The equation of line that would graph his salary over time will be;
⇒ y = 1/685x - 38.89
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
After 4 years, he makes $56,785; after 9 years, he makes $60,210.
Now,
Since, After 4 years, he makes $56,785; after 9 years, he makes $60,210.
Hence, The equation of line passes through the points (56,785, 4) and
(60,210, 9).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (9 - 4) / (60210 - 56785)
m = 5 / 3425
m = 1/685
Thus, The equation of line with slope 1/685 is,
⇒ y - 4 = 1/685 (x - 56,785)
⇒ y - 4 = 1/685x - 42.89
⇒ y = 1/685x - 42.89 + 4
⇒ y = 1/685x - 38.89
Therefore, The equation of line that would graph his salary over time will be;
⇒ y = 1/685x - 38.89
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ1
The domain of a certain exponential function is all real numbers. The range of the function is all real
numbers greater than -3. The graph of the function has a horizontal asymptote at y = -3.
Select a graph or graphs to fit the description of the function.
One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.
How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x + c.
In which:
a is the initial value.b is the rate of change.c is the horizontal asymptote.The graph of the function has a horizontal asymptote at y = -3, hence:
c = -3.
For a and b, they can assume any non-negative values, hence we attribute these following values:
a = 1, b = 2.
The graph is given at the end of the answer.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
because of different units being used for various data series, which fit statistic can be used across different series that are in fact measured in different units?
The fit statistic that can be used across different series that are in fact measured in different units is; MAPE
What statistic can be used?There are different statistics models in this regards such as;
Mean Absolute Error (MAE)
Mean Absolute Scaled Error (MASE)
Accuracy Percent (Accuracy %)
Mean Squared Error (MSE)
Root Mean Squared Error (RMSE)
Mean Absolute Percent Error (MAPE)
Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.
The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.
Read more about statistics at; https://brainly.com/question/15525560
#SPJ1
if there are 720 different classes in one quarter, each in its own room, how many different rooms will be required?
if there are 720 different classes in one quarter at time, each in its own room, different rooms will be required 720 rooms.
To answer this question, we need to understand that each class needs its own room. Therefore, the number of rooms required will be equal to the number of classes. In this case, there are 720 different classes in one quarter, so 720 different rooms will be required. Each room can accommodate one class at a time, so the total number of rooms needed is 720.
Number of Classes = 720
Number of Rooms Required = Number of Classes = 720
Learn more about time here
https://brainly.com/question/28050940
#SPJ4
6.0 percent of a population are infected with a certain disease. there is a test for the disease, however the test is not completely accurate. 90.0 percent of those who have the disease test positive. however 3.1 percent of those who do not have the disease also test positive (false positives). a person is randomly selected and tested for the disease. what is the probability that the person has the disease given that the test result is positive?
Probability of the person has the diseases and the test result is positive = 1/90 = 0.011
What is probability?Probability refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.
How can we calculate probability?Given, percentage of people who have disease and test result positive =90
percentage of people who has not disease but test result positive =3.1
Suppose 6.0 percent of population are infected
Now, probability of a randomly selected person who has diseases and test positive
= 1/90
= 0.011
To learn about Probability visit:
https://brainly.com/question/13810637
#SPJ4
The expression (x + 3)(x + 2) is the product of two binomials. Which expression is also
a product of binomials?
The expression which has product of two binomials is (5-n)(n+7).
What is Expression?An expression is combination of variables, numbers and operators.
Binomials are expressions containing the sum (or difference) of two terms.
The expression (x + 3)(x + 2) is the product of two binomials.
(pq)(qp), (5-n)(n+7), 3x(2x+5), 6x-2y
(pq)(qp) is not the product of binomials because pq and qp are products.
3x(2x+5) is not the product of binomials because 3x is not a sum or difference.
6x-2y is also not because it is one binomial, not two multiplied together.
(5-n)(n+7) is the product of two binomials.
Hence, (5-n)(n+7) is the expression which has product of two binomials.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ1
sqrt{ 45 Multiplyed bysqrt 10
Answer:
Step-by-step explanation:
when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5
When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13 degrees
The distance between point a to point b = 5.3 feet
The length of the top side = 3 feet
Therefore, it will form a right triangle
Here we have to use trigonometric function
Here adjacent side and the hypotenuse of the triangle is given
The trigonometric function that suitable for the given conditions is
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos θ = 3 / 5
θ = cos^-1(3 / 5)
θ = cos^-1(0.6)
θ = 53.13 degrees
Therefore, the value of θ is 53.13 degrees
Learn more about trigonometric function here
brainly.com/question/25618616
#SPJ4
PLS HELP WILL GIVE BRAINLIEST!
