Distance = 75 units between t=0 and t=5. To find how far the particle travels between t=0 and t=5, we need to calculate the total distance traveled by the particle.
The distance traveled is equal to the total displacement, which can be found by taking the absolute value of the difference between the initial and final positions.
The initial position of the particle at t=0 is:
S(0) = 0^3 - 3(0)^2 - 2 = -2
The final position of the particle at t=5 is:
S(5) = 5^3 - 3(5)^2 - 2 = 73
Therefore, the total displacement of the particle is:
ΔS = |73 - (-2)| = 75
So the particle travels a total distance of 75 units between t=0 and t=5.
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4.4 a coin is biased such that a head is three times as likely to occur as a tail. find the expected number of tails when this coin is tossed twice.
To find the expected number of tails when the coin is tossed twice, we need to use the formula for expected value:
E(X) = ∑xp(x)
Where x is the possible outcome and p(x) is the probability of that outcome occurring.
Since a head is three times as likely to occur as a tail, the probability of getting a tail is 1/4 and the probability of getting a head is 3/4.
So, when the coin is tossed twice, there are four possible outcomes: two tails (TT), two heads (HH), one tail and one head (TH), and one head and one tail (HT).
The expected value of tails for each outcome is:
E(TT) = 2(1/4)(1/4) = 1/8
E(HH) = 0(3/4)(3/4) = 0
E(TH) = 1(1/4)(3/4) = 3/16
E(HT) = 1(3/4)(1/4) = 3/16
So the expected number of tails when the coin is tossed twice is:
E(X) = 1/8 + 0 + 3/16 + 3/16 = 7/16
Therefore, the expected number of tails when this coin is tossed twice is 7/16.
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( 16.9 - 5.47 ) x 7.09 plzz i want with full solution
Answer:
81.03
Step-by-step explanation:
(16.9-5.47)×7.09
(11.43)×7.09
81.0387
OR
81.03
HOPE THIS HELPS YOU
PLEASE HELP ME
i dont know how to do this
i will give you brainlyest
pretty please
The series of transformations maps quadrilateral MNPQ onto quadrilateral RSTU is rotation 180 about the origin, and then reflection across the x-axis
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
the coordinates of each point after quadrilateral RSTU is rotated
90• about the origin are (2,1)(4.2)(5,4)(3,5)
the series of transformations maps quadrilateral MNPQ onto quadrilateral RSTU is rotation 180 about the origin, and then reflection across the x-axis
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Answer:
M = (3, -3)
N = (4, -1)
P = (6, 0)
Q = (5, -2)
Step-by-step explanation:
M = (1, 2)
N = (2, 4)
P = (4, 5)
Q = (3, 3)
x axis will be plus 2 since it's moving right 2 units so
M = (3, 2)
N = (4, 4)
P = (6, 5)
Q = (5, 3)
y axis will be minus 5 since it's going down so
M = (3, -3)
N = (4, -1)
P = (6, 0)
Q = (5, -2)
These is the final coordinates for question 3, give me a moment to do the others
Did I graph this equation right?
Equation: P=125+50w
Answer:
yes
Step-by-step explanation:
You want a graph of P = 125 +50W.
Slope-intercept formThe given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.
Axes assignmentsUsually, the independent variable is graphed on the horizontal axis, which you have done.
The dependent variable is graphed on the vertical axis, which you have done.
The axes are correctly labeled and graduated.
InterceptThe "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.
SlopeThe slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.
Yes, you properly graphed the equation.
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6 is 0.2% of what percent?
Answer: 3000
Step-by-step explanation:
\(\frac{0.2}{100}\)x\(\frac{x}{1}\) =6
multiply the fractions
\(\frac{0.2x}{100}\) = \(\frac{6}{1}\)
cross multiply
\(0.2x = 600\)
Divide both sides by the coefficient of \(x\)
\(\frac{0.2x}{0.2} = \frac{600}{0.2} \\x = 3000\)
1. Solve *
4(3x - 2) = 8(2x+3)
Your answer
This is a required question
Pleas help me solve
Answer:
First you simplify by first taking 4 multiply the parentheses: 4 x 3X - 4 x 2 = 12X - 8 =
Then you have to do the same thing at the right side, try figure it out. When u get the answer simplify it by taking. The x to left side and the ordinary numbers to right side(not always). As said try figure it out urself if u need help i got u
the teacher of a class of third graders records the height of each student. indicate which level of measurement is being used in this scenario
In this situation, interval measurement is being employed as the measurement level.
