The compound interest on ₹20,000 for 3 years at 10% per annum compounded annually is ₹6,620.
To calculate the compound interest on a principal amount of ₹20,000 for 3 years at 10% per annum compounded annually, we can use the formula
A = P(1 + R/100)^n
Where,
A = final amount after n years
P = principal amount
R = annual interest rate
n = number of years
In this case, P = ₹20,000, R = 10%, and n = 3 years.
So, applying the formula
A = 20000(1 + 10/100)^3
= 20000(1.1)^3
= 20000(1.331)
= ₹26,620
The final amount after 3 years is ₹26,620. Therefore, the compound interest is
Compound Interest = Final Amount - Principal Amount
= ₹26,620 - ₹20,000
= ₹6,620
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I have solved the question in general, as the given question is incomplete.
The complete question is:
Find the compound interest on ₹ 20,000 for 3 years at 10% per annum compounded annually.
find two positive numbers that satisfy the given requirements. the sum of the first and twice the secind is 100 and the product is a maximum
Answer: The two positive numbers that satisfy the given requirements are 25 and 50.
Step-by-step explanation:
Let's call the two positive numbers x and y. We want to maximize their product while satisfying the condition that "the sum of the first and twice the second is 100", or mathematically:
x + 2y = 100
We can use algebra to solve for one of the variables in terms of the other:
x = 100 - 2y
Now we want to maximize the product xy:
xy = x(100 - 2y) = 100x - 2xy
Substituting x = 100 - 2y:
xy = (100 - 2y)y = 100y - 2y^2
To find the maximum value of this expression, we can take the derivative with respect to y and set it equal to zero:
d(xy)/dy = 100 - 4y = 0
Solving for y gives:
y = 25
Substituting y = 25 into the equation x + 2y = 100, we get:
x + 2(25) = 100
x = 50
Therefore, the two positive numbers that satisfy the given requirements are x = 50 and y = 25, and their product is:
xy = 50(25) = 1250
If F1 = 4y - 6, F2 = 9y + 3 and F3 = -y - 8, simplify F1 × F2 - F3 in terms of y.
Answer:
To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.
F1 × F2 can be expanded using the distributive property:
F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3
= 36y^2 + 12y - 54y - 18
= 36y^2 - 42y - 18
Now we can subtract F3 from the result:
F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)
= 36y^2 - 42y - 18 + y + 8
= 36y^2 - 41y - 10
Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.
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In a certain company, employees contribute to a welfare fund at the rate of 4% of the first $1000 earned, 3% of the next $1000, 2% of the next $1000 and 1% of any extra monies. How much will an employee who earned $20,000 contribute to the fund?
The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.
An employee who earned $20,000 will contribute $260 to the welfare fund.
To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.
The first $1000 will have a contribution rate of 4%.
Contribution for the first $1000 = 4% of $1000 = $40.
The next $1000 will have a contribution rate of 3%.
Contribution for the next $1000 = 3% of $1000 = $30.
The next $1000 will have a contribution rate of 2%.
Contribution for the next $1000 = 2% of $1000 = $20.
The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.
Contribution for the remaining amount = 1% of $17,000 = $170.
Now, let's sum up the contributions for each tier:
$40 + $30 + $20 + $170 = $260.
Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.
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Venell put together a model train with 25 train cars. Each train car is 80 millimeters long. How many meters long is Venell's model train if there are no gaps between cars? (1 meter = 1,000 millimeters)
Answer: 2 meters
Step-by-step explanation:
The length of one train car is 80 millimeters. Therefore, the length of the entire train is:
25 cars × 80 mm per car = 2000 mm
To convert millimeters to meters, we need to divide by 1000:
2000 mm ÷ 1000 = 2 meters
Therefore, Venell's model train is 2 meters long.
in nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)
where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.
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Complete question:
In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'
B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---
C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°
D. ΔY = f(x₁ +Xq, X2, Xk).
Pls help There is a 20% chance that a customer walking into a store will make a purchase. A computer was used to generate 5 sets of random numbers from 0 to 9, where the numbers 0 and 1 represent a customer who walks in and makes a purchase.
A two column table with title Customer Purchases is shown. The first column is labeled Trial and the second column is labeled Numbers Generated.
