how all work.
A) What is the average rate of change of the function g(x) = 14x + 6 over the interval [0, 5]?
B) What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval [0,5]?
C) How does this compare to your Answers for Problem 4?

Answer:

40,000 ft²

Step-by-step explanation:

area = 200 ft * 200 ft = 40,000 ft²

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{6!}\\\large\textsf{= 6}\times\large\textsf{5}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{6(5) = \bf 30}\\\large\textsf{= 30}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{30(4) = \bf 120}\\\large\textsf{= 120}\times\large\textsf{3}\times\large\textsf{2}\times\textsf{1}\\\large\textsf{120(3) = \bf 360}\\\large\textsf{= 360}\times\large\textsf{2}\times\large\textsf{1}[/tex]

[tex]\large\textsf{360(2) = \bf 720}\\\large\textsf{720}\times\large\textsf{1}\\\large\textsf{= \bf 720}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Therefore, your answer is: \bf 720}\huge\textsf{ (option B)}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

-2

-1

-2

Step-by-step explanation:

really ? this is a problem ? why ?

f(0) means the functional value for x = 0.

is x = 2 ? no.

so, automatically the other case applies, and f(0) = -2

f(2) means x=2

is x = 2 ? yes.

so that case applies, and f(2) = -1

f(5) means x=5

is x = 2 ? no.

so again, the case for x <> 2 applies, f(5) = -2

Answer:

It is a mathematical method and with it gives a fitted trend line for the set of data in such a manner that the following tow conditions are satisfied. The sum of the deviation of the actual values of Y and the computed values of Y is zero.

Answer:

15. 52

16. 6

17. 59

18. 11

Step-by-step explanation:

Answer:

Hence there are 6 different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men.

Step-by-step explanation:

We know that,

Total males = 3,

Total Females = 2,

Now we want 2 males and a female.

Then the choices are,

           [tex]= ^{3} C_{2} \times ( ^{2} C_{1} )\\\\= 3 \times 2\\\\=6[/tex]

Answer:

mana saya tau iwnisbagcayabaonsoanuwvsybwiwnusvwuagwyvwkwnwibsyafa

include the notation and just do the work on the page

Answer:

use gauthmath

Step-by-step explanation:

you will thank me later

This question is incomplete, the complete question is;

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

What proportion of the students scored at least 23 points on this test, rounded to five decimal places?

Answer:

proportion of the students that scored at least 23 points on this test is 0.30850

Step-by-step explanation:

Given the data in the question;

mean μ = 22

standard deviation σ = 2

since test closely followed a Normal Distribution

let

Z = x-μ / σ      { standard normal random variable ]

Now, proportion of the students that scored at least 23 points on this test.

P( x ≥ 23 ) = P( (x-μ / σ) ≥  ( 23-22 / 2 )

= P( Z ≥ 1/2 )

= P( Z ≥ 0.5 )

= 1 - P( Z < 0.5 )

Now, from z table

{ we have P( Z < 0.5 ) = 0.6915 }

= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850

P( x ≥ 23 ) = 0.30850

Therefore, proportion of the students that scored at least 23 points on this test is 0.30850

Answer:

question 1

if you want x to stand alone

you will take the -3 off by crossing it to the other side

NB when a negative number crosses the equal sign it becomes positive

x =10+3= ×=13 is the final answer

Step-by-step explanation:

question 2

you will divide both sides by 2(because we want x to stand alone)

so final answer is ×=4

9514 1404 393

Answer:

Step-by-step explanation:

Assuming the dimensions are integer numbers of feet, you're looking for factors of 580 that have a difference of 9.

 580 = 1×580 = 2×290 = 4×145 = 5×116 = 10×58 = 20×29

The last pair of factors differs by 9, so ...

  the length is 29 feet; the width is 20 feet.

Answer:

7/0

Step-by-step explanation:

This is because if a number is divided by 0 then there is no answer or it is undefined

Think of it like this,

You have 7 apples and wanted to give it to zero friends, is it possible?

Hope this helped :)

Answer:

Second option (7÷0)

Explanation:

Dividing by zero is considered undefined since you can't divide something by nothing. It's like saying you have a pizza and you want to divide it between 7 people but since you're dividing by zero, you're not splitting the pizza between anyone.

Answer:

i dont know

Step-by-step explanation:

hmmm

Answer:

0.6826 = 68.26% probability Z will be within one standard deviation of average.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

What is the probability Z will be within one standard deviation of average?

This is the p-value of Z = 1 subtracted by the p-value of Z = -1.

Z = 1 has a p-value of 0.8413.

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability Z will be within one standard deviation of average.

Answer: 0.86 and -2800 (choice A)

Explanation:

Think of the given equation as y = 0.86x - 2800

Then compare it to y = mx + b

We see that m = 0.86 is the slope and b = -2800 is the y intercept.

Answer:

Slope: 0.86 , Y-intercept:-2800

Step-by-step explanation:

Linear equations go by the form of y=mx + c

where m is the gradient(slope of the graph) and c is the y-intercept

Answer:

0.5665 = 56.65% probability of less than four twos.

