The correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given that:-
A study was conducted on the year and the number of honeybees in a beekeeper’s hive. After using the averaging method for the line of best fit, the two representative points found were (10, 250) and (20, 500).The equation of the line will be calculated as:-
The intercept of the line will be;-
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{500-250}{20-10}=25[/tex]
The equation of the line is given as:-
y - y₁ = m( x - x₁ )
Putting the coordinates:-
y - 250 = 25 ( x - 10 )
y - 250 = 25x - 250
y = 25x
Therefore the correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.
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the area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units if we increase the length by 3 units and the breadth by 2 units then the area is increased by 67 square units find the dimensions of the rectangle.
length = 17 units, breadth = 9 units
Step-by-step explaination:-
Let the length and the breadth of the rectangle be x units and y units respectively.
Then the area of rectangle = xy square units
According to given conditions, we have
(x -5)(y + 3) = xy - 9 and (x + 3)(y + 2) = xy + 67
=> xy + 3x - 5y - 15 = xy - 9
and xy + 2x + 3x + 6 = xy + 67
=> 3x - 5y - 6 = 0......eqn(i)
and 2x + 3y - 61 = 0.....eqn(ii)
Multiplying equation (i) by 2 and equation (ii) by 3, we get...
6x - 10y - 12 = 0....eqn(iii) and,
6x + 9y - 183 = 0....eqn(iv)
Subtracting equation (iii) from equation (iv), we get...
19y - 171 = 0 => y = 9.
Substituting this value of y in equation (ii), we get
2x + 3 × 9 - 61. = 0 => 9x - 34 = 0 => x = 17.
Hence, the length of rectangle = 17 units and
breadth = 9 units.
Hope it helps you!!Graph the function.
f(x)=3z-5
Use the Line tool and select two points to graph
The plot of the graph is attached and points have been determined
The two among them are (5,-2) ,(15,4).
What is a Line Function ?
A line function is what can be written in the form of
y =mx +c
where m is the slope and c is the intercept on y axis.
The equation given here is y = (3/5)x -5
m = 3/5
c = -5
The plot of the graph is attached and points have been determined
The two among them are (5,-2) ,(15,4)
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I need help ASAP PLEASE > How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3? (Please explain with your on words)
Answer:
The graph has been moved 7 units to the left and 8 units down.
Step-by-step explanation:
When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.
When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.
Pls help meee!!!!!!!!!
Pls show your work pls and thank u
Answer: x = 40
Step-by-step explanation:
these two angles are vertical angles, they will equal each other
therefore, move numbers and variables to the opposite sides of the = sign to isolate the X
3x-10 = 2x + 30
+10 +10 move the -10 by doing opposite
_____________
3x = 2x + 40
-2x -2x move -2x by doing opposite
____________
x = 40
you can check your work by substituting 40 in place of x
3(40) - 10 = 2(40) +30
120-10 = 80 + 30
110 = 110
answer is correct
Answer:
x = 40
Step-by-step explanation:
The given angles are vertical angles, hence they are equal.
=============================================================
Solving for x :
⇒ 3x - 10 = 2x + 30
⇒ 3x - 2x = 30 + 10
⇒ x = 40
find the area of the shaded polygons
Answer:
4 square units
Step-by-step explanation:
The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.
__
formulaPick's theorem tells you the area is ...
A = i +b/2 -1
where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).
applicationUsing the counted values in the formula, we find the area to be ...
A = 0 +10/2 -1 = 4
The area of the polygon is 4 square units.
_____
Additional comment
There are several other ways to find the area. Here are a couple:
decompose the figure
A horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...
A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2
The triangle has base 1 and height 3, so its area is ...
A = 1/2bh = 1/2(1)(3) = 3/2
Then the total area is 5/2 +3/2 = 8/2 = 4 square units.
subtract empty space
The figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...
A = s² -1/2bh -1/2bh
A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units
Use the spinner below to find the probability of getting the following number after 1 spin. P(multiple of 3) = (Round to 4 decimal places)
The value of the probability P(multiple of 3) is 0.3333
How to determine the probability?The spinner that completes the question is added as an attachment
From the attached spinner, we have:
Total section = 12Multiples of 3 = 4The probability is then calculated as:
P(multiple of 3) = Multiples of 3/Total
This gives
P(multiple of 3) = 4/12
Evaluate
P(multiple of 3) = 0.3333
Hence, the value of the probability is 0.3333
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Integration questions .