1) the slope of the line x=8 is ______
2) the domain and range of a linear function are _________
Answer:
I tried as I can to solve it
find the value of x.
And bottom says solve for X someone help me
Answer:
2(x+8)=126
Step-by-step explanation:
GD is the bisector of CGE and 126 and the angle CGE are equal
g there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join?
there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join is 120
A fractional factorial experiment utilizes subset of combinations that are gotten from the full factorial experiment. They are applicable when there are too many inputs to screen practically or cost or time would be excessive.
Also, using the fractional factorial experiment makes running the experiments faster and cheaper.
10C3 = 10! / (7!*3!)
= 10*9*8/6
= 120
learn more about of factorial here
https://brainly.com/question/17201051
#SPJ4
help plss and if u could plot the point as well thats better
TY
The linear functions defined in this problem are given as follows:
1. y = -x + 3.
2. y = x - 3.
3. y = 3x + 1.
4. y = -2x - 2.
How to define the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
The coefficients and their meaning are given as follows:
m is the slope, representing the rate of change of the output variable y relative to the input variable x.b is the y-intercept, representing the value of y when the graph of the function touches or crosses the y-axis.From the second bullet point above, the intercepts for each function in this problem are given as follows:
1. b = 3.2. b = -3.3. b = 1.4. b = -2.The slopes are given as follows:
1: m = -1, when x increases by 1, y decays by 1.2: m = 1, when x increases by 1, y increases by 1.3. m = 3, when x increases by 1, y increases by 3.4: m = -2, when x increases by 1, y decays by 2.Missing Information
The problem is incomplete, hence we just define the linear functions.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
the difference between the sample statistic and the population parameter when sampling is done correctly is referred to as what?
A sampling error is the difference between a population parameter and a sample statistic.
Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.
Thus, the difference is defined as sampling error.
To learn more about statistics check the link below:
https://brainly.com/question/15525560
#SPJ4
I need to know the question to a problem 10”=14,521
Answer:
The value of n in this equation is 5.
Step-by-step explanation:
This can be determined by using the property of exponents that states that x^n * x^m = x^(n+m). In this case, 10^n * 10^5 = 14,521, so 10^(n+5) = 14,521. Solving for n, we get n = 5.
A rocket will launch in 3. 75 hour and the launch time i 11:20 am. What time i it now??
The time presently is 8:15 a.m, and the rocket will launch in 3.75 hours, at 11:20 a.m.
What is subtraction?Subtraction (represented by the minus sign) is one of four mathematical operations, the others being addition, multiplication, and division. Subtraction is the procedure of removing items from a collection. Subtraction may be thought of as the inverse of addition. Counting forwards helps children learn to add. To subtract, they just count backwards.
Here,
launch time=11:20 am
time left to launch=3.75 hour
=0.75*60
=45 minutes
= 3 hours 45 minutes
=11 hours 20 minutes-3 hours 45 minutes
=8 hours 15 minutes
=8:15 AM
The time right now is 8:15 AM when rocket will launch in 3. 75 hour and the launch time is 11:20 am.
To know more about subtraction,
https://brainly.com/question/25114508
#SPJ4
Will give brainliestttt PLEASE I NEED HELP :((((
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 4)(2, 8)(3, 16)(4, 32)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work. (4 points)Part C: Determine the average rate of change between station 2 and station 4. Show your work. (4 points)
Step-by-step explanation:
A
for a linear function the slope ratio has to be the same between every pair of data points.
between (1, 4) and (2, 8) we have
x changes by +1 (from 1 to 2).
y changes by +4 (from 4 to 8).
the slope is
+4/+1 = 4
between e.g. (2, 8) and (3, 16) we have
x changes by +1 (from 2 to 3).
y changes by +8 (from 8 to 16).
the slope here is +8/+1 = 8.
which is not the same as 4.
so, it is not a linear function.
it is an exponential function.
B.
the function is actually
f(x) = y = 2^(x+1)
an exponential function is of the form
y = a^x
in our case we have
4 = a¹ = 2²
8 = a² = a¹×2 = 2² × 2 = 2^(2+1)
16 = a³ = a²×2 = a¹×2×2 = 2²×2×2
we see
f(n) = a1×2^(n-1) = 2²×2^(n-1) = 2^(n+1)
C.
the average rate of change is
(the difference of the function results at the interval ends) / (the difference of the interval ends).
so, in our case
(f(4) - f(2))/(4 - 2) = (32 - 8)/2 = 24/2 = 12
the average rate of change between stations 2 and 4 is 12 (or 12/1).
