Answers
So, the correct statement will be:
To change the shape of a function you need to stretch or compress it.
Thus, option C is the correct answer.
Related Questions
Please help me with coordinates. IT'S DO IN 3 HOURS
Answers
Get graphs (standard X,Y graphs) and start placein the numbers in the following format (x,y) If they are negative, it will be placed to the left of the graph, if positive to the right of the graph
hey can you please help me posted picture of question
Answers
The original relation would be: [tex] x^{2} -2[/tex] with domain equal to the range of the given inverse and range equal to the domain of the given inverse.
The relation passes the vertical line test, so it will be a function. So the statement is true
A system with 6 independent components is such that the system will fail if at least one of the individual components fail. the probability that a component fails is 0.02. let a be the event that the system fails. what is the probability of a ?
Answers
[tex]\mathbb P(A)=\mathbb P(A_1\cup\cdots\cup A_6)=\mathbb P(A_1)\times\cdots\times\mathbb P(A_6)[/tex]
The [tex]A_i[/tex] are independent and identically distributed, so [tex]\mathbb P(A_i)=\mathbb P(A_j)[/tex] for all [tex]i,j[/tex]. So
[tex]\mathbb P(A)=\mathbb P(A_1)^6=0.02^6=6.4\times10^{-11}=0.000000000064[/tex]
What percent of 7 is 2?
Answers
Q # 2 please find the area
Answers
Hope this makes sense :)
area = 15 yd²
Explanation:
The area of the triangle can be calculated as follows:
area of triangle = 0.5 * base * height
In the given, we have:
base = 10 yd
height = 3 yd
Substitute with the givens in the above equation to get the area as follows:
area of triangle = 0.5 * 10 * 3 = 15 yd²
Hope this helps :)
Value of m varies directly as value of n and n=5 when m=12. What is n when m=18?
Answers
m = 12 & n = 5
m = 6 & n = 2.5 (divided each number by 20)
Now m is a factor of 18. Multiply each number by 3.
Answer: m = 18 & n = 7.5
hey can you please help me posted picture of question
Answers
y² = 64 -(x -2)²
y² = 64 -(x² -4x +4)
y² = -x² +4x +60
The answer is ...
D. y² = -x² +4x +60
twenty milligrams of the drug lincomycin is to be given for each kilogram of a person's weight. The drug is to be mixed with 250 cc of a normal saline solution, and the mixture is to be administered intravenously over a 1 hour period. Clyde Dexter, who weighs 196 lb, is to be given the drug. Determine the dosage of the drug he will be given?
Answers
To determine the dosage of lincomycin for Clyde Dexter, his weight is first converted to kilograms (88.9 kg), then the prescribed dosage of 20 mg/kg is applied, resulting in a required dosage of 1778 mg.
Explanation:To calculate the dosage of lincomycin for Clyde Dexter, we first need to convert his weight from pounds to kilograms. Knowing that there are approximately 2.20462 pounds in a kilogram, we can calculate his weight in kilograms. Following this, we will calculate the dosage of lincomycin required based on the prescribed 20 milligrams per kilogram of body weight.
Step 1: Convert Weight to Kilograms
Clyde’s weight in pounds: 196 lb
Conversion factor: 1 kg = 2.20462 lb
Clyde’s weight in kilograms: 196 lb / 2.20462 = 88.9 kg (approximately)
Step 2: Calculate Dosage
Prescribed dosage: 20 mg/kg
Clyde's weight: 88.9 kg
Required dosage of lincomycin: 88.9 kg * 20 mg/kg = 1778 mg
The calculated dosage of lincomycin for Clyde Dexter, based on his body weight, is therefore 1778 mg. This dose is to be mixed with 250 cc of normal saline solution and administered intravenously over a 1 hour period.
Factor completely.
3x squared + 2xy - y squared
Answers
[tex]3 x^{2} +2xy- y^{2} \\ \\ 3 x^{2} +3xy-xy- y^{2} \\ \\ 3x(x-y)-y(x-y) \\ \\ (x-y)(3x-y) [/tex]
Carlos has $50 in his savings account. He deposits $100 on his birthday, and then another $25 every month. Which equation can be used to find the number of months it would take him to reach a balance of $500? Let m = number of months.
