The simplification of the function is r(x)=10x - 95.
We are given that;
s(x) = -85 and a(x) = 10(x - 1)
Now,
To create a function that combines them, you can substitute these expressions into the formula above:
r(x) = s(x) + a(x) r(x) = (-85) + 10(x - 1)
You can simplify this function by distributing the 10 and combining the constants:
r(x) = -85 + 10x - 10 r(x) = 10x - 95
Therefore, the function will be r(x)=10x - 95.
Learn more about function here:
https://brainly.com/question/2253924
#SPJ1
Please help me!
Which of these graphs represent a function?
Answer:
X
Step-by-step explanation:
You want to identify the graph that represents a function.
Vertical line testA graph represents a function if no vertical line intersects the graph in more than one place.
W – the line x=0 intersects the graph at y = -4 and at y = 4. This graph is not the graph of a function.
X – At points where the graph might overlap, one point is identified as not include, (1, -1) for example, while the other point is identified as included (1, 1) for example. This means there is only one function value at that point, so this is the graph of a function.
Y – The vertical line x=-2 intersects the graph in an infinite number of points. This graph is not the graph of a function.
Z – The vertical line x=0 intersects the graph at y = -2, y = 0, and y = 2. This graph is not the graph of a function.
<95141404393>
For each graph below, state whether it represents a function. I don’t know if I got them right
Answer:
Step-by-step explanation:
Use the vertical line test. If you can draw a vertical line that cuts more than one point then the graph is not a function.
The only one that is incorrect is graph 4. It is a function (no vertical line will cut the graph more than once).
1/2x^2+3x-5 min or max
The function f(x) = (1/2)x^2 + 3x - 5 has a minimum value
Classifying the function as min or maxTo determine whether the function f(x) = (1/2)x^2 + 3x - 5 has a minimum or maximum value, we can use the fact that the vertex of a quadratic function represents the minimum or maximum point of the function.
To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.
In this case, a = 1/2 and b = 3, so we have:
x = -b/2a = -(3)/(2(1/2)) = -3
To find the corresponding y-coordinate, we can substitute x = -3 into the function:
f(-3) = (1/2)(-3)^2 + 3(-3) - 5 = -9.5
Since the coefficient of the quadratic term is positive, we know that the parabola opens upward and the vertex represents a minimum value.
Therefore, the minimum value of the function is -9.5, which occurs at x = -3.
Read more about quadratic function at
https://brainly.com/question/30660734
#SPJ1
If the function y=e−2x is vertically compressed by a factor of 3, reflected across the y-axis, and then shifted down 2 units, what is the resulting function? Write your answer in the form y=ceax+b
The resulting function is given as follows:
[tex]y = \frac{e^{2x}}{3} - 2[/tex]
How to obtain the resulting function?The parent function in the context of this problem is given as follows:
[tex]y = e^{-2x}[/tex]
When the function is vertically compressed by a factor of 3, we have that it is divided by three on the range, hence:
[tex]y = \frac{e^{-2x}}{3}[/tex]
When the function is reflected across the x-axis, we multiply by -1 on the domain, hence:
[tex]y = \frac{e^{2x}}{3}[/tex], as -2x x -1 = 2x.
When it is shifted down two units, we subtract by two on the range, hence:
[tex]y = \frac{e^{2x}}{3} - 2[/tex]
More can be learned about functions at https://brainly.com/question/2456547
#SPJ1
The value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m2 – 3,500m + 18,000, where m is the approximate number of months since the start of 2020.
Over what period was the value of the card declining?
< m
If the value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m² – 3,500m + 18,000, the value of the card was declining over the period 0 < m < 7.
To determine when the value of the collectible card was declining, we need to look for when the first derivative of the function is negative. If the first derivative of the function is negative over a certain period, then the function is decreasing over that period. The first derivative of the function V(m) is:
V'(m) = 500m - 3,500
To find when the value of the card was declining, we need to solve the inequality V'(m) < 0. Solving for m, we get:
500m - 3,500 < 0
500m < 3,500
m < 7
Therefore, the value of the card was declining over the period 0 < m < 7. This corresponds to the months from January 2020 to July 2020. During this period, the first derivative of the function V(m) is negative, which means the value of the card was decreasing.