Answer:
Um in an old question of mine you said "its been forever". That was my elijahmiraclechild account. I don't really remember you but I would like to
Step-by-step explanation:
Question 4
The weights for 12-month-old baby boys are normally distributed with a mean of 22.5 pounds and a standard deviation of 2.2 pounds.
Find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds.
ANSWER -
Answer:
70.5%
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 22.5Standard deviation σ = 2.2Therefore, if the weights of the 12-month-old baby boys are normally distributed:
[tex]\boxed{X \sim\text{N} \left(22.5,2.2^2 \right)}[/tex]
where X is the weight of the baby boy.
To find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds find P(19.7 ≤ X ≤ 24.4).
Calculator input for "normal cumulative distribution function (cdf)":
Upper bound: x = 19.7Lower bound: x = 24.4σ = 2.2μ = 22.5[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=0.704548741[/tex]
[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=70.5\%[/tex]
Therefore, the percentage of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds is 70.5% (nearest tenth).
If C is ¼ of the distance from A to D if A is (3,7) and D is (11,11) where is C?
Answer:
(8.25, 9.75)
Step-by-step explanation:
To find the point that is ¼ of the distance from A to D, we first need to find the coordinates of D. Since A is located at the point (3, 7) and D is located at the point (11, 11), we can use the distance formula to find the distance between these two points. The distance formula is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have x1 = 3, y1 = 7, x2 = 11, and y2 = 11, so the distance between A and D is:
distance = √((11 - 3)^2 + (11 - 7)^2) = √(8^2 + 4^2) = √(64 + 16) = √80 = 8.944
Now that we know the distance between A and D, we can use this information to find the point that is ¼ of the distance from A to D. Since C is ¼ of the distance from A to D, it is located ¼ of the way along the line between A and D. This means that we can find the coordinates of C by taking the average of the coordinates of A and D, weighted by ¼ and ¾, respectively. In other words, the coordinates of C are given by:
C = ¼ * A + ¾ * D
where A and D are the coordinates of points A and D, respectively. Plugging in the coordinates of A and D, we get:
C = ¼ * (3, 7) + ¾ * (11, 11) = (0.75 * 3 + 2.25 * 11, 0.75 * 7 + 2.25 * 11) = (8.25, 9.75)
Therefore, the point C is located at the coordinates (8.25, 9.75).
Determine the period.
Enter
Answer:
Your answer should be [tex]\frac{\pi }{7}[/tex]
Step-by-step explanation:
Looking at the x-axis we can say that is our b.
Period Formula: 2π/b.
x-axis is from 0 to 20.
b = 14 because of the rise to rise.
2π/14 = π/7
True
False
ܘ ܗ
10
15-
f(x)
0
3
The range of the given function in the figure is R - {0, 1, 2, 3}.
What is the range of a function?The range of a function is represented by the set of output values for the given input values.A range for a function depends on the domain of the function. Where the domain is nothing but the set of input values to the function.If a function is given by y = f(x), then the range is given by R = {y: x ∈ D of f}D - the domain of the function; R - the range of the functionCalculation:The given mapping shows a function f(x).
There are 4 inputs to the function and 5 outputs.
So, the domain set for the given function is written as D = {0, 5, 10, 15}
And the range set for the given function is written as R = {0, 1, 2, 3}
(Since the 5th output is repeating, in the range it is considered only once).
Learn more about the range of the function here:
https://brainly.com/question/10197594
#SPJ1
A radioactive isotope has a half life of 1 month. It begins with 500 grams. After 8 months, how many grams would it have. Round to the nearest two decimal places.
Answer:
t1/2=1m => 30days
A0=500g =0.5kg
t=8m = 240days
A=?
λ=ln2÷t1/2
λ=0.6931÷30
λ=0.0231033333
A=A0×e^-λ×t
A=0.5×e^-0.0231033333×240
A=1.953125grams
The fraction 5/6 * i is equivalent to what percent ? Round your percent to the nearest tenth. 5/6 is approximately 96
It is approximately equal to 83.3%
What are percentages?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”
Given here, 5/6 thus in percentage terms it will be = 5/6 × 100
= 83.3%
Hence the answer is 83.3%
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
Which equation represents twenty-nine is one-third of the number n?