What is the experimental probability that at least one of the first three customers that walks into the store will make a purchase?
A) 60%
B) 13%
C) 40%
D) 22%
The experimental probability that at least one of the first three customers that walks into the store will make a purchase is 60%.
What is experimental probability?It is determined by counting the number of times an event occurs in a given experiment and dividing the total number of trials by the number of successful outcomes.
The experimental probability that at least one of the first three customers that walks into the store will make a purchase is calculated by dividing the total number of customers who make a purchase by the total number of customers who enter the store.
In this case, there are 3 trials and 2 customers who make a purchase.
The experimental probability is 3 by 5 which is the total number of trials.
Thus, the experimental probability
=3/5
= 60%.
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Asaad invests $6800 in two different accounts. The first account paid 14 %, the second account paid 11 % in interest. At the end of the first year he had earned $856 in interest. How much was in each account?
Answer:
Step-by-step explanation:
Let x be the amount invested in the first account, which pays 14% interest. Then the amount invested in the second account, which pays 11% interest, is 6800 - x.
The interest earned on the first account is 0.14x, and the interest earned on the second account is 0.11(6800 - x). The total interest earned is the sum of these two amounts, so we have:
0.14x + 0.11(6800 - x) = 856
Simplifying and solving for x, we get:
0.14x + 748 - 0.11x = 856
0.03x = 108
x = 3600
Therefore, Asaad invested $3600 in the first account and $3200 (6800 - 3600) in the second account.
Y=3x-4 4x+3y=1 what does X and y equal?
Answer:
{y,x}={-1,1}
to leave and take
what the answer of this
The correct option for this question is (d) "No, none of the sides are parallel."
why it is and what is a Quadrilateral?
To determine if quadrilateral CDEF is a trapezoid, we need to check if it has exactly one pair of parallel sides.
We can find the slopes of the line segments CD and EF as follows:
slope of CD = (5 - (-6)) / (-8 - (-1)) = 11 / (-7) = -1.57 (approx.)
slope of EF = (8 - 5) / (3 - 4) = 3 / (-1) = -3
Since the slopes are different, CD and EF are not parallel, and therefore, CDEF is not a trapezoid.
Alternatively, we can also find the slopes of the line segments CF and DE as follows:
slope of CF = (-5 - (-6)) / (4 - (-1)) = 1/5
slope of DE = (8 - 5) / (3 - (-8)) = 3/11
Since the slopes are different, CF and DE are not parallel, and therefore, CDEF is not a trapezoid.
Therefore, the answer is option (d) "No, none of the sides are parallel."
A quadrilateral is a geometric shape that has four straight sides and four vertices (corners). It is a two-dimensional polygon with four sides and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.
There are many types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.
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The triangle shown has an area of 46 square centimeters. Find the measure of the base (segment AB ). Triangle A B C. A line goes from point C to point D on side A B. Side A C is 11 centimeters, C B is 9 centimeters, and A B is question mark.
By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
the length of the base AB,
Area = (1/2) * base * height
[tex]CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\[/tex]
We also know that the area of the triangle is:
[tex]46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\[/tex]
[tex]8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\[/tex]
[tex]AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\[/tex]
Therefore, the length of the base AB is approximately 20.88 centimeters.
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What percent of 28 is 77?
Answer:
36.3636364%
or 36.36
Step-by-step explanation:
Tell me which brand or which size is a better buy.
Answer:
The answer is brand B
Step-by-step explanation:
You divide $14.88 by 24 which equals 68 cents per item.
Then brand B is 60 cents per item which is the better buy!
Need help answering all 3 of these please anyone
a. The slope of AB is [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. The mid-point of Diagonal AC is [tex](0, -1/2)[/tex]
What are the Quadrilaterals?A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.
a.
Slope is given by
[tex]A = (-2, 3) and B = (-5, 0)[/tex]
[tex]m = 1[/tex]
[tex]B = (-5, 0) and C = (2, -4)[/tex]
[tex]m = -4/7[/tex]
Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex] .
