Let T be the event that an adult admits to texting while driving and N be the event an adult does not admit to texting while driving. We previously determined
P(T) = 0.61
and
P(N) = 0.39.
Since three adults are chosen randomly, we have the following simple events.
TTT TTN TNT NTT TNN NTN NNT NNN
The adults were randomly selected, indicating these can be seen as independent events. Therefore, the multiplication rule can be used. Recall the multiplication rule states that for independent events, the probability that they all occur is the product of their respective probabilities. Let x be the number of adults who admit to texting while driving. Since three adults are randomly selected, then x can take on the values 0, 1, 2, or 3.
When x = 0, then no adult in the group of three admits to texting while driving. This corresponds to the simple event NNN whose probability is calculated as below.
P(x = 0) = P(NNN)
= P(N)P(N)P(N)
= 0.39(0.39)(0.39)
=
When x = 1, then only one adult in the group admits to texting while driving. This corresponds to the simple events TNN, NTN, and NNT. First, calculate the probability of each simple event by multiplying the individual probabilities. Then sum the three simple events to find
P(x = 1).
Calculate
P(x = 1).
P(x = 1) = P(TNN) + P(NTN) + P(NNT)
= P(T)P(N)P(N) + P(N)P(T)P(N) + P(N)P(N)P(T)
= 0.61(0.39)(0.39) + 0.39(0.61)(0.39) + 0.39(0.39)(0.61)
=
Find the remaining probabilities
P(x = 2)
and
P(x = 3).
P(x = 2) = P(TTN) + P(TNT) + P(NTT)
= P(T)P(T)P(N) + P(T)P(N)P(T) + P(N)P(T)P(T)
= 0.61(0.61)(0.39) + 0.61(0.39)(0.61) + 0.39(0.61)(0.61)
=
P(x = 3) = P(TTT)
= P(T)P(T)P(T)
= 0.61(0.61)(0.61)
=

Answer:

Step-by-step explanation:

On the graph of two inequalities, solution of two inequalities is defined by the common shaded area.

That means all the points which lie in this area will satisfy both the inequalities.

From the graph attached,

Points given in the options (0, 0), (0, -1) and (1, 1) are not lying in the solution area.

Since, ordered pair given in 4th option is not clear in the picture, Option (4) may be the answer.

Answer:

1.25. It would be 1.25 if ur just talking about dividing in general which is pretty tough

Answer:

\dfrac54=-4c+\dfrac14 4 5 ​ =−4c+ 4 1 ​ start fraction, 5, divided by, 4, end fraction, equals, minus, 4, c, plus, start fraction, 1, divided by, 4, end fraction

Step-by-step explanation:

Answer:

Part 1)

10,000 different numbers.

Part 2)

A) 1 in 10,000.

Step-by-step explanation:

Part 1)

Since there are four digits and there are ten choices for each digit (0 - 9) and digits can be repeated, then we will have:

[tex]T=\underbrace{10}_{\text{Choices For First Digit}}\times\underbrace{10}_{\text{Second Digit}}\times\underbrace{10}_{\text{Third Digit}}\times \underbrace{10}_{\text{Fourth Digit}} = 10^4=10000[/tex]

Thus, 10,000 different numbers are possible.

Part 2)

Since there 10,000 different tickets possible, the chance of one being the correct combination will be 1 in 10,000.

This is equivalent to 0.0001 or a 0.01% chance of winning.

Answer:

Question 1: x = 6

Question 2: Correct!

Question 3: x = 11

Question 4: Correct!

Step-by-step explanation:

Question 1:

Angle 22x - 2 DOESN'T equal 50 degrees. Only Alternate Interior Angles will equal each other. These two angles are Same Side Interior Angles, meaning if you added them together, they would equal 180 degrees.