[tex]\\\\\ \textbf{a)}\\\\~~~\displaystyle \int (6x- \sin 3x) ~ dx\\\\=6\displaystyle \int x ~ dx - \displaystyle \int \sin 3x ~ dx\\\\=6 \cdot \dfrac{x^2}2 - \dfrac 13 (- \cos 3x) +C~~~~~~~~~~~;\left[\displaystyle \int x^n~ dx = \dfrac{x^{n+1}}{n+1}+C,~~~n \neq -1\right]\\\\ =3x^2 +\dfrac{\cos 3x}3 +C~~~~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \sin (mx) ~dx = -\dfrac 1m ~ (\cos mx)+C \right]\\[/tex]
[tex]\textbf{b)}\\\\~~~~\displaystyle \int(3e^{-2x} +\cos (0.5 x)) dx\\\\=3\displaystyle \int e^{-2x} ~dx+ \displaystyle \int \cos(0.5 x) ~dx\\\\\\=-\dfrac 32 e^{-2x} + \dfrac 1{0.5} \sin (0.5 x) +C~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx}~dx = \dfrac 1m e^{mx} +C \right]\\\\\\=-\dfrac 32 e^{-2x} + 2 \sin(0.5 x) +C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \cos(mx)~ dx = \dfrac 1m \sin(mx) +C\right]\\\\\\=-1.5e^{-2x} +2\sin(0.5x) +C[/tex]
2)[tex]\textbf{a)}\\\\y = \displaystyle \int \cos(x+5) ~ dx\\\\\text{Let,}\\\\~~~~~~~u = x+5\\\\\implies \dfrac{du}{dx} = 1+0~~~~~~;[\text{Differentiate both sides.}]\\\\\implies \dfrac{du}{dx} = 1\\\\\implies du = dx\\\\\text{Now,}\\\\y= \displaystyle \int \cos u ~ du\\\\~~~= \sin u +C\\\\~~~=\sin(x+5) + C[/tex]
[tex]\textbf{b)}\\\\y = \displaystyle \int 2(5x-3)^4 dx\\\\\text{Let,}\\~~~~~~~~u = 5x-3\\\\\implies \dfrac{du}{dx} = 5~~~~~~~~~~;[\text{Differentiate both sides}]\\\\\implies dx = \dfrac{du}5\\\\\text{Now,}\\\\y = 2\cdot \dfrac 1 5 \displaystyle \int u^4 ~ du\\\\\\~~=\dfrac 25 \cdot \dfrac{u^{4+1}}{4+1} +C\\\\\\~~=\dfrac 25 \cdot \dfrac{u^5}5+C\\\\\\~~=\dfrac{2u^5}{25}+C\\\\\\~~=\dfrac{2(5x-3)^5}{25}+C[/tex]
3)[tex]\textbf{a)}\\\\y = \displaystyle \int xe^{3x} dx\\\\\text{We know that,}\\\\ \displaystyle \int (uv) ~dx = u \displaystyle \int v ~ dx - \displaystyle \int \left[ \dfrac{du}{dx} \displaystyle \int ~ v ~ dx \right]~ dx\\\\\text{Let}, u =x~ \text{and}~ v=e^{3x} .\\\\y= \displaystyle \int xe^{3x} ~dx\\\\\\~~= x\displaystyle \int e^{3x} ~ dx - \displaystyle \int \left[\dfrac{d}{dx}(x) \displaystyle \int e^{3x}~ dx \right]~ dx\\\\\\[/tex]
[tex]=x\displaystyle \int e^{3x}~ dx - \displaystyle \dfrac 13 \int \left(e^{3x} \right)~ dx\\\\\\=\dfrac{xe^{3x}}3 - \dfrac 13 \cdot \dfrac{ e^{3x}}3+C\\\\\\= \dfrac{xe^{3x}}{3}- \dfrac{e^{3x}}{9}+C\\\\\\=\dfrac{3xe^{3x}}{9}- \dfrac{e^{3x}}9 + C\\\\\\= \dfrac 19e^{3x}(3x-1)+C[/tex]
Problem is in the picture
Given that m2Q=63 and DQ-7, find z rounded to the nearest tenth.
Answer:
Ali is a boy
Step-by-step explanation:
Ali is a good boy
The revenue from selling x necklaces is r(x) =10x. The cost of buying x necklaces is c(x)=4x+15. The profit from selling x necklaces is p(x)=r(x)-c(x).
Answer:
the revenue is 280 by 190
The triangles shown below must be congruent.
