Andrew owns stock in Hyren Airlines and as a result gets paid dividends worth $539.70 every year. If Andrew owns 105 shares of Hyren Airlines, how big is the dividend each share yields?
Answer: $5.14
Step-by-step explanation:
divide $539.70 by 105 to get the answer
so 539.70 divide by 105 is 5.14
step1 get rid of the decimal but you will ad it later so
53970
/ 105
=514
step2 move the decimal 2 places to the left.
Anna received a gift of $5,000 from her grandmother and decided to invest it. The expression 5000(1.0005)^12t represents the amount of money Anna is earning on her investment. Select all of the following that are equivalent expressions so that Anna can better understand how her money is invested.
a) 5000(1.0005^12)^t
b) 5025^12t
c) 5000(1+0.0005)^12t
d) 5000(1.0005^t)^12
e) (5000+2.5)^12t
f) 5000(1+0.06/12)^12t
The equivalent expression that represents the amount Anna can better understand how her money is invested is 5000(1+0.0005)^12t.
The correct answer option is option c.
What is the equivalent expression of Anna's investment?Based on the expression given, Anna's investment is compounded monthly.
The formula for calculating future value:
FV = P (1 + r)^(nm)
Where,
FV = Future valueP = Present valueR = interest ratem = number of compoundingn = number of years5000(1.0005)^12t
Given options:
a) 5000(1.0005^12)^t
False
b) 5025^12t
False
c) 5000(1+0.0005)^12t
= 5,000(1.0005)^12t
True
d) 5000(1.0005^t)^12
False
e) (5000+2.5)^12t
False
f) 5000(1+0.06/12)^12t
= 5000(1 + 0.005)^12t
= 5000(1.005)^12t
False
In conclusion, the expression equivalent to Anna's investment is 5000(1+0.0005)^12t
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Help please!!!!!!!!!!!!!!
4/9 - 1/2 Subtract.
- Simplest form.
-1/9 - (-2/5) Evaluate.
- Simplest form.
Answer:
Step-by-step explanation:
Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18
The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.
in how many ways can a math team of 6 students be chosen from a math club which consists of 6 seniors and 14 juniors if the team must consist of 2 seniors and 4 juniors? a) 24,024 b) 225 c) 1,002,001 d) 84 e) 15,015 f) none of the above.
There are 84 ways.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.
acc to our question-
Number of commities: If now any sinyour then N1 = C6,4 = 15. If one sinyour then number of commities is =N2 = C4,1C6,3 = 4·20 = 80.hence,There are 84 ways.
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. A cash register contains nickels and dimes. There are 12 nickels in the
cash register. The total amount of money in the cash register is $2.30.
How many dimes are in the cash register?
Answer: 17 Dimes.
Step-by-step explanation:
algebra 2 help needed!
As per the given equation of the parabola, the directrix of the parabola is equal to y = -2.5.
What is directrix?
A directrix in mathematics is a curve which is associated with the process generating a geometric object, such as:
Directrix - conic section
Directrix - generatrix
Directrix - rational normal scroll
The equation of a quadratic function, with vertex (h,k), is:
y = (a)(x - h)² + k
In which, a is the leading coefficient.
The directrix is: y = k + 4a.
In this problem, the equation of parabola is given as:
y = (1/8)(x-2)² - 3
The coefficients in the given equation are a = 1/8 = 0.125,
h = 2, k = -3,
Hence the directrix is given by:
y = -3 + 4 x 0.125
y = -3 + 0.5
y = -2.5.
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123 1/23 +(−123 1/23 )
Answer: positive
Step-by-step explanation:
123 1/23 + (-123 1/23)
123 1/23 - 123 1/23 = 0
0 is a positive number and not negative so the answer is negative
10. On a school trip the ratio of the number of teachers to the number of students is 1 : 15
The ratio of the number of male students to the number of female students is 7:5
Work out what percentage of all the people on the trip are female students.
Give your answer correct to the nearest whole number.
There are 39% of all the people on the trip are female students on a school trip.
What is meant by the term ratio?Mathematicians use the term "ratio" to compare two numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities being compared using division in a ratio.One to fifteen teachers are assigned to every hundred students.
and there are 7:5 more female students than male students.
Let's say there are x teachers. Students multiply by 15 as a result.
