If x is the number of defective cameras in the 2-size sample, that means that:
P(x = 0) = 0 (since there are no 2 cameras that can be selected without replacement that are not defective)
P(x = 1) = 5/15 = 1/3 (since there are 15 total ways to select a distinct sample and only 5 of these would have the non-defective one in them)
P(x = 2) = 10/15 = 2/3 (since there are 15 total ways to select a distinct sample and 10 of these would NOT have the non-defective one in them)
the perimeter of regular hexagon equals the perimeter of an equilateral triangle. if the area of the triangle is 10, what is the area of the hexagon?
If the perimeter of the regular hexagon equals to the perimeter of an equilateral triangle then the area of the hexagon is 18.
A hexagon can be be known as a polygon that has six sides and angles. Regular hexagons have six equal sides and angles and are composed of six equilateral triangles. first we have to write down the formula for finding the area of a hexagon if you know the side length. Since a regular hexagon is comprised of six equilateral triangles, the formula for finding the area of a hexagon is derived from the formula of finding the area of an equilateral triangle.
Let a be the side of equilateral triangle ∴ [tex]\sqrt{3}[/tex] /4 [tex]a^{2}[/tex] = 12
Perimeter of triangle = 3a = Perimeter of Hexagon
3a=6h ,where h is the side of hexagon.
⇒ h = 1/2 a
The area of the hexagon =6× [tex]\sqrt{3}[/tex]/4 [tex]h^{2}[/tex]
=6× [tex]\sqrt{3}[/tex]/4 . ( a/2 ) 2 = 6/4 ×12
= 18
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If ST =
2v 59, RU= -v + 83, and PQ = v, what is the value of v?
Answer:
El valor de la variable b se corresponde con:
a) b = 0,25
b) b = 9
c) b = 125
please help me solve this linear expression
Answer:
substitute a=-5 and c=5 into a=-3c
Step-by-step explanation:
a= -3c
(-5)= -3(5)
-5= -15
A cylindrical container has radius 1 m.
The cylinder contains 628 litres of water.
Calculate depth of water in the cylinder giving your answer in cm
take pi to be 3.14
The depth of water in the cylinder is 20 cm
How to calculate depth of water in the cylinderFrom the question, we have the following parameters that can be used in our computation:
Volume = 628 litres
Radius = 1 m
Convert litres and meters to cm cube and cm
So, we have the following representation
Volume = 628000 cm cubed
Radius = 100 cm
The volume is the calculated as
V = πr²h
So, we have
628000 = 3.14 * 100² * h
Evaluate
628000 = 31400 * h
Divide by 31400
h = 20
Hence, the height is 20 cm
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in need some help. i cant figure this out.
Answer:
x = 1.28
Step-by-step explanation:
Given equation:
[tex]3 \frac{1}{2}x-6=2-2\frac{3}{4}x[/tex]
Add 2³/₄x to both sides of the equation:
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2-2\frac{3}{4}x+2\frac{3}{4}x[/tex]
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2[/tex]
Add 6 to both sides of the equation:
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6+6=2+6[/tex]
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x=8[/tex]
Rewrite the mixed numbers as improper fractions:
[tex]\implies \dfrac{3 \cdot 2+1}{2}x+\dfrac{2 \cdot 4+3}{4}x=8[/tex]
[tex]\implies \dfrac{7}{2}x+\dfrac{11}{4}x=8[/tex]
Make the denominators of the fractions the same:
[tex]\implies \dfrac{7 \cdot 2}{2 \cdot 2}x+\dfrac{11}{4}x=8[/tex]
[tex]\implies \dfrac{14}{4}x+\dfrac{11}{4}x=8[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{14+11}{4}x=8[/tex]
[tex]\implies \dfrac{25}{4}x=8[/tex]
Multiply both sides by 4:
[tex]\implies 4 \cdot \dfrac{25}{4}x=4 \cdot8[/tex]
[tex]\implies 25x=32[/tex]
Divide both sides by 25:
[tex]\implies \dfrac{25x}{25}=\dfrac{32}{25}[/tex]
[tex]\implies x=\dfrac{32}{25}[/tex]
Convert the improper fraction to a mixed number:
[tex]\implies x=1 \frac{7}{25}[/tex]
The value of x as a decimal:
[tex]\implies x=1.28[/tex]
Consider a game in which each play costs one nickel (1¢). During each play, the game dispenses a coin to the player to keep. The game machine contains equal numbers of pennies (1¢), nickels, dimes (10¢), and quarters (25¢). The nickels that the player inserts do not go into the same pool of "reward" coins. What is the expected profit, in cents, for a player who plays five games in a row?
