For a recent evening at a small, old-fashioned movie theater, 35% of the moviegoers were female and 65% were male. There were two movies playing that evening. One was a romantic comedy, and the other was a World War II film. As might be expected, among the females the romantic comedy was more popular than the war film: 70% of the females attended the romantic comedy. Among the male moviegoers, the romantic comedy also was more popular: 60% of the males attended the romantic comedy. No moviegoer attended both movies. Let F denote the event that a randomly chosen moviegoer (at the small theater that evening) was female and ¯F denote the event that a randomly chosen moviegoer was male. Let R denote the event that a randomly chosen moviegoer attended the romantic comedy and ¯R denote the event that a randomly chosen moviegoer attended the war film. Fill in the probabilities below, and then answer the question that follows. Do not round any of your responses
P(F)=0.35
P(F and R)=
P(F and ¯R)=
P(¯R|F)=
P(R|¯F)=0.60
P(¯F and R)=
P(¯F and ¯R)=
P(¯F)=
What is the probability that a randomly chosen moviegoer attended the romantic comedy?

Answers

Answer 1

Answer:

[tex]P(F\ and\ R) = 0.21[/tex]

[tex]P(F\ and\ R^{-}) = 0.14[/tex]

[tex]P(R^{-}|F)= 0.40[/tex]

[tex]P(F^{-} and\ R) = 0.39[/tex]

[tex]P(F^{-}\ and\ R^{-}) =0.26[/tex]

[tex]P(F^{-}) =0.65[/tex]

Step-by-step explanation:

The variables have been defined in the question as:

[tex]F = Female\ Moviegoer[/tex]

[tex]F^{'} = Male\ Moviegoer[/tex]

[tex]R = Romantic\ Comedy[/tex]

[tex]R^{'} = War\ File[/tex]

Also, we have the following given parameters:

[tex]P(F) = 0.35[/tex]

[tex]P(F^{-}) =0.65[/tex]

[tex]P(R) =0.60[/tex]

[tex]P(R^{-}) = 0.40[/tex]

The solution is as follows:

[tex]a.\ P(F\ and\ R)[/tex]

[tex]P(F\ and\ R) = P(F) * P(R)[/tex]

Substitute values for P(F) and P(R)

[tex]P(F\ and\ R) = 0.35 * 0.60[/tex]

[tex]P(F\ and\ R) = 0.21[/tex]

[tex]b.\ P(F\ and\ R^{-})[/tex]

[tex]P(F\ and\ R^{-}) = P(F) * P(R^{-})[/tex]

Substitute values for P(F) and P(R-)

[tex]P(F\ and\ R^{-}) = 0.35 * 0.40[/tex]

[tex]P(F\ and\ R^{-}) = 0.14[/tex]

[tex]c.\ P(R^{-}|F)[/tex]

[tex]P(R^{-}|F)=\frac{P(R^{-}\ and\ F)}{P(F)}[/tex]

[tex]P(R^{-}|F)=\frac{P(R^{-})\ *\ P(F)}{P(F)}[/tex]

Substitute values for P(F) and P(R-)

[tex]P(R^{-}|F)=\frac{0.40 * 0.35}{0.35}[/tex]

[tex]P(R^{-}|F)= 0.40[/tex]

This implies that both events are independent

[tex]d.\ P(F^{-} and\ R)[/tex]

[tex]P(F^{-} and\ R) = P(F^{-}) * P(R)[/tex]

Substitute values for P(F-) and P(R)

[tex]P(F^{-} and\ R) = 0.65 * 0.60[/tex]

[tex]P(F^{-} and\ R) = 0.39[/tex]

[tex]e.\ P(F^{-}\ and\ R^{-})[/tex]

[tex]P(F^{-}\ and\ R^{-}) =P(F^{-}) * P(R^{-})[/tex]

Substitute values for P(F-) and P(R-)

[tex]P(F^{-}\ and\ R^{-}) =0.65 * 0.40[/tex]

[tex]P(F^{-}\ and\ R^{-}) =0.26[/tex]

[tex]f.\ P(F^{-})[/tex]

[tex]P(F^{-}) =0.65[/tex] --- Given


Related Questions

I save 100 a month to go to Tokyo and rent a hotel
Which costs 1,391 for a flight and 34 for a hotel
What is the constant rate of proportionality?