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y
Thus, Diagonal [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]
Midpoint [tex]= ((-2 + 2), (3 + -4))[/tex]
[tex]= ((0), (-1))[/tex]
Now divide them by 2
[tex]= ((0/2), (-1/2))[/tex]
[tex]= (0, -1/2)[/tex]
Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]
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Construct triangle PQR in which angle Q = 30 deg , angle R=60^ and PQ + QR + RP = 10cm
We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm, here is a guide:
Draw a line segment AB = 10 cm.Construct angle 30° at point A and angle 60° at point B.Draw angle bisectors to angles A and B.Make sure these angle bisectors intersect at point P.Draw perpendicular bisector to line segment AP.Let this bisector meet AB at Q.Then draw perpendicular bisector to line segment BP.Let this bisector meet AB at R.Join PQ and PR.PQR is the required triangle.What is a triangle?A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.
Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.
Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.
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Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formula.
In response to the stated question, we may state that Therefore, the trigonometry exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
Using the given triangle, we can find the values of sin(u), cos(u), and tan(u) as follows:
sin(u) = opposite / hypotenuse = 4 / 5
cos(u) = adjacent / hypotenuse = 3 / 5
tan(u) = opposite / adjacent = 4 / 3
To find the values of sin(2u) and cos(2u), we can use the double angle formulas:
[tex]sin(2u) = 2 sin(u) cos(u)\\cos(2u) = cos^2(u) - sin^2(u)\\sin(2u) = 2 (4/5) (3/5) = 24/25\\cos(2u) = (3/5)^2 - (4/5)^2 = -7/25[/tex]
sin(t/2) = ± [tex]\sqrt((1 - cos(t)) / 2)[/tex]
We need to determine the sign of the square root based on the quadrant in which t/2 lies. Since 7t/2 is in the second quadrant (between pi and 3pi/2), t/2 is in the second quadrant as well (between pi/2 and pi). In the second quadrant, sine is positive and cosine is negative. Therefore, we take the positive square root:
[tex]sin(t/2) = \sqrt((1 - cos(t)) / 2)\\= \sqrt((1 - (-3/5)) / 2)\\= \sqrt(8/10)\\= \sqrt(4/5)\\[/tex]
= 2/√5
= 2√5 / 5
Therefore, the exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.
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P, Q, R, S, T and U are different digits.
PQR + STU = 407
Step-by-step explanation:
There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:
P = 2
Q = 5
R = 1
S = 8
T = 9
U = 9
With these values, we have:
PQR = 251
STU = 156
And the sum of PQR and STU is indeed 407.
Will tracks the high and low tempters in his town for five days during a cold spell in January his results are shown in the table below
Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.
Define change in temperaturecalculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.
Change in temperature on Monday from High to low
=15-10=5°F
Change in temperature on Tuesday from High to low
=8-(-4)=12°F
Change in temperature on Wednesday from High to low
=-2-(-5)=3°F
Change in temperature on Thursday from High to low
=-3-(-7)=4°F
Change in temperature on Friday from High to low
=-1-(-12)=11° F
Days when change in temperature more than 10° F are Tuesday and Friday.
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The Complete question is attached below:
graph each system of equations. solve each system and clearly mark the solutions on your graph. assume 0\le \theta \le 2\pi : r
The system of equation is now written as:
y = −2x−8
y = x+ 1
First, we will plotting two system of equations on the same axis, and then we'll explore the different factors to consider when plotting two linear inequalities on the same axis. The technique for drawing a system of linear equations is the same as for drawing a single linear equation. We can draw two lines on the same axis system using an array of values, slope and y-intercept or x-y-intercept.
Now,
these using slope-intercept form on the same set of axes. Remember that slope-intercept form looks like
y = mx+ b, so we will want to solve both equations for y.
First, solve for y in 2x+y=−8
2x+ y = −8
OR, y = −2x− 8
Second, solve for y in
x− y = −1
Or, y = x+1
The system is now written as
y = -2x - 8
y = x + 1
Now you can plot the two equations using their slope and intercept on the same set of axes as shown in the figure below. Note that these charts have one thing in common. It is their intersection, the point that lies on the two lines. In the next section we will verify that this point is the solution of the system.
Complete Question:
Graph each system of equations. Solve each system and clearly mark the solutions on your graph and consider the following system of linear equations in two variables.