The expected profit, in cents, for a player who plays 1 game is 5.25 cents.
How to obtain the expected profit?The distribution that models the profit of a player for a single game is given as follows:
P(X = -4 cents) = 0.25. -> pays 5 cents, wins 1 cent, loses 4 cents.
P(X = 0 cents) = 0.25. -> pays 5 cents, wins 5 cents.
P(X = 5 cents) = 0.25. -> pays 5 cents, wins 10 cents.
P(X = 20 cents) = 0.25. -> pays 5 cents, wins 25 cents.
The expected value of a discrete distribution is computed by adding the total of each outcome and multiplying it by its probability, as follows:
E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25
E(X) = 5.25 cents.
Hence, the expected profit is 5.25 cents
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Which of the following statements is true for all real symmetric matrices Mcq?All the eigenvalues are realAll the eigenvalues are positiveAll the eigenvalues are distinctSum of all the eigenvalues is zero
Option A is the correct answer. All the eigenvalues of a real symmetric matrix are always real.
Symmetrix matrix: A matrix is said to be a Symmetrix matrix if A=A^T the matrix should be equal to the transpose of A.
All the eigenvalues of the Symmetric matrix are real. Eigenvectors corresponding to distinct eigenvalues are orthogonal.
Skew-Symmetrix matrix: A matrix 'A' is said to be a Skew-Symmetrix matrix if A=-A^T
Eigenvalues of the skew-symmetric matrix are zero or purely imaginary.
Skew-Hermitian matrix: A square matrix is said to be a Skew-Hermitian matrix if it is equal to the negotiation of its complex conjugate transpose.
A=-(A)^T
Eigenvalues of the Skew-Hermitian matrices are zero or imaginary.
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The vector field F = [tex](3x^2y + z^3, x^3 + 2yz, y^2 + 3xz^2)[/tex] has a nonzero divergence and a nonzero curl, indicating that it is not a conservative vector field. F cannot be expressed as the curl of another vector field.
To compute the divergence of F, we take the partial derivatives of each component with respect to their corresponding variables and sum them up. The divergence of F is given by div(F) = ∇·F = (∂/∂x)[tex](3x^2y + z^3)[/tex] + (∂/∂y)[tex](x^3 + 2yz)[/tex] + (∂/∂z)[tex](y^2 + 3xz^2)[/tex]. Evaluating these partial derivatives, we find div(F) = 6xy + 3z^2 + 2yz + 6xz.
To compute the curl of F, we take the curl operator (cross product of the del operator with F) and expand the determinant. The curl of F is given by curl(F) = ∇×F = (∂/∂y)[tex](y^2 + 3xz^2)[/tex] - (∂/∂z)[tex](x^3 + 2yz)[/tex], (∂/∂z)[tex](3x^2y + z^3)[/tex] - (∂/∂x)[tex](y^2 + 3xz^2)[/tex], (∂/∂x)[tex](x^3 + 2yz)[/tex] - (∂/∂y)[tex](3x^2y + z^3)[/tex]. Simplifying these expressions, we obtain curl(F) = [tex](-2xz, -3z^2, -6xy)[/tex].