Answers
Before one month, you will know that Carlos has a minimum of $150, because he deposited $100 to his already $50 account. The following equation is true: [FILL] $500 = 25m + $150
Have a wonderful day, and may God bless you! :D
Answer:
[tex]150+25m = 500[/tex]
Step-by-step explanation:
Given : Carlos has $50 in his savings account. He deposits $100 on his birthday, and then another $25 every month.
To Find: Which equation can be used to find the number of months it would take him to reach a balance of $500?
Solution:
Carlos has $50 in his savings account.
He deposits $100 on his birthday.
Let m be the number of months
He save $25 every month
So, he saves in x months = 25 m
Now wants to reach a balance of $500.
So, equation becomes:[tex]50+100+25m = 500[/tex]
:[tex]150+25m = 500[/tex]
Hence Equation can be used to find the number of months it would take him to reach a balance of $500 is [tex]150+25m = 500[/tex]
Can someone help me with this problem? please explain.
Answers
You have weight (5.76 pounds) and density (0.08 pounds/in³). The units of volume (in³) are in the denominator of the density, but we want them in the numerator of a number that gives the volume of the brick. At the same time, we want to cancel units of pounds. We can do all that by dividing weight by density.
volume = weight/density
volume = (5.76 pounds)/(0.08 pounds/in³) = (5.76/0.08) in³ = 72 in³
We know the volume of a rectangular prism (brick) is given by the product of its length, width, and height. We now have enough information to find the height.
volume = length*width*height
72 in³ = (8 in)*(2.25 in)*height . . . . . substitute known numbers
72 in³/((8*2.25) in²) = height . . . . . .. solve for height
72/18 in = height = 4 in . . . . . . . . . . . do the arithmetic. (in³)/(in²) = in
The height of the brick is 4 inches.
A multivitamin tablet contains 16.5mg of calcium. How much calcium does a bottle of 20 tablets contain
Answers
Final answer:
To find the total calcium in a bottle of 20 tablets, multiply the calcium content of one tablet (16.5 mg) by the number of tablets (20), resulting in 330 mg of calcium in the entire bottle.
Explanation:
To calculate the total amount of calcium in a bottle of 20 multivitamin tablets, you simply multiply the amount of calcium in one tablet by the number of tablets. If one tablet contains 16.5mg of calcium, the total amount of calcium in a bottle can be found with the following calculation:
Total amount of calcium = Amount of calcium per tablet × Number of tablets
Total amount of calcium = 16.5 mg/tablet × 20 tablets = 330 mg
So, a bottle of 20 tablets contains 330 mg of calcium.
Can you guys please help me posted picture of question
Answers
Number of outcomes from the spinner = 8
First we have to draw the 6 leaves to represent the 6 outcomes of rolling the die. Next on each of these leaves 8 possible outcomes of the spinner will be drawn using leaves.
So 6 leaves are being divided into further 8 leaves.
Thus total number of leaves will be = 6 x 8 = 48 leaves
Therefore, the correct answer is option D
A brother and a sister are in the same math class. There are 8 boys and 10 girls in the class. One boy and one girl are randomly chosen. What is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form.
Answers
[tex] |\Omega|=8\cdot10=80\\ |A|=1\\\\ P(A)=\dfrac{1}{80} [/tex]
Use the information to answer the questions. In triangle ABC, a = 11 in., m
Answers
m<B=70, and c=9 in. Which information about the triangle is given.
======================================================
Solution:
Given the following:
a = 11 in , ∠B = 70° , c = 9 in
The given information can be used in the cosine law.
Which is ⇒⇒⇒ b² = a² + c² - 2 a c * cos (B)
The correct answer is the third option.
A farmer wishes to build a rectangular plot with 800 meters of wire fencing. use calculus to find the maximum area that can be enclosed by the fence
Answers
200²=40 000 m²
Answer:
40,000 meters squared
Step-by-step explanation:
Find the optimum and constraint equations. (They are just fancy terms for the two equations you need).
The Constraint is 2x + 2y= 800 (As the plot is a normal rectangle and there is 800 m to make a fence, you would use the perimeter formula for a rectangle)
The optimum is xy= A. The area equals length times width (or in this case) xy.
