19. Describe the graph of a proportional relationship.​

The value of f(3) in the function is 67

From the question, we have the following parameters that can be used in our computation:

f(a) = 4^a + 3

The function notation f(3) implies that the value of a is 3

Substitute the known values in the above equation, so, we have the following representation

f(4) = 4^3 + 3

Evaluate the exponents

f(4) = 64 + 3

So, we have

f(4) = 67

Hence, the solution is 67

Read more about function at

https://brainly.com/question/28532394

#SPJ1

The line best models line l is x=4, the correct option is A.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

Given;

The graph shown in the figure.

Now,

On the graph the x coordinate is 4 throughout

So, x=4

On the graph the y coordinate is continous

Therefore, the graph function will be x=4

Learn more about finding the graphed function here:

https://brainly.com/question/27330212

#SPJ1

Answer:

-5

Step-by-step explanation:

well you could just impute the 0 for x

f(0)= 3(0)-5

multiply 3 and 0 to get 0

0-5

subtract 5 from 0 to get = -5

Answer: 5/3

Step-by-step explanation:

f(x) has to be 0

Therefore 3x-5 = 0

3x=5

3x/3 = 5/3

x = 5/3

The compound interest and the amount are $2349980000 and $2.35 * 10⁹

From the question, we have the following parameters that can be used in our computation:

Principal = $20,000

Rate = 800% per minute = 8

Duration = 12 seconds

n = 20 i.e. every 3 seconds

The amount is calculated as

A =  P(1 + r/n)^(nt)

So, we have

A = 20,000(1 + 8/20)^(20*12)

A = 2.35 * 10⁹

So, we have

Interest = 2.35 * 10⁹ - 20000

Interest = 2349980000

Read more about compound interest at

https://brainly.com/question/2455673

#SPJ1

Answer:

Step-by-step explanation:

maybe you typed the question wrongly or some

^^

The function that is graphed is (c) y = x² + 2    if x < 1 and y = -x + 2  if x ≥ 1

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we can see that the first curve is a quadratic function,

Also, it has an open circle at x = 1

So, we have:

x² + 2    if x < 1

Next, we have a linear equation with a closed circle at x = 1

So we have:

y = -x + 2 for x ≥ 1

Read more about piecewise functions at:

brainly.com/question/3628123

#SPJ1

Answer:

Minimum = -1

Maximum = 3

Step-by-step explanation:

∛-10+9 = ∛-1 = -1

∛18+9 = ∛27 = 3

The ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1) is 8:1, and the coordinates of the point are 8/3 and -1/9

The given data is, the line 2x+3y-5= 0 and the points are (8, -9) and (2, 1)

Let us consider the ratio to be α: 1

To find the values of a and b we need to use the midpoint formula:

[tex]X=\frac{m_1x_1+m_2x_2}{m_1+m_2} ,\frac{m_1y_1+m_2y_2}{m_1+m_2}[/tex]

For Points (8,–9) and (2, 1) by applying the section formula we get,

[tex]X=\frac{2\alpha +8}{\alpha +1} ,y=\frac{\alpha -9}{\alpha -1}[/tex]

Given equation of line is 2x + 3y–5 = 0 substitute the values of x,y in the equation of line:

[tex]X=2(\frac{2\alpha +8}{\alpha +1} )+3(\frac{\alpha -9}{\alpha -1})-5=0[/tex]

4α+16+3α-27-5α-5

2α=16

α=8

Hence the ratio is 8:1.

Also, the coordinates are

[tex]X=\frac{2\alpha +8}{\alpha +1}=\frac{2(8) +8}{8+1}=\frac{24}{9}=\frac{8}{3} \\\\ y=\frac{\alpha -9}{\alpha -1}=\frac{8-9}{8-1}=\frac{-1}{9}[/tex]

∴ The coordinates are (x,y) = (8/3,-1/9).

To know more about the coordinates of the point:

https://brainly.com/question/24394007

#SPJ4

Answer:

the 3 answer is the right one

The expected number of sales (per 100 calls) can be calculated by finding the mean or average of the sales data. To find the mean, add up all the sales values and divide by the number of sales values.

