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3 years ago

Dustin has a collenction of quarters and pennies. The total value is $4.65. Th

Mathematics

1 answer:

Hitman42 [59]3 years ago

6 0

Answer:

Dustin has 18 quarters and 15 pennies.

Step By Step Solution:

(See image above)

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Alona [7]

$15

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3 years ago

Read 2 more answers

Find the midpoint between -7+4i and 3-2i

lana [24]

(-2,3) i believe this is correct

6 0

3 years ago

Hat is the solution to the system of equations?

Dima020 [189]

Answer:

(–19, 55)

Step-by-step explanation:

y = –3x – 2 equation 1

5x + 2y = 15 equation 2

using equation 1 in equation 2 we have:

5x + 2(–3x – 2) = 15

5x –6x – 4 = 15

-x = 15+4

x=-19

using equation 1:

y = -3(-19)- 2

y= 57-2

y= 55

5 0

3 years ago

Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert

Setler [38]

Answer:

$P(x \ge 5) = 1.000$ ---- At least 5 from marketing departments are extroverts

$P(x=15) = 0.013$ ---- All from marketing departments are extroverts

$P(x = 0) = 0.002$ ---------- None from computer programmers are introverts

Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$(a):\ P(x \ge 5)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

Using the complement rule, we have:

$P(x \ge 5) = 1 - P(x < 5)$

So, we have:

$P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)$

$P(x = 0) = ^{15}C_{0} * (75\%)^0 * (1 - 75\%)^{15 - 0} = 1 * 1 * (0.25)^{15} = 9.31 * 10^{-10}$

$P(x = 1) = ^{15}C_{1} * (75\%)^1 * (1 - 75\%)^{15 - 1} = 15* (0.75)^1 * (0.25)^{14} = 4.19 * 10^{-8}$

$P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}$

$P(x = 3) = ^{15}C_{3} * (75\%)^3 * (1 - 75\%)^{15 - 3} = 455* (0.75)^2 * (0.25)^{12} = 0.0000153$

$P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103$

So, we have:

$P(x < 5) = (9.31 * 10^{-10}) + (4.19 * 10^{-8}) + (8.80 * 10^{-7}) + 0.0000153 + 0.000103$

$P(x < 5) = 0.00011922283$

Recall that:

$P(x \ge 5) = 1 - P(x < 5)$

$P(x \ge 5) = 1 - 0.00011922283$

$P(x \ge 5) = 0.9998$

$P(x \ge 5) = 1.000$ --- approximated

$(b)\ P(x = 15)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x=15) = ^{15}C_{15} * 0.75^{15} * (1 - 0.75)^{15-15}$

$P(x=15) = 1 * 0.75^{15} * (0.25)^{0$

$P(x=15) = 0.013$

$(c)\ P(x = 0)$

$n=5$ ---------- computer programmers

$p = 70\%$ --- proportion that are introverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}$

$P(x = 0) = 1 * 1 * (0.30)^5$

$P(x = 0) = 0.002$

3 0

2 years ago

Which of the following accurately depicts the transformation of y= x^2 to the function shown below? y=2(x-3)^2+5

sweet [91]

Answer:

Which of the following accurately depicts the transformation of y= x^2 to the function shown below? y=2(x-3)^2+5

A. Shift left 3 units, shrink vertically to 1/2 of the original height, then shift up 5 units.

B. Shift right 3 units, stretch vertically by a factor of 2, then shift up 5 units.

C. Shift up 3 units, stretch horizontally by a factor of 2, then shift left 5 units.

D. Shift 5 units right, stretch vertically by a factor of 3, then shift up 2 units.

Step-by-step explanation:

For f(x) = 4x+1 and g(x)= x^2-5, find (f/g) (x).

6 0

3 years ago