Knowing that adding 22x - 2 and 50 will equals 180 degrees, here's how we solve for x:

First, subtract 50 from 180 to find what angle 22x - 2 will equal:

180 - 50 = 130

130 = 22x - 2

Now use basic algebra to solve for x:

130 = 22x - 2

(add 2 to both sides)

132 = 22x

(divide both sides by 22)

x = 6

Question 3:

Angle 5x + 15 DOESN'T equal 9x + 11. They make up a line, which is 180 degrees, so they are supplementary angles.

With that in mind, to solve for x, add the two equations and set it equal to 180:

5x + 15 + (9x + 11) = 180

Now use basic algebra to solve for x:

5x + 15 + 9x + 11 = 180

(add like terms)

14x + 26 = 180

(subtract 26 from both sides)

14x = 154

(divide 14 from both sides)

x = 11

Hope it helps (●'◡'●)

Answer:

37 buses and 1 van.

Step-by-step explanation:

The cost to rent a van is $1200 for 50 students and 3 chaperones, while a bus for 10 students and a chaperone is $100 .

The cost of renting buses for 50 students is $500

What we do is rent 37 buses and 1 van

37 buses will take in 370 students with empty 2 spaces in 2 buses for chaperones since the chaperones are 36.

Then rent 1 van to take in 50 students and 1 chaperone.

The total cost here will be

$3700 + $1200 = $ 4900

This will help to safe cost.

Answer:

0.96784

Step-by-step explanation:

17-13.3/2

=1.85

p(x<1.85)

=0.96784

The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.

Mean [tex]\mu[/tex]=13.3 minutes

Standard deviation[tex]\sigma[/tex]=2 minutes

The value of the z-score tells you how many standard deviations you are away from the mean.

So, the z-score of the above data

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{17-13.3}{2}[/tex]

[tex]z=1.85[/tex]

From the standard normal table, the p-value corresponding to z=1.85

Or, p(x<1.85)=0.9678 or 96.78%

Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.

To get more about the z-score visit:

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Answer:

  A. 5 should have been subtracted in step 4

Step-by-step explanation:

No question is stated, so there is no "answer."

__

If we assume the question is, "What error did Keith make?" then choice A properly describes it.

Step 4 should look like ...

  x -5 = 7y . . . . . . . 5 should be subtracted from both sides

and the final result should be ...

  g(x) = (x -5)/7

Answer:

Choosing a card randomly and noting its suit

Step-by-step explanation:

Choosing a card randomly and noting its suit

This is because binomial distributions only work for bernoulli trials (a trail in which there are only two outcomes)

Answer:

2424.5

904.16

Step-by-step explanation:

the mean = ∑frequency /n

∑f = 5+17+36+115+125+81+47+45+22+7 = 500

∑xf = 1212250

∑x²f = 3347037625

sample mean = 1212250/500

= 2424.5

variance = 1/500-1[3347037625 - 1212250²]

= 815710.02

standard deviation is = √variance

standard deviation = √815710.02

= 904.16

Answer: (f-g)(x) = - 5^x + 3x - 2

Step-by-step explanation:

if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)

(f-g)(x) = -5^x - 4 - (-3x - 2)

(f-g)(x) = -5^x - 4 + 3x + 2

(f-g)(x) = - 5^x + 3x - 2

Answer:

(a) 3178

(b) 14231

(c) 33152

Step-by-step explanation:

Given

[tex]y = \frac{269573}{1+985e^{-0.308t}}[/tex]

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*8}}[/tex]

[tex]y = \frac{269573}{1+985e^{-2.464}}[/tex]

[tex]y = \frac{269573}{1+985*0.08509}[/tex]

[tex]y = \frac{269573}{84.81365}[/tex]

[tex]y = 3178[/tex] --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*13}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.004}}[/tex]

[tex]y = \frac{269573}{1+985*0.01824}[/tex]

[tex]y = \frac{269573}{18.9664}[/tex]

[tex]y = 14213[/tex] --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

[tex]y = \frac{269573}{1+985e^{-0.308*16}}[/tex]

[tex]y = \frac{269573}{1+985e^{-4.928}}[/tex]

[tex]y = \frac{269573}{1+985*0.00724}[/tex]

[tex]y = \frac{269573}{8.1314}[/tex]

[tex]y = 33152[/tex] --- approximated

Answer:

9:2

Step-by-step explanation:

Answer:

mean life = 8264.5 s

Step-by-step explanation:

k = - 0.000121

The relation is given by

[tex]m = mo e^{kt}[/tex]

Now, the mean life is the life time for which the sample retains.