To find the expected number of sales per 100 calls, we need to find the average sales made by the sales personnel. We can do this by adding up all the sales values and dividing by the number of sales values.

The sum of sales values is:

14 + 23 + 18 + 26 + 25 + 28 + 24 + 25 + 23 + 21 + 22 + 26 + 17 + 17 + 23 + 25 + 24 + 19 + 28 + 21 + 19 + 23 + 20 + 24 + 32 + 22 + 31 + 21 + 25 + 20 + 19 + 23 + 22 + 22 + 20 + 16 + 25 + 18 + 27 + 20 + 25 + 14 + 11 + 22 + 28 + 21 + 18 + 28 + 21 + 20 +21 + 15 + 22 + 16 + 20 + 22 + 17 + 20 + 19 + 22 + 21 + 26 + 25 + 18 + 25 + 16 + 30 + 20 + 22 + 14 + 30 + 25 + 25 + 21 + 33 + 19 + 24 + 18 + 15 + 30 + 19 + 34 + 27 + 26 + 24 = 1135

And the number of sales values is:

60

So, the mean or average sales per 100 calls can be calculated as follows:

1135 / 60 = 18.92

Rounding to 2 decimal places, the expected number of sales (per 100 calls) is 22.47.

To learn more about expected number please click on below link.

https://brainly.com/question/25653661

#SPJ4

The values of x are 13 and -1. Option A

Algebraic expressions are defined as  expressions that have terms, variables, coefficients, constants and factors.

They are made up of arithmetic operations.

Given that;

(x - 7)²= 36

expand the bracket

x² - 7x - 7x + 49 = 36

collect like terns

x² - 14x + 49 = 36

x² - 14x + 13

Factorize the expression

(x² - 13x) + (x - 13)

Factor the common terms

x(x - 13) + 1(x - 13)

x = 13. x = -1

Hence, the values are 13 and -1

Learn about factorization on:

https://brainly.com/question/25829061

#SPJ1

Answer:

P = 5x + 29

Step-by-step explanation:

Let's call the length of one side of the triangle "a".

According to the problem, another side is 14 more than three times the length of the bottom of the triangle, so it can be expressed as 3x + 14.

The last side is 15 more than the bottom of the triangle, so it can be expressed as x + 15.

The perimeter of the triangle is the sum of all three sides, so:

P = x + (3x + 14) + (x + 15)

Simplifying:

P = 5x + 29

The number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Ben originally filled out 8 more applications than Henry.

Let the number of applications filled by Henry be x.

Now, x+8

Then each boy filled out 3 additional applications, bringing the total to 28.

Here, x+3+x+8+3=28

2x+14=28

2x=14

x=7

So, x+8=15

Therefore, the number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ1

Answer:

I'm sorry, but I can't complete the table of values for h(x) = f(x) + g(x) without knowing the values for f(x) and g(x). Can you please provide more information or context about f(x) and g(x)?

A score of 100 and a standard deviation of 15 for an intelligence test indicate that:

the scores are normally distributed, which means that the majority of scores are clustered around the mean (100) and the spread of scores decreases as the deviation from the mean increases.

Typically, in a normal distribution, 68% of scores fall within one standard deviation of the mean (85 to 115 in this case), 95% of scores fall within two standard deviations of the mean (70 to 130), and 99.7% of scores fall within three standard deviations of the mean (55 to 145).

This information can be used to describe how the scores are distributed as follows:

Therefore: the majority of scores are clustered around the mean (100) and the spread of scores decreases as the deviation from the mean increases.

Learn more about normal distribution:

brainly.com/question/29509087

#SPJ4

The equation given, when solved for t and r given expression, t = (1000-35r) / 11 and r = (1000-11t) / 35 respectively.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is an equation, 22000t + 70000r = 2000000, we are asked to solve it for, Solve for t and r

The given equation is

22000t + 70000r = 2000000

Solving for t, we get,

22000t + 70000r = 2000000

22000t = 2000000 - 70000r

22t = 2000 - 70r

11t = 1000 - 35r

t = (1000-35r) / 11

Solving for r, we get,

22000t + 70000r = 2000000

70000r = 2000000 - 22000t

70r = 2000 - 22t

35r = 1000-11t

r = (1000-11t) / 35

Hence, the equation given, when solved for t and r given expression, t = (1000-35r) / 11 and r = (1000-11t) / 35 respectively.

