Answer:
$12,276.24
Step-by-step explanation:
22000 / (1 + 0.105/12)^4*12
12276.24
If the profit function for a product is
P(x) = 2400x + 105x^2 − x^3 − 167,000
dollars, selling how many items, x, will produce a maximum profit?
x = items
Selling 80 items will produce maximum profit if the profit function is [tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex].
What is the value of x that produces maximum profit?To find value of x that produces maximum profit, we must get critical points of the profit function and determine which one corresponds to a maximum.
The profit function is given as:
[tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex]
Taking the derivative of P(x) with respect to x, we get:
[tex]P'(x) = 2400 + 210x - 3x^2[/tex]
Setting P'(x) equal to zero and solving for x, we get:
[tex]0 = 2400 + 210x - 3x^2\\3x^2 - 210x - 2400 = 0\\x^2 - 70x - 800 = 0\\(x - 80)(x + 10) = 0[/tex]
Here, the critical points are x = 80 and x = -10.
To determine one that corresponds to a maximum, we can use the second derivative test. Taking the derivative of P'(x), we get:
[tex]P''(x) = 210 - 6x[/tex]
Evaluating P''(80), we get:
[tex]P''(80) = 210 - 6(80)\\P''(80) = 210 - 420\\P''(80) = -330[/tex]
Since P''(80) is negative, the critical point x = 80 corresponds to a maximum. So, selling 80 items will produce maximum profit.
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Which of the following new vehicle borrowers is likely to be offered the lowest APR?
A.Stephanie who is buying a new vehicle and has a FICO score of 780
B. Tyler who is buying a used vehicle and has a FICO score of 780
C. Emily who is buying a new vehicle and has a FICO score of 600
D. Daniel who is buying a used vehicle and has a FICO score of 600
Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.
Since, When it comes to APR for a new or used vehicle loan, a borrower's credit score is one of the main factors considered by lenders.
The higher the credit score, the very more likely that a borrower is to be offered a lower APR.
Hence, In this case,
Tyler has a FICO score of 780 which is considered excellent, and is buying a used vehicle.
This combination of a high credit score and a used vehicle purchase makes Tyler the most likely candidate to be offered the lowest APR.
Thus, Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.
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Which of the following sets of numbers could not represent the three sides of a right
triangle?
11, 60, 61}
{14, 48, 50
{46, 60, 75}
(39,80,89}
Answer: D
Step-by-step explanation: it equals 181
I need help to get the residual plot from this data 13.8 1.42 16.7 3.21 0.7 1.11 18 4 16.7 3.21 20 4 18 3.8 19.5 3.78 21.9 3.69 0.7 1.11
Answer:
To create a residual plot, you need to first fit a model to the data. Without any information about the problem you are trying to solve or the model you are fitting, I will assume that you are trying to fit a linear regression model to these data points.
First, you would need to find the equation of the line that best fits the data using a regression analysis software or by hand. Let's assume that the equation of the line is:
y = 0.2x + 2.5
where y is the response variable (dependent variable) and x is the predictor variable (independent variable).
Next, you would calculate the predicted values of y (i.e., the values that the model predicts) for each value of x in your dataset, using the equation of the line. For example, for the first data point (13.8, 1.42), the predicted value of y would be:
y_predicted = 0.2 * 13.8 + 2.5 = 5.06
The residual for this data point would be the difference between the actual value of y and the predicted value of y:
residual = 1.42 - 5.06 = -3.64
You would repeat this process for each data point in your dataset, to get a list of residuals.
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).
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I would be thankful if you help
To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:
[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]
Understanding MatrixThe solution provided above uses a method of matrix called Echelon.
Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.
By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.
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5. Which box-and-whisker plot represents this set of data? (1 point)
90, 98, 75, 84, 89, 91, 70, 81, 93, 84, 100
allison jogged around lions park for one hour and according to her pedometer she covered 4.5 miles. if allison jogs at the same rate for 1 and a half hours how many miles will she jog?
If Allison jogs at the same rate for 1 and a half hours, the number of miles that she would jog is 6.75 miles.
What is speed?In Mathematics and Science, speed is the distance covered by a physical object per unit of time.
How to calculate the speed?In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Speed = 4.5/1
Speed = 4.5 miles per hour.
Making distance the subject of formula, we have:
Distance, d(t) = speed × time
Distance, d(t) = 4.5 × 1.5
Distance, d(t) = 6.75 miles.
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Correct answer gets brainliest!!!!
It is a point and point is zero dimensional. Therefore the right options are A and C respectively.
Understanding Point in MathematicsPoint is a basic geometric object that represents a location or a position in space. It is often represented as a dot or a small circle.
Points have no size, shape, or dimension. They are considered to be zero-dimensional objects, and they are often used as a building block for more complex geometric structures.