• A. True
• B. False
Answer:
TRUEStep-by-step explanation:
When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.
in this case there is a rotation same angles and same sides
your answer is: TRUE
A football club is the only one in its region and is therefore able to behave like a monopolist. It sells tickets to Adults (a) and Juniors (j), whose demand curves are given by:
Pa = 200 − Qa
Pj = 160 − Qj
Additionally, the club’s total costs are given by = 20Qi
The club hires an economist to consider its pricing strategy and receives the advice that it should charge different prices to each type of supporter. Find the prices it sets in both markets, the sales (output) in each and its overall level of profit and illustrate profit maximising outputs and prices of each consumer type on a graph (one graph for each type of consumer). Calculate consumer surplus in this case.
Answer:
Adult market
price: 110sales: 9900profit: 8100consumer surplus: 9000Junior market
price: 90sales: 6300profit: 4900consumer surplus: 5600Total profit: 13000
Total consumer surplus: 14600
Step-by-step explanation:
Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.
RevenueEach demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).
R = QP = Q(Pmax -Q)
ProfitThe profit is the difference between revenue and cost.
Profit = R - C = Q(Pmax -Q) -20Q
Profit = Q(Pmax -20 -Q)
Writing the demand equation in terms of P, we find ...
Q = Pmax -P
Substituting this into the Profit equation gives ...
Profit = (Pmax -P)(Pmax -20 -(Pmax -P))
Profit = (Pmax -P)(P -20)
The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:
Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10
PricesIn the adult market, Pmax = 200, so the profit-maximizing ticket price is ...
Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market
In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...
Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market
SalesUsing the revenue equation, we find the sales in each market to be ...
Qa = 200 -Pa = 200 -110 = 90
Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market
Qj = 160 -Pj = 160 -90 = 70
Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market
Overall ProfitThe profit in each market is ...
Adult market profit = 90(110 -20) = 8100
Junior market profit = 70(90 -20) = 4900
The overall profit will be the sum of the profits in each market:
Overall profit = 8100 +4900 = 13000
Consumer surplusThe consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.
CSa = (1/2)(200)Qa = 100(90) = 9000
CSj = (1/2)(160)(Qj) = 80(70) = 5600
The total consumer surplus is ...
CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus
Graph
The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.
The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.
Which number line represents the solution set for the inequality -4(x + 3) ≤-2-2x?
++
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4
5 6 7
O
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1
2
3
4
6 7
ليا
نی
für
fe
LO
5
Answer:
x<_-5
Step-by-step explanation:
-4(x+3)<_-2-2x
-4x-12<_-2-2x
-4x+2x<_-2+12
-2x<_+10
divide both side by -2
-2x/2<_10/-2
x<_-5
it is D
The figure above shows the probability density function for the random variable x. What is P(3≤x<7)?
The value of the probability P(3≤x<7) is 1
How to evaluate the probability expression?The expression is given as: P(3≤x<7)
This is calculated using:
P(3 ≤ x < 7) = P(3) + P(4) + P(5) + P(6)
Using the figure of the probability density function (see attachment), we have:
P(3 ≤ x < 7) = 0.30 + 0.30 + 0.20 + 0.20
Evaluate
P(3 ≤ x < 7) = 1
Hence, the value of the expression is 1
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The radius of Circle A is 3 ft. The radius of Circle B is 3 ft greater than the radius of
Circle A. The radius of Circle C is 3 ft greater than the radius of Circle B. The radius of Circle D is 2 ft
less than the radius of Circle C. What is the area of each circle? How many times greater than the
area of Circle A is the area of Circle D?
Answer:
Step-by-step explanation:
Ar of circle
A= 49π
B=100π
C=169π
D=121π
Ar of circle A is less than Ar of circle D
The surface area of a right cone which has a base diameter of 6 units and a height of 8 units is:
75 units squared.
108 units squared.
151 units squared.
188 units squared.
The area of a 2D form is the amount of space within its perimeter. The surface area of the cone is 108.79967 units².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given the diameter of the cone is 6 units, therefore, the radius of the cone is 3 units, and the height of the cone is 8 units. Thus, the surface area of the right cone is,
A=πr [r+√(h²+r²)]
A = 108.79967 units²
Hence, the surface area of the cone is 108.79967 units².
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calculate volume of a planet if radius is 6050 and answer in scientific notation
to the 2 significant number
Answer:
9.3*10^11
Step-by-step explanation:
4/3πr^3=9.3*10^11
A hockey season ticket holder pays $88.56 for her tickets plus $5.00 for a program each game. A second person pays $19.76 for a ticket to every game, but doesn't buy programs. In how many games will they have paid the same amount?
Answer: x = 6
Step-by-step explanation: If you take 88.56 + 5x = 19.76x, an equation, you should first rearrange the variables to the left side of the equation: 5x - 19.76x = -88.56.