The divergence of F is nonzero, indicating that F does not satisfy the divergence theorem, which states that a vector field with zero divergence is conservative. Additionally, the curl of F is nonzero, indicating that F does not satisfy the curl theorem, which states that a vector field with zero curl is conservative. Therefore, F is not conservative and cannot be expressed as the curl of another vector field.
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a cylindrical water tank 5 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level. how much work is done in pumping a full tank of water up to ground level? (the water weighs 9800 newtons per cubic meter.)
The work is done in pumping a full tank of water up to ground level is 470400πNm.
Tank sizes variety from 6 ft. to one hundred twenty ft. in diameter with a roof, and as much as two hundred toes in diameter as an open pinnacle tank. Tanks with a roof have capacities starting from seven-hundred gallons to 500,000 gallons at the same time as the open pinnacle tanks may be constructed with even large capacities
The radius of the layer = 2m
V= pi (2)^2 (Delta y) m^3 = four pi Delta y m^3V=π(2) 2 (Δy)m 3 =4πΔym 3
Weight of the layer =9800 (four pi Delta y)=9800(4πΔy)
Weight of the water = 9800 frac=9800 m 3 N
So, weight of the layer = 39200 pi Delta y=39200πΔy
distance layer is moved =5-y=5−y
W=int_^{four} (5-y)(39200 pi dyW=∫ 04 (5−y)(39200πdy
=39200 pi int_^{four} (5-y) dy=39200π∫ 04 (5−y)dy
=39200 pi left[ 5y - frac y^2 right]_^{four}=39200π[5y− 21 y 2 ] 04
=-39200 pi (12) = 470400 pi Nm=−39200π(12)= 470400πNm.
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Stella is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $0.75 per mile driven. How much would a taxi ride cost if Stella is riding for 7 miles? How much would a taxi ride cost that is m miles long?
Cost of ride, 7 miles:
Cost of ride , m miles:
The amount that would a taxi ride cost for 7 miles is $7.75 and The amount that would a taxi ride cost that is m miles long is $(2.5 + 0.75m).
What is the equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.
Given:
The taxi charges $2.50 just for the pickup and then an additional $0.75 per mile driven,
Write the equation for the following statement,
y = 2.5 + 0.75x
Here, y is the total amount and x is the number of miles,
Calculate the cost of the ride, put x = 7
y = 2.5 + 0.75 × 7
y = 7.75
Calculate the cost of the ride, put x = m
y = 2.5 + 0.75m
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Complete the table to find 430 percent of 90.
A=
B=
100%
90
100%
90
Percent
100%
90
Using a
100%
90
a Diagram
30%
A
Total
430%
B
Answer:
387
Step-by-step explanation:
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
21. Calculate the future value of a $7,000 after 9
years, when there is an interest rate of 2.05%
with quarterly simple interest payments.
[A] $7,322.88
[D] $8,419.30
[B] $8,414.35
[E] $7,527.31
[C] $6,148.05
The solution is Option A.
The amount after 9 years with an investment of $ 7000 at a simple interest calculated quarterly at rate 2.05 is $ 7,322.88
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Now , the amount invested P = $ 7,000
The rate of interest R = 2.05 %
The time period t = 9 years
Since the interest is calculated quarterly , t= T/4
Now , the simple interest is calculated by the formula
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Substituting the values in the equation , we get
Simple Interest I = [ ( 7000 x 2.05 x 9 ) / 4 ] / 100
On simplifying the equation , we get
Simple Interest I = ( 129150 ) / 400
Simple Interest I = $ 322.875
I = $ 322.88
Now , the amount after 9 years = initial amount P + Interest I
Amount after 9 years = 7,000 + 322.88
Amount after 9 years = $ 7,322.88
Hence , the amount after 9 years is $ 7,322.88
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Multiply. 4x(y + x + 2)
Step-by-step explanation:
4xy + 4x² + 8x
Can also be rearranged as
4x²+8x+4xy
under what circumstances is a discretized b state matrix equivalent to a continuous time b state matrix
A continuous time system can behave roughly throughout a variety of periods using a discretized state matrix. A continuous time condition matrix should be used in its place if these requirements are not satisfied since a discretized state matrix might not adequately depict the performance of a continuous time system.