Answers

Answer:

the c.o.p is 14.25

Step-by-step explanation:


Based on the P's and Q's of this polynomial (The Rational Zero Theorem), which of the following could NOT be a zero of the polynomial 4x3 + 4x2 - 11x-6?

Answers

Answer:

4

Step-by-step explanation:

P are the factors of the last coefficient (6) and Q are the factors of the first coefficient (4). Since p is divided by q, we could have 3/1, 6/1, 2/1, and 1/1, but not 4/1 since 4 is not a factor of 6

Which of the following points are in the third quadrant of the xy-plane? Check
all that apply.

Answers

Answer: D and E

Step-by-step explanation:

The x and y-values in the 3rd quadrant are both negative.

Remember this:

1st quadrant- x= + y= +

2nd quadrant- x= - y= +

3rd quadrant- x= - y= -

4th quadrant- x= + y= -

Write a function formula for g using the function f.
g(x)=

Write a function formula for f using the function g.
f(x)=


Answers

Answer:

g(x) = -f(x+3)

f(x) = -g(x-3)

Step-by-step explanation:

Transformations

Function f can be obtained by knowing function g and vice-versa.

Suppose we know the expression of function f. If we reflect f across the x-axis, we get function g but displaced 3 units to the right.

Thus, we only have to translate the reflected f 3 units to the left:

g(x) = -f(x+3)

Similarly, if g(x) is reflected across the x-axis and translated by 3 units to the right, we get f(x), thus:

f(x) = -g(x-3)

Help!!! Just those two, please

Answers

A. Multiply the area of the original store by the percent increase then add that to the original amount.

1200 x 0.75 = 900

1200 + 900 = 2100

Answer: 2,100 square feet.

B. 2000 x 0.30 = 600

2000 + 600 = $2,600

2600 x 0.05 = 130

2600 + 130 = 2,730

Rent :$2,730

Which of the following slopes of a line passes through points (2, 3) and (4,7) ?
5
2
3
O

Answers

Answer:

2

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (7 - 3)/(4 - 2)

slope = 4/2 = 2

Answer: 2

Sad Ariana Grande Facts/Moments pt.2
Ariana preformed in Pittsburg, Mac millers hometown. Not only did they split up, but he passed. She sang Thank u, next (more emotional than you might think) and was in tears :( i cry inside when i see her like thissss

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awww that is so sweet!!

Two angles are complementary. The measure of the larger angle is LaTeX: 30^\circ30 ∘more than 4 times the measure of the smaller. Find the measure of both angles.

Answers

BI This year sucks and all but it wouldn’t be that bad if everyone just made themselves some bear shaped pancakes

pages in a book are numbered from 1 to 1001. How many times does the number 0 appear?

Answers

Answer:

192 times

Step-by-step explanation:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100  - 11 times

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125

126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175

176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200  - 31 times

201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225

226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250

251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275

276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300  - 51 times

301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325

326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350

351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375

376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400  - 71 times

401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425

426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450

451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475

476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500  - 91 times

501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525

526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550

551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575

576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600  - 111 times

601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625

626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650

651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675

676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700  - 131 times

701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725

726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750

751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775

776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800  - 151 times

801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825

826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850

851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875

876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900  - 171 times

901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925

926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950

951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975

976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000  - 192 times

What are the solutions?
y=k^2-16k-4

Answers

Answer:

y−k

​2

​​ +16k+4=0

2 Use the Quadratic Formula.

k=\frac{-16+2\sqrt{y+68}}{-2},\frac{-16-2\sqrt{y+68}}{-2}k=

​−2

​−16+2√

​y+68

​​  

​​ ,

​−2

​−16−2√

​y+68

​​  

​​  

3 Simplify solutions.

k=8-\sqrt{y+68},8+\sqrt{y+68}k=8−√

​y+68

​​ ,8+√

​y+68

​​  

Step-by-step explanation:

Jon invests $4,100 into an account that pays 5 percent simple interest each year. What is the total balance in the account after 3 years?

