According to the information in the table, it can be inferred that the trend of the results is positive but does not have an exact linear fit (option B).
How to calculate the average of the results?To calculate the average of the results we must add all the results and divide the result by the number of years as shown below.
503 + 504 + 506 + 508 + 511 + 512 + 511 + 514 = 40694069 ÷ 8 = 508.6Additionally, to identify if the trend is positive or negative, we must see if the results increase or decrease year after year. From the above, it is possible to infer that it is a positive trend.
On the other hand, it can be stated that it does not have an exact linear fit because the increase is not constant each year.
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The function that represents the Scooter Company's total profit is given by:
P(x) = -2x² + 250x - 2,000.
How to calculate the profit function?The profit function is calculated by the revenue function subtracted by the cost function, hence:
P(x) = R(x) - C(x).
In this problem, we have that:
The revenue function is: R(x) = 400x - 2x².The cost function is: X(x) = 150x + 2000.Hence the profit function is:
P(x) = R(x) - C(x).
P(x) = 400x - 2x² - (150x + 2000).
P(x) = -2x² + 250x - 2,000.
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Complete the coordinate proof of the theorem.
The coordinate of C( a+c , b) , AC are ((a+c)/2 , b/2) , BD are ((a+c)/2 , b/2)
What are Coordinates ?Coordinates is the value assigned to a point in a x-y graph to determine its location.
The coordinates of parallelogram is
A ( 0,0) B (a,0) , C ( __ , ___) , D ( c , b)
The y coordinate is same as D as b
and the x coordinate will be a+c
C( a+c , b)
The coordinate of the mid point of AC are ((a+c)/2 , b/2)
The coordinate of the mid point of BD are ((a+c)/2 , b/2)
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One third of all guitars that are sold in the shop is a Stratocaster, one fourth of them are Telecasters, and one fifth of them is a Les Paul. If Jamie goes and buys a guitar, what are the chances she gets a telecaster or a Les Paul?
A. 58%
B. 53%
C. 45%
D. 43%
The probability that Jamie buys a telecaster or a Less Paul is 45% or forty-five percent.
How to find out the probability?1. Find the individual probabilities:
Probabilities to buy a telecaster:
1/ 4 = 0.25Probabilities to buy a Les Paul:
1/ 5 = 0.22. Add the probabilities:
0.25 + 0.2 = 0.453. Multiply by 100:
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1. What is the length of XU?
X
U
Y
36 in
V
Z
W
23 in
Answer: 49 in
Step-by-step explanation:
[23 + XU]/2 = 36 [trapezoid midsegment theorem]23 + XU = 72 [multiply both sides by 2]XU = 49 [subtract 23 from both sides]PLEASEEEEEE HELPPPPPPP!!! 50 POINTSSSSSS
12 = 6^2 + 7^2 - 2 (6) (7) (cosA)
solve for the cosA
Step-by-step explanation:
please mark me as brainlest
A piecewise function is shown here:
f(x) = {-3x +5 if x <2
{1/2x - 4 if 2 < or = to x < or = to 8
{2 if x > 8
Use the piecewise function to find each value given below.
f(0) =
f(-4) =
f(6) =
f(9)=
f(2) =
f(0) = -3(0) + 5 = 5
f(-4) = -3(-4) + 5 = 17
f(6) = ½(6) - 4 = -1
f(9) = 2
f(2) = ½(2) - 4 = -3
Using the restraints, find which equation the f(x) function validates and plug it in.
Calculate the number of two-person committees that can be formed from a group of 10 people
Bikash borrowed Rs150,000 from Anish at the rare 21% per year at the end of 9 month. How compound interest should he pay compound half yearly.
in a study of birth orders and intelligence, IQ test were given to 18 and 19 years old men to estimate the size of difference, if any, between the main IQs of firstborn sons and second born sons. The following data for 10 firstborn sons and 10 second born sons are consistent with the means and standard deviation's reported in the article. It is reasonable to assume that the samples come from populations that are approximately normal. First born numbers are 107, 113, 84, 126, 99, 95, 98, 109, 91, 90. Second born numbers are 112, 92, 102, 86, 97, 106, 105, 116, 109, 95. construct a 95% confidence interval for the difference in mean IQ between first born and second born sons. Let them one denote the main IQ of firstborn sons.
