Ryan exponential function of the form f(t)= a×b^t to represent the following situation. assume t is in years. an account has an initial investment of $91,000, increasing by 3.76% per year. F(T)=_________​

The function would be \(f(x)=\frac{1}{2}x + 1 \ and\ f(x)=\frac{1}{2}x - \frac{1}{2}\)

What is linear function?

A linear function is one with one or two variables that does not have exponents. It is a function that has a straight line graph.

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. To find the equation of the linear function given the values of x and f(x), we can use two points and use the slope-intercept form of the equation.

A way to find the equation of the linear function is to use the point-slope form: f(x) = m(x-x1) + f(x1), where (x1,f(x1)) is a point on the line.

If we use the points (-4,-2) and (0,0) we can find the slope:

m = (0 - (-2)) / (0 - (-4)) = 2/4 = 1/2

then using point-slope form:

f(x) = 1/2(x - (-4)) + (-2)

f(x) = 1/2x + 1

so the equation of the linear function is f(x) = 1/2x + 1

Alternatively, we can use the two points (-2,-1) and (0,0) we can find the slope:

m = (0 - (-1)) / (0 - (-2)) = 1/2

then using point-slope form:

f(x) = 1/2(x - (-2)) + (-1)

f(x) = 1/2x - 1/2

so the equation of the linear function is f(x) = 1/2x - 1/2.

Therefore, equation f(x) = 1/2x+1 and f(x) = 1/2x - 1/2 represents the given values of x and f(x)

To know more about linear functions visit,

https://brainly.com/question/2248255

#SPJ1

Option B

Because the average points scored in the night is more than that of the day

1. The solution of 5(r-2)² = 35 is r = ±√7 + 2.

2. The solution of -4(k-8)² = 16 is k =  (16 ± √(-16)) / 2.

1. 5(r-2)² = 35

First, divide both side by 5 we get

5(r-2)²/5 = 35 /5

(r-2)² = 7

Take square root on both side

r-2 = ±√7

r = ±√7 + 2

2. -4(k-8)² = 16

Divide both side by -4 we get

(k-8)² = -4

k² + 64 - 16k + 4 = 0

k² - 16k + 68 = 0

On solving the quadratic equation we get

k =  (16 ± √(-16)) / 2

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ1

Answer:

The true mean contents of the cans being filled by this machine with 95% confidence is between 11.891 ounces and 11.949 ounces.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 35 - 1 = 34

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 34 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.032

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.032\frac{0.085}{\sqrt{35}} = 0.029\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 11.92 - 0.029 = 11.891 ounces.

The upper end of the interval is the sample mean added to M. So it is 11.92 + 0.029 = 11.949 ounces.

The true mean contents of the cans being filled by this machine with 95% confidence is between 11.891 ounces and 11.949 ounces.

Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

The required feet added to both the length and width of the patio is 6 feet.

Given that,
A square patio had the same number of feet added to its length and width. The equation A(x) = x² + 12x + 36 represents the area of the new patio in square feet, where 'x' was the length and width of the original patio, in feet.

Here,

According to the question,
A(x) = x² + 12x + 36
A(x) = x² + 6x + 6x + 36
A(x) = (x + 6)(x + 6)

Length = width = x + 6

Thus, the required feet added to both the length and width of the patio is 6 feet.

Learn more about the area here:

https://brainly.com/question/27934373
#SPJ1

Answer:

a)  The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

b)  P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

c) P ( z = 0 ) = 0.6

  P ( z = 1 ) = 0.4

Step-by-step explanation:

Number of head on first toss = Z

Total Number of heads on 2 tosses = W

% of head occurring = 40%

% of tail occurring = 60%

P ( head ) = 2/5 ,    P( tail ) = 3/5

a) Determine the joint probability distribution of W and Z

P( W =0 |Z = 0 ) = 0.6         P( W = 0 | Z = 1 ) = 0

P( W = 1 | Z = 0 ) = 0.4        P( W = 1 | Z = 1 ) = 0.6

P( W = 1 | Z = 0 ) = 0           P( W = 2 | Z = 1 ) = 0.4

The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

B) Marginal distribution of W

P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

C) Marginal distribution of Z ( pmf of Z )

P ( z = 0 ) = 0.6

P ( z = 1 ) = 0.4

Part(a): The required joint probability of W and Z is ,

\(P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16\)

Part(b): The pmf (marginal distribution) of W is,

\(P(w=0)=0.36,P(w=1)=0.48,P(w=2)=0.16\)

Part(c): The pmf (marginal distribution) of Z is,

\(P(z=0)=0.6,P(z=1)=0.4\)

Part(a):

The joint distribution is,

\(P(w=0\z=0)=0.6,P(w=1|z=0)=0.4,P(w=2|z=0)=0\)

Also,

\(P(w=0\z=1)=0,P(w=1|z=1)=0.6,P(w=2|z=1)=0.4\)