2x+ y = −8 and x− y = −1
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Kingsley knows that 1inch is about 2.45 centimeters. He wants to write an equation he can use to convert any given length in inches (i) to centimeters (c)
How should Kingsley write his equation?
A.) c/i = 2.54
B.) c = 2.54i
C.) i = c/2.54
Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
What is equation ?
An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.
Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.
Let's call the length in inches "i" and the length in centimeters "c".
We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:
1 inch = 2.45 centimeters
To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:
c = 2.45i
This is the equation Kingsley can use to convert any given length in inches to centimeters.
Alternatively, we can rearrange this equation to solve for i:
c = 2.45i
Divide both sides by 2.45:
c/2.45 = i
So the equation for converting from centimeters to inches is:
i = c/2.45
Therefore, since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
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Let f be the function given by f(x) = e-2x2.
a) Find the first four nonzero terms and the general termof the power series for f(x) about x = 0.
b) Find the interval of convergence of the power series forf(x) about x = 0. Show the analysis that leads to yourconclusion.
c) Let g be the function given by the sum of the first fournonzero terms of the power series for f(x) about x = 0. Show thatabsolute value(f(x) - g(x)) < 0.02 for -0.6<= x <=0.6.
a) The first four nonzero terms of the power series for f(x) about x=0 are
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is (-2)^n (2x)^(2n) / (2n)!
b) The interval of convergence of the power series is (-∞, ∞).
c) To estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series, we can use the Lagrange form of the remainder
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
a) To find the power series for f(x) about x = 0, we can use the Maclaurin series formula
f(x) = Σ[n=0 to ∞] (fⁿ(0)/n!) xⁿ
where fⁿ(0) denotes the nth derivative of f evaluated at x=0.
In this case, we have
f(x) = e^6(-2x^2)
fⁿ(x) = dⁿ/dxⁿ(e^6(-2x^2)) = (-2)^n(2x)^ne^6(-2x^2)
So, we can write the power series as
f(x) = Σ[n=0 to ∞] ((-2)^n(2x)^n e^6(0))/n!)
= Σ[n=0 to ∞] ((-2)^n (2x)^n /n!)
To find the first four nonzero terms, we substitute n = 0, 1, 2, and 3 into the above formula
f(0) = e^6
f'(0) = 0
f''(0) = 24
f'''(0) = 0
So, the first four nonzero terms of the power series are:
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is
(-2)^n (2x)^(2n) / (2n)!
b) To find the interval of convergence of the power series, we can use the ratio test
lim [n→∞] |((-2)^(n+1) (2x)^(2n+2) / (2n+2)! ) / ((-2)^n (2x)^(2n) / (2n)!)|
= lim [n→∞] |-4x^2/(2n+1)(2n+2)|
= lim [n→∞] 4x^2/(2n+1)(2n+2)
Since this limit depends on the value of x, we need to consider two cases
i) If x = 0, then the power series reduces to the constant term e^6, and the interval of convergence is just x=0.
ii) If x ≠ 0, then the series converges absolutely if and only if the limit is less than 1 in absolute value
|4x^2/(2n+1)(2n+2)| < 1
This is true for all values of x as long as n is sufficiently large. So, the interval of convergence is the entire real line (-∞, ∞).
c) We can use the Lagrange form of the remainder to estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
where M is an upper bound for the fifth derivative of f(x) on the interval [-0.6, 0.6].
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What quadratic function is represented by the graph?
A. f(x) = −2x²+x+6
B. f(x) = 2x²x+6
C. f(x) = 2x²+x+6
D. f(x) = − 2x² - x - 6
Answer:
Answer: C. f(x) = 2x²+x+6
Use the diagram shown. Lines p and q are parallel.
How many degrees is the measure of ∠4?
Answer:
61°
Step-by-step explanation:
∠4 is the vertical angle to the 61° angle. This means they will have the same measure, so ∠4 is 61°.
complete the table below.
4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569
Answer:
?
Step-by-step explanation:
I will mark you brainiest!
If the triangles above are reflections of each other, then BC ≅ to:
A) DE.
B) ED.
C) EF.
D) DF.
E) AC.