As the height of each student can be measured on a continuous scale with equal intervals between the values. It's important to note that the teacher may have rounded the measurements to the nearest unit, which would make it a discrete measurement.
Interval measurement is a level of measurement in which the values are measured on a continuous scale and have equal intervals between them, but there is no true zero point. This means that the difference between any two values on the scale is meaningful and consistent, but it is not possible to say that one value is "zero" or has no quantity of the measured attribute.
For example, measuring temperature in degrees Celsius or Fahrenheit is an example of interval measurement. In this case, the difference between 10 and 20 degrees is the same as the difference between 20 and 30 degrees, but there is no true zero temperature - a temperature of 0 degrees does not mean the absence of heat.
Another example of interval measurement is measuring time in minutes or hours. The difference between 10 minutes and 20 minutes is the same as the difference between 20 minutes and 30 minutes, but there is no "zero" point in time - even if nothing is happening, time continues to pass.
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Does an X or y-axis scale have to always start at zero?.
No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero
Define axis.A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.
Given,
No, X or y-axis scale does not have to always start at zero.
A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.
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Look at this rectangular prism:
Answer:
3 : 1
Step-by-step explanation:
volume = length * width * height
The volume of the solid as it is shown is:
volume = 10 m * 6 m * 10 m = 600 m^3
old volume = 600 m^3
Now we triple the length.
The length becomes 3 * 10 m = 30 m
The new volume is:
volume = length * width * height
volume = 30 m * 6 m * 10 m = 1800 m^3
new volume = 1800 m^3
ratio of new volume to old volume = 1800 m^3 : 600 m^3
Divide both sides of the ratio by 600 m^3.
Ratio = 3 : 1
Answer: 3 : 1
When a problem is said to be decidable or undecidable give an example of an undecidable problem?
Example of an undecidable problem is given by the problems in the system created by computer viruses.
What is decidable and undecidable problems?According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.
A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.
When is a problem said to be decidable or undecidable?
whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.
If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.
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Find the measurement of angle x.
The measure of angle x in the right triangle is approximately 14.6 degrees.
What is the measure of angle x?The figure in the image is that of two right angles.
First, we determine the hypotenuse of the left-right angle.
Angle θ = 30 degrees
Adjacent to angle θ = 10 cm
Hypotenuse = ?
Using the trigonometric ratio.
cosine = adjacent / hypotenuse
cos( 30 ) = 10 / hypotenuse
hypotenuse = 10 / cos( 30 )
hypotenuse = \(\frac{20\sqrt{3} }{3}\)
Using the hypotenuse to solve for x in the adjoining right triangle:
Angle x =?
Adjacent to angle x = \(\frac{20\sqrt{3} }{3}\)
Opposite to angle x = 3
Using the trigonometric ratio.
tan( x ) = opposite / adjacent
tan( x ) = 3 / \(\frac{20\sqrt{3} }{3}\)
tan (x ) = \(\frac{3\sqrt{3} }{20}\)
Take the tan inverse
x = tan⁻¹( \(\frac{3\sqrt{3} }{20}\) )
x = 14.6 degrees
Therefore, angle x measures 14.6 degrees.
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A daycare facility is enclosing a rectangular area along the side of their building for the children to play outdoors. They need to maximize the area using 180ft of fencing on three sides of the yard. The quadratic equation A=−2x2+180x gives the area, A, of the yard for the length, x, of the building that will border the yard. Find the length of the building that should border the yard to maximize the area, and then find the maximum area.
Answer:
a) length x = 45ftb) maximum area = 4050 ft²Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
Hence the length of the building that should border the yard to maximize the area is 45 ft
To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
Hence the maximum area of the yard is equal to 4050 ft²
how many samples of size n=2 can be drawn from this population
The samples of size n = 2 that can be drawn from this population is 28
How many samples of size n=2 can be drawn from this populationFrom the question, we have the following parameters that can be used in our computation:
Population, N = 8
Sample, n = 2
The samples of size n = 2 that can be drawn from this population is calculated as
Sample = N!/(n! * (N - n)!)
substitute the known values in the above equation, so, we have the following representation
Sample = 8!/(2! * 6!)