To learn more about equation click on,
https://brainly.com/question/31533526
#SPJ1
Suppose that the function f is defined as follows.
Answer:
Step-by-step explanation:
Please help me understand this
Answer:
To find the value of y, we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
We know that the slope is 5, and the two points on the line are (5,y) and (4,1). We can substitute these values into the slope formula to get:
5 = (y - 1) / (5 - 4)
Simplifying this equation gives:
5 = y - 1
Adding 1 to both sides gives:
y = 6
Therefore, the value of y is 6.
Step-by-step explanation:
Jermaine invested $3,200 in a defined-contribution account. Assuming he is in a 20% marginal tax bracket, how much did he lower his income taxes with the investment
Jermaine's income tax was lowered by $640 as a result of the investment.
Investment calculationAssuming that the defined contribution account is a tax-deferred retirement account, Jermaine can lower his income taxes by the amount of his contribution multiplied by his marginal tax rate. The formula for this tax savings is:
Tax savings = Contribution × Marginal tax rate
Using the given values, Jermaine's contribution to the account is $3,200 and his marginal tax rate is 20%. Substituting these values into the formula, we get:
Tax savings = $3,200 × 0.20 = $640
Therefore, Jermaine can lower his income taxes by $640 by contributing $3,200 to the defined contribution account.
More on investment can be found here: https://brainly.com/question/15353704
#SPJ1
Simplify. Simplify. Express your answer as a single term, without a denominator.
pls helpppppp
Simplifying further, you can move any negative exponents to the denominator by changing their sign:
t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)
what is denominator ?
In a fraction, the denominator is the bottom number that represents the total number of equal parts into which the whole is divided. For example, in the fraction 3/4, the denominator is 4, which indicates that the whole has been divided into four equal parts.
In the given question,
When multiplying two terms with the same base, you can add their exponents, so:
t⁻¹ u v⁴* t⁻¹ u⁻⁷ v⁰ = t⁻² u⁻⁶ v⁴
Simplifying further, you can move any negative exponents to the denominator by changing their sign:
t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)
To know more about denominator , visit:
https://brainly.com/question/7067665
#SPJ1
what is the x-intercepts of y=-3x(4-x)
The x-intercepts of the given function y = -3x(4-x) are x = 0 and x = 4.
As we know that the x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses
To determine the x-intercepts of a function, we need to set y=0 and solve for x.
In this case, we have:
y = -3x(4-x)
0 = -3x(4-x)
0 = 3x(x-4)
Therefore, the x-intercepts occur when either 3x=0 or x-4=0.
Solving for x, we get:
3x = 0, x = 0
x - 4 = 0, x = 4
Therefore, the x-intercepts of y=-3x(4-x) are x=0 and x=4.
Learn more about the x-intercept here:
https://brainly.com/question/14180189
#SPJ1
According to a recent poll, 22% of US adults get an average of 7 or more hours of sleep per night. Assume this is the parameter value for the population. Suppose you select a simple random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night. Let p(hat) = the proportion in the sample who get an average of 7 or more hours of sleep per night.
Assuming the polling information is true, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night is ?
answer is .3664
If needed, use the z-table to answer the question.
assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
The mean of the sample proportion distribution is given by:
μp(hat) = p = 0.22
The standard deviation of the sample proportion distribution is given by:
σp(hat) = sqrt((p*(1-p))/n) = sqrt((0.22*0.78)/50) = 0.0802
To find the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night, we need to find the z-score corresponding to this value:
z = (0.20 - 0.22) / 0.0802 = -0.2494
Using a standard normal table or calculator, we find that the probability of obtaining a z-score of -0.2494 or less is 0.4019. Therefore, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night,
Hence assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
Learn more about probability, by the following link.
brainly.com/question/24756209
#SPJ1
CAN SOMEONE PLEASE HELP me with the correct answer!!!!! I need this done please help like please
please help
What is the distance to the earth’s horizon from point P?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
x =
mi
The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.