Answer:
D
Step-by-step explanation:
If their reflections are congruent to each other then looking at the diagram we can see a reflection just like a mirror where its flipped on the other side of the dotted line. When flipping it and aligning one triangle to the other we find that BC is congruent to DF
The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble??
A) 11
B) 33
C) 32
D) 22
The number οf times that Greg chοοses a yellοw pebble is 22 times.
Thus, option D is correct.
Finding the number οf chοices:Tο find the number οf pοssible chοices, calculate the number οf chances in the tοtal number οf οutcοmes.
Since we need tο find the number οf chοices that are expecting a yellοw pebble, find the tοtal number οf yellοw pebbles in the number οf pebbles in bοth Claire and Laura's cases and find the tοtal number οf yellοw pebbles.
Here we have
A table belοw shοws the number οf painted pebbles by Claire and Laura
Frοm the table,
Number οf pebbles that Laura painted = 8 yellοw, 7 green, 10 blue
Number οf pebbles that Claire painted = 14 yellοw, 5 green, 6 blue
Tοtal number οf yellοw pebbles = 8 + 14 = 22
Given that
Greg chοοses a pebble at randοm frοm the bοx 75 times, and each time replaces the pebble
Hence, the number οf time that Greg get yellοw pebble = number οf yellοw pebbles
Therefοre, The number οf times that Greg chοοses a yellοw pebble is 22 times.
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Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = e−8/√n lim n→[infinity] an =
The sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex], is convergent sequence because the limit of an exists, that is as n approaches infinity, so the sequence an approaches 1 ( finite value).
The sequence can be convergent if the limit is zero, or if the limit is finite. The divergent sequence is one whose limit is not finite. The limit can be found suing the limit properties or by simplification method, as applicable. We have, an sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex]. We have to check whether the sequence converges or diverges. Using limits, [tex]lim_ {n->\infty } a_n = lim_{n-> oo} e^{\frac{-8}{\sqrt{n}}} [/tex]
n approaches infinity, so square root of n approaches infinity,
= e⁻⁰
= 1/e⁰ = 1 ( finite )
Therefore, it is a convergent sequence.
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Use Synthetic Division to find the quotient of the division between
x4-2x3+2x2-9x +10 and (x-2).
x^3 + 2x - 5
x^3 + x + 4
x^4 + 2x - 5
x^2 - 2x + 5
Using synthetic division for the given dividend and divisor the required quotient is given by option a. x^3 + 2x - 5.
Dividend is equal to,
x^4-2x^3+2x^2-9x +10
Divisor is equal to,
( x - 2 )
Using synthetic division we have,
Use double equals to method to simplify the dividend we have,
x^4-2x^3+2x^2-9x +10
= x^4 - 2x^3 + 2x^2 - 4x -5x + 10
= x^3 (x -2) + 2x ( x -2 ) - 5 ( x - 2 )
= ( x - 2 ) ( x^3 + 2x - 5 )
Now ,
Simplify by dividing it,
( x^4-2x^3+2x^2-9x +10 ) ÷ ( x - 2 )
= ( x - 2 ) ( x^3 + 2x - 5 ) ÷ ( x -2 )
= ( x^3 + 2x - 5 )
Therefore, the quotient of the synthetic division for the given dividend is equal to option a . ( x^3 + 2x - 5 ).
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A pyrotechnician is running a test for a fireworks display he is providing for an event downtown. He launches a test shell from the top of a tower. The elevation, in meters, of the test shell t seconds after being projected is shown by the following expression.
Look at the picture attached and then choose your answer pls!
Select the best description of the term 29.4 in the expression.
A. the total time the test shell is in the air
B. the initial velocity of the test shell
C. the highest elevation the test shell reaches
D. the initial elevation of the test shell
The best description of that term 29.4 in the expression is the initial velocity of the test shell. That is option B.
Who is a pyrotechnician?A pyrotechnician is defined as the individual that has been trained for safe storage, handling, and functioning of pyrotechnics such as fireworks.
While testing the display of the fireworks, he took note of the following:
The elevation in meters
The time in seconds
The change in velocity should be noted as the velocity of distance covered by a moving object with time.
Therefore, the term 29.4 is the initial velocity of the fireworks he projected.