You will need to plug in the simplified constraint into the optimum.
2y= -2x + 800 (divide by two next)
y= -x + 400
Plug in this to the Optimum
x(-x + 400)
this equals -xsquared + 400x
Find the derivative of it
-2x plus 400
Set it equal to )
x=200, this is only one of the lengths of the side.
In order to find the other, plug in x=200 to the constraint
-x + 400
-200 + 400
y = 200 also
So, going back to the Optimum 200 times 200 equals 40,000.
This means that the maximum area is in fact 40,000 meters squared.
find the solution of this system of equation 8x-4y=-32 -3x 4y=42
Answers
simplify the expression (-5)2. -10 10 -25 25
Answers
_____
There are an even number of negative factors, so the result is positive.
Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose money on the deal. Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. Based on this information, which system of inequalities could be used to determine how many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?
Answers
30 + 5x
Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. So the total charges at Movie Time for x movies will be:
25 + 6x
Anna wants her plan to her amount y which is more than Movie Time but Less than Movie Mania. So we can set up the equation as:
Cost at Movie Time < y < Cost at Movie Mania
Using the values, we can write:
25 + 6x < y < 30 + 5x
Using this system of inequalities Anna can determine how many movies need to be rented for a customer on her plan
Answer:D. y<5x+30/x
y>6x+25/x
Step-by-step explanation:
got right on edmentum
what is the first 10000 numbers of pi
Answers
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959 5082953311 6861727855 8890750983 8175463746 4939319255 0604009277 0167113900 9848824012 8583616035 6370766010 4710181942 9555961989 4676783744 9448255379 7747268471 0404753464 6208046684 2590694912 9331367702 8989152104 7521620569 6602405803 8150193511 2533824300 3558764024 7496473263 9141992726 0426992279 6782354781 6360093417 2164121992 4586315030 2861829745 5570674983 8505494588 5869269956 9092721079 7509302955 3211653449 8720275596 0236480665 4991198818 3479775356 6369807426 5425278625 5181841757 4672890977 7727938000 8164706001 6145249192 1732172147 7235014144 1973568548 1613611573 5255213347 5741849468 4385233239 0739414333 4547762416 8625189835 6948556209 9219222184 2725502542 5688767179 0494601653 4668049886 2723279178 6085784383 8279679766 8145410095 3883786360 9506800642 2512520511 7392984896 0841284886 2694560424 1965285022 2106611863 0674427862 2039194945 0471237137 8696095636 4371917287 4677646575 7396241389 0865832645 9958133904 7802759009 9465764078 9512694683 9835259570 9825822620 5224894077 2671947826 8482601476 9909026401 3639443745 5305068203 4962524517 4939965143 1429809190 6592509372 2169646151 5709858387 4105978859 5977297549 8930161753 9284681382 6868386894 2774155991 8559252459 5395943104 9972524680 8459872736 4469584865 3836736222 6260991246 0805124388 4390451244 1365497627 8079771569 1435997700 1296160894 4169486855 5848406353 4220722258 2848864815 8456028506 0168427394 5226746767 8895252138 5225499546 6672782398 6456596116 3548862305 7745649803 5593634568 1743241125 1507606947 9451096596 0940252288 7971089314 5669136867 2287489405 6010150330 8617928680 9208747609 1782493858 9009714909 6759852613 6554978189 3129784821 6829989487 2265880485 7564014270 4775551323 7964145152 3746234364 5428584447 9526586782 1051141354 7357395231 1342716610 2135969536 2314429524 8493718711 0145765403 5902799344 0374200731 0578539062 1983874478 0847848968 3321445713 8687519435 0643021845 3191048481 0053706146 8067491927 8191197939 9520614196 6342875444 0643745123 7181921799 9839101591 9561814675 1426912397 4894090718 6494231961