Answers

Answer:

615

Step-by-step explanation:

4100*3 then you have to multiply by the rate in decimal form which is 0.05!

Answer:

a.

Step-by-step explanation: if i’m wrong lmk

Use slope-intercept form, y= mx+b to find the equation of the line that passes through the points (-6,1) and (3,4).

Answers

The equation will be y=1/3+3

Sergio claims that 20/20 equals 1% . Which statement is true regarding his claim? A .Sergio is correct because 20/20 equals 1% B . Sergio is correct because 20 out of 20 represents 1 whole. C. Sergio is incorrect because 20/20 equals 100/100 D.Sergio is incorrect because the ratio simplifies to 0.

Answers

Step-by-step explanation:

Percentage = (20/20) * 100% = 100%.

Hence Sergio is incorrect because 20/20 equals 100/100, so it would be 100% instead of 1%. (C)

Answer:

Percentage = (20/20) * 100% = 100%.

Step-by-step explanation:

13. I have 22 nickels, dimes and quarters worth $3.45. There are twice as many quarters as nickels. Find the number of each coin.

Answers

Answer:

12 nickels 4 dimes 3 quaters

Step-by-step explanation:

what is 2 + 2= i need to know

Answers

4 :))))) hope this helps ya out
Explain:

Answer:

4 but what 1x1

Step-by-step explanation:

What is the greatest common factor for 12 and 54? enter your answer in the box.

Answers

Answer:

6

Step-by-step explanation:

Factors for 12: 1, 2, 3, 4, 6, 12

Factors for 54: 1, 2, 3, 6, 9, 18, 27, 54

It's 6.

The greatest common factor of the numbers 12 and 54 will be 6.

Given that:

Numbers, 12 and 54

The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The factors of the numbers 12 and 54 are calculated as,

12 = 2² x 3

54 = 2 x 3³

The value of the greatest common factor is calculated as,

GCF = 2 x 3

GCF = 6

More about the greatest common factor link is given below.

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As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than 10 hours per week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and
x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply.

Answers

Answer:the line x+y<10 has a negative slope and a positive y intercept

The line representing 20x+25y>200 is solid and the graph is shaded above line

The overlapping region contains the point (4,5)

Step-by-step explanation:

;)

Answer:

The answers are B, C, and E.

Step-by-step explanation:

I got it right on edge

For this problem we will use the complex numbers 3 - 6i and 9 + i
What is the conjugate of each complex number?



What is the sum of the complex numbers? Show all work.



What is the sum of the conjugates of the complex numbers? Show all work.

Answers

Conjugate is just changing the sign on the imaginary number, so the conjugates here are 3+6i and 9-i

The sum of the original complex numbers is (3-6i)+(9+i)=12-5i

The sum of the conjugates is (3+6i)+(9-i)=12+5i

PLS HELP I DONT UNDERSTAND :( WILL GIVE BRAINLIEST + 25 POINTS!!

Answers

Answer:

it is f

Step-by-step explanation:

The price of admission to the Everglades Historical Museum is $11 more for non-members than for members of the museum’s Friends of the Museum program.

If a group of 3 members and 4 non-members pays a total of $79 to visit the Museum, what is the cost, in dollars, of the ticket for one non-member?

Select one:
A. $9.00
B. $11.00
C. $15.00
D. $16.00

Answers

Answer:

d. $16.

Step-by-step explanation:

3 members (m) + 4 nonmembers (n) = $79

nonmembers = $11 more or n=m+11 so...

3m + 4(m+11)=79   [replace "n" with "m+11"]

3m + 4m + 44=79

7m + 44 = 79

7m=35 and reduced m=5 so members pay $5 and nonmembers pay 5+11=$16

If you have five red balls and five blue balls in a jar what’s the probability of the first ball being red?