Evaluate
Sample = 28
Hence, the number of samples is 28
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Complete question
A finite population consists of 8 elements.
10,10,10,10,10,12,18,40
How many samples of size n = 2 can be drawn this population?
Write an equation that describes the following relationship: y varies inversely as the fourth power of x and when x=2, y=2
We rewrite the staement into a methematical expression:
\(\begin{gathered} y\text{ }\propto\text{ }\frac{1}{fourth\text{ opower of x}} \\ \text{where }\propto\text{ represents varies} \\ fourth\text{ power of x }=x^4 \\ \\ y\text{ }\propto\text{ }\frac{1}{x^4} \\ \text{removing the varies symbol i to an equation:} \\ \text{The equation beomes:} \\ y\text{ = k}\frac{1}{x^4} \\ \text{where k = constant of proportion} \end{gathered}\)\(\begin{gathered} to\text{ get the alue of k, we substitute for x and y in the equation we got above:} \\ \text{when x = 2, y = 2} \\ y\text{ = k}\frac{1}{x^4} \\ 2\text{ = k}\frac{1}{2^4} \\ 2\text{ = }\frac{k}{2^4} \end{gathered}\)\(\begin{gathered} 2\times(2^4)\text{ = k} \\ k=2^1\times2^4=2^{+4} \\ k=2^5 \end{gathered}\)The equation describing the relationship between the variables:
\(\begin{gathered} y=2^5\frac{1}{x^4} \\ y\text{ = }\frac{2^5}{x^4}^{} \end{gathered}\)how many grams of pure zinc oxide powder must be added to 450 g of a 1.5% ointment to make a 11% zinc oxide ointment? round to one decimal place.
The amount of zinc oxide need to be added to 450 g of 1.5% ointment to make a 11% zinc oxide ointment is 48 gram.
A fraction represent the number of parts in total or whole. Fraction is sometimes denoted in percentage, e.g. 20% means a fraction of 20/100.
In the given problem, let w is the amount of zinc oxide need to be added.
Original weight of Zinc oxide = 1.5% x 450 g
After adding w gram of zinc oxide, weight of zinc oxide = 1.5% x 450 + w
Original weight of ointment = 450 g
After adding w gram of zinc oxide, weight of ointment = 450 + w
Hence, the new fraction of zinc oxide:
(1.5% x 450 + w) / (450 + w) = 11%
1.5% x 450 + w = 11% x 450 + 11% w
9.5% x 450 = 89% w
w = 48
Hence, the amount of zinc oxide need to be added is 48 gram.
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does -7+5x=5x+9 have infinite solutions?
Hi there!
»»————- ★ ————-««
I believe your answer is:
No, it does not have infinite solutions.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
While both sides do share a term, it does not mirror each other. For an equation to have infinite solutions, it must be an identity.⸻⸻⸻⸻
\(-7+5x=5x+9\\\rule{150}{0.5}\\\\\rightarrow -7 + 5x = 5x + 9\\\\\rightarrow -7 + 5x - 5x = 5x - 5x +9\\\\\rightarrow -7 = 9\)
⸻⸻⸻⸻
The result is a contradiction. It has no real solutions.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Find the magnitude of the net electric field at the origin (created by charges q1 and q2).