5679452080 9514655022 5231603881 9301420937 6213785595 6638937787 0830390697 9207734672 2182562599 6615014215 0306803844 7734549202 6054146659 2520149744 2850732518 6660021324 3408819071 0486331734 6496514539 0579626856 1005508106 6587969981 6357473638 4052571459 1028970641 4011097120 6280439039 7595156771 5770042033 7869936007 2305587631 7635942187 3125147120 5329281918 2618612586 7321579198 4148488291 6447060957 5270695722 0917567116 7229109816 9091528017 3506712748 5832228718 3520935396 5725121083 5791513698 8209144421 0067510334 6711031412 6711136990 8658516398 3150197016 5151168517 1437657618 3515565088 4909989859 9823873455 2833163550 7647918535 8932261854 8963213293 3089857064 2046752590 7091548141 6549859461 6371802709 8199430992 4488957571 2828905923 2332609729 9712084433 5732654893 8239119325 9746366730 5836041428 1388303203 8249037589 8524374417 0291327656 1809377344 4030707469 2112019130 2033038019 7621101100 4492932151 6084244485 9637669838 9522868478 3123552658 2131449576 8572624334 4189303968 6426243410 7732269780 2807318915 4411010446
Answer:
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 38095 25720 10654 85863 27886 59361 53381 82796 82303 01952 03530 18529 68995 77362 25994 13891 24972 17752 83479 13151 55748 57242 45415 06959 50829 53311 68617 27855 88907 50983 81754 63746 49393 19255 06040 09277 01671 13900 98488 24012 85836 16035 63707 66010 47101 81942 95559 61989 46767 83744 94482 55379 77472 68471 04047 53464 62080 46684 25906 94912 93313 67702 89891 52104 75216 20569 66024 05803 81501 93511 25338 24300 35587 64024 74964 73263 91419 92726 04269 92279 67823 54781 63600 93417 21641 21992 45863 15030 28618 29745 55706 74983 85054 94588 58692 69956 90927 21079 75093 02955 32116 53449 87202 75596 02364 80665 49911 98818 34797 75356 63698 07426 54252 78625 51818 41757 46728 90977 77279 38000 81647 06001 61452 49192 17321 72147 72350 14144 19735
Step-by-step explanation:
i cant add the rest
Which polynomial represents the difference below?
Answers
Correct answer is B.
The difference between given two polynomials is [tex](- x^{2} + 12x + 3)[/tex].
What is a polynomial?"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."
Given two polynomials are [tex](5x^{2} + 9x + 3)[/tex] and [tex](6x^{2} - 3x)[/tex].
Therefore, the difference between these two polynomials
[tex]= (5x^{2} + 9x + 3) - (6x^{2} - 3x)\\= (5x^{2} - 6x^{2}) + (9x + 3x) + 3\\= - x^{2} + 12x + 3[/tex]
Learn more about polynomial here:
https://brainly.com/question/21610884
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Name the pattern block used to cover 1 third of the hexagon
Answers
See the attached figure
By sketching a hexagon and dividing it to 3 equal shapes.
we will shading one of the 3 equal shapes.
So, the shaded area is a parallelogram with equal sides which is called rhombus
The correct answer is:
The pattern block used to cover 1 third of the hexagon is rhombus
WHAT IS 1/3 OF 97.50
Answers
1. A line passes through the ordered pairs (7,2) and (5,4). What is the slope? please show work
2. A sphere has a diameter od 20 cm. What would be the volume of sphere?
Answers
since the sphere has a diameter of 20, its radius is half that, or 10.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ r=10 \end{cases}\implies V=\cfrac{4\pi (10)^3}{3}[/tex]
Two cars leave at the same time from points A and B, the distance between them is 280 km. If the cars meet each other, they’ll meet in 2 hours. But if they go in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of both of the cars?
Answers
[tex]2x + 2y = 280[/tex]
[tex]14x - 14y = 280[/tex]
x represents car A's speed, and y represents car B's speed.
We'll use elimination to solve this system of equations. Multiply the first equation by 7:
[tex](2x + 2y = 280) * 7 = 14x + 14y = 1960[/tex]
[tex]14x - 14y = 280[/tex]
Combine both equations:
[tex]28x = 2240[/tex]
Divide both sides by 28 to get x by itself:
[tex]x = 80[/tex]
The speed of car A is 80 mph.
Since we now know the value of one of the variables, we can plug it into the first equation:
[tex]2(80) + 2y = 280[/tex]
[tex]160 + 2y = 280[/tex]
Subtract 160 from both sides.