How to find the distance to the earth horizon from a given point
In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:
x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]
x = 284.372 mi
The distance x is equal to 284.372 miles.
To learn more on Pythagorean theorem: https://brainly.com/question/14930619
#SPJ1
From the observation deck of a skyscraper, Brandon
The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
How to solveGiven that:-
The angle is = 45
The height of the skyscraper is 1140 feet.
The horizontal distance will be calculated by applying the angle property in the right angle triangle.
tan45 = ( P / B )
B = P / tan45
B = P Since ( tan45 =1 )
B = 1140 feet.
Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
Read more about distance here:
https://brainly.com/question/2854969
#SPJ1
From the observation deck of a skyscraper, Brandon measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Factor the expression. x^2-14x-32
Answer:
[tex](x-2)(x+16)[/tex]
Step-by-step explanation:
Use graphing calculator and find the x-intercepts.
Hawk thinks his heartrate will increase as he increases his skateboarding speed. To see if this relationship exists, he records six different speeds and models it with a scatterplot and regression output.
A scatterplot is shown with the x axis labeled Speed, miles per hour, and the y axis labeled Pulse, beats per minute. The points on the graph increase from 9.5 and 68 to 15.8 and 116.
Regression Statistics
Multiple R 97.28153%
R Square 94.63696%
Adjusted R Square 93.29620%
Standard Error 4.806846736
Observations 6
df SS MS F
Regression 1 1,630.910231 1,630.910231 70.58453
Residual 4 92.42310217 23.10577554
Total 5 1,723.333333
Coefficients Standard Error t Stat p-Value
Intercept 1.301246992 10.66036651 0.122064001 0.908735
Speed 7.315685846 0.870763656 8.401459797 0.001098
Part A: Write the equation of the regression line using the regression output. (2 points)
Part B: What do the slope and intercept parameters mean using the context of the problem? (4 points)
Part C: Compute the margin of error that Hawk should use if he wants to provide a 99% confidence interval for the slope. Assume that conditions for inference are satisfied. (4 points)
The equation of the regression line is Pulse = 1.301 + 7.316 * Speed. The slope parameter represents how pulse rate changes with skateboarding speed. The margin of error for a 99% confidence interval for the slope is 2.517.
Explanation:Part A: The equation of the regression line can be written as: Pulse = 1.301 + 7.316 * Speed
Part B: The slope parameter of 7.316 means that for every 1 unit increase in skateboarding speed, the pulse rate increases by an average of 7.316 beats per minute. The intercept parameter of 1.301 represents the pulse rate at a speed of 0 miles per hour (which doesn't have a specific meaning in this context).
Part C: To compute the margin of error for a 99% confidence interval for the slope, we use the formula: margin of error = critical value * standard error. The critical value for a 99% confidence interval is approximately 2.896. Plugging in the values, we get margin of error = 2.896 * 0.870 = 2.517 (rounded to three decimal places).
Learn more about Regression analysis here:https://brainly.com/question/31873297
#SPJ2
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:
B. 2.3p – 10.1 = 6.49p – 4
C. 230p – 1010 = 650p – 400 – p
How to determine the required equations?From the information provided, we have the following equation:
2.3p – 10.1 = 6.5p – 4 – 0.01p
Next, we would simplify the given equation by collecting like terms as follows;
2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4
2.3p - 10.1 = 6.49p - 4
What is the multiplication property of equality?In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.
By multiplying both sides of the given equation by 100, we have the following;
100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)
230p - 1010 = 650p - 400 - p
Read more on multiplication property of equality here: brainly.com/question/17565345
#SPJ1
An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 are white, and 30 are pink. If he reaches into the bag randomly and removes one at a time, what is the probability that the first three cases are all pink? Please help I have no clue how to do this at all. I listen in math class but this is hard!
The probability of drawing a pink case on the first draw is 30/80.