The direction of the net magnetic field is \($167.36^{\circ}$\)
How to find the magnitude?\(q_1=-4 \mathrm{nC} \text { at }(0.6,0.8)\)
\($q_2=6 \mathrm{nC}$\) at (0.6,0)
\($r_1=$\)Distance of \($q_1$\) from origin\($=\sqrt{0.6^2+0.8^2}$\)
\($r_2=$\) Distance of \($q_2$\) from origin \($=0.6$\)
\($\mathrm{k}=$\) Coulomb constant\($=9\)times \(10^9 \mathrm{Nm}^2 / \mathrm{C}^2$\)
Electric field is given by
\(&E_1=\frac{k q_1}{r_1^2} \\\)
\(&\Rightarrow E_1=\frac{9 \times 10^9 \times 4 \times 10^{-9}}{\sqrt{0.6^2+0.8^2}} \\\)
\(&\Rightarrow E_1=36 \mathrm{~N} / \mathrm{C}\)
\(&\theta=\tan ^{-1} \frac{0.8}{0.6} \\\)
\(&\Rightarrow \theta=53.13^{\circ} \\\)
\(&E_1=36 \cos 53.13^{\circ} \hat{i}+36 \sin 53.13^{\circ} \hat{j} \\\)
\(&\Rightarrow E_1=21.6 \hat{i}+28.8 \hat{j}\)
\(&E_2=\frac{k q_2}{r_2^2} \\\)
\(&\Rightarrow E_2=\frac{9 \times 10^9 \times 6 \times 10^{-9}}{0.6^2} \\\)
\(&\Rightarrow E_2=150 \mathrm{~N} / \mathrm{C}\)
The charge \($q_2$\) is on the \($\mathrm{x}$\) axis itself and it is pointing towards the origin (left side) so the sign will be negative
\(E_2=-150 \hat{i}\)
Resultant electric field
\(&E=E_1+E_2 \\\)
\(&\Rightarrow E=21.6 \hat{i}+28.8 \hat{j}+(-150 \hat{i}) \\\)
\(&\Rightarrow E=-128.4 \hat{i}+28.8 \hat{j}\)
Magnitude of electric field is given by
\(&|E|=\sqrt{(-128.4)^2+28.8^2} \\\)
\(&\Rightarrow|E|=121.6 \mathrm{~N} / \mathrm{C}\)
Magnitude of the net electric field is \($121.6 \mathrm{~N} / \mathrm{C}$\)
Direction is given by
\(\theta=\tan ^{-1} \frac{128.4}{28.8}=77.36^{\circ}\)
From the -x axis
\((90+77.36)^{\circ}=167.36^{\circ}\)
The direction of the net magnetic field is \($167.36^{\circ}$\)
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Picture below has question/answer choices!!
The statements that is true about the similarity of the two triangles the option D
D. ΔMNO and ΔJKL are not similar triangles
What are similar triangles?Similar triangles are triangles which have proportional corresponding sides
The parameters in the question are;
The length of segment MN = 20
Length of segment NO = 12
Length of segment OM = 25
Measure of angle ∠O = 56°
Length of segment LJ =- 15
Length of segment JK = 12
Length of segment KL = 9
Measure of angle ∠L = 56°
Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included angle between the two sides are congruent
The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL
However, the ratio of the sides LK to ON and JL to MO are;
9/12 ≠ 15/25
Therefore, the triangles are not similar
The correct option is option D
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alex stocks up for winter . he buys 36 cans of vegetables. He pays 80 cents per can for tomatoes and 40 cents per can for corn, for a total cost of $20.8. How many cans of corn does he buy?
Answer:
Therefore, Alex buys 20 cans of corn.
Step-by-step explanation:
Let's assume Alex buys x cans of tomatoes and y cans of corn.
Given that he buys 36 cans in total, we can write the equation:
x + y = 36 ----(1)
The cost of tomatoes per can is 80 cents, and the cost of corn per can is 40 cents. The total cost is $20.8, which can be expressed as 2080 cents.
The cost of the tomatoes (80 cents per can) multiplied by the number of tomato cans (x) gives the cost of tomatoes, and the cost of corn (40 cents per can) multiplied by the number of corn cans (y) gives the cost of corn. The sum of these costs should equal 2080 cents.
80x + 40y = 2080 ----(2)
Now we have a system of equations (equations (1) and (2)) that we can solve to find the values of x and y.
To solve the system, we can use substitution or elimination. Let's use the substitution method here.
From equation (1), we have:
x = 36 - y
Substituting this value of x into equation (2), we get:
80(36 - y) + 40y = 2080
Expanding and simplifying:
2880 - 80y + 40y = 2080
2880 - 40y = 2080
-40y = 2080 - 2880
-40y = -800
y = (-800) / (-40)
y = 20
Therefore, Alex buys 20 cans of corn.
Answer:
20
Step-by-step explanation:
Let x be the number of cans of corn Alex buys.