In a study of birth orders and intelligence, IQ tests were given to 18 and 19 years old men to estimate the size of the difference, we have that [tex]|t|=0.618\leq t_c =2.101[/tex] and for this reason, we cannot reject the null hypothesis.
What are the Test Statistics?Null and Alternative Hypotheses
[tex]H_o: \mu_{1} = \mu_{2}\\\\Ha: \mu_1 \neq \mu_2 .[/tex]
Since the population standard deviations are unknown, we will apply a t-test on the means of the two populations, using two independent samples.
The degrees of freedom are df = 18, and the significance threshold is set at alpha = 0.05, based on the data presented. If we assume that the population variances are the same, we can calculate the degrees of freedom in this way:
The rejection region for this two-tailed test is R = \{t : |f| > 2.101}
Therefore the Test Statistics is
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
t=0.618
In conclusion. we have that [tex]|t|=0.618\leq t_c =2.101[/tex]
For this reason, we cannot reject the null hypothesis.
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What is
162divide[6 multiply (7-4) to the second power]
help please
Answer:
please mark me brainlist
Step-by-step explanation:
i need it
Answer:
3^1 multiplied by 3^2 = 3^(1 + 2) = 3^3
162
Simplify ——————
(2•3^3)
Canceling out 2 as it appears on both sides of the fraction line
3^4 divided by 3^3 = 3^(4 - 3) = 3^1 = 3
Step-by-step explanation:
hope this helps you ♡
Evaluate the integral
-7x³
x³ +1
Note: Use an upper-case "C" for the constant of integration.
I
dx
The value of the integration is
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.
We know that finding the area of the curve's undersurface is the process of integration. To do this, cover the area with as many tiny rectangles as possible, then add up their areas. The sum gets closer to a limit that corresponds to the area under a function's curve. Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral over the domain is finite with the given bounds, then the integration is definite.
Here, we have to determine the value of the given integral
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx[/tex].
So,
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx = 7 \int {\frac{1-x^{3}-1 }{x^{3}+1} } \, dx[/tex][tex]= 7 \int [{1-\frac{1 }{x^{3}+1} } ]\, dx =7\int \, dx - 7 \int {\frac{1 }{x^{3}+1} } \, dx[/tex] ...(1)
Now,
[tex]\frac{1}{x^{3} +1} = \frac{1}{(x+1)(x^{2} -x+1)}[/tex]
We can write
[tex]\frac{1}{(x+1)(x^{2} -x+1)}=\frac{A}{(x+1)} + \frac{Bx+C}{(x^{2} -x+1)}[/tex]
i.e. [tex]1 = A(x^{2} -x+1)+(Bx+C)(x+1)[/tex]
i.e. [tex]1 = Ax^{2} -Ax + A+Bx^{2} +Bx+Cx+C[/tex]
i.e. [tex]1=(A+B)x^{2} +(-A+B+C)x +(A+C)[/tex]
Comparing both sides, we get
[tex]A+B=0 \implies B = -A[/tex] ...(2)
[tex]-A+B+C = 0 \implies -A+(-A)+C=0 \implies -2A+C=0[/tex] ...(3)
[tex]A+C=1[/tex] ...(4)
Subtracting (3) from (4),
[tex]A+C+2A-C=1-0 \implies 3A=1 \implies A=\frac{1}{3}[/tex]
From (4), [tex]C= 1-\frac{1}{3} =\frac{3-1}{3} =\frac{2}{3}[/tex]
From (2), [tex]B =-\frac{1}{3}[/tex]
We get
[tex]\frac{1}{x^{3}+1 } =\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{3} \frac{x-2}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-4}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1-3}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{3}{6} \frac{1}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{1}{2} \frac{1}{x^{2} -x+1}[/tex]
Integrate both sides,
[tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \int \frac{1}{(x+1)} \, dx - \frac{1}{6} \int \frac{2x-1}{x^{2} -x+1}\, dx+\frac{1}{2} \int \frac{1}{x^{2} -x+1}\, dx[/tex]
i.e. [tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \ln(x+1) - \frac{1}{6} ln (x^{2} -x+1)+\frac{\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })[/tex]
From (1),
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex]
Therefore, the value of the integration is
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.
