Answer:
Discount: $30 off
New Sale Price: $270
Step-by-step explanation:
$300*10% =
30
$300-30=
$270
or
$300*.1=
30
$300-30=
$270
The Rangers won five of the first six games. how many of the next 30 games must the rangers wins have twice as many wins as losses?
Using proportions, it is found that they must win 19 of their next 30 games.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
We want a win-to-loss proportion of 2:1, which is equivalent to a win-to-total proportion of 2:3. We have that:
The team will have won 5 + x games.The team will have played 36 games.Hence:
[tex]\frac{5 + x}{36} = \frac{2}{3}[/tex]
3(5 + x) = 72
15 + 3x = 72
3x = 57
x = 19.
The Rangers must win 19 of their next 30 games.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180
The true options regarding the triangle diagram are;
m∠5 + m∠6 = 180°
m∠2+ m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
How to prove congruent angles?We see the attached image showing ΔABC with Exterior angles as;
∠ 1 , ∠ 4 ,and ∠ 6
Now, the exterior angle property of triangles states that; An exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior ∠1 we have;
∠1 = ∠5 + ∠3 (Exterior angle Property of Triangle)
Similarly,
For Exterior ∠ 4 we have;
∠4 = ∠5 + ∠2 (Exterior angle Property of Triangle)
For Exterior ∠6 we have;
∠6 = ∠2 + ∠3 (Exterior angle Property of Triangle)
From Triangle Sum Property, we know that the sum of the measures of angles in a triangle is equal to 180°. Thus;
m∠2 + m∠3 + m∠5 = 180° (Triangle Sum Property)
Linear Pair of angles states that the measure of a straight angle is 180° and as such a linear pair of angles must add up to 180°. Thus;
m∠5 + m∠6 = 180° (Linear Pair)
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you received an invoice for 3,000 with terms of 3/10 1/20 n/30. how much will you have to pay if you the bill in 12 day
The customer will to pay $2,970 in 12 days.
What does 3/10 mean?
3/10 is cash discount term which means that a discount of 3% would be given to the customer if payment for the goods purchased is made within 10 days of purchase.
In this case, 3% is not applicable since the payment was made after 12 days.
What does 1/20 mean?
1/20 is cash discount term which means that a discount of 1% would be given to the customer if payment for the goods purchased is made within 20 days of purchase, the payment is within this range, hence, a 1% discount would be applied to invoice price so as to determine the cash payable
cash payable=$3,000*(1-1%)
cash payable=$3,000*0.99
cash payable=$2,970
What does n/30 mean?
It means a payment is expected latest after 30 days which does not entitle the customer no discount.
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Hey can someone tell me the steps to solving a system of equations with graphing
Answer:
Let's go through the following example to show how to solve a system of equations by graphing. I won't solve this system, I will just show how to.
[tex]8x-3y = 17\\4x+y=21[/tex]
If you can use an online graphing calculator...
If you have an online grapher (like Desmos) at your disposal, then you can put each equation in it as it is.
Lines intersect -> Put your cursor over the point of intersection to get the solution.Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines are the same and have infinite solutionsIf you have a physical graphing calculator (like TI-84)
1. Get both equations in the form [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
2. Put both equations in the graphing calculator
Lines intersect -> Find the intersection point using your graphing calculator's mechanics (each one is a little different)Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines have the same equation and have infinite solutionsIf you just have graphing paper...
1. Get both equations into the form [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
2. Plug in a few different points for x and calculate their y-values.
3. Plot those points on the graph paper
Lines intersect -> Find the intersection point's coordinates to get the solution for x and y.Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines have the same equation and have infinite solutions.A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 4 or more customers at this bank in one hour.
Using the Poisson distribution, there is a 0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.A bank gets an average of 12 customers per hour, hence the mean is [tex]\mu = 12[/tex].
The probability that there will be 4 or more customers at this bank in one hour is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-12}12^{0}}{(0)!} \approx 0[/tex]
[tex]P(X = 1) = \frac{e^{-12}12^{1}}{(1)!} \approx 0[/tex]
[tex]P(X = 2) = \frac{e^{-12}12^{2}}{(2)!} = 0.0004[/tex]
[tex]P(X = 3) = \frac{e^{-12}12^{3}}{(3)!} = 0.0018[/tex]
Then:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0.0004 + 0.0018 = 0.0022.
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0022 = 0.9978[/tex]
0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.
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I need some help with this question for a self-taught course
The support pole must be approximately 7.8 meters long.
What is the length of the support pole?