Next, you should combine your like terms. So, -14.76 = -88.56.
Then, divide both sides of the equation by the coefficient of variable. So, x = -88.56 / -14.76./
Lastly, calculate. Determine the sign for multiplication or division, so x = 88.56 / 14.76. Multiply both the numerator and denominator with the same integer. So, x = 8856 / 1476. Cross out the common factor, then you get your answer of x = 6
Carol has some dimes and quarters. If she has 19 coins worth a total of $3.10, how many of each type of coin does she have?
10+u-17u=14 - I already have the answer which is 3/8, but I need to know how they got that answer. Please help! :)
Answer:
Step-by-step explanation:
hope this helps !
Answer:
Step-by-step explanation:
10+u-17u=14
Starts by combining like terms:
u-17u=14-10
Solve:
-16u=4
u=-16/4
u= -4
please help!!!! needs to be submitted
The coordinates of the image of triangle are transformation are X = (1,3), Y = (5,-3) and Z = (-1, -7)
How to determine the transformation?From the figure, the coordinates of the triangle are:
A = (-1, -1)
B = (1, 2)
C = (-2,4)
The transformation rule is given as:
[tex]\triangle XYZ = T_{ < 3,1 > }(R_{x-axis}(D_2(\triangle ABC)))[/tex]
This means that, we start by dilating the triangle by a scale factor of 2.
So, we have:
A' = (-2, -2)
B' = (2, 4)
C' = (-4,8)
Next, we rotate the triangle across the x-axis
So, we have:
A'' = (-2, 2)
B'' = (2, -4)
C'' = (-4,-8)
Lastly, we translate the triangle by (x + 3,y + 1) to get the triangle XYZ
So, we have:
X = (1,3)
Y = (5,-3)
Z = (-1, -7)
See attachment for the image of the transformation
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Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.
2-5x=2x-3
The solution to the equation below to the nearest fourth of a unit is 0.7142
Equations and expressions
Given the equation as shown below;
2-5x=2x-3
Collect the like terms
-5x - 2x = -3 - 2
-7x = -5
Divide both sides by -7
x = -5/-7
x = 5/7
x= 0.7142
Hence the solution to the equation below to the nearest fourth of a unit is 0.7142
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Joan has 7/8 of her book left to read. If she reads ¼ each day, how many days will it take her to finish?
Answer:
4 days
Step-by-step explanation:
first convert 1/4 to eighths
2/8=1/4
to make 2/8 equal 7/8
you have to multiply by 4 for it to be 8/8
it cant be 7/8 because that would be three and a half days and they only read 1/4 each day
so it would take 4 days to finish
Triangle P Q R is shown. Angle Q P R is a right angle. The length of Q P is 8 StartRoot 3 EndRoot and the length of P R is 8.
Consider triangle PQR. What is the length of side QR?
Answer: Length of side QR is 16 units.
Step-by-step explanation: Given that dimensions of PQR
QPR= 90degrees
Determine the angle of elevation if the slope is 0.3415
Using the slope concept, considering it's value of 0.3415, it is found that the angle of elevation is of 18.86º.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Hence, we have that:
[tex]\tan{\alpha} = 0.3415[/tex]
[tex]\alpha = \arctan{0.3415} = 18.86^\circ[/tex]
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Round 0.007492 to four decimal places.
The square below represents one whole.
Express the shaded area as a fraction, a decimal, and a percent of the whole.
The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively
Fractions, Decimals and PercentagesFrom the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.
In the diagram, there are 100 total squares and 23 of them are shaded
Expressing the shaded area as a fraction, we get
[tex]\frac{23}{100}[/tex]
Expressing the shaded area as a decimal, we get
[tex]\frac{23}{100}[/tex] = 0.23
Expressing the shaded area as a percent , we get
[tex]\frac{23}{100}\times 100\%[/tex] = 23%
Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively
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PLS help me with my math
i dont know either your on your own
Step-by-step explanation:
i just dont know
A box contains 7 plain pencils and 5 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected?
Write your answer as a fraction in simplest form
Answer:
5/24
Step-by-step explanation:
Probability of selecting a pen :
⇒ Number of pens / Total items in Box 1
⇒ 5 / 7 + 5
⇒ 5/12
=============================================================
Probability of selecting a crayon :
⇒ Number of crayons / Number of items in box 2
⇒ 4 / 4 + 4
⇒ 4/8
⇒ 1/2
===========================================================
Probability (of both events) :
⇒ 5/12 × 1/2
⇒ 5/24
Emma makes 14 dozen cookies in one hour how many individual cookies can she make in 4.5 hours