In addition to representing locations in space, points are also used in other areas of mathematics, such as in coordinate systems and in topology. In geometry, points are used to define lines, planes, and other geometric shapes.
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Abel starts walking from Point A at a speed of 4 km/h, 2 hours later, from Point A,
Jack rides his bicycle at 8 Km/h along the same route.
a) When will Jack overtake Abel?
b) How far will they have travelled by the time Jack overtake Abel?
Answer:
a) In 2 hours
b) 16 km
Step-by-step explanation:
Let's first find out how far Abel has traveled in 2 hours. We can use the formula:
distance = speed x time
distance = 4 km/h x 2 h = 8 km
So when Jack starts cycling, Abel has already covered 8 km.
Now, let's say it takes Jack t hours to catch up to Abel. During this time, Abel has continued walking for t + 2 hours. So we can write:
distance covered by Abel = distance covered by Jack
4 km/h x (t + 2 h) = 8 km/h x t
Simplifying this equation, we get:
4t + 8 = 8t
4t = 8
t = 2
So Jack will overtake Abel after 2 hours of cycling. To find out how far they will have traveled, we can use the formula:
distance = speed x time
distance = 8 km/h x 2 h = 16 km
Therefore, when Jack overtakes Abel, they will have traveled 16 km in total.
A side of the triangle below has been extended to form an exterior angle of 125°. Find the value of
From the given triangle, x has a value of 35°.
As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.
Which angles are adjacent?Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.
According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.
Now, 125°+ y =180°
y = 180°-125°
y = 55°
As a result, the supplied triangle's value for y is 55°.
The sum of the triangle law,
55°+ 90° + x = 180°
x = 35°
Therefore the value of x = 35°
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Select the correct answer.
Consider functions f and g.
f(z) = log (x - 1)
g(x)
²-4
Which statement gives the best approximation of the solutions of the equation f(x) = g(z)?
OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642
-3.464 and z≈ 3.642.
OB.
The solutions are where the graphs of the functions cross the x-axis at z
O C.
The solutions are where the graphs of the functions intersect at
-3.464 and z≈ 3.464
O D.
The solutions are where the graphs of the functions cross the x-axis at z ≈ -4 and ≈ 0.422
The statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:
option A. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.
How did we get the value?To find the solutions of the equation f(x) = g(x), set f(x) = g(x) and then solve for x. Using the given functions, we have:
log(x - 1) = (⅓x² - 4)
Exponentiating both sides:
x - 1 = e^(⅓x²-4)
Solve for x:
x = e^(⅓x²-4) + 1
Therefore, the solutions to the equation f(x) = g(x) are given by the values of x for which the graphs of the functions intersect. To find these points of intersection, plot the graphs of the functions and look for the points where they intersect. In other way round, solving for x numerically:
Based on the given functions, it is clear that g(x) is an upward-facing parabola with its vertex at (0, -4) and x-intercepts at (-2√3, 0) and (2√3, 0). The function f(x) is defined only for x > 1, and its graph is a monotonically increasing curve that approaches infinity as x approaches 1 from the right.
Therefore, there is only one point of intersection between the graphs of f(x) and g(x), which occurs to the right of x = 1. This point of intersection can be found numerically using a calculator or computer software, and it is approximately x ≈ 3.642.
Thus, the statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:
OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.
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i need the answer for this +explanation it had me confused
Answer:
The surface area of the square pyramid is 18 km².
Step-by-step Explanation:
What is the surface area of a square pyramid with a slant height?
The surface area of a square pyramid with a slant height can be determined by the product of the base perimeter with the slant height divided by two.
Mathematically, it can be expressed as:
Surface Area S.A = P × l/2
where;
Side length (a) = 3
Base perimeter (P) = 4a = 4(3) = 12km
Slant length (l) = 3 km
Surface Area (S.A) = 12 × (3/2)
Surface Area (S.A) = 12 x 1.5 = 18 km²
Therefore, the surface area of the same pyramid is 18 square km.
[tex]\sf SA_{Pyramid} =\boxed{\sf 27km^{2}}.[/tex]
Step-by-step explanation:We're asked to calculate the surface area (SA) of a pyramid. Surface area of a tridimensional shape isn't more than calculating the area of all of its "faces" and then adding them all together. Some of these tridimensional shapes already have equations that provide a direct calculation of this parameters, without the need to add together the area of the different parts of the shape.
There's a developed formula for directly calculating the surface area of square pyramids, but in this case it is easier to just calculate the individual areas of each face and add them all together.
1. Calculate the area of the base.This is pretty easy to calculate, as the base forms the shape of a square. Therefore, multiplying the length and width of this square will give us that area:
[tex]\sf A_{Base} =lw=3km*3km=\boxed{\sf 9km^{2}} .[/tex]
Check attached image 1 to see where we got these values from.