Based on all the information given in the statement, we prepare a geometric diagram that describes the system formed by the high-security fence and the support pole. The representation is attached below. Lastly, the length of the pole is found by using the law of sines:
l/sin 84° = 6 m /sin 50°
l = 6 m × (sin 84°/sin 50°)
l ≈ 7.790 m
The support pole must be approximately 7.8 meters long.
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A rectangle has corners E, F, G, D, starting from top left and going clockwise. Point H is halfway between E and F. 2 lines are inscribed in the rectangle. One line goes from D to H and another goes from H to G. Angle E D H is (5 x) degrees and angle H D G is (4 x) degrees. Angles E D G and F G D are right angles. What is the measure of Angle EDH? 10° 40° 50° 90°
The measure of Angle EDH = 50°.
How to estimate the measure of Angle EDH?The angle EDH exists given as 5x° and the angle HDG exists given as 4x°. The angles EDG and FGD exist at right angles. That signifies both angles exist equivalent to 90°.
Angle EDH = 5x°
Angle HDG = 4x°
Angle EDG = 90°
5x + 4x = 90
9x = 90
Divide both sides by 9
x = 90/9
x = 10°
Angle EDH = 5x = 5 × 10 = 50°
The measure of Angle EDH = 50°.
Therefore, the correct answer is option c) 50°.
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Consider a situation that you might need to use your understanding of probability to make an informed
decision.
• What sorts of information would you collect?
How might you use what you have learned about probability to determine a course of action?
What are the possible benefits and limitations of this approach?
The information that can be collected to make an insurance policy will be information regarding the drivers.
How to illustrate the information?It should be noted that the probability simply means the likelihood of the occurence of an event.
In this case, when choosing a car insurance policy, we can use the probability to determine the likelihood for the need to file a claim.
The course of action is to survey a number of drivers to get information from them.
Also, the benefit of this approach is that the food drivers can pay less premium while the disadvantage can be the cost that's involved.
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1. A situation that can use probability to make an informed decision is when deciding on an insurance policy to take.
2. The information that you would collect for an insurance policy decision includes insurance:
PremiumPolicy coveragePolicy limitsDeductiblesDiscounts.3. An understanding of probability helps the policyholder to:
Analyze different insurance policies to determine the best plan to choose amid uncertainty.Measure the likelihood of an event occurring and its consequences.Determine the level of risk involved.4. Possible Benefits and Limitations of Probability:Using probability, the insurance policyholder enjoys these benefits:
Measure outcomesReduce uncertaintyOptimize policiesSpread risk coveragePredict future losses and events.However, the limitations of probability in measuring insurance risks become prominent under the following situations:
Presence of an infinite number of possible outcomes. Where the outcomes are not equally likely.Thus, probability analyzes insurance policies to determine the best plans and their deductible amounts.
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Select the correct answer.
What is the range of the function shown in the graph?
keeping in mind that the range is vertical values covered by the function, Check the picture below.
Which choice is equivalent to the quotient shown here for acceptable values of x?
The expression [tex]\sqrt{\frac{5}{x-1} }[/tex] is equivalent to the given quotient.
Option A is correct.
When we divide one number by another, the result is a quotient. Although a quotient can be greater than the divisor, it will never be greater than the dividend.
In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor.
After the division has been done, the quotient is obtained. This signifies that the quotient is the result of dividing a dividend by a divisor.
According to the question,
[tex]\sqrt{25(x-1)}[/tex] ÷ [tex]\sqrt{5(x-1)^{2} }[/tex] = 5[tex]\sqrt{x-1}[/tex] ÷ (x-1)[tex]\sqrt{5}[/tex]
= [tex]\sqrt{\frac{5}{x-1} }[/tex]
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A box contains 5 red marbles and 2 yellow marbles. Consider the two–stage experiment of randomly selecting a marble from a box, NOT replacing it, and then selecting a second marble. Determine the probabilities of the following events:
a. Selecting 2 red marbles.
P (red) =
b. Selecting a red marble on the first draw and a yellow marble on the second.
P (red then yellow) =
c. Selecting at least 1 yellow marble.
P (at least 1 yellow) =
Answer:
a) 10/21 b) 5/21 c)1/21
Step-by-step explanation:
a) your have 7 choice and 5 or them or red, 5/7. You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3. We multiple these two numbers together:
5/7(2/3) = 10/21
b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7. The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified). We multiply these together.
5/7(1/3) =5/21
c) I am assuming that you are still selecting 2 marbles. The first draw would be 2/7. This time I am selecting yellow and there are only 2 choices for yellow. My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6. We multiply these together
2/7(1/6) = 2/42 or 1/21
What is the product?