Then, the number of cans of tomatoes he buys is 36-x.
The cost of the cans of tomatoes is:
\((36 - x) \times 0.80\)
The cost of the cans of corn is:
\(x \times 0.40\) dollars
The total cost is:
\((36-x) \times 0.80 + x \times 0.40 = 20.8 dollars\)
Simplifying the expression, we get:
28.8 - 0.40x = 20.8
0.40x = 8
x = 20
Therefore, Alex buys 20 cans of corn.
hope it helps...
Assume that in the US 20% of the population works in government laboratories, i.e., NA/N=.20. GDP per capita in the United States grows at 2 percent per year, and the population grows at 1% per year.
Consider the following National Income and Product Account Data for 2020. Reorganize the accounts according to the model to determine the values of
i. C/GDP
ii. G/GDP
iii. K/GDP
iv. X/GDP (Note X is model investment.)
v. rk/Y.
GDP per capita in the United States grows at 2 percent per year, and the population grows at 1% per year then answer is i. C/GDP = 0.7 ii. G/GDP = 0.2 iii. K/GDP = 0.3 iv. X/GDP = 0.4 v. rk/Y = 0.06
To reorganize the accounts according to the model, we can use the following equations:
C = cY
G = gY
I = kY
X = rX
M = mY
where c is the marginal propensity to consume, g is the government spending multiplier, k is the investment multiplier, r is the marginal propensity to import, and m is the import multiplier.
We can solve for the values of c, g, k, r, and m using the following information:
The population grows at 1% per year.
GDP per capita grows at 2% per year.
NA/N = 0.20, which means that 20% of the population works in government laboratories.
We can use the following steps to solve for the values of c, g, k, r, and m:
Set Y = $15,000.
Set GDP per capita = $15,000 / 1.01 = $14,851.
Set c = (GDP per capita - mY) / Y = (14,851 - 0.1Y) / Y = 0.694.
Set g = (G - NA) / Y = (2,000 - 0.2Y) / Y = 0.196.
Set k = (I - NA) / Y = (4,000 - 0.2Y) / Y = 0.392.
Set r = (X - M) / Y = (3,000 - 1,000) / Y = 0.667.
Once we have solved for the values of c, g, k, r, and m, we can use the following equations to calculate the values of C/GDP, G/GDP, K/GDP, X/GDP, and rk/Y:
C/GDP = cY/Y = 0.694
G/GDP = gY/Y = 0.196
K/GDP = kY/Y = 0.392
X/GDP = rX/Y = 0.667
rk/Y = rk/Y = 0.06
Therefore, the values of C/GDP, G/GDP, K/GDP, X/GDP, and rk/Y are 0.7, 0.2, 0.3, 0.4, and 0.06, respectively.
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The probability distribution for the number of defective items in a random sample is as follows: x: 0 1 2 3 4 p(x) : 1 0.15 13 07 0.55
calculate:
expected value of X = ____
From the probability distribution for the number of defective items in a random sample, the expected value of X is 2.82.
To calculate the expected value of X, we need to multiply each possible value of X by its corresponding probability and sum them up.
The expected value of X, denoted as E(X) or μ, is calculated using the formula:
E(X) = ∑ (x * p(x))
where x represents each possible value of X and p(x) represents the corresponding probability.
In this case, the probability distribution for X is given as follows:
x: 0 1 2 3 4
p(x): 0.1 0.15 0.13 0.07 0.55
To calculate the expected value, we perform the following calculations:
E(X) = (0 * 0.1) + (1 * 0.15) + (2 * 0.13) + (3 * 0.07) + (4 * 0.55)
E(X) = 0 + 0.15 + 0.26 + 0.21 + 2.2
E(X) = 2.82
The expected value represents the average value or mean of the probability distribution. In this case, it represents the average number of defective items we expect to find in a random sample based on the given probabilities.
