We have to calculate the present value PV of a annuity.
The payment is yearly and it is P=60,000.
The interest rate is 5% (r=0.05), compounded annually (m=1).
The number of periods is n=20 years.
Then, we can use the formula for the present value of a annuity:
[tex]\begin{gathered} PV=P\cdot\frac{1-\frac{1}{(1+r)^n}}{r} \\ PV=60000\cdot\frac{1-\frac{1}{1.05^{20}}}{0.05} \\ PV\approx60000\cdot\frac{1-\frac{1}{2.653}}{0.05} \\ PV\approx60000\cdot\frac{1-0.377}{0.05} \\ PV\approx60000\cdot\frac{0.623}{0.05} \\ PV\approx60000\cdot12.462 \\ PV\approx747720 \end{gathered}[/tex]Answer: the company must set aside $747,720.
use the point slope formula and the given points to choose the correct linear equation in slope intercept form (0,7) and (4,2)
We have to write the equation of the line that passes through (0,7) and (4,2) in point-slope form.
We start by using the points to calculate the slope m:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-7}{4-0}=-\frac{5}{4}[/tex]Then, if we use point (0,7), we can write the equation in point-slope form as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-7=-\frac{5}{4}(x-0) \\ y=-\frac{5}{4}+7 \end{gathered}[/tex]Answer: the equation is y = -(5/4)*x + 7
Consider the equation. Y=x^2+1The next step in graphing a parabola is to find points that will determine the shape of the curve. Find the point on the graph of this parabola that has the x-coordinated x= -2
The graph is
[tex]y=x^2+1[/tex]its a upword parabola and vertex of graph is (0,1)
the point on a graph x=-2
[tex]\begin{gathered} y=x^2+1 \\ y=(-2)^2+1 \\ y=4+1 \\ y=5 \end{gathered}[/tex]so graph of function is :
(B)
the coordinate of graph then x=1
[tex]\begin{gathered} y=x^2+1 \\ y=1^2+1 \\ y=2 \end{gathered}[/tex]the value of y is 2 then value of x=1
Rectangle CARD has a length of 2x-5 and a width of 6x+10. Triangle BEST has a length of 10x+3 and a width of 4x-7. Find the difference between triangle CARD and triangle BEST. *
Given:
Rectangle CARD: {length = 2x-5 and width = 6x+10}
Triangle BEST: {length = 10x+3 and width = 4x-7}
To find the differnce, let's first the perimeter of both.
Perimeter of rectangle CARD: 2(length + width)
= 2(2x - 5 + 6x + 10)
= 2(2x + 6x - 5 + 10)
= 2(8x + 5)
= 16x + 10
Perimeter of triangle BEST: 2(length + width)
2(10x + 3 + 4x - 7)
= 2(10x + 4x + 3 - 7)
= 2(14x - 4)
= 28x - 8
Therfore, the difference between both of them is calculated below:
(28x - 8) - (16x + 10)
= 28x - 8 - 16x + 10
= 28x - 16x - 8 10
= 12x - 18
ANSWER:
12x -
Using Calculus with Data in a tablePlease let me know if you have any questions regarding the material, thanks!
ANSWER
g'(0.1) = 4
EXPLANATION
As stated, g(x) is a composition of two functions: f(x) and 2x. To find its derivative, we have to use the chain rule,
[tex]g^{\prime}(x)=f^{\prime}(x)\cdot(2x)^{\prime}=f^{\prime}(2x)\cdot2[/tex]So, the derivative of g(x) = f(2x) is twice the derivative of f(x) and, therefore,
[tex]g^{\prime}(0.1)=f^{\prime}(2\cdot0.1)\cdot2=f^{\prime}(0.2)\cdot2=2\cdot2=4[/tex]Hence, g'(0.1) = 4.
a turtle swims 15 kilometers in 9 hours how long does it take the turtle to swim 18 kilometers?
Answer:
10.8 hours or 648 minutes
Step-by-step explanation:
1. Find a factor of 15 and 18 kilometers. A similar factor is 3.
2. Find how long it will take the turtle to swim 3 kilometers.
3. Divide 9 by 5 which is how long it takes to swim three hours. (Keep it in a fraction for now)
4.Multiply 9/5 by 6 to get 18 hours; which is 10.8 hours.
Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 12 minutes. Consider 49 of the races.
Let
X = the average of the 49 races.