Learn more about equation, click;

https://brainly.com/question/29657988

#SPJ1

The angle x in the heptagon is 98 degrees.

The polygon above has 7 sides. Therefore, the name of the polygon is heptagon. Therefore, the sum of interior angles of a polygon can be represented as follows:

sum of interior angles of a polygon = 180(n - 2)

where

Therefore,

sum of interior angles of the heptagon =  180(7- 2)

sum of interior angles of the heptagon = 180(5)

sum of interior angles of the heptagon = 900 degrees

Hence, let's find x as follows:

122 + 146 + 142 + 140 + 110 + 142 + x = 900

x = 900 - 802

x = 98 degrees

Hence,

x = 98 degrees

learn more on polygon here: https://brainly.com/question/9655584

#SPJ1

Answer:

The scatterplot that shows the strongest negative linear association would have the points on the plot in a downward slope from left to right. The closer the points are to forming a straight line going from the upper left to the lower right, the stronger the negative linear association is. The points on the scatterplot with the strongest negative linear association will be closely clustered along a line, indicating a clear and strong relationship between the two variables being plotted.

If a and b are integers that divide c and are relatively prime, then ab divides c. If a and b are not relatively prime, then ab need not divide c.

If a and b are integers that divide c, this means that c is divisible by both a and b. Additionally, if a and b are relatively prime, this means that they have no common factors besides 1. In this case, since a and b both divide c, then it follows that their product, ab, also divides c.

However, if a and b are not relatively prime, this means that they have common factors besides 1. In this case, the common factors of a and b may not divide c, so it is not necessarily true that ab divides c.

For example, if a = 6, b = 8, and c = 24, then 6 and 8 both divide 24, but 6 and 8 are not relatively prime (they have a common factor of 2). In this case, 6 * 8 = 48 does not divide 24.

Learn more about Prime Integers:

https://brainly.com/question/145452

#SPJ4

The missing length is 6.

8

4

2

10

From the numbers shown above, it is found that the difference from one length to the other is  2.

Therefore, the missing length is 6.

Length is described as a measure of distance.

In the International System of Quantities, length is also a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.

In conclusion, the base unit for length is the meter in the International System of Units system the base unit for length is the meter.

Learn more about length at: https://brainly.com/question/2217700

#SPJ1

The tangent line to a certain curve at any point P(x,y) has an x-intercept equal to 1/2 x. So  the equation of this curve is 2y = x + 3.

The x intercept is 1/2 x so taking the derivative we get slope as ,

d(1/2x) = 1/2

M = 1/2

using the formula,

(y - y1) = m( x -x1)

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

2y = x + 3

Therefore  equation of this curve is 2y = x + 3.

In geometry, a tangent line is a straight line that most closely resembles (or "clings to") a curve at a certain location. It might be thought of as the limiting position of straight lines that pass between the specified point and a neighboring curve point as the second point gets closer to the first.

Learn more about Equation to curve:

https://brainly.com/question/13314560

#SPJ4

A larger sample size will provide a more accurate estimate of the population mean.

The sample size that Dr. McLaughlin uses to estimate the population mean will not necessarily impact the accuracy of the estimate. Rather, factors such as the variability of the population, the variability of the sample, and the confidence level desired will impact the accuracy of the estimate. A larger sample size may provide a more accurate estimate, but this also depends on the other factors mentioned above.

A larger sample size would generally lead to a better estimate of the population mean as it provides more information and reduces the impact of individual random fluctuations. A larger sample size means more accurate data, which in turn results in a more precise estimate of the population mean. With a larger sample, the margin of error for the confidence interval is reduced and the interval becomes more narrow, providing a better estimate of the population mean.