2. Calculate the area of one triangular face.So these faces form the sape of a triangle. Therefore, mul;tiplying their lengh by width and then dividing by 2 should give us the area.
[tex]\sf A=\dfrac{lw}{2} =\dfrac{(3km)(3km)}{2}=4.5km^{2}.[/tex]
Check attached image 2 to see where we got these values from.
This is the area of an individual triangular face of the pyramid, but we have a total of 4 faces. Hence, let's multiply this area by 4 to find the total area of all triangular faces:
[tex]4.5km^{2} *4=\boxed{\sf 18km^{2}}.[/tex]
3. Calculate the total surface area.So the total surface area, as stated at the beginning of this answer, is given by the addition of all individual areas from all the faces of the shape, so let's do just that:
[tex]\sf SA_{Pyramid} =9km^{2} +18km^{2}=\boxed{\sf 27km^{2}}.[/tex]
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The Venn diagram below shows the 14 students in Ms. Cooper's class.
The diagram shows the memberships for the Chess Club and the Science Club. (ALL SHOWN IN PHOTO BELOW) **AM GIVING BRAINLIEST AND 30 POINTS!!!**
Answer:
Step-by-step explanation:
Suppose that the function f is defined as follows.
A graph of the piecewise function is shown on the coordinate plane in the image attached below.
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals such as -1 < x ≤ 0.
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Gruden Company produces golf discs which it normally sells to retailers for $7 each. The cost of manufacturing 20,000 golf discs is:
Answer:
$140,000
Step-by-step explanation:
7*20,000 = 140,000
help me solve this please 2x+5y
Answer:
35
Step-by-step explanation:
Simply plug in the value of your 'x' and 'y':
x = 4.5
y = 5.2
[tex]2(4.5)+5(5.2)=9+26=35[/tex]
Please help!!!!!!!!!!!!
The calculated values of the sum of interior angles of the shapes are 1080 degrees and 360 degrees
Calculating the sum of interior angles of the shapesThe formula of the sum of interior angles of a polygon is
Sum = (n − 2) * 180
For the octagon, we have
n = 8
This means that
Sum of angles = (8 − 2) * 180
Evaluate
Sum of angles = 1080
For the square, we have
n = 4
This means that
Sum of angles = (4 − 2) * 180
Evaluate
Sum of angles = 360
Hence, the sum of interior angles of the shapes are 1080 degrees and 360 degrees
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PLEASE HELP!
For a group of objects made of the same material, the weight of an object varies directly with its volume. If an object that has a volume of 20 cubic inches weighs 28 ounces, what is the constant of variation?
20
5/7
7/5
28
The constant of variation that exists between the weight and the volume of the objects would be = 7/5. That is option C.
How to calculate the constant of variation?A measurement is said to vary directly with another when the increase in proportion of the object leads to a direct decrease to the other one.
That is for the given object;
Weight is directly proportional to Volume
Therefore, weight = k Volume
K = constant of variation
make k the subject of formula;
k= weight/volume
but weight = 28
volume = 20
k = 28/20
= 7/5
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what is pi * 12 * 2
Answer: 3.14 x 12 x 2
= 75.36
Step-by-step explanation:
Suppose that the function is defined as follows.
Answer:
Step-by-step explanation:
Based on the results, whaBased on the results,, what is the probability of needing fewer than 4 rolls to get doublest
The probability of needing fewer than 4 rolls to get doubles is 13/25.
What is Probability?Probability is a branch of mathematics that deals with the likelihood of something happening. It is used in many areas such as finance, engineering, and even gambling. Probability is the measure of how likely an event is to take place. This is usually expressed as a number between 0 and 1, where a 0 indicates an impossible event, and a 1 indicates an event that is certain to happen. Probability is an important component of decision making, as it allows us to calculate the chances of different outcomes.
This can be calculated by using the binomial probability formula. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of trials. In this case, the number of successes is 2 (the number of doubles required to win the game) and the number of trials is 4 (the maximum number of rolls necessary to win the game).
Using the formula P(x) = nCx * pˣ* qⁿ⁻ˣ, where n is the number of trials, x is the number of successes, p is the probability of success and q is the probability of failure, we can calculate the probability of needing fewer than 4 rolls to get doubles as follows:
P(2) = 4C2 * (1/2)² * (1/2)⁴⁻² = 4 * ( 1/4 ) * (1/4) = 1/4
P(1) = 4C1 * (1/2)¹ * (1/2)⁴⁻¹= 4 * (1/2) * (1/2) = 1/4
The total probability of needing fewer than 4 rolls to get doubles is the sum of the probabilities of needing 1 or 2 rolls to get doubles, which is 1/4 + 1/4 = 1/2, or 13/25.