What is probability?Probability is a branch of mathematics that deals with the measurement and analysis of random phenomena. It is the study of the likelihood or chance of an event occurring. It involves analyzing and predicting the likelihood of certain outcomes based on the available information and the rules of probability theory. Probability is used extensively in various fields, including statistics, physics, finance, engineering, and computer science, among others.
In the given question,
The probability of drawing a pink case on the first draw is 30/80. Since the cases are not replaced, the probability of drawing a pink case on the second draw is 29/79 (there are now 29 pink cases left out of 79 total cases). Similarly, the probability of drawing a pink case on the third draw is 28/78. Therefore, the probability of drawing three pink cases in a row is:
(30/80) * (29/79) * (28/78) = 0.0412 or about 4.12%.
So, the probability that the first three cases are all pink is 0.0412 or about 4.12%.
To know more about probability, visit:
https://brainly.com/question/11234923
#SPJ1
Read the piccture and thank you
HOW TO SOLVE LINEAR REGRESSIONS
A scientist has two solutions, which she has labeled solution a and solution
b. each contains salt. she knows that solution a is 65% salt and solution b is 80% salt. she wants to obtain 150 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?
Consider the function.
f(x)=2log5(x−2)+1
On what interval is the function positive?
Enter your answer in the box. Round to the nearest hundredth.
on any day ,the probability that marcus will get a seat on the schoo bus is 0.93 . what is the probability that he does not get a seat on the school bus?
Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .
what is probability ?The prospect of an event happening is assessed by probability. It is a number between zero and 1, where 0 denotes an improbable occurrence and 1 denotes a certain occurrence. For instance, if we flip a fair coin, the odds of obtaining heads are 0.5, or 50%, and the odds of receiving tails are also 0.5, or 50%. In each case, there are various ways to compute probability. In general, if an event has n equally possible results and k of them are favourable, the likelihood that the event will occur is: Event P = k/n . All possible outcomes are thought to be equally likely under what is referred to as the classical probability.
given
Simply put, the likelihood that Marcus won't obtain a seat on the school bus is the complement of the likelihood that he will.
By deducting the probability from 1, one can determine the complement of a probability. So:
Chance of not being seated equals one less than the likelihood of being seated.
The likelihood of not getting a seat is equal to 1 - 0.93.
0.07 percent of people will not receive a seat.
Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
If $4,500 is invested at an interest rate of 5.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a) 4 years
(b) 8 years
(c) 12 years
a) The value of the investment after 4 years is $5,544.90.
b) The value of the investment after 8 years is $6,849.42.
c) The value of the investment after 12 years is $8,453.35.
The formula for calculating the value of an investment that is compounded continuously is given by:
A = [tex]Pe^{(rt)[/tex]
where A is the final value of the investment, P is the initial investment amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time period in years.
(a) To find the value of the investment after 4 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05254)[/tex]
A = 4500[tex]e^{0.21[/tex]
A = 45001.2322
A = $5,544.90
(b) To find the value of the investment after 8 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05258)[/tex]
A = 4500[tex]e^{0.42[/tex]
A = 45001.5221
A = $6,849.42
(c) To find the value of the investment after 12 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.052512)[/tex]
A = 4500[tex]e^{0.63[/tex]
A = 45001.8785
A = $8,453.35
To learn more about interest click on,
https://brainly.com/question/23092865
#SPJ1
Which expression represents the volume of a shipping box? s(2^3) (8 + 2)3 (8x2)3 8+23
As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.
what is volume ?A tri object's volume is a measurement of how much space it takes up. The usual measurement tool is a cubic unit, such as a cubic metre (m3) or cubic foot (ft3). The formula used to determine a solid item's volume depends on the shape of the object. For instance, the volume of a cube is determined by multiplying the length of a single of its sides by six, whereas the capacity of a cylinder is determined by dividing the area of its base by the diameter. Engineering, mathematics, and architecture are just a few of the disciplines where the idea of volume is crucial.
given
The formula used to calculate a shipping box's volume is based on the box's dimensions.
The box's volume can be expressed as follows if its side length is s:
[tex]V = s^3[/tex]
As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.