A continuous time condition matrix is a matrix that is used to indicate the state of a system at any moment, as opposed to a discretized state matrix, which is used to describe the status of a system at discrete time intervals. Under the following conditions, a discrete-time state matrix is identical to a time series state matrix:
The system may be regarded as being in stable equilibrium at each time point since the time gaps between every discretization are short enough. This indicates that the behavior of the system does not drastically vary from one-time point to the next.
Over the time frames between each discretization, a linear model accurately predicts the behavior of the system. This means that the behavior of the system can be precisely predicted by a linear equation of the type "Ax = Bu," where A as well as B are matrices and x as well as u are vectors that, respectively, represent the system's state and input.
Over the intervals between each discretization, the system's input remains constant. This indicates that the system's input does not drastically vary from one-time point to the next.
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What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
-3/4
Step-by-step explanation:
equation of a line : y=mx+c
m= slope= 4/3
perpendicular slope is the inverse of m
this is because m1 * m2 = -1
thus perpendicular slope = -3/4
in the triangle below, with right angle
Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?
On a coordinate plane, the point (0, 3) is graphed.
On a coordinate plane, the point (0, 4) is graphed.
On a coordinate plane, the point (3, 0) is graphed.
On a coordinate plane, the point (4, 0) is graphed.
The graph that represents Ramon's initial step is, On a coordinate plane, the point (0, 3) is graphed.
What is an ordered pair?The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.
Pair in Order = (x, y) where x represents the abscissa, the measure of a point's separation from the main axis, and y represents the ordinate, the measure of a point's separation from the secondary axis.
Given, Ramon is graphing the function f(x) = 3 + (4)x.
We know the initial value of a function is determined when the independent variable is set to zero.
Here the independent variable is 'x'.
Now, at x = 0,
f(0) = 3 + (4)(0).
f(0) = 3.
So, The ordered pair is (0, 3).
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Answer:
a
Step-by-step explanation:
Find g(x), where g(x) is the reflection across the x-axis of f(x)=4x+10
Answer:
To find the reflection of a function across the x-axis, we simply need to change the sign of the y-coordinates of the function's points. Therefore, the reflection of f(x) = 4x + 10 across the x-axis is g(x) = -(4x + 10) = -4x - 10.
Step-by-step explanation:
To find the reflection of a function across the x-axis, we can follow these steps:
Start with the equation of the original function, which in this case is f(x) = 4x + 10.Change the sign of the y-coordinates of the function's points. This means that we need to multiply the entire equation by -1.Substitute the result from step 2 into the original equation to find the reflected function. In this case, we get g(x) = (-1)(4x + 10) = -4x - 10.Here is an example of how this works in practice. Let's say that the original function f(x) has the points (1,14) and (2,18).
The reflection of these points across the x-axis would be (1,-14) and (2,-18), respectively.
To find the equation of the reflected function g(x), we would simply substitute these points into the equation from step 3 to get g(x) = -4x - 10.
Super Express Couriers charges a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30.
If Kevin's postage fee was 150 less than 5 times the weight of his parcel, how much did his parcel weigh?
Answer:
Step-by-step explanation:
я хз
The weight of Kevin's parcel is 60 g.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30. and Kevin's postage fee was 150 less than 5 times the weight of his parcel,
Let the weight of the parcel be x
Establishing the equations,
5x - 150 = 30 + 2x
5x - 2x = 30 + 150
3x = 180
x = 180/3
x = 60
Hence, the weight of Kevin's parcel was 60g
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Mark’ mother i planning to borrow $25,000 to remodel the retaurant he own. He contacted everal loan companie, and he i comparing two different option. Company 1 offer an interet rate of 5. 25%. Company 2 offer an interet rate of 8. 5%. Both loan option involve imple interet and mut be repaid in exactly 3 year. How much more will mark’ mother pay in interet if he chooe to borrow the money from company 2?