The mean life is the reciprocal of the decay constant.  

The relation between the mean life and the decay constant is

[tex]\tau =\frac{1}{k}\\\\\tau = \frac{1}{0.000121} = 8264.5 seconds[/tex]

Answer:

Yes.

Step-by-step explanation:

.

Answer:

64 Bottles

Step-by-step explanation:

that is the procedure above

Answer:

x = 22

Step-by-step explanation:

In order to solve this, we need to understand that in an isosceles triangle the two angles that are located at its base are equal to each other.

base - (the side that is not one of the two sides that are equivalent to each other)

Knowing this we can see that ∠ACB will equal ∠BAC, therefore ∠ACB will be equal to x°. Since the sum of all inner angles of a triangle is equal to 180°, we can make the following equation...

x° + x° + (3x + 70)° = 180°

2x° + 3x° + 70° = 180°

5x° = 180° - 70°

5x° = 110°

x° = 110° / 5

x° = 22°

x = 22

Therefore, x = 22.

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Answer:

  6,364.8 lb

Step-by-step explanation:

The centroid of the plate is its center, so is 1.5 ft above the bottom of the pool, or 8.5 ft below the surface. The area of the plate is (3 ft)(4 ft) = 12 ft². Then the fluid force is ...

  (62.4 lb/ft³)(8.5 ft)(12 ft²) = 6,364.8 lb

Answer:

0.7513 = 75.13% probability that no more than 1 employee was over 50

Step-by-step explanation:

The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4 + 16 = 20 employees, which means that [tex]N = 20[/tex]

4 over 50, which means that [tex]k = 4[/tex]

5 were dismissed, which means that [tex]n = 5[/tex]

What is the probability that no more than 1 employee was over 50?

Probability of at most one over 50, which is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]

[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]

0.7513 = 75.13% probability that no more than 1 employee was over 50

Answer:

B

Step-by-step explanation:

(6)^1/2 × (8)^1/2

6^1/2 × 2 (2)^1/2

4 (3)^1/2

Answer:

Volume = 63 feet

Step-by-step explanation:

To find the volume of a cube or a rectangular prism, the formula is

(L x W x H)/3. In other words, it is the length of the prism, times the width of the prism, times the height of the prism, whole divided by three, since it has a "triangular shape."

Let's substitute in values for these letters, L, W, and H. You said the length was 7, the width was 6, and the height was 4.5. Therefore, it will result in

(7 x 6 x 4.5)/3. That results in 189/3, which is 63.

Hope this helped!!!

Answer:

Plastic is 22.5 pounds and aluminum is 32.5 pounds.

Step-by-step explanation:

total junk = 55 pounds

Value of plastic = $ 1.60 per pound

Value of aluminum = $ 1.28 per pound

Total value= $ 77.60

Let the plastic is p and the aluminum is 55 - p.

Total cost

77.60 = 1.6 p + (55 - p) x 1.28

77.60 =  1.6 p + 70.4 - 1.28 p

7.2 = 0.32 p

p = 22.5 pounds

So, plastic is 22.5 pounds and aluminum is 32.5 pounds.

Answer:

2.409

Step-by-step explanation:

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\ln 200 = log_{e}200[/tex]

[tex]log_{9}200 = \frac{log_{e}200}{log_{e}9}[/tex]

           = [tex]\frac{5.3}{2.2}[/tex]

           = 2.409

The approximate value of log 200 would be; 2.409

When we raise a number with an exponent, there comes a result.

Let's say you get  a^b = c Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows [tex]b = \log_a(c)[/tex]'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We have given the values in 9 = 2.2 and 200 – 5.3

We need to find the approximate value of log, 200.

