Please help! Variables!!

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:

Yes.

Step-by-step explanation:

.

Answer:

B

Step-by-step explanation:

(6)^1/2 × (8)^1/2

6^1/2 × 2 (2)^1/2

4 (3)^1/2

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:

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.

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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:

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

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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:

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: …

Step-by-step explanation: you need an image

Answer:

what expression?

Step-by-step explanation:

Answer:

Hello?

Step-by-step explanation:

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:

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:

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%.

Answer:

The minimum score required for an A grade is 80.

Step-by-step explanation:

According to the Question,

A: Top 12% of scores

B: Scores below the top 12% and above the bottom 57%

C: Scores below the top 43% and above the bottom 19%

D: Scores below the top 81% and above the bottom 5%

F: Bottom 5% of scores Scores on the test

And The normally distributed with a mean of 66.5 and a standard deviation of 9.9.

Now,

we have μ=66.5 , σ=9.9  

Top 12%, so at least the 100-12 = 88th percentile, which is the value of X when Z has a p-value of 0.88. So it is X when Z = 1.175.

⇒ Z = (X-μ)/σ

⇒ 1.175×9.9 = X-66.5

⇒ X=78.132

Rounding to the nearest whole number, the answer is 80.

The minimum score required for an A grade is 80.

Answer:

x = 27

Step-by-step explanation:

I'm assuming the equation looks like this:

[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]

Here's how to solve for x:

[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]

(subtract 5 from both sides)

[tex]\frac{2}{3}x-\frac{1}{9}x=15[/tex]

(Find the GCF of 3 and 9, which is 3. Multiply 2/3 by 3/3. You get 6/9)

[tex]\frac{6}{9}x-\frac{1}{9}x=15[/tex]

(add like terms)

[tex]\frac{5}{9}x=15[/tex]

(multiply 9/5 to both sides, which is the same as dividing both sides by 5/9)

x = 27

Hope it helps (●'◡'●)

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).

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Answer:

the value of x is 29°

hope it helps

have a nice day

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:

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:

221

Step-by-step explanation:

Given sequence is ,

> 5 , 6 , 7 , 8 , 9.

The common difference is 6-5 = 1 .

Therefore , the 221st number will be

> 221 st term = 221 × 1 = 221 .

Hence the 221 st term is 221 .

Answer:

225

Step-by-step explanation:

d = 6 - 5 = 1 (common differences)

a = 5 (first term)

221st term

a+(n-1)d

5 +(221 - 1) 1

5 + 220 =225

Therefore the answer is 225

Answer:

64 Bottles

Step-by-step explanation:

that is the procedure above

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:

9:2

Step-by-step explanation:

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:

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

9514 1404 393

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

9514 1404 393

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