If Mark’s mother borrows the money of $25,000 from company 2 which offers a rate of 8.5% for 3 years, she needs to pay the charge of $6375.
How to calculate the simple interest?Interest is the cost of borrowing or saving money. Simple interest is an easy method to calculate the interest charge on a loan.
As its name, calculating the simple interest is simple and quick. We only multiply the money we borrow or deposit, by the period, then multiply them by the interest rate applied by the bank or any financial institution chosen.
The formula for calculating the simple interest is
P x R x T
P means principal or how much money we borrow or save
R means rate or how many percentages of interest applied
T means time or how long we borrow or save the money
By using the formula mentioned before, the simple interest would be
$25,000 x 8.5% x 3 = $6375
Thus, the amount of simple interest paid is $6375 and the total amount paid is $25000 + $6375 = $31,375
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7.6u-(30 divided by 6) + 12
Answer:
7.6u+7
Step-by-step explanation:
7.6u-(30/6)+12
30/6=5
7.6u-5+12
7.6u+7
The table below shows that the number of miles driven by Hakeem is directly proportional to the number of gallons he used.
\text{Gallons Used}Gallons Used \text{Miles Driven}Miles Driven
3636 1274.41274.4
4141 1451.41451.4
4545 15931593
\text{What is the rate of gas usage, in miles per gallon?}
What is the rate of gas usage, in miles per gallon?
The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, A table below shows that the number of miles driven by Hakeem is directly proportional to the number of gallons he used.
According to the table,
There are 36, 41, 45 gallons of gas are used for 1274.4 mile, 1451.4 and 1593 miles respectively,
So, for finding unit rates, we will divide the total mile to total gallons used, in one journey,
unit rate = 1593/45 = 1274.4/36 = 1451.4/41 = 35.4
Hence, The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.
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The library ha enough DVD’ to diplay equal number of them in group of 3, 5, or 9. What i the leat number of DVD the library can have?
The library ha enough DVD’ to diplay equal number of them in group of 3, 5, or 9. then the least number of DVD the library can have is 45
What is the function of DVD?
Short for digital versatile disc or digital video disc, a DVD or DVD-ROM is a disc capable of storing a significant amount more data than a standard compact disc. DVDs are widely used for storing and viewing movies and other data.
45 is the least common multiple of 3, 5, and 9.
45 can be equally divided by 3, 5, and 9:
45 ÷ 3 = 15
45 ÷ 5 = 9
45 ÷ 9 = 5
the least number of DVD the library can have is 45
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bonjour
voici un programe de calcul
.choisir un nombre relatif
.multiplier par-3
.ajouter -5
1quel nombre obtient-on avec ce programme lorsqu'on choisit au départ:
a.7 ? b.-4 ?
2. Léa a obtenu 1avec ce programme de calcul.
quel nombre avait-elle choisi au départ
Answer:
1a. -26
1b. -17
2. -2
Step-by-step explanation:
1.
a.
7
7 × (-3) = -21
-21 + (-5) = -26
b.
-4
-4 × 3 = -12
-12 + (-5) = -17
Formule:
r = -3n - 5
2.
r = -3n - 5
1 = -3n - 5
-3n = 6
n = -2
if a and b are independent events with p(a) = 0.35 and p(b) = 0.20, then, p(a è b) =
The probability of a intersection b, represented by P(a ∩ b) is equal to 0.07.
What is independent probabilityOne of the axioms of probability states that is two events say A and B are independent that is the probability of occurrence of one of them is not affected by the occurrence of the other, then P(A ∩ B) = P(A) × P(B)
We have from the question two events a and b which are said to be independent events,
P(a) = 0.35
P(b) = 0.20
then;
P(a ∩ b) = 0.35 × 0.20
P(a ∩ b) = 0.07
Therefore, the value 0.07 is the probability of the intersection of the two independent events a and b.
