Ask question

Ask question

All categories

miss Akunina [59]

2 years ago

5

A garden table and a bench cost $450 combines. The cost of the garden table is two times the cost of the bench. What is the cost

of the bench?

1 answer:

nordsb [41]2 years ago

5 0

Answer:

150

Step-by-step explanation:

You might be interested in

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 is equivalent to sec2θ−1sec2θ for all values of θ for which sec2θ−1sec2θ is defined?

galina1969 [7]

Answer:

$2 sin^2 \theta$

Step-by-step explanation:

According to the scenario, the following information is given:

$= \frac{sec^2 \theta - 1 }{sec^2 \theta}$

$= (\frac{1}{\frac{cos^2\theta}{\frac{1}{cos^2\theta} }} - 1)$

$= 1 - cos^2\theta\\\\= 1 - (1 - 2 sin^2 \theta)\\\\= 2 sin^2 \theta$

Therefore for the given equation, the answer is $2 sin^2 \theta$

5 0

2 years ago

Solve the following equation by factoring. <br><br> 2x2−7x+3=0

slava [35]

Answer:

x=3

Step-by-step explanation:

Step 1: Factor left side of equation.

(2x−1)(x−3)=0

Step 2: Set factors equal to 0.

x−3=0

ANSWER:

x=3

8 0

3 years ago

Can someone help me with this Please

horrorfan [7]

Answer:

314 cm²

Step-by-step explanation:

To find the area of a circle, use the formula A = πr² by substituting r = 10.

A = πr² = π10² = 314 cm²

8 0

3 years ago

Find the area of the figure below

tatuchka [14]

Step-by-step explanation:

(3×6) + (2×6)

= 18 + 12

= 30 in²

4 0

2 years ago