Sr-203r-40
O 157-8
0157-8
O 15/+14-8
0152²-140-8
Find the area. This is a trapezoid, with bases that measure 5 feet and 10 feet, and a height of 4 feet.
Answer:
A = 30 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases , then
A = [tex]\frac{1}{2}[/tex] × 4 × (5 + 10) = 2 × 15 = 30 ft²
A sales agent gets 15%commission for each motivational book he sells. if he sold books worth #284000,how much commission will he get?
Answer:
$42,600
Step-by-step explanation:
284000 x .15
Triangle PQR is rotated, translated, and dilated to obtain triangle P'Q'R' as shown. An Image of triangle PQR and PQR prime are displayed. The Triangle PQR intersects P at (minus 2, 0.5), R at (minus 2, minus 2.5) and Q at (0, minus 1.5). Similarly P, R, Q prime at (1.5,minus 1.5), (1.5,3), and (minus 1.5,1.5). Which statement about the two figures is correct? A. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. B. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. C. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent. D. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
How to determine the true statements?The transformations are given as:
RotationTranslationDilationRotation and translation would preserve the lengths and the angles of the triangles. Because they are rigid transformations.
Dilation would only preserve the angle of the triangles. Because it is a nonrigid transformation.
The above means that the angles of triangle PQR and triangle P'Q'R' are congruent
Hence, the true statement is (d)
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Robin can make 8 puppets with the material she already has. For each additional sheet of felt she buys, she can make 5 more puppets. What is an equation that shows how the total number of puppets she can make, y, depends on the number of sheets of felt she buys?
A motorboat travels 132 km in 4 hours going upstream. It travels 196 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer:
Step-by-step explanation:
x = speed of the boat
y = speed of the current
x + y = 162/3 = 54 mph
x - y = 132/3 = 44 mph
Add the two equations to get
2x = 98
x = 49 mph
y = 54 - x = 54 - 49 = 5 mph or something
Bruce pitches for his little brother's baseball team. He has observed that the number of pitches a batter hits varies and is given by the function f(x) = x – 11, where x is the number of pitches and f(x) is the number of hits. If batters get {4, 12, 14, 27, 42} hits, how many pitches did Bruce throw? A. {13, 21, 24, 26, 44} B. {17, 24, 27, 28, 35} C. {20, 27, 32, 33, 45} D. {15, 23, 25, 38, 53}
Answer:
D.{15,23,25,38,53}
Step-by-step explanation:
Replace f(x) with any other variables of your choice.
Substitute the value of the variable for the given set of hits
that is {4,12,14,27,42}
Solve for x for each value of the variable from the above set
Put all the solution for x in a set that is inside {,} brackets.
The correct option should be D
if x+4/4= y+3/3 then y/3=
The value of y / 3 in the equation is x / 4.
How to use equation to find y / 3 ?Therefore,
x + 4 / 4 = y + 3 / 3
then y / 3 can be found as follows,
x + 4 / 4 = x / 4 + 4 / 4 = x / 4 + 1
y + 3 / 3 = y / 3 + 3 / 3 = y / 3 + 1
x / 4 + 1 = y / 3 + 1
subtract 1 from both sides of the equation
x / 4 + 1 - 1 = y / 3 + 1 - 1
x / 4 = y / 3
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How large an equilateral triangle can you fit inside a 2-by-2 square?
Answer:
An equilateral triangle with a length of 2
Step-by-step explanation:
A 2-by-2 square implies that the square has a length and width of 2. Since equilateral triangles have the same length for all sides, it tells you that if one side is a certain length, all the other sides must have the same length. The largest length we can fit into this square would be 2 because any larger, the sides of the triangles would not fit into the square. Under the assumption that the length needs to be a whole number, the answer would be 2.
17. The Bricklayer needs 100 pieces of angle, each to be cut 54 3/16" long. 1 point
How many can be cut from a 20% length (do not include waste or thickness of
cut)? How many pieces of 20' angle are needed in order to have the 100
pieces?