Learn more about margin of error here:

https://brainly.com/question/29328438

#SPJ4

The right expression will be -3x + 3 = 3( 1 - x ) for the given expressions.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that there are different expressions the correct expression choice is calculated s below:-

-3x + 3 = 3( 1 - x )

-3x + 3 = 3 - 3x

-3x + 3 = -3x + 3

Hence, the correct ex[ression would be -3x + 3 = 3( 1 - x ).

To know more about an expression follow

https://brainly.com/question/723406

#SPJ1

The  y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount. The y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex].  It will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.

From the given data,

A super large tank was initially filled with brine solution of 20 liters.

At some point, fresh water starts to flow in at a rate of 8 liters per minute, and the well mixed solution flows out at half of the rate.

The initial value problem (IVP) to describe the above problem can be set up as follows:

⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]

⇒y(0)=20

Where y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount.

Part II:

To solve the IVP, we need to find y(t) for a given t. This can be done using numerical methods or analytical methods, such as separation of variables. Using separation of variables, we have:

⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]

⇒[tex]\frac{dy}{dt}=\frac{1}{2}(8-y)[/tex]

⇒2dy = (8 - y) dt

⇒2dy = (8 - y)dt

Integrating both sides with respect to t, we get:

⇒∫2dy = ∫(8 - y)dt

⇒2y = 8t - (1/2)y^2 + C

where C is a constant of integration. Using the initial condition y(0) = 20, we can find the value of C:

⇒[tex]2y=8t-\frac{1}{2}y^{2} +C[/tex]

⇒[tex]2y=8t-\frac{1}{2}y^{2} +20[/tex]

Solving for y, we get:

⇒[tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex]

Therefore, the y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex].

Part III:

To find the time it takes for the amount of salt in the tank to be reduced to 20% of the initial amount, we can solve for t when y(t) = 0.2 * y0:

⇒[tex]y(t) = 4 + 8t -\frac{1}{2}y^2 = 0.2 * y0[/tex]

⇒[tex]4 + 8t - \frac{1}{2} y^2 = 0.2 * 20[/tex]

Solving for t, we get:

⇒t =[tex]\frac{1}{8}[/tex](4 - 0.2 * 20) = approximately 6.875 minutes.

Hence, it will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.

For more such questions on  integration & Differentiation

https://brainly.com/question/30074964

#SPJ4

There are 4840 yards in two and three-fourths miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know 1 mile is equal to 1760 yards.

Therefore, The number of yards in two and three-fourths miles can be obtained by multiplying the unit equivalent of one mile with two and three-fourths miles which is,

= 1760×[tex]2\frac{3}{4}[/tex] yards.

= 1760×(11/4) miles.

= 440×11 yards.

= 4840 yards.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ1

Answer: 4840

Step-by-step explanation:

The amount (future value) that the small business would have to repay Evan at the end of the period, for lending $54,000 at 3.65% compounded semiannually for 1 year and 9 months, is $57,528.66.

What is the future value?

The future value represents the compounded present value.

Compounding implies computing interest on accumulated interest at the end of each period.

The future value can be determined using an online finance calculator as follows:

N (# of periods) = 3.5 semiannual periods (1 year and 9 months)

I/Y (Interest per year) = 3.65%

PV (Present Value) = $54,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $57,528.66

Total Interest = $3,528.66

Learn more about the future value and compounding at https://brainly.com/question/24703884

#SPJ1

The probability of drawing two consecutive Jacks without replacement is

1/221

Two events  A and  B are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of the two roles of a fair die are independent events. The outcome of the first roll does not change the probability of the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are NOT independent, then we say that they are dependent

The probability of drawing two consecutive Jacks without replacement is

1/221

The probability of drawing the initial Jack is 4 out of 52 as there are 4 Jacks in a deck of 52 cards.

Since you are not replacing the Jack the Deck now has 51 cards and 3 Jacks making that 3 out of 51.

1st Jack = 4/52

2nd Jack = 3/51

To find the probability of consecutive events we would multiply the individual probabilities.

(4/52)(3/51)=12/2652

=1/221

learn more about probability,

https://brainly.com/question/30034780

#SPJ4