[tex]2y = 120[/tex]
Divide both sides by 2 to get y by itself:
[tex]y = 60[/tex]
The speed of car B is 60 mph.
Hey can you please help me posted picture of question
Answers
F(x)= (x-1)^2+3
First the graph is shifted right by 1 unit which can be expressed as:
(x - 1)²
Next the function is shifted up by 3 units, so the final function can be expressed as:
F(x) = (x - 1)² + 3
So, the correct answer is option B
Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2
Answers
[tex]u(x,y)=xy[/tex]
[tex]v(x,y)=\dfrac xy[/tex]
The Jacobian for this transformation is
[tex]\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}[/tex]
and has a determinant of
[tex]\det\mathbf J=-\dfrac{2x}y[/tex]
Note that we need to use the Jacobian in the other direction; that is, we've computed
[tex]\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}[/tex]
but we need the Jacobian determinant for the reverse transformation (from [tex](x,y)[/tex] to [tex](u,v)[/tex]. To do this, notice that
[tex]\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}[/tex]
we need to take the reciprocal of the Jacobian above.
The integral then changes to
[tex]\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\frac12\int_{v=}^{v=}\int_{u=}^{u=}\frac{e^u}v\,\mathrm du\,\mathrm dv=\frac{(e^4-e)\ln2}2[/tex]
The population standard deviation of the numbers 3, 8, 12, 17, and 25 is 7.563 correct to 3 decimal places. what happens if each of the five numbers is multiplied by 3
Answers
Step One
Find the new five numbers.
3*3, 8*3, 12*3, 17*3, 25*3
9 , 24 , 36, 51, 75
Step 2
Find the average
(9 + 24 + 36 + 51 + 75)/5 = 195/5 = 39
Step 3
Subtract the individual numbers from the average
(39 - 9) = 30
(39 -24) = 15
(39 - 36) = 3
(39 - 51) = - 12
(39 - 75) = -36
Step 4
Square the results from Step 3
30^2 = 900
15^2 = 225
3^2 = 9
(-12)^2 = 144
(-36)^2 = 1296
Step 5
Take the average of the results from step 4
(900 + 225 + 9 + 144 + 1296)/5
2574 / 5 = 514.8
Step 6
Take the square root of the result from step 5
deviation = sqrt(514.8)
deviation = 22.689
Step seven
Compare the two standard deviations.
s2/s1 = 22.689 / 7.563 = 3
Conclusion
If you are given 1 set of numbers to find a population standard deviation and you multiply each member by a, then the result will be a * the standard population deviation of the first set of numbers.
Note
Your calculator will do this as well, but you have to know how to enter the data into your calculator. That requires that you follow the directions carefully.
Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. what is the probability that in a randomly selected hour the number of watches produced is greater than 500
Answers
z=(x-μ)/σ
where:
x=500
μ=500
σ=100
thus
z=(500-500)/200=0
Thus:
P(x>500)=1-P(x<500)=1-P(z<0)=1-0.5=0.5
Answer: 0.5~50%
Answer: 0.5
Step-by-step explanation:
Given : The number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100.
i.e. [tex]\mu = 500\text{ and } \sigma= 100[/tex]
Let x be the number of watches produced every hour.
Then, the probability that in a randomly selected hour the number of watches produced is greater than 500 will be :
[tex]P(x>500)=1-P(x\leq500)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{500-500}{100})\\\\=1-P(z\leq0)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.5\ \ [\text{ By z-table}]\\\\=1-0.5=0.5[/tex]
Hence, the probability that in a randomly selected hour the number of watches produced is greater than 500 =0.5.
37% of a certain country's voters think that it is too easy to vote in their country. you randomly select 12 likely voters. find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.
Answers
The probability that the number of likely voters who think that it is too easy to vote is:
a) exactly three = 0.17422
(b) at least 4 = 0.70533
(c) less than eight = 0.96406
How to use binomial probability theorem?
The general formula for binomial probability theorem is:
P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾
Where:
n = 12
p = 0.37
(a) exactly three,
P(x = 3) = ¹²C₃ * 0.37³ * 0.93⁹
= 0.17422
(b) at least 4,
P(4 ≤ x ≤ 12) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)
= 0.70533
(c) less than eight.
P(x < 8) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)
= 0.96406