The number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5
How to determine the number
From the information given;
The bricklayer needs = 100 pieces of angle
The number of cuts = 54
Length of cuts = 3/ 16'' Inches
a. To determine the number of cuts form a 20% length, we have to multiply the length by the percentage and by the initial number of cuts
= 20/ 100 × 3/ 16 × 54
= 0. 2 × 0. 1875 × 54
= 2. 0
The number of cuts would be 2
b. To determine the number of pieces of 20' angle to have 100 pieces we would divide the initial number of pieces by the angle
= 100/ 20
= 5 pieces
The number of pieces of 20' angle is 5
Thus, the number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5
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In general, in y=asjn[k(x-d)]+c the equation of the axis of the curve is determined by
the value of
a) d
b) k
c) c
d) a
The equation of the axis of the curve is determined by (c) c
How to determine the equation of the axis?The equation is given as:
y= a sin[k(x - d)] + c
In the above equation, the midline is
y = c
This represents the equation of the curve axis
Hence, the equation of the axis of the curve is determined by (c) c
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The slope of the line is 8. Write the point-slope equation for the line using
the coordinates of the labeled point.
The point-slope equation of the line is: y - 2 = 8(x - 2).
How to Write the Point-Slope Equation of a Line?The point-slope equation is: y - b = m(x - a), where:
m = slope(a, b) is a point.Using the coordinates of the point shown in the graph, substitute (a, b) = (2, 2) and m = 8 into y - b = m(x - a):
y - 2 = 8(x - 2)
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− 2 x − 2 > 4 OR − 8 x − 7 ≤ − 23
interval notaton and plot on line graph
The interval notation of the possible values of x according to.the given inequalities is; -3 > x and x>= 2.
What is the interval notation of the inequalities given in the task content?The interval notation of the given inequalities which describes the possible value of x according to the task content are as follows;
For − 2 x − 2 > 4; we have;
− 2 x > 4 +2
-2x > 6
x < -3.
For − 8 x − 7 ≤ − 23; we have;
− 8 x ≤ − 23 +7
-8x ≤ -16
x >= 2.
Consequently, the interval notation of the given inequalities is; -3 > x and x >= 2.
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Find the area of the trapezoid. 15ft 10ft 20ft
Answer: 175 ft squared
Step-by-step explanation: A= a + b / 2h= 20 + 152 · 10 = 175
La siguiente figura 1, ilustra el salto de una rana sobrepuesto en un plano cartesiano. La longitud del salto es de 9 ft y la altura máxima con respecto al suelo es 3 ft. Encuentra la ecuación estándar a fin de calcular la trayectoria de la rana.
3. La salinidad de los océanos se refiere a la cantidad de material disuelto que se encuentra en una muestra de agua marina. La salinidad S se puede calcular a partir de la cantidad C de cloro en agua de mar con la ecuación S = 0.03 + 1.805 C, donde S y C se miden por peso en partes por millar. Calcula la C si S es 0.35.
4. El arco de un puente es semielíptico, con eje mayor horizontal. La base del arco mide 50 ft de un lado al otro y la parte más alta del arco mide 15 ft arriba de la calzada horizontal. Encuentre la altura del arco a 12 ft del centro de la base.
Investiga la hipérbola con centro en el origen y fuera del origen. Eje focal en x y en y.
2. De las expresiones que se indican a continuación, Identifica si es una recta o ecuación lineal,
una ecuación cuadrática o de segundo grado, una ecuación de tercer grado, una
circunferencia, una hipérbola, justifica tu respuesta y elabora su respectiva gráfica.
3x – 2y + 4= 0
4x + y2 -7 = 0
x2 + y2 = 16
y = x3 - 3x +1
x2 + 4y2 = 4
3. A partir de tu investigación resuelve los siguientes ejercicios:
a) Traza la gráfica
9x2 – 4 y2 = 36
Encuentra los focos y ecuaciones de las asíntotas.
b) Traza la gráfica
4y2 – 2 x2 = 1
Encuentra los focos y ecuaciones de las asíntotas.
c) Dadas las siguientes ecuaciones, decir qué cónica representan:
9 x2 - 4 y2 - 54 x - 16 y + 29 = 0
4 x2 + 2 y2 - 7 x + y - 5 = 0
x2 - 6 x + 5 y - 11 = 0
Debido a restricciones de longitud invitamos cordialmente a leer la explicación de esta pregunta para aprender sobre las cuestiones de las ecuaciones cónicas.
¿Cómo analizar y aplicar las ecuaciones cónicas?
Según la geometría analítica, existen cinco tipos de secciones cónicas: recta, circunferencia, elipse, parábola e hipérbola. Aquí se presentan problemas que emplean este tipo de ecuaciones.
1) La trayectoria de la rana describe la forma de una parábola. Asumimos que el punto máximo de la trayectoria de la rana es de la forma (h, k) = (0, k), entonces tenemos que la ecuación de la parábola es:
y - k = C · x² (1)
Donde C es la constante del vértice.