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Can someone help me this is hard
Answer:
m ≥ 28.5
Step-by-step explanation:
He wants to bike at least 28.5 miles, like he did last year
also whats up with the anime tab TT no judgement tho
What is the perimeter, in units, of ΔABC
Δ
A
B
C
with A(−1,−6)
A
(
−
1
,
−
6
)
, B(7,−6)
B
(
7
,
−
6
)
, and C(3,−3)
C
(
3
,
−
3
)
?
Answer:
To find the perimeter of triangle ABC, we need to find the lengths of all three sides of the triangle. To do this, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).
Applying this formula, we can find the lengths of the sides of the triangle as follows:
AB = sqrt((7 - (-1))^2 + (-6 - (-6))^2) = sqrt(8^2 + 0^2) = sqrt(64) = 8
BC = sqrt((3 - 7)^2 + (-3 - (-6))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
AC = sqrt((-1 - 3)^2 + (-6 - (-3))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
Thus, the perimeter of triangle ABC is 8 + 5 + 5 = 18 units.
I need help ive been trying to figure them out for an hour and i also want to know if some are correct
The correct answer for question 1 is C) CA=XY
what is congruence in triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure.
Given here ΔABC≅XYZ
Therefore AB=XY , BC=YZ , AC=XZ & ∠A=∠X , ∠B=∠Y , ∠C=∠Z but clearly CA≠XY
The full diagram is attached please refer to the diagram for clarity
Hence, option c is the correct answer.
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ELYSE OWNS 2,000 SHARES OF A
CORPORATION THAT PAYS A QUARTERLY
DIVIDEND OF $0.51 PER SHARE. HOW MUCH
SHOULD SHE EXPECT TO RECEIVE IN A YEAR?
Using the mathematical operations of multiplication, if Elyse owns 2,000 shares of a corporation that pays a quarterly dividend of $0.51 per share, she should expect yearly dividends of $4,080.
What are mathematical operations?Mathematical operations involve the use of operands and mathematical operators to solve mathematical problems.
Mathematical operations follow the PEMDAS rule, which states that Parentheses, Exponents, Multiplication, and Divisions in that order should be solved first before Additions and Subtractions.
The number of shares owned = 2,000
Quarterly dividend per share = $0.51
Quarters in a year = 4
Yearly dividends = $4,080 (2,000 x $0.51 x 4)
Thus, applying the multiplication operation, the annual dividend Elyse should receive is $4,080.
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The universal set, &, and sets F and G
are defined below.
{integers from 1 to 14 inclusive}
F = {x: 1≤ x <5}
G = {x:3 < x≤ 9}
A value is chosen at random from §.
Work out P(FG).
Give your answer as a fraction in its
simplest form.
-
Answer:7/8
Step-by-step explanation:your mom
The ratio of the same side interior angles of two parallel lines is 1:14. find the measures of all eight angles formed by the parallel lines and transversals.
Answer:
x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees.
Step-by-step explanation:
The ratio of the same side interior angles of two parallel lines is 1:14, which means that for every one degree of the first angle, the second angle measures 14 degrees. If the first angle is x degrees, then the second angle is 14x degrees.
Since the lines are parallel and the angles are on the same side of the transversal, the alternate interior angles are congruent, so the measure of the third angle is also x degrees, and the measure of the fourth angle is also 14x degrees.
Since the lines are parallel, the alternate exterior angles are also congruent, so the measure of the fifth angle is also x degrees, and the measure of the sixth angle is also 14x degrees.
Finally, the measures of the seventh and eighth angles can be found by adding the measures of the adjacent angles. The seventh angle is adjacent to the third and fifth angles, so its measure is x + x = 2x degrees. The eighth angle is adjacent to the fourth and sixth angles, so its measure is 14x + 14x = 28x degrees.
In summary, the measures of the eight angles formed by the parallel lines and transversal are x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees. The value of x can be determined by knowing the measure of one of the angles, or by using other information about the angles or the parallel lines.