Take the ratio of male to female as 7 years for the male and 5 years for the female.
The total student trip is made up of both male and female pupils.
Thus,
15x = 7y + 5y
15x = 12y
5x = 4y
x = 4/5y ...eq 1
Then, the percentage of the female students.
5y/(x + 5x)×100
5y/16x ×100
Put the value of x from eq 1
625/ 16 = 39%
Thus, there are 39% of all the people on the trip are female students.
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A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 58°. A guy wire is to be attached to the top of the tower and to the ground, 175 m downhill from the base of the tower. The angle in the figure is determined to be 13°. Find the length of cable required for the guy wire. (Round your answer to the nearest meter.)
Answer:
ii think that the figure will be determined by 13#
Step-by-step explanation:
you have to round up to the nearest meter
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=8.4 and x=7.3 and passes through the point (0,8.2).
Formula of parabola for given values is F(x) = 7.5(x^2-15.7x+61.32)
What is parabola?The general equation of a parabola in math is: y = a(x-h)^2 + k ,where (h,k) denotes the vertex. The standard equation of a the parabola is y^2 = 4ax.
According to given data:We have, horizontal intercepts x=8.4 and x=7.3, passes through point(0, 8.2)
As we parabola is quadratic function,
f(x) = a(x-8.4)(x-7.3)
It is passing through the point (0, 8.2)
8.2 = a(-8.4)(-7.3)
a = 8.2/61.32 =7.5 (approx)
Now, equation of parabola is
F(x) = 7.5(x-8.4)(x-7.3)
f(x) = 7.5(x^2-7.3x-8.4x+61.32)
F(x) = 7.5(x^2-15.7x+61.32)
Thus, required equation of parabola is F(x) = 7.5(x^2-15.7x+61.32).
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You have eight marbles. all the marbles weigh the same, except for one, which is heavier than all the others. the marbles are otherwise indistinguishable. you may make no assumptions about how much heavier the heavy marble is. the task is to find the heavy marble by using a two-pan balance what is the minimum number of weighings required to identify the heavy marble?
A minimum of 3 weighings are required to identify the heavy marble out of 8 marbles.
As all the marbles weigh the same except one which is heavier, therefore firstly 8 marbles are divided into half. 4 marbles are placed in one pan while the other 4 are placed in another pan. In this two-pan balance, the pan which is lower than the other contains a heavier marble.
Now, the pan with heavier marble has 4 marbles which are again divided into half. 2 marbles are placed in each pan. Similarly, the pan with heavier marble goes down as compared to another pan with 2 marbles of the same weight. Now the final weighing is done by placing 1 marble in each pan out of 2 marbles taken from the pan which went down before as compared to another pan.
The pan with heavier marble will move down and thus with 3 weighings, a heavier marble is identified.
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Expand using Pascal's triangle: (x + 1)4.
Answer:
[tex] {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 1[/tex]
Step-by-step explanation:
as shown in photo attached :")
Consider the system of equations : 2a + 3b - 4c = 7,
a - b + 2c = 6
(a) Find an ordered tripe of numbers (a,b,c) that satisfies both equations.
(b) Can you find a second ordered triple that satisfies both equations.
(c) Solve for b in terms of a, and solve for c in terms of a. How many solutions does this system have?
Answer:
a. 87 b. 9 c. 4
Step-by-step explanation:
24m/s into mph. If your answer is a decimal, give it to 1 d.p
24 meters per second = 53.6865 miles per hour
53.6865 to 1 d.p = 53.7
Answer: 53.7
how many real fourth roots does -1 have?
There are zero or null real fourth roots of -1.
What are real fourth roots?This means that the square root of the square root of a number is equal to the number's fourth root. Symbolically, the fourth root is also represented by multiplying the radical by 4, creating the number 4. The fourth root of 16, for instance, is 2, which means that 2 2 2 2 = 16. n, also known as the degree of the root, is a positive integer in this situation. The terms "square root" and "cube root" are used to describe roots of degree 2 and 3, respectively. The ordinal numbers fourth root, twentieth root, etc. are used to refer to roots of higher degree. It is a root extraction to calculate the nth root. A integer y such that y2 = x is referred to as the square root of an x in mathematics.
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8. The length of a rectangle is 3 feet longer than the width. If the width is x feet, how long is the rectangle?