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If f(x)=16x- 30 and g(x)= 14x-6, for which value of x does (f-g)(x)=0?
Answer:
x=12
Step-by-step explanation:
16x-30-(14x-6)=2x-24=0. add 24 on both sides to get 2x=24. divide by 2 on both sides to get x=12
Find the area of triangle PQR.
Step-by-step explanation:
To get the angle of QPR, we subtract 90-60=30. This proves that the triangle is a 30,60,90, as angle QRP must be 60°. To get the area, we must know the length and width. These can be derived from a known relationship within 30,60,90 triangles.
[tex]qp = \frac{\sqrt{3}}{2} n[/tex]
[tex]qr = \frac{1}{2} n[/tex]
[tex]pr = n[/tex]
because half of pr is 10, we can conclude that n is 20. So we plug 20 into N for QP and QR, and get values of
[tex]qp = 5 \sqrt{3} [/tex]
[tex]qr = 5[/tex]
Now we multiply (l*w)/2 and get:
[tex] \frac{(5 \sqrt{3} \times 5)}{2} = 21.65 \: units[/tex]
????????????????????
Answer:
[tex]\text{C.} \ \ \ {\left(\textit{AB}\right)}^{2} \ = \ \left(\textit{AC}\right)\left(\textit{AD}\right)[/tex]
Step-by-step explanation:
This problem uses the concept of the tangent-secant theorem which describes the relationship of the segments a secant line and a tangent line with the associated circle. This theorem is found as Proposition 36 in Book 3 of Euclid's Elements.
As shown in the figure attached below, segment AB (in blue) forms a tangent with the circle BCD and segment AD (in orange) is the secant where it intersects the circle at point C.
Furthermore, let two segments (in green) be drawn one from point C and point D.
To show that [tex]\triangle ABC[/tex] is similar to [tex]\triangle ADB[/tex], notice that both triangles share a common angle [tex]\angle BAC[/tex]. Additionally, by the alternate segment theorem, [tex]\angle ABC[/tex] is equal to [tex]\angle ADB[/tex]. Therefore, [tex]\angle ACB[/tex] is also equal to [tex]\angle ABD[/tex].
Hence, [tex]\triangle ABC[/tex] is indeed similar to [tex]\triangle ADB[/tex]. This implies the ratio of the sides of both triangles is the same. Particularly,
[tex]\displaystyle{\frac{AB}{AD} \ \ = \ \ \frac{AC}{AB}}[/tex].
Then, performing cross multiplication yields
[tex]{\left(AB\right)}^{2} \ \ = \ \ \left(AC\right)\left(AD\right)[/tex].
Therefore, the product of the lengths of the secant segment and its external segment is equal to the square of the length of the tangent segment.
Change a Relation to Make It a Function The relation R is shown below as a list of ordered pairs. R = { (1, 4), (1, 3), (-1, 3), (2, 15) } Which ordered pairs prevent this relation from being a function? (1, 4) and (1, 3), because they have the same x-value (1, 3) and (–1, 3), because they have the same y-value
Answer: (1,4) and (1,3) because the have the same x-value
Step-by-step explanation:
A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).
If f(x) = 2x+6 and g(x)= x3 what is (g f)(0)?
Answer:
[tex]27[/tex]
Step-by-step explanation:
[tex]g(f(0))=g(2(0)+3)=g(3)=3^3=27[/tex]
Use the zero x = 5, to help find the remaining zeros of x4 - 4x3 - 14x² + 36x + 45. Select one:
O a. x = 5, 3, and -3
O b. x = -1, 3, and -3
O c. None of these
O d. x = 1, 3, and -3
Answer:
huh
Step-by-step explanation:
Jdnjdbbdidbd
1 + 1/3=
Answer:
[tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]1 + \frac{1}{3} \\= \frac{3}{3} + \frac{1}{1}\\= \frac{4}{3}[/tex]
(if the question is asking for the simplified form , it is [tex]1\frac{1}{3}[/tex]
Math: One to One function...help!