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Using the normal distribution and the central limit theorem, it is found that:
a) The distribution is approximately N(145, 1.71).
b) P(143 < X < 148) = 0.8389.
c) The 70th percentile of the distribution is of 145.90 minutes.
d) The median is of 145 minutes.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In the context of this problem, the parameters are defined as follows:
[tex]\mu = 145, \sigma = 12, n = 49, s = \frac{12}{\sqrt{49}} = 1.71[/tex]
The distribution of sample means is approximately:
N(145, 1.71) -> Insert the mean and the standard error.
The normal distribution is symmetric, hence the median is equal to the mean, of 145 minutes.
For item b, the probability is the p-value of Z when X = 148 subtracted by the p-value of Z when X = 143, hence:
X = 148:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (148 - 145)/1.71
Z = 1.75
Z = 1.75 has a p-value of 0.9599.
X = 143:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (143 - 145)/1.71
Z = -1.17
Z = -1.17 has a p-value of 0.1210.
Hence the probability is:
0.9599 - 0.1210 = 0.8389.
The 70th percentile is X when Z has a p-value of 0.7, so X when Z = 0.525, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
0.525 = (X - 145)/1.71
X - 145 = 0.525(1.71)
X = 145.90 minutes.
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A)State the angle relationship B) Determine whether they are congruent or supplementary C) Find the value of the variable D) Find the measure of each angle
Answer:
a) Corresponding
b) Congruent, since they have the same measure.
c) p = 32
d) 90º
Step-by-step explanation:
Corresponding angles:
Two angles that are in matching corners when two lines are crossed by a line. They are congruent, that is, they have the same measure.
Item a:
Corresponding
Item b:
Congruent, since they have the same measure.
Item c:
They have the same measure, the angles. So
3p - 6 = 90
3p = 96
p = 96/3
p = 32
Item d:
The above is 90º, and the below is the same. So 90º
Which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
In general, a function f(x) means that the input is x and the output is f(x) (or simply f).
Therefore, in our case, the input is the length of the race and the outcome is the time.
The better option is Time(length), option A.Junior's brother is 1 1/2 meters tall. Junior is 1 2/5 of his brother's height. How tall is Junior? meters
To determine Junior's height you have to multiply Juniors height by multiplying 3/2 by 7/5his brother's height by 1 2/5.
To divide both fractions, first, you have to express the mixed numbers as improper fractions.
Brother's height: 1 1/2
-Divide the whole number by 1 to express it as a fraction and add 1/2
[tex]1\frac{1}{2}=\frac{1}{1}\cdot\frac{1}{2}[/tex]-Multiply the first fraction by 2 to express it using denominator 2, that way you will be able to add both fractions
[tex]\frac{1\cdot2}{1\cdot2}+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex]Junior's fraction 1 2/5
-Divide the whole number by 1 to express it as a fraction and add 2/5
[tex]1\frac{2}{5}=\frac{1}{1}+\frac{2}{5}[/tex]-Multiply the first fraction by 5 to express it using the same denominator as 2/5, that way you will be able to add both fractions:
[tex]\frac{1\cdot5}{1\cdot5}+\frac{2}{5}=\frac{5}{5}+\frac{2}{5}=\frac{5+2}{5}=\frac{7}{5}[/tex]Now you can determine Junior's height by multiplying 3/2 by 7/5
[tex]\frac{3}{2}\cdot\frac{7}{5}=\frac{3\cdot7}{2\cdot5}=\frac{21}{10}[/tex]Junior's eight is 21/10 meters, you can express it as a mixed number:
[tex]\frac{21}{10}=2\frac{1}{10}[/tex]y = -x +3
x+y = 17
Are these parallel?
Answer:
Yes
Step-by-step explanation:
The equations need to be in slope intercept form. The first equation is but the second one isn't. Solve the second equation for y to put it in slope intercept form.
x + y = 17
x - x + y = 17 - x
y = -x + 17
To determine if they are parallel the slopes need to be the same.
y = -1x + 3
y = -1x +17
The slope are both -1, so they are parallel
Answer:
Yes
Step-by-step explanation:
A pair of parallel lines is cut by a transversal, as shown (see figure):Which of the following best represents the relationship between angles p and q?p = 180 degrees − qq = 180 degrees − pp = 2qp = q
we know that
In this problem
that means
answer isp=qWhat is the domain of the function represented by the graph?
All real numbers (In interval form (-∞,∞) )
Given,
From the graph,
To find the domain of the function.
Now,
We know that a domain of a function is the set of the all the x-values for which the function is defined.
By looking at the graph of the function we see that it is a graph of a upward open parabola and the graph is extending to infinity on both the side of the x-axis this means that the function is defined all over the x-axis i.e. for all the real values.