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ASAP PLEASE
Vertex of angle DCF:
Endpoint of ray DF:
Upper endpoint of segment BF:
Vertex of angle AGB:
Vertex of angle BAE:
Endpoint of ray FC:
Vertex of angle DCF: (9, 8)
Endpoint of ray DF: (6, 6)
Upper endpoint of segment BF: (9, 10)
Vertex of angle AGB: (7, 9)
Vertex of angle BAE: (5, 8)
Endpoint of ray FC: (9, 5)
How to Interpret Geometry Coordinates?From the given diagram, we can say that;
1) Vertex is the meeting point of a pair of sides in this case and so, we have that the Vertex of angle DCF is; (9, 8)
2) Endpoint of ray DF is at point D which is; (6, 6)
3) Upper endpoint of segment BF is at point B which is; (9, 10)
4) Vertex of AGB is at point G which is; (7, 9)
5) Vertex of angle BAE is at point A which is (5, 8)
6) Endpoint of ray FC is point C which is (9, 5)
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In the figure shown, triangle RST undergoes reflections across two line. R''S''T’’ is the final image of RST
Triangle RST is first reflected across the line x=0 and then across line
a. x=0
b. y=0
c. y=x
d. y=-x
======================================================
Explanation:
Point T is at (-2,1)
When we reflect it over the line x = 0, aka the y axis, we use the rule \((x,y) \to (-x,y)\) so T(-2,1) becomes T ' (2, 1). The x coordinate flipped in sign, while the y coordinate stays the same.
Then the final transformation is reflecting over y = -x using the rule \((x,y) \to (-y, -x)\). Therefore, the point (2,1) moves to (-1, -2) which is where T'' is located in the diagram.
You apply the same two transformations for the points R and S to get R'' and S'' respectively.
Note: A composition of two reflections, where the lines of reflection aren't parallel, form a rotation. In this case, we have a 90 degree counterclockwise rotation when going from triangle RST to triangle R''S''T''.
Helppppppppppppppppppp I’ll mark you brainlist don’t respond if you’re going to put something random I will report you :)
Answer:
-3, -13, -23, -33, -43
Step-by-step explanation:
An atithmetic sequence has a common difference between each term
in -3, -13, -23, -33, -43
the difference between terms is a constant -10
what is -1/4 - 8 > -12
Answer:
It is true.
Step-by-step explanation:
Suppose Jason read an article stating that in a 2005–2006 survey, the average American adult woman at least 19 years old drank an average of 1.06 liters of plain water per day with a standard deviation of 0.06 liters. Jason wants to find out if the women at his college drink a similar amount per day. He asks 60 of his female classmates in his Introductory Statistics class to record the amount of water they drink in one day, and he is willing to assume that the standard deviation at his college is the same as in the 2005–2006 survey. Jason wants to construct a 95% confidence interval for u, the average amount of water the women at his college drink per day. Have the requirements for constructing a z-confidence interval for a mean been met? Mark all of the following requirements that have been met with yes, and all the requirements that have not been met with no. - The sample is a simple random sample. - The population standard deviation is known. - The population from which the data are obtained is normally distributed, or the sample size is large enough. - The requirements for constructing a z-confidence interval for a mean have been met. Answer Bank yes no
The requirements for constructing a z-confidence interval for a mean have been met since the sample size is large enough and the population standard deviation is known
To construct a z-confidence interval for a mean, the following requirements must be met
The sample size should be large enough (n > 30).
The population standard deviation is known, or the sample standard deviation can be used as an estimate of the population standard deviation.
In this case, Jason has asked 50 of his male classmates to record the amount of water they drink in one day, so the sample size is large enough (n = 50) to meet the first requirement. Additionally, Jason is willing to assume that the standard deviation at his college is the same as in the 2003-2004 survey, which meets the second requirement.
Therefore, the requirements for constructing a z-confidence interval for a mean have been met, and Jason can proceed with constructing a 99% confidence interval for the average amount of water the men at his college drink per day using the formula:
CI = x ± z × (σ/√n)
where x is the sample mean, σ is the population standard deviation (or the sample standard deviation), n is the sample size, and z is the critical value from the standard normal distribution for a 99% confidence level.
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The given question is incomplete, the complete question is:
Suppose Jason read an article stating that in a 2003-2004 survey, the average American adult man at least 19 years old drank an average of 1.37 liters of plain water per day with a standard deviation of 0.05 liters. Jason wants to find out if the men at his college drink a similar amount per day. He asks 50 of his male classmates in his Introductory Physics class to record the amount of water they drink in one day, and he is willing to assume that the standard deviation at his college is the same as in the 2003-2004 survey. Jason wants to construct a 99% confidence interval for the average amount of water the men at his college drink per day Have the requirements for constructing a z-confidence interval for a mean been met?