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Complete questions as follows-
Based on the results, what is the probability of needing fewer than 4 rolls to get doubles? 13/25.
How do you leave 6.92820323 in three significant numbers
Answer:
6.92
Step-by-step explanation:
When ever there are also of decimal places you must at least write the first 2 only.
Hope this helps
please mark me brainliest ♥️
i need answer for this with explanation
Answer:
53yd
Step-by-step explanation:
SA1 = 2(4×2)
= 2×8
= 16
SA2 = 2(4×3)
= 2×12
= 24
SA3 = 2(3×2)
= 2×6
= 12
TOTAL SA
16+24+13
= 53
Correct answer gets brainliest!!!!
Answer:
A is incorrect because points are: (length [x], height [y])
B is correct because a point is not a size, it is a position, and they have no dimensions, as they are a dot.
C is incorrect, as I explained above.
D is incorrect, also as I explained above.
Select the bolded answers, as the question asks which are false
Imma get that brainliest ;)
Answer:
It's has to be D) because it says it depends on their dimensions.
Step-by-step explanation:
a) says they have no length or high which is almost the same thing as B).
Cuz B) they have no size or dimension
which that means that if you have to check if they all apply they all have to be the same thing in different words.
C) says their size variety which variety means it could be different types it could be without dimension it could be tall or etc
And D) says their size depends on their dimension all the others say don't have size or dimension. I hope this helps you
The whole page tysmmmm plsss step by step explanation
Answer:
Step 1:
a.) 16 pets in total (1 + 0 + 2 + 0 + 3 + 8 + 0 + 2)
b.) the mean is 2 (16 is the total number of pets, divide that by 8 which is the total number of students asked, 16/8 = 2)
Step 2:
a.) 0, 0, 0, 1, 2, 2, 3, 8 (zero, one, two, three, four, five, six, seven, eight.)
b.) 0 and 3 are the middle numbers (center.)
c.) 3/2 = 1.5 (0+3 = 3 divided by 2 = 1.5)
Step 3:
- most of the students did not have any pets, so the mode would be 0 (it is zero because zero appears in the set of numbers 3 times. More than any other number).
Step 4:
They should use the mean of the amount of pets the students have; this is because the mean is the average amount of pets counting everyone in class—regardless on if there were zeros in the list.
evaluate the expression
After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.
To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:
On substituting the values,
We get,
= 2x² - y¹ + 3x⁰
= 2(3)² - 7¹ + 3(1)
= 2(9) - 7 + 3
= 18 - 7 + 3
= 14
Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.
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Suppose that the functions f and g are defined as follows.
Answer:
[tex]\dfrac{f}{g}(x) = \boxed{\dfrac{7}{x\left(x-3\right)}\\\\}[/tex]
Domain of [tex]\dfrac{f}{g}: \boxed{\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \dfrac{7}{x} , g(x) = x - 3[/tex]
[tex]\dfrac{f}{g} = \dfrac{f(x)}{g(x)} = \dfrac{7}{x} \div x - 3\\\\= \dfrac{7}{x} \times \dfrac{1}{x-3}\\\\ = \dfrac{7}{x\left(x-3\right)}[/tex]
To find the domain of
[tex]\dfrac{f}{g} = \dfrac{7}{x\left(x-3\right)}[/tex]
note that this function is defined everywhere in the range (- ∞, ∞) except for x = 0 and x = 3
At these two points, the function is undefined since the denominator becomes 0 and division by 0 is undefined
Therefore the domain consists of three parts expressed in inequality and interval forms
-∞ < x < 0 (-∞, 0)
0 < x < 3 (0, 3)
3 < x < ∞ (3, ∞)
Therefore the domain is obtained by combining these three intervals
- ∞ < x < 0 or 0 < x < 3 or x > 3
In interval notation with union:
[tex]\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)[/tex] ANSWER
Please solve this for me!
Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7
Step-by-step explanation:
What is the circumference of the circle in terms of pi? (C = td) О Тл О 147 О 21л * 28 л
The circumference of the circle with a radius of 10 cm is 20π cm, option (C) is correct.
A circle's perimeter, or the distance encircling it, is known as its circumference. It is determined by multiplying the circle's diameter by pi. But in this case, we are given the radius of the circle, which is half of the diameter.
To get a circle's circumference, use the following formula:
C = 2πr
where;
r = radius of the circle
π = mathematical constant pi (approximately equal to 3.14).
Given the radius of the circle as 10 cm, we can use the formula to find its circumference:
C = 2πr
C = 2π(10 cm)
C = 20π cm
Hence, option C is correct.
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The correct question is:
What is the circumference of the circle with radius = 10 cm (leave your answer of π).
A) 10π cm
B) 5π cm
C) 20π cm
D) 10π cm