Therefore,

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\\\ln 200 = log_{e}200[/tex]

Using the logarithm property;

[tex]log_{9}200 = \dfrac{log_{e}200}{log_{e}9}\\ = \dfrac{ln 200}{ln 9}\\ = \dfrac{5.3}{2.2}[/tex]

=  2.409

Hence, the approximate value of log, 200 would be; 2.409

Learn more about logarithm here:

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Answer:

0.534375

45328

36763

-6

-78

The values of x and y that satisfy the graphs are:

(-1, 0), and (-5, 0).

A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

We can start by simplifying the quadratic equation:

y = (x + 3)² – 4

y = x² + 6x + 9 - 4

y = x² + 6x + 5

Now, we can use various methods to find values of x and y that satisfy this equation. Here are five possible values:

If we substitute x = -1, we get:

y = (-1)² + 6(-1) + 5

y = 0

So, one solution is (-1, 0).

If we substitute x = 0, we get:

y = 0² + 6(0) + 5

y = 5

So, another solution is (0, 5).

If we substitute x = -5, we get:

y = (-5)² + 6(-5) + 5

y = 0

So, another solution is (-5, 0).

To find rational solutions, we can factor in the quadratic expression:

y = x² + 6x + 5

y = (x + 1)(x + 5)

So, the solutions are x = -1 and x = -5. Substituting these values into the equation, we get:

For x = -1, y = (-1)² + 6(-1) + 5 = 0

For x = -5, y = (-5)² + 6(-5) + 5 = 0

So, the solutions are (-1, 0) and (-5, 0).

To learn more about the quadratic equation;

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Answer:

The probability of getting two good coils is 77.33%.

Step-by-step explanation:

Since a batch consists of 12 defective coils and 88 good ones, to determine the probability of getting two good coils when two coils are randomly selected (without replacement), the following calculation must be performed:

88/100 x 87/99 = X

0.88 x 0.878787 = X

0.77333 = X

Therefore, the probability of getting two good coils is 77.33%.

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Answer:

  (c)  2^r = a

Step-by-step explanation:

The relationship between log forms and exponential forms is ...

  [tex]\log_2(a)=r\ \Leftrightarrow\ 2^r=a[/tex]

__

Additional comment

I find this easier to remember if I think of a logarithm as being an exponent.

Here, the log is r, so that is the exponent of the base, 2.

This equivalence can also help you remember that the rules of logarithms are very similar to the rules of exponents.

Answer: Choice C)  [tex]2^r = a[/tex]

This is the same as writing 2^r = a

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

Explanation:

Assuming that '2' is the base of the log, then we'd go from [tex]\log_2(a) = r[/tex] to [tex]2^r = a[/tex]

In either equation, the 2 is a base of some kind. It's the base of the log and it's the base of the exponent.

The purpose of logs is to invert exponential operations and help isolate the exponent. A useful phrase to help remember this may be: "if the exponent is in the trees, then we need to log it down".

The general rule is that [tex]\log_b(y) = x[/tex] converts to [tex]y = b^x[/tex] and vice versa.

Answer:

Hello?

Step-by-step explanation:

Answer:

a)  [tex]h=286.8ft[/tex]

b)  [tex]\frac{dh}{dt}=5.7ft/s[/tex]

Step-by-step explanation:

From the question we are told that:

Angle [tex]\theta=35[/tex]

a)

Slant height [tex]h_s=500ft[/tex]

Generally the trigonometric equation for Height is mathematically given by

[tex]h=h_ssin\theta[/tex]

[tex]h=500sin35[/tex]

[tex]h=286.8ft[/tex]

b)

Rate of release

[tex]\frac{dl}{dt}=10ft/sec[/tex]

Generally the trigonometric equation for Height is mathematically given by

[tex]h=lsin35[/tex]

Differentiate

[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]

[tex]\frac{dh}{dt}=10sin35[/tex]

[tex]\frac{dh}{dt}=5.7ft/s[/tex]

Answer:

I will say 2,000 yes so that is what I am putting