A one-to-one function has an inverse. The inverse is another function that undoes the action of the first one, so if we evaluate a function [tex]f[/tex] at some point [tex]x[/tex] to get the number [tex]f(x)[/tex], evaluating the inverse at [tex]f(x)[/tex] will recover the original input [tex]x[/tex]. In other words,
[tex]f^{-1}(f(x)) = x[/tex]
The process works in the opposite direction, too:
[tex]f\left(f^{-1}(x)\right) = x[/tex]
From the given definition of [tex]g[/tex], we have [tex]g(-4) = 3[/tex], so taking inverses on both sides, we find
[tex]g(-4) = 3 \implies g^{-1}(g(-4)) = g^{-1}(3) \implies \boxed{g^{-1}(3) = -4}[/tex]
Given [tex]h(x)=2x-13[/tex], evaluating [tex]h[/tex] at its inverse will recover [tex]x[/tex], so that
[tex]h\left(h^{-1}(x)\right) = x \implies 2h^{-1}(x) - 13 = x \implies \boxed{h^{-1}(x) = \dfrac{x+13}2}[/tex]
[tex](h\circ h^{-1})(x)[/tex] is another way of writing the compound function [tex]h\left(h^{-1}(x)\right)[/tex]. As already discussed, this reduces to [tex]x[/tex], so
[tex]\boxed{\left(h\circ h^{-1}\right)(-9) = -9}[/tex]
Line l passes through point (−2,37) and line p is the graph of y+3=−5(x+4) .
If l is parallel to p what is the equation of l ?
The slope of line p is -5, so substitute into point-slope form, we get
[tex]\boxed{y-37=-5(x+2)}[/tex]
Britney sells mattresses at a furniture store. She makes a 9.75% commission on each mattress she sells. Last week, Britney sold four mattresses. The sale price of each mattress is shown in the table.
How much did Britney earn last week?
Enter your answer in the box.
$
Mattress sale Amount
Mattress 1 $2400
Mattress 2 $3200
Mattress 3 $1900
Mattress 4 $800
Answer:
$809.25
Step-by-step explanation:
→ Find the sum of the sales amount
2400 + 3200 + 1900 + 800 = 8300
→ Find the amount that s commission
( 9.75 × 8300 ) ÷ 100 = $809.25
Calculate this logarithmic expression
The solution of the logarithmic expression [tex]\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})[/tex] is [tex]\log_2[270][/tex]
How to solve the logarithmic expression?The expression is given as:
[tex]\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})[/tex]
Apply the product law of logarithm
[tex]\log_2[(17 -\sqrt{19}) *(17 +\sqrt{19})]\\[/tex]
Apply the difference of two squares
[tex]\log_2[(17^2 -(\sqrt{19})^2][/tex]
Evaluate the squares
[tex]\log_2[(289 -19][/tex]
Evaluate the difference
[tex]\log_2[270][/tex]
Hence, the solution of the logarithmic expression [tex]\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})[/tex] is [tex]\log_2[270][/tex]
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HELP ASAP
8. The tubes on the frame of this road bike form a triangle. The owner's manual
identifies some of the angle measures formed by the bike frame. Based on the
information in the diagram below, determine which tube is the longest.
top tube
seat tube
top tube
30%
7
55
C
down tube
Part I: Classify the triangle formed by the three bike frame tubes as equilateral,
isosceles, or scalene. Find the measure of ZB and explain your classification. (3
points; 1 point for classification, 1 point for the angle measure, and 1 point for
explanation)
seat tube
down tube
Answer:
See below
Step-by-step explanation:
Longest is the down tube.....it is opposite the largest angle (95°) angle in the triangle . This is a SCALENE triangle ( all sides of different length)
The longest tube that we have here is the down tube. The triangle that is formed id the scalene triangle
What is the scalene triangle
A scalene triangle is a type of triangle where all three sides have different lengths. In other words, no two sides of a scalene triangle are equal in length. Additionally, the angles of a scalene triangle are also different from each other.
The term "scalene" comes from the Greek word "skalenos," which means "uneven" or "unequal." This name reflects the defining characteristic of the scalene triangle, which is the absence of any equal sides or angles.