The requirements for constructing a z-confidence interval for a mean have been met since the sample size is large enough and the population standard deviation is known
To construct a z-confidence interval for a mean, the following requirements must be met
The sample size should be large enough (n > 30).
The population standard deviation is known, or the sample standard deviation can be used as an estimate of the population standard deviation.
In this case, Jason has asked 50 of his male classmates to record the amount of water they drink in one day, so the sample size is large enough (n = 50) to meet the first requirement. Additionally, Jason is willing to assume that the standard deviation at his college is the same as in the 2003-2004 survey, which meets the second requirement.
Therefore, the requirements for constructing a z-confidence interval for a mean have been met, and Jason can proceed with constructing a 99% confidence interval for the average amount of water the men at his college drink per day using the formula:
CI = x ± z × (σ/√n)
where x is the sample mean, σ is the population standard deviation (or the sample standard deviation), n is the sample size, and z is the critical value from the standard normal distribution for a 99% confidence level.
Learn more about z-confidence interval here
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The given question is incomplete, the complete question is:
Suppose Jason read an article stating that in a 2003-2004 survey, the average American adult man at least 19 years old drank an average of 1.37 liters of plain water per day with a standard deviation of 0.05 liters. Jason wants to find out if the men at his college drink a similar amount per day. He asks 50 of his male classmates in his Introductory Physics class to record the amount of water they drink in one day, and he is willing to assume that the standard deviation at his college is the same as in the 2003-2004 survey. Jason wants to construct a 99% confidence interval for the average amount of water the men at his college drink per day Have the requirements for constructing a z-confidence interval for a mean been met?
A company's total cost, in millions of dollars, is given by ????(????) = 120 − 80????−???? where t = time in years. Find the marginal cost when t = 4.
The derivative of the given function is 80e^-t. By evaluating this expression at t=4, we get 80e^-4. When t = 4 the marginal cost is approximately $14.874 million.
C(t) = 120 − 80e^-t
dC/dt = 0 - (-80)(-e^-t)
= 80e^-t
80e^-4 ≈ 80(0.01832) [using e^-4 ≈ 0.01832]
≈ 1.4656
However, the question asks for the answer in millions of dollars
1.4656 / 1 million ≈ 0.014874
Rounding this to three decimal places, we get the answer as approximately $0.015 million or $15,000.
Therefore, the marginal cost when t = 4 is:
dC/dt | t=4 = 80e^-4
dC/dt | t=4 ≈ 14.874
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The complete question is:
A company's total cost, in millions of dollars, is given by C(t) = 120 − 80e^-t where t = time in years. Find the marginal cost when t = 4.
working with a manufacturing process which produces compsites having a fiber volume fraction a (msi) and a matrix with a matrix modulus b (msi). determine the fiber modulus required to produce a composite with longitudinal modulus of c (msi).
The fiber modulus required to produce a composite with longitudinal modulus of c is 56.93.
What is manufacturing process?
Manufacturing process management is a group of tools and techniques that specify how goods should be produced. MPM is distinct from ERP/MRP, which is used to schedule manufacturing, gather cost information, and organize the ordering of supplies and other resources.
What is matrix?
A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns. is a matrix having two rows and three columns, for instance.
As a result, if we look at the formula for the relationship between the fiber modulus and the matrix's volume fraction, composite modulus, and fiber vol fraction, we have:
C = (M x B) / [(1-A)M + A x B]
where M denotes the fiber's modulus.
If you provide the corresponding letter values,
40 = M X 0.5 / [(1-0.7)M + 0.7 X 0.5]
M = 56.93
Hence,the fiber modulus required to produce a composite with longitudinal modulus of c (msi) is 56.93
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find the coordinates of the image of point (5,2) after a reflection in the line y=x
Answer:
the answer is 5,-2
Step-by-step explanation:
Write the equation of the line shown. Be sure to use the correct variable.
Equation:
Answer:
y = -9Step-by-step explanation:
As per diagram, y = -9 for any value of x, so it is the line with equation:
y = -9