Answer:
29=n/3
Step-by-step explanation:
Answer:
29 = n/3
Step-by-step explanation:
[tex]29 = \frac{1}{3} of \: n \\ 29 = \frac{1}{3} \times n \\ 29 = \frac{n}{3} [/tex]
Line a passes through the points (0, 4)
and (4, 0). Line b passes through the
points (0, 7) and (7, 0). Are the lines
parallel? Explain.
Answer:
Yes, the lines are parallel. This is because the lines have the same slope. The slope of a line is a measure of how steep the line is, and it is calculated by taking the difference of the y-coordinates of two points on the line and dividing it by the difference of the x-coordinates of the same two points. In this case, the slope of line a is -1, and the slope of line b is also -1. Because the lines have the same slope, they are parallel to each other.
This week, a pack of tomato plants costs $25. Next week, the plants are on sale for 15% off.
Larissa wants to know the price of the tomato plants if she buys them next week.
How much is the discount?
Price This Week
%
$
$
Price Next Week
%
25
$
Discount
15
?
%
The discount is $3.75 and the amount next week will be $21.25
How to illustrate the percentage?This has to do with a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the pack of tomato plants costs $25. Next week, the plants are on sale for 15% off. Larissa wants to know the price of the tomato plants if she buys them next week.
The discount will be:
= 15% × $25
= $3.75
The amount next week will be:
= $25 - $3.75
= $21.25
Learn more about percentages on:
brainly.com/question/24877689
#SPJ1
Solve the equation by subtracting the appropriate number from both sides and enter the value of x below. x + 2551 = 3105
Answer:
554
Step-by-step explanation:
x + 2551 - 2551 = 3105 - 2551
x = 554
Answer:
[tex]x + 2551 = 3105 \\ x + 2551 - 2551 = 3105 - 2551 \\ x = 554[/tex]
A city has a 5% sales tax. What is the constant of proportionality?
Answer: 0.05
Step-by-step explanation:
The equation is k = y/x, which is a constant change rate
Take 5 divided by 100 = 0.05
5% = 0.05
So the constant of proportionality is 0.05
You need to determine where to place the beams so that the chains are fastened to the rollercoaster at a height of 25 feet. Write the equation you would need to solve to find the horizontal distance each beam is from the origin. (10 points).
Using the roller coaster as an example, draw a right triangle.
The equation used to find the horizontal distance: h² = 30² - 25².16.58 feet is the horizontal distance.What are ways to arrive at the equation?25 feet is listed as the height.The answer to the whole question is that the roller coaster measures 30 feet long.Use h to symbolize the horizontal distance.
The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.
30² = h² + 25².
Assemble similar phrases.
h² = 30² - 25².
horizontal separation
In (a), there is:
h² = 30² - 25².
This results:
h² = 275
Take both sides' roots.
h = 16.58
Consequently, 16.58 feet are the horizontal distance.
To know more about the right triangle, here
https://brainly.com/question/25016594
#SPJ4
The diagram below is used to sort out numbers.
Type each number in the correct location on the diagram.
3
30
333
3001
two-digit
numbers
multiples
of 3
three-digit
numbers
The solution is given as,
Two-digit numbers Multiples of 3 Three-digit numbers
30 3,30, 333, 333
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Place the given number in the appropriate place.
Numbers are 3, 30, 333, 3001,
Two digit number among the numbers = 30
Multiples of 3 among numbers = 30, 333, 3
Three-digit numbers among the numbers = 333
Thus, It is shown that the numbers are placed in their appropriate positions.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
One ector of a circle ha an area of 121 quare centimeter and an arc meaure of 36'. What i the area of the circle to the nearet
quare centimeter
The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]
Given in the question,
The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]
The measure of an arc = is 36 inches.
According to the attached figure,
Let us consider the arc length = L
Let radius = r
As per the question L = 36'
Let the radius be
To calculate the length of the arc we need to use the formula,
L = r x θ
36 = r x θ
θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1
Now according to the area of the sector of the circle,
A = [tex]r^{2}[/tex] x θ / 2
121 = [tex]r^{2}[/tex] x θ / 2
[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )
[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex] ----- equation 2
r = [tex]\frac{2 * 121 }{36}[/tex]
r = 6.72 cm.
Now if the radius is = 6.72 cm
Diameter = 2 x radius
= 2 x 6.72
= 13.44 cm
Area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi[/tex] x 6.72 x 6.72
= 144.87 [tex]cm^{2}[/tex]
Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]
To know more about the Area of the circle,
https://brainly.com/question/12269818
#SPJ4