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A company decides to offer a monetary incentive for employees who log a specified number of hours spent exercising in an attempt to improve employee health. The average health score (higher = better) of the 75 employees who logged enough hours was 87. The mean health score for all employees (population) was 85, with a population standard deviation of 6.5. Calculate the standard error of the mean
The standard error will be equal to 0.75.
What is the standard error?The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.
The standard error will be calculated by using the formula:-
SE = [tex]\sigma[/tex] / √n
Here [tex]\sigma[/tex] is the standard deviation and n is the sample number.
SE = 6.5 / √75
SE = 0.75
Therefore the standard error will be equal to 0.75.
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Each phrase in the table describes two variables whick are strongly correlated. Select all phases that imply correlation without causation.
The complete question is attached below.
The most correct phases that imply correlation without causation are 1, 5, and 6.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.
The most correct phases imply correlation without causation are;
The number of stuffed animals produced at a factory and the number of newborn babies.
The number of videos rented and the number of films in the theater.
The number of pets in the neighborhood and the amount of grass nearby.
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The set of all numbers greater than or equal to −5 and less than 5.
Answer:
No. greater than of equal to (-5) = -4,-3,-2,-1,0,1,2,3,4,5,6...........
No. less than 5 = 4,3,2,1 ,0,-1......
{ -4,-3,-2,-1,0,1,2,3,4}
if m=p/2+3r. find the value of p if r=1 and m=5
Answer:
p = 4
Step-by-step explanation:
[tex]m =\frac{p}{2} +3r[/tex]
[tex]\Longrightarrow m-3r=\frac{p}{2}[/tex]
[tex]\Longrightarrow 2m-6r=p[/tex]
[tex]\Longrightarrow p = 2m-6r[/tex]
If m = 5 and r = 1
Then
p = 2(5) - 6(1)
= 10 - 6
= 4
Basically look at the picture I don’t even know what to say
Answer:
C
Step-by-step explanation:
x = [tex]\frac{2}{3}[/tex] πr³ ( multiply both sides by 3 to clear the fraction )
3x = 2πr³ ( divide both sides by 2π )
[tex]\frac{3x}{2\pi }[/tex] = r³ ( take cube root of both sides )
[tex]\sqrt[3]{\frac{3x}{2\pi } }[/tex] = r
Answer:
[tex]r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
Step-by-step explanation:
This question make look scary, but don't judge its book by its cover.
[tex]x=\frac{2}{3} \pi r^{3} \\\frac{2}{3} \pi r^{3}=x\\r^{3} =x / \frac{2\pi }{3} \\r^{3} =x*\frac{3}{2\pi } \\r^{3} =\frac{3x}{2\pi } \\r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo.
What are the dimensions of the cropped photo?
8 inches by 8 inches
9 inches by 9 inches
12 inches by 12 inches
13 inches by 13 inches
Answer:
x = 9 or B
Step-by-step explanation:
Formula
(x + 2)^2 = 121
Comment
The easiest way to do this is to take the square root immediately, which is usually possible.
Solution
√(x + 2)^2 = √121 Take the square root
x + 2 = 11 Subtract 2 from both sides
x + 2 - 2 = 11 - 2
x = 9
Answer: B) 9 inches by 9 inches
Step-by-step explanation:
Edg 2022
Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.
Melissa and Corey started on different trails.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa and Corey crossed paths between 60 and 90 minutes.
Corey began his descent before Melissa.
As Melissa’s time increased from 0 to 60 minutes, her elevation decreased.
The true statements are (A), (B) and (D)
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
As, from the given table we can see that
Melissa and Corey started on different trails.Melissa hiked up the trail for a longer period of time than Corey.Corey began his descent before Melissa.Learn more about this concept here:
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The graphs below have the same shapes. What is the equation for the red graph?
The equation for the red graph is f(x) = -x².
How to depict the equation?From the information given, g(x) = 4 - x².
The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:
(x, y) = (x, y -4).
The equation of the function will be:
f(x) = g(x) - 4
f(x) = (4 - x²) - 4
f(x) = -x²
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