Answers

Answer:

red balls = 5

blue balls = 5

total balls = 5 blue+5 red

= 10

[tex]p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls} [/tex]

[tex]p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2} [/tex]

Answer:

Step-by-step explanation:

Total number of red balls = 5

Total number of blue balls = 5

Total number of balls in jar = 5 + 5

                                             = 10

Probability of the first ball being red = total number of the red ball/total number of balls in the jar

                                                             = [tex]\frac{5}{10}[/tex]

                                                             = [tex]\frac{1}{2}[/tex]

Therefore, the probability of the first ball being red = [tex]\frac{1}{2}[/tex], 50% or 0.5 (in any way you are instructed to write it in)

Half a bottle of lemonade is shared between 3 friends . What fraction will each child get ?

Answers

Answer:

1/3

Step-by-step explanation:

i hope this helped !!!!!!!!!

1/6 fraction of bottle of lemonade will each friend gets.

What is Fraction?

A fraction represents a part of a whole.

Given,

Half a bottle of lemonade is shared between 3 friends .

Half means 1/2.

One divided by two is half.

This half is shared between three friends.

So we need to divide half by three of friends.

1/2/(3/1)

When a fraction is divided by another fraction, the denominator is multiplied as reciprocal to numerator.

1/2×1/3

1/6

Hence, 1/6 fraction of  bottle of lemonade will each friend gets.

To learn more on Fractions click:

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If 65% of students in a class like Mathematics, what percent of the students do not like Mathematics

Answers

Answer:

forty five percent 45% go for it

each package of paper contains 100 sheets. At the beginning of the school year, each of Mr.Castillo 's 34 students brought in one package of paper. How many sheets of paper did the students bring in altogether??

Answers

Answer:

3400

Step-by-step explanation:

Just multiply 100 by 34.

plz help! will give brainliest!!!

Answers

Answer:

c

Step-by-step explanation:

1) What is the constant of proportionality that relates y to x
х
Y
8
6
20
15
28
21
a. 1.33
6,48
0.0.75
b. 14
f

Answers

Answer:  The Answer Is A Because if u just add the numbers then divide them

Evaluate the function.

g(x)=10x+3

g(19.6)=

Answers

Answer:

199

Step-by-step explanation:

plug in x=19.6, then

g(19.6) = 10 * 19.6 +3= 199

______ an antiques dealer, paid $150 for a painting. She wants to sell the painting for
atleast 25 percent more than what she paid for it. Which of ___________ selling prices are atleast
25 percent more than the price the dealer paid for the painting?
______________ such selling prices

Answers

Answer:

plzzzzz

Step-by-step explanation:

lolzzzz

Answer:

25% of 150 is $37.50

Any dollar amount greater than or equal to $187.50 would be at least a 25% increase

Step-by-step explanation:

Given the side lengths of 20,23 and 41, determine whether the triangle is acute, right, obtuse, or not a triangle.

Answers

Answer:  Obtuse triangle

=====================================================

Explanation:

In this case, a triangle is possible since adding any two sides leads to a sum larger than the third side

20+23 = 43 is larger than 4120+41 = 61 is larger than 2323+41 = 64 is larger than 20

I'm using the triangle inequality theorem here.

----------------------------

To determine what kind of triangle we have, we'll use the converse of the Pythagorean theorem. Specifically, we'll use a corollary of it.

Consider a triangle with sides a,b,c. Let c be the longest side.

We have three possible cases:

If a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 > c^2, then the triangle is acute.If a^2+b^2 < c^2, then the triangle is obtuse.

For this problem, we have a = 20, b = 23, c = 41.

We see that a^2+b^2 = 20^2+23^2 = 929 and c^2 = 41^2 = 1681.

In short, a^2+b^2 = 929 and c^2 = 1681.

Since 929 < 1681, this means a^2+b^2 < c^2.

Therefore, this triangle is obtuse.

how do you find a slope

Answers

Answer:

rise/run

Step-by-step explanation:

rise meaning the y value, run meaning the x value

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