Therefore,

\(P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16\)

Learn More: https://brainly.com/question/13127182

Answer:

f(x) = -5/3x + 5/3

Step-by-step explanation:

if x = 4 ; f(x) = -5

if x = -2 ; f(x) = 5

f(x) = ax + b

-5 = 4a + b (1)

and

5 = -2a + b (2)

(1) + (2)

2a + 2b = 0

a = -b

(1) -5 = 4a - a

-5 = 3a

a = -5/3

Answer :

f(x) = -5/3x + 5/3

Answer:

3

I used to be an olimpic runner and I ran the 400 all the time and I did cross country

Answer:

No

Step-by-step explanation:

For the smaller figure to be a scaled copy, the figure would have to be half as wide as well,

Answer:

$17.53

Step-by-step explanation:

385.66 / 22 = 17.53

Answer:

Interval Notation:

( −∞,−13]

Set-Builder Notation:

{ x| x≤−13}

Step-by-step explanation:

We have the following:

Therefore we can conclude that from step 1 to step 2, it is a rotation because it moves on its own axis and from step 2 to 3, it is a reflection

Answer:

---------------

Let the radius be r.

Use circumference formula and find the value of r:

Find the area using the circle area formula:

The matching choice is (B).

Answer:

Step-by-step explanation:

Answer:

\(0.7\) is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory

Step-by-step explanation:

The two events are independent of each other.

Hence the probability of choosing satisfactory piston from Machine 1 and unsatisfactory piston from Machine 2 is equal  probability of choosing satisfactory piston from Machine 1 + probability of choosing unsatisfactory piston from Machine 2

Substituting the given values we get

Probability of choosing satisfactory piston from Machine 1 and unsatisfactory piston from Machine 2 =\(\frac{174}{174 +116} + \frac{20}{180 +20}\)

=\(\frac{174}{174 +116} + \frac{20}{180 +20}\)

=\(= \frac{174}{290} + \frac{20}{200}\\= 0.6 + 0.1\\= 0.7\)

Answer:

The cash flow statement paints a picture as to how a company’s operations are running, where its money comes from, and how money is being spent. So i think D is the answer

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

y=4/3x-4

Step-by-step explanation:

For this problem, we will apply a slope-intercept form of the equation which is:
y=mx+b

where m is slope and b is the y-intercept

We are given that:

m=4/3

b=-4

Substitute these values into slope-intercept form of equation as:

y=4/3x-4

Answer:

Step-by-step explanation:

A standard deck of cards has 52 cards, including 4 queens. If you are certain to get a queen when selecting 49 cards from a shuffled deck, it means that one of those 49 cards must be a queen, and the remaining 48 cards can be any of the remaining 48 cards in the deck.

So, the probability of selecting a queen from a shuffled deck of cards is:

probability = number of favorable outcomes / total number of possible outcomes

Since we are certain to get a queen, the number of favorable outcomes is 4 (the number of queens in the deck), and the total number of possible outcomes is 49 (the number of cards selected from the deck).

Therefore, the probability of selecting a queen is:

probability = 4/49

This fraction cannot be simplified any further. Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.0816.

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

To learn more about percentages visit the link below:

https://brainly.com/question/30399396

Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

Read more about percentage

https://brainly.in/question/21062337#:~:text=Answer%3A,has%20no%20unit%20of%20measurement.

Answer:

1. intersecting

2. paralle

3. perpendicular

4. intersecting

Answer:

Parallel box and whisker plots are regular box and whisker plots, but drawn "one-above-the other" on the piece of paper. To enable to do this easily, draw an x-axis which is big enough for the largest value in the data, and small enough for the smallest value in the data (in the entire collection of data). Plot each box-and-whisker diagram below each other.

Step-by-step explanation:

pls mark

Answer:

Parallel box and whisker plots are regular box and whisker plots, but drawn "one-above-the other" on the piece of paper.

Step-by-step explanation:

Answer: (2y+3)(3x+y-1)

Step-by-step explanation:

First regroup the terms.

6xy+9x+2y^2+y-3

Second factor 3x out of 6xy+9x

3x(2y)+9x+2y^2+y-3

3x(2y)+3x(3)+2y^2+y-3

And you get

3x(2y+3)+2y^2+y-3

Third factor by grouping

Answer:6.05

Step-by-step explanation:

6 is the ones place. 0 is the tenths place. 5 is the hundredths place.

Answer:

  30 ft

Step-by-step explanation:

The Pythagorean theorem can be used to find the length of the unknown side. It tells you the sum of the squares of the legs is equal to the square of the hypotenuse.

  12² +a² = 13²

  a² = 169 -144 = 25

  a = √25 = 5

The sum of the side lengths is ...

  (12 +5 +13) ft = 30 ft

The perimeter is 30 feet.

Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.