:
A(0) = 1320, r = 0.2.
Hence the equation is:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 1320(1 + 0.2)^t[/tex]
[tex]A(t) = 1320(1.2)^t[/tex]
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