Answer:
Let the width be x feet. As length is 3 feet longer, it is x+3 feet. As perimeter is twice of te sum of length and width, it is 2×(x+3+x)=2×(2x+3)=4x+6 feet.
Step-by-step explanation:
A, B and C are points on the circumference of a circle.
XY is a tangent to the circle at the point A.
Angle BAY = 72° and angle ABC = 54°.
Prove that triangle ABC is an isosceles
triangle.
You must give a reason for any statement
that you make or any calculation that you
carry out.
By using tangent property of circle, it has been proved that [tex]\Delta[/tex] ABC is isosceles
What is tangent to a circle?
At first it is important to know about circle.
Circle is a two dimensional round figure in which every point of the circle maintains a fixed distance from a point known as the center. The fixed distance is called the radius of the circle.
The straight line which touches the circle at any point is known as the tangent to a circle.
Tangent property of circle is used here
[tex]\angle BAY = 72^{\circ}[/tex]
[tex]\angle ABC = 54^{\circ}[/tex]
[tex]\angle ACB = 72^{\circ}[/tex] [Angle in alternate segment are equal]
[tex]\angle BAC = 180 - (54 + 72)\\[/tex] [Sum of three angles of a triangle is 180°
= 180 - 126
= 54°
[tex]\Delta ABC[/tex] is isosceles
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if three sides of a trapezoid are 10 inches long, how long should the fourth side be if the area is a maximum?
The area of the trapezoid is maximum when the fourth side be 20 inches.
What is meant by trapezium?Trapezoids are quadrilaterals with two parallel and two oblique sides. It is also known as a trapezium. A trapezoid is a four-sided closed shape or figure with a perimeter that covers some area.
By applying Pythagorean theorem,
[tex]c^2=a^2+b^2[/tex]
[tex]10^2=h^2+x^2[/tex]
[tex]100=h^2+x^2[/tex]
[tex]h^2=100-x^2[/tex]
[tex]h=\sqrt{100-x^2}[/tex]
Area of the trapezoid is,
[tex]A=\frac12 \times h\times (b_1+b_2)[/tex]
By substituting the values of h, b1, and b2 in the above equation,
[tex]A=\frac12 \times \sqrt{100-x^2} \times (10+2\times x+10)[/tex]
[tex]A=\sqrt{100-x^2} \times (x+10)[/tex]
If we take the derivative of both sides of the equation in relation to x, we get
[tex]\frac{dA}{dx}=\frac{d}{dx}[\sqrt{100-x^2} \times (x+10)][/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} \ \frac{d}{dx} (x+10) + (x+10) \ \frac{d}{dx} \sqrt{100-x^2}[/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\frac {dA}{dx}=0[/tex]
[tex]0=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\sqrt{100-x^2} = \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
100-x²=x²+10x
2x²+10x-100=0
x²+5x-50=0
(x-5)(x+10)=0
If, x+10=0
x=-10
The above value is not accepted because it is a negative value,
If, x-5=0
x= 5
The value is accepted because it is positive value
The length of the trapezium which should be fourth is,
b₂=2x+10
b₂= 2(5)+10
b₂=20
The area of the trapezoid is maximum when the fourth side be 20 inches
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PLEASE HELP MEE!
Solve x2 – 2x = 15 by applying the quadratic formula.
HELP MEEE PLEASEEEEE
Answer:
XY = 12.4 cm
Step-by-step explanation:
a² + b² = c²
(4 cm)² + (XY)² = (13 cm)²
16 cm² + XY² = 169 cm²
XY² = 153 cm²
XY = √(153 cm²)
XY = 12.4 cm
a concert venue is determining the ticket price for concerts in a particular series. the sales team finds that at a price of $38 per ticket, attendance averages 1,000 people per concert. each decrease in price of $5 adds 50 people to the average attendance. find an equation for revenue, r, as a function of p, the price of tickets. what is r(25)?
An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
Given that;
The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,
Let 'T' be the number of times the price is decreased.