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The mean time to admit an emergency patient to the Mount Nittany Medical Center is 5 minutes with a standard deviation of 3 minutes. Only trauma patients are admitted to this center. Also, assume that the admission process is in fact the radiography process via an X-Ray machine.
(a) What is the natural coefficient of variation for one patient?
C0 : ______________
(b) If the admission times of patients are independent, what will be the mean and variance of admitting a group of 50 emergency patients? What will be the coefficient of variation of a group of 50 emergency patients?
t0 : ______________ σ02 : ______________ C0 :______________
(c) The X-Ray machine in the center may fail at any time randomly. The time to failure is exponentially distributed with a mean of 80 hours and the repair time is also exponentially distributed with a mean of 4 hours. What will be the effective mean and coefficient of variation of the admission time for a group of 50 trauma patients?
te : ______________ σe 2 :____________ Ce :______________
(d) Determine the variability class of the squared-coefficients of variation in Parts a-c (e.g., low variability, moderate variability, or high variability.)
C0 2(Part a): ______________ C0 2(Part b): ______________ Ce 2(Part c): ______________
(e) In two sentences, describe how the manager of center can improve the inflated effective admission time in Part c?
(a) The natural coefficient of variation for one patient is the ratio of the standard deviation to the mean, expressed as a percentage:
C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.
(b) If the admission times of patients are independent, the mean and variance of admitting a group of 50 emergency patients can be calculated as follows:
mean = n x mean time = 50 x 5 = 250 minutes
variance = n x variance of individual patient / sample size = 50 x (3)^2 / 50 = 9
The coefficient of variation for a group of 50 emergency patients is the ratio of the standard deviation to the mean, expressed as a percentage:
C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.
(c) The effective mean and coefficient of variation of the admission time for a group of 50 trauma patients can be calculated using the following formula:
te = n x mean time / (1 - p1 x p2)
where p1 is the probability of machine failure and p2 is the probability of repair completion. Assuming the machine can fail at any time, p1 can be calculated as 1 / (mean time between failures / mean admission time) = 1 / (80 x 60 / 5) = 0.001042. Assuming the repair time is also exponentially distributed, p2 can be calculated as 1 / mean repair time = 1 / 4 = 0.25. Therefore, te = 50 x 5 / (1 - 0.001042 x 0.25) = 250.14 minutes. The variance of the admission time can be calculated using the formula:
σe^2 = n x variance of individual patient / (1 - p1 x p2)^2 = 50 x (3)^2 / (1 - 0.001042 x 0.25)^2 = 10.81. The coefficient of variation for a group of 50 trauma patients is the ratio of the standard deviation to the mean, expressed as a percentage:
Ce = (standard deviation / mean) x 100% = (sqrt(10.81) / 250.14) x 100% = 2.60%.
(d) The variability class of the squared coefficients of variation can be determined as follows:
C0² (Part a): (0.6)^2 = 0.36 (low variability)
C0² (Part b): (0.6)^2 = 0.36 (low variability)
Ce² (Part c): (0.026)^2 = 0.000676 (low variability)
(e) The manager of the center can improve the inflated effective admission time in Part c by implementing preventive maintenance measures to reduce the probability of machine failure, such as regular inspection and cleaning of the X-Ray machine, and by improving the repair process to reduce the mean repair time, such as hiring more skilled technicians or improving the repair procedures.
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pounds each, and the small boxes weigh 35 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4925 pounds in boxes, how many of each type of box is it carrying?
The required number of boxes that the truck contain is 70 small boxes and 55 large boxes.
What is simplification?In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Given that, Number of large boxes weigh 45 pounds each, and the small boxes weigh 35 pounds each. There are 125 boxes in all, the truck is carrying a total of 4925 pounds
Let the number of large boxes will be l and the number of small boxed be s,
According to the question,
l + s = 125
l = 125 - s - - - - - (1)
Again,
45l + 35s = 4925
put 1 in the above equation,
45[125 - s] + 35s = 4925
5625 - 45s + 35s = 4925
10s = 700
s = 70
Now,
l = 125 - 70
l = 55
Thus, the required number of boxes that the truck contain is 70 small boxes and 55 large boxes.
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