Also, we know that the function will be a quadratic polynomial since the equation of a parabola is a quadratic equation and as we know polynomial is well defined for all the real value of x.
The domain of the function is:
Hence, All real numbers (In interval form (-∞,∞) )
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Find two points on the graph of this function other than the origin that fits in the given grid express each coordinate as an integer or simplified fraction or around four decimal places as necessary another coordinates to plot points on
Substitute arbitrary values of x for which -10 < h(x) < 10.
In this instance, we can use x = 1, and x = -1
[tex]\begin{gathered} h(x)=-\frac{5}{8}x^5 \\ h(1)=-\frac{5}{8}(1)^5 \\ h(1)=-\frac{5}{8} \\ h(1)=-0.625 \\ \\ h(x)=-\frac{5}{8}x^{5} \\ h(-1)=-\frac{5}{8}(-1)^5 \\ h(-1)=\frac{5}{8} \\ h(-1)=0.625 \end{gathered}[/tex]Therefore, the points that fits in the grid in the function h(x) are (1, -0.625) and (-1, 0.625).
Open the most convenient method to graft the following line
You have the following expression:
3x + 2y = 12
the best method to graph the previous expression is by intercepts.
In this case, you make one of the variables zero and solve for the other one. Next, repeat the procedure wi
Determine the probability of flipping a heads, rolling a number less than 5 on a number cube and picking a heart from a standard deck of cards.
1/12
16/60 or 4/15
13/156
112
The probability of flipping a heads is 1/2, probability of rolling a number less than 5 is 2/3, and probability of picking a heart from a standard deck of cards is 1/4.
What is probability?
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is always a number b/w 0 and 1, with 0 approximately says impossibility and 1 says surity.
We can find probability using the formula:
P = required out comes/ total outcomes
In first case the required out come is only one which is heads and total outcomes include both heads and tails,
Therefore, required outcome = 1
total outcome = 2
Probability = 1/2
In second case the required out come are number less than five which are 1, 2, 3, 4 and a number cube have numbers till 6.
Therefore, required outcome = 4
total outcome = 6
Probability = 4/6 = 2/3
In third case the required out come hearts card and there are 13 hearts card in a card deck and total outcomes include all types of cards which are 52,
Therefore, required outcome = 13
total outcome = 52
Probability = 13/52 = 1/4
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Which statement best describes the area of the triangle shown below?
ANSWER
Option D - The area of this triangle is one-half of that of a square that has area of 12 square units
EXPLANATION
We want to the best description of the area of the triangle given.
To do this, we have to first find the area of the triangle.
The area of a triangle is given as:
[tex]A\text{ = }\frac{1}{2}(b\cdot\text{ h)}[/tex]Where b = base and h = height
From the diagram, we have that:
b = 4 units
h = 3 units.
Therefore, the area of this triangle is:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}(4\cdot\text{ 3)} \\ A\text{ = }\frac{1}{2}(12) \\ A\text{ = 6 square units} \end{gathered}[/tex]Checking through the options, we see that the only correct option is Option D.
This is because the area of this triangle (6 square units) is one-half of that of a square that has area of 12 square units
A car used 15 gallons of gasoline when driven 315 miles. Based on this information, which expression should be used to determine the unit rate of miles per gallon of gasoline?
Given trhat a car used 15 gallons of gasoline to cover 315 miles.
The expression that will be used to determine the unit rate of miles per gallon of gasoline is:
[tex]\frac{315\text{ miles}}{15\text{ gallons}}[/tex]ANSWER:
[tex]\frac{315\text{ miles}}{15\text{ gallons}}[/tex]3. Solve using the Laws of Sines Make a drawing to graphically represent what the following word problem states. to. Two fire watch towers are 30 miles apart, with Station B directly south of Station A. Both stations saw a fire on the mountain to the south. The direction from Station A to the fire was N32 W. The direction from Station B to the fire was N40 ° E. How far (to the nearest mile) is Station B from the fire?
Let's make a diagram to represent the situation
The tower angle is found by using the interior angles theorem
[tex]\begin{gathered} 50+58+T=180 \\ T=180-50-58=72 \end{gathered}[/tex]It is important to know that the given directions are about the North axis, that's why we have to draw a line showing North to then find the interior angles on the base of the triangle formed.
To find the distance between the fire and Station B, we have to use the law of sines.
[tex]\frac{x}{\sin58}=\frac{30}{\sin 72}[/tex]Then, we solve for x
[tex]\begin{gathered} x=\frac{30\cdot\sin 58}{\sin 72} \\ x\approx26.75 \end{gathered}[/tex]Hence, Station B is 26.75 miles far away from the fire.(c) Given that q= 8d^2, find the other two real roots.