So, price;
p = 38 – 5x
x = (38 - p) / 5
And as per the given condition attendance;
a = 1000 + 50x
So, the Revenue is;
To develop an equation for revenue (r) as a function of p, the price of tickets;
R = p * a
R= p * (1000 + 50x)
But, x = (38 - p) / 5
Then,
R = P * (1000 + 50(38 - p)/5)
= p * (1000 + 380 - 10p)
= p * (1380 – 10p)
= 1380p - 10p² → (I)
To get R(25) from (I);
R(25) = 1380(25) - 10(25)²
= 34500 - 6250
= 28250
Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
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A utility pole has a support wire that reaches from the top of the pole to the ground, forming a right triangle. Ryan has measured the angle of elevation to the top of the pole formed by the wire and the ground to be 59°. He also knows that the horizontal distance from the base of the pole to the wire is 7 meters. What is the approximate height of the utility pole? A. 8 meters B. 12 meters C. 11 meters D. 14 meters
The height of utility poles is B. 12 meters.
The height of the utility pole will be calculated by the formula -
tan theta = perpendicular ÷ base, where theta is the angle of elevation, perpendicular is the height of utility pole and base is the distance from the base of pole to the wire.
Keep the values in formula to find the height of utility pole.
tan 59 = perpendicular ÷ 7
Perpendicular = tan 59 × 7
Perpendicular = 1.66 × 7
Performing multiplication on Right Hand Side of the equation
Perpendicular = 11.65 metres
On rounding off, we get 12 metres.
Thus, the height is B. 12 meters.
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Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter, what is the total amount she earned?
The total amount of the money earned by Paige will be $1591.92.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.
The total amount of earnings will be,
TA = ( 50 x 30 ) + ( 0.02 x 4596)
TA = 1500 + 91.92
TA = $1591.92
Therefore, the total amount of the money earned by Paige will be $1591.92.
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There are approximately 420 national parks in the United States. A survey
showed that 85% of the national parks allow overnight camping. Based on
this information, how many national parks allow overnight camping?
Answer:
357 national parks
Step-by-step explanation:
420x85/100
420x17/20
21x17=
357
Is -1 8/9 a repeating decimal or Terminating
Calculate S16 for the arithmetic sequence defined by (an) = {5/8-5/16n}
65/
2
65/
8
-65/
8
-65/
2
The sum of the first 16 terms of the defined arithmetic sequence is given as follows:
-520/16.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, being called common difference d.
The nth term of an arithmetic sequence is given by the equation presented as follows, called general equation:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the arithmetic sequence.
The sum of the first n terms is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The sequence in this problem is defined as follows:
[tex]a_n = \frac{5}{8} - \frac{5}{16}n[/tex]
The first term is of:
[tex]a_1 = \frac{5}{8} - \frac{5}{16} = \frac{5}{16}[/tex]
Hence the 16th term of the sequence is of:
[tex]a_{16} = \frac{5}{8} - \frac{5}{16}(16) = \frac{5}{8} - 5 = -\frac{35}{8}[/tex]
Hence the sum of the first 16 terms of the arithmetic sequence is defined as follows:
[tex]S_{16} = 8\left(\frac{5}{16} - \frac{35}{8}\right) = 8 \times \left(-\frac{65}{16}\right) = -\frac{520}{16}[/tex]
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Can someone help me on this
The algebra properties associated to each case are listed below:
Case 1: Distributive property
Case 3: Associative property (multiplication)
Case 5: Existence of inverse (addition)
What algebra properties are used in algebraic expressions?
In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:
Reflexive property of equalities.Symmetric property of equalities.Transitive property of equalities.Compatibility property (addition, multiplication)Commutative property (addition, multiplication).Associative property (addition, multiplication).Existence of inverse (addition, multiplication).Modulative property (addition, multiplication).Distributive property.Now we proceed to determine the property associated to corresponding operation:
Case 1
9 · (x + y) = 9 · x + 9 · y → Distributive property
Case 3
[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)
Case 5
(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)
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A line segment is shown on the coordinate grid.
What is the domain displayed on the line graph above?
Answer: x = -2 through 1
Step-by-step explanation:
The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!
cual es el interes que genera $600, colocados al 8% anual durante 1 año 4 meses?
The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64
Simple InterestThe formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.
Simple interest formula is given as:
S.I = P(1 + rt)
S.I = Simple InterestP = principalr = rate t = timeSubstituting the values into the formula
S.I = 600(1 + 0.08 * 16)
S.I = 664
The interest generated is $64
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Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?