Si sabemos que (h, k) = (0, 3) y (x, y) = (9, 0), entonces la ecuación de la parábola es:
C = (0 - 3) / 9²
C = - 1 / 27
La ecuación de la parábola es y - 3 = (- 1 / 27) · x².
2) Se determina el tipo de categoría de cada ecuación:
a) 3 · x - 2 · y + 4 = 0: Recta (a · x + b · y + c = 0)
b) 4 · x + y² - 7 = 0: Parábola ((y² - k) = 4 · p · (x - h))
c) x² + y² = 16: Circunferencia ((x - h)² + (y - k)² = r²)
d) y = x³ - 3 · x + 1: Ecuación cúbica
e) x² + 4 · y² = 4: Elipse (b² · (x - h)² + a² · (y - k)² = a² · b²)
3) Se debe hallar el valor C de la función lineal tal que S = 0.35 por medios algebraicos:
0.35 = 0.03 + 1.805 · C
0.32 = 1.805 · C
C = 0.32 / 1.805
C = 0.177
4) El arco semielíptico tiene una longitud de semieje mayor de 25 pies (paralelo al eje x) y una longitud de semieje menor de 15 pies (paralelo al eje y). Si consideramos que el centro de la elipse está en el origen, entonces tenemos que la ecuación es:
x² / 25² + y² / 15² = 1
y = 15 · √(1 - x² / 25²)
y = 15 · √(1 - 12² / 25²)
y = 13.159 pies
5) a) y b) Ahora graficamos la hipérbola y presentamos las ubicaciones de los focos y las asíntotas correspondientes. a) Las ecuaciones de las asíntotas son y = ± (3 / 2) · x, b) Las ecuaciones de las asíntotas son y = ± (√ 2 / 2) · x.
c) Se puede determinar la naturaleza de cada ecuación por métodos algebraicos:
9 · x² - 4 · y² - 54 · x - 16 · y + 29 = 0
[9 · x² - 2 · 9 · (3 · x) + 81] - [4 · y² - 2 · 8 · (2 · y) + 64] = 116
(3 · x - 9)² - (2 · y - 8)² = 116
9 · (x - 9)² - 4 · (y - 4)² = 116
(x - 9)² /12.889 - (y - 4)² / 29 = 1 - Hipérbola
4 · x² + 2 · y² - 7 · x + y - 5 = 0
[4 · x² - 2 · (7 / 4) · (2 · x) + 49 / 16] + [2 · y² + 2 · (√2 / 2) · (√2 · y) + 1 / 2] = 5
(2 · x - 7 / 4)² + (√2 · y + √2 / 2)² = 5
4 · (x - 7 / 8)² + 2 · (y + 1 / 2)² = 5
(x - 7 / 8)² / 1.25 + (y + 1 / 2)² / 2.5 = 1 - Elipse
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There are 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class. The students need to be placed on teams of equal size with students from only their own class. What's the largest size of a team?
The largest size of a team according to the task content is; 20 kids.
What is the largest size of a team?It follows from the task content that the population is; 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class.
However, since, the team forming condition states that students be placed on teams of equal size with students from only their own class.
It therefore follows that the largest size of a team is 20 as only 20 students are in Mrs. Tanya's class hence leaving 4 kids in Mrs. Olga's class without a team.
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According to the tables used by insurance companies, a 47-year old woman has a 0.179% chance of passing away during the coming year. An insurance company charges $204 for a life insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance?
The expected value for the person buying the insurance is -25.
How the expected value is calculated?The expected value is the average gain or loss of an event if the event is repeated a number of times.
Expected value = ∑xP(x)
Calculation:It is given that,
The probability of a 47-year-old woman passing away during the coming year is 0.179% = 0.00179
The death benefit = $100,000 - $204 = $99,796
The loss from living = -204
Then the expected value = 99796(0.00179) + (-204)(0.99821) = -25
Therefore, the expected value for the person buying the insurance is -25.
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Find the area of the figure.
After defeating the fire breathing dragon, the knight decides
to celebrate his victory with a celebratory goblet made out of Dragon Alloy #17, which is 36% gold, 9% silver, and 55% magic steel. The dwarves have Dragon Alloy #11, which is 36% gold, 28% magic steel, and the rest silver. They also have Dragon Alloy #15, which is 36% gold and 64% magic steel. How many grams of each
alloy should the dwarves combine to get 1 kg of Dragon Alloy #17?
250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of alloy #11 and y represent the amount of alloy #15, hence:
(0.36x) + (y * 0.36) = 1(0.36) (1)
Also:
0.28x + 0.64y = 1(0.55) (2)
From both equations:
x = 0.25, y = 0.75
250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.
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