Step-by-step explanation:

For each roll, there are only two possible outcomes. Either it is a two, or it is not a two. The probability of a roll ending up in a two is independent of any other roll, which means that the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

A die is rolled 20 times

This means that [tex]n = 20[/tex]

One out of six sides is 2:

This means that [tex]p = \frac{1}{6} = 0.1667[/tex]

Probability of less than four twos:

This is:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.1667)^{0}.(0.8333)^{20} = 0.0261[/tex]

[tex]P(X = 1) = C_{20,1}.(0.1667)^{1}.(0.8333)^{19} = 0.1043[/tex]

[tex]P(X = 2) = C_{20,2}.(0.1667)^{2}.(0.8333)^{18} = 0.1982[/tex]

[tex]P(X = 3) = C_{20,3}.(0.1667)^{3}.(0.8333)^{17} = 0.2379[/tex]

So

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0261 + 0.1043 + 0.1982 + 0.2379 = 0.5665[/tex]

0.5665 = 56.65% probability of less than four twos.

Answer:

the slope-intercept form for any line is y = mx + b, where m is the slope and b is the y-intercept.

now, let's calculate the slope:

=  

here is the equation we currently have solved: y = x + b

now we have to solve for the y-intercept. to do this, we substitute one of the given points into the equation, and solve for b.

let's use (8, 2). in this ordered pair, the 8 is the x, and the 2 is the y.

2 = 8 + b

2 - 8 = b

b = -6

and now we have our final equation!  

y = x - 6

hope this helped! please let me know if you are confused about anything i did smiley

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the slope first:

Use point-slope form and the coordinates of one of the points:

Answer:

x<7

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

if zero toppings is an option, then there would be 5 possibilities for toppings

0,1,2,3,or 4

the server randomly chose 3 toppings so that would be one out of 5 or 20%.

(If the server did not have the option to put zero toppings on then there would be only 4 options 1,2,3, or 4 toppings and the correct answer would be one out of 4 or 25%.)

Answer:

(a) 23000(1-15%)^t

(b) about 12006.14375

Step-by-step explanation:

(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t

And with the values, we get the exponential model 23000(1-15%)^t

(b) From question (a) we already have the model and the time period given here is 4 years. So putting it in the formula we get,

23000(1-15%)^4

=23000(1-15/100)^4

=23000(0.85)^4

=23000x0.52200625

=12006.14375     (Ans)

Answer:

0.3898 = 38.98% probability that there will be 4 failures

Step-by-step explanation:

A sequence of Bernoulli trials forms the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

Let the probability of success on a Bernoulli trial be 0.26.

This means that [tex]p = 0.26[/tex]

a. In five Bernoulli trials, what is the probability that there will be 4 failures?

Five trials means that [tex]n = 5[/tex]

4 failures, so 1 success, and we have to find P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{5,1}.(0.26)^{1}.(0.74)^{4} = 0.3898[/tex]

0.3898 = 38.98% probability that there will be 4 failures

i think the answer is 2.24

Answer:

[tex]cos(45)=\frac{\frac{7\sqrt{2} }{2} }{x} \\\\cos(45)x=\frac{7\sqrt{2} }{2}\\\\\frac{\sqrt{2} }{2}x=\frac{7\sqrt{2} }{2}\\\\x=\frac{\frac{7\sqrt{2} }{2}}{\frac{\sqrt{2} }{2}} =\frac{7\sqrt{2} }{2}*\frac{2}{\sqrt{2}} =7[/tex]

[tex]y^{2} +(\frac{7\sqrt{2} }{2} )^{2} =x^{2} \\\\y^{2} =7^{2}-(\frac{7\sqrt{2} }{2} )^{2} \\\\y^{2}=49-\frac{49(2)}{4} =49-\frac{49}{2}=\frac{49(2)}{2}-\frac{49}{2}=\frac{98-49}{2}=\frac{49}{2} \\\\y=\sqrt{\frac{49}{2} } =\frac{7}{\sqrt{2} } =\frac{7\sqrt{2}}{\sqrt{2}(\sqrt{2})} =\frac{7\sqrt{2}}{2}[/tex]

A = 0.5*b*h

60 = 0.5*10*h

60 = 5h

5h = 60

h = 60/5

h = 12

Answer: The height is 12 meters.

Answer:

6 m

Step-by-step explanation:

Since the area is 60 m squared and the base is 10 m, the height is 12.

Formula: base x height / 2 = area

= 10 x height / 2= 60 m squared

60 / 10 = 6 x 2 = 12.

Hope this helps!

9514 1404 393

Answer:

  C.  837

Step-by-step explanation:

The remaining angle is ...

  C = 180° -A -B = 180°-62° -67° = 51°

The law of sines tells us that the length AC is ...

  AC/sin(B) = AB/sin(C)

  AC = AB·sin(B)/sin(C) = 40·sin(67°)/sin(51°)

Using the area formula given, we now have ...

  area = 1/2(AB)(AC)sin(A)

  = (1/2)(40)(40·sin(67°)sin(62°)/sin(51°) ≈ 836.7

The area of the triangle is about 837 square units.