To know more about volume visit :-
https://brainly.com/question/1578538
#SPJ1
B as a % of A is equal to A as a % of (A+B). Find B as a % of A.
Option (b), 62% is correct.
How to solveBy the given condition,
B/A = A/(A + B) ..... (1)
Now to find the percentage of A = B, we consider B = Ax. From (1), we get
Ax/A = A/(A + Ax)
or, x = 1/(1 + x)
or, x² + x - 1 = 0
Using the quadratic formula, we get
x = {- 1 ± √(1 + 4)}/2
= (- 1 ± √5)/2
Since x cannot be negative, we take
x = (- 1 + √5)/2
≈ 0.62
Therefore the required percentage is
= 0.62 × 100%
= 62%
Read more about percentage here:
https://brainly.com/question/24877689
#SPJ1
B as a percentage ofAis equal to Aas a
percentage of(A+B). How much percent
of A is B?
(a) 60%
(b) 62%
(C) 64%
(d) 66%
Need help. What is the x value pic attached below
The value of x in the function f(x) = (1/3)^x - 2 such that f(x) = 7 is -2
Calculating the value of xFrom the question, we have the following equation that can be used in our computation:
f(x) = (1/3)^x - 2
When the value of f(x) is 7, we have
(1/3)^x - 2 = 7
So, we have
(1/3)^x = 9
Take the log of both sides
x = log(9)/log(1/3)
Evaluate
x = -2
Hence, the value of x is -2
Read more about exponential functions at
https://brainly.com/question/2456547
#SpJ1
PLS HELP THIS IS DUE TOMORROW
Answer: y = -|x + 1| + 1
Step-by-step explanation:
Since this is a "V" shaped graph, we know it uses the absolute value function. This is the parent function:
y = |x|
This represents the transformations:
➜ a is amplitude
➜ h is horizontal shift
➜ k is vertical shift
f(x) = a | x - h | + k
Next, we see it is shifted one unit upwards.
y = |x| + 1
Then, we see it is also shifted one unit left.
➜ Note that this shift is -h units, so we will use positive for moving left.
y = |x + 1| + 1
Lastly, we see this graph is flipped and has a negative slope, or amplitude.
y = -|x + 1| + 1
Confusing Calculus Parametric Equations Question
Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.
what is acceleration?The rate at which an object's velocity varies with respect to time is known as its acceleration. It is a vector quantity whose definition is the product of the velocity change and the time period during which the change takes place. Depending on the direction and size of the velocity change, acceleration may be positive, negative, or zero. Acceleration in physics is frequently represented by the letter "a," and its SI unit is metres per second squared (m/s2).
To find when the bullet will hit the ground, we need to find the time at which y = 0.
y = vo sin(a) t - (1/2)g[tex]t^2[/tex], where g is the acceleration due to gravity (9.8 m/s^2).
Setting y = 0, we get:
0 = vo sin(a) t - (1/2)g[tex]t^2[/tex]
Solving for t using the quadratic formula, we get:
Since we want the time when the bullet hits the ground, we take the positive root:
t = (vo sin(a) + √((vo sin(a))^2 + 2gy)) / g
Plugging in the values given, we get:
t = (550 m/s * sin(a) + √((550 m/s * sin(a))^2 + 2 * 9.8 m/s^2 * 0)) / 9.8 m/s^2
Simplifying, we get:
t = (550 m/s * sin(a)) / 9.8 m/s^2
t = 35.27 seconds (rounded to two decimal places)
To find how far from the gun the bullet will hit the ground, we need to find the value of x at this time:
x = vo cos(a) t
Plugging in the values given, we get:
x = 550 m/s * cos(a) * 35.27 s
x = 18602.57 meters
Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.
to know more about acceleration:
https://brainly.com/question/30660316
#SPJ1
I need help with this econ question. Thank you.
Answer:
c + 3.6 + 3.4 + 4.1 + 2.3 = 18.6
c + 13.4 = 18.6
c = 5.2
$5.2 trillion was spent on consumption.