Polynomials
Given the equation:
[tex]x^5-3x^4+mx^3+nx^2+px+q=0[/tex]Where all the coefficients are real numbers, and it has 3 real roots of the form:
[tex]x_1=\log _2a,x_2=\log _2b,x_3=\log _2c[/tex]It has two imaginary roots of the form: di and -di. Recall both roots must be conjugated.
a) Knowing the sum of the roots must be equal to the inverse negative of the coefficient of the fourth-degree term:
[tex]\begin{gathered} \log _2a+\log _2b+\log _2c+di-di=3 \\ \text{Simplifying:} \\ \log _2a+\log _2b+\log _2c=3 \\ \text{Apply log property:} \\ \log _2(abc)=3 \\ abc=2^3 \\ abc=8 \end{gathered}[/tex]b) It's additionally given the values of a, b, and c are consecutive terms of a geometric sequence. Assume that sequence has first term a1 and common ratio r, thus:
[tex]a=a_1,b=a_1\cdot r,c=a_1\cdot r^2[/tex]Using the relationship found in a):
[tex]\begin{gathered} a_1\cdot a_1\cdot r\cdot a_1\cdot r^2=8 \\ \text{Simplifying:} \\ (a_1\cdot r)^3=8 \\ a_1\cdot r=2 \end{gathered}[/tex]As said above, the real roots are:
[tex]x_1=\log _2a,x_2=\log _2b,x_3=\log _2c[/tex]Since b = a1*r, then b = 2, thus:
[tex]x_2=\log _22=1[/tex]One of the real roots has been found to be 1. We still don't know the others.
c) We know the product of the roots of a polynomial equals the inverse negative of the independent term, thus:
[tex]\log _2a_1\cdot2\cdot\log _2(a_1\cdot r^2)\cdot(di)\cdot(-di)=-q[/tex]Since q = 8 d^2:
[tex]\begin{gathered} \log _2a_1\cdot2\cdot\log _2(a_1\cdot r^2)\cdot(di)\cdot(-di)=-8d^2 \\ \text{Operate:} \\ 2\log _2a_1\cdot\log _2(a_1\cdot r^2)\cdot(-d^2i^2)=-8d^2 \\ \log _2a_1\cdot\log _2(a_1\cdot r^2)=-8 \end{gathered}[/tex]From the relationships obtained in a) and b):
[tex]a_1=\frac{2}{r}[/tex]Substituting:
[tex]\begin{gathered} \log _2(\frac{2}{r})\cdot\log _2(2r)=-8 \\ By\text{ property of logs:} \\ (\log _22-\log _2r)\cdot(\log _22+\log _2r)=-8 \end{gathered}[/tex]Simplifying:
[tex]\begin{gathered} (1-\log _2r)\cdot(1+\log _2r)=-8 \\ (1-\log ^2_2r)=-8 \\ \text{Solving:} \\ \log ^2_2r=9 \end{gathered}[/tex]We'll take the positive root only:
[tex]\begin{gathered} \log _2r=3 \\ r=8 \end{gathered}[/tex]Thus:
[tex]a_1=\frac{2}{8}=\frac{1}{4}[/tex]The other roots are:
[tex]\begin{gathered} x_1=\log _2\frac{1}{4}=-2 \\ x_3=\log _216=4 \end{gathered}[/tex]Real roots: -2, 1, 4
PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
start at 4 on the positive y axis, then go up 3 and 5 to the left
Which question can be answered by finding the quotient of ?
A. Jared makes of a goodie bag per hour. How many can he make in of an hour?
B. Jared makes of a goodie bag per hour. How many can he make in of an hour?
C. Jared has of an hour left to finish making goodie bags. It takes him of an hour to make each goodie bag. How many goodie bags can he make?
D. Jared has of an hour left to finish making goodie bags. It takes him of an hour to make each goodie bag. How many goodie bags can he make?
Below question can be answered by finding the quotient of :
C. Jared has of an hour left to finish making goodie bags. It takes him of an hour to make each goodie bag. How many goodie bags can he make?
What is quotient ?In arithmetic, a quotient is a number obtained by dividing two numbers. A quotient is widely used throughout mathematics and is often referred to as the whole number or fraction of a division or ratio.
The number we get when we divide a number by another is the quotient. For example, 8 ÷ = 2; here the result of division is 2, so it is a quotient. 8 is the dividend and is the divisor.
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The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. How long will it take for the Ferris wheel to make one revolution?
We have the function d, representing the distance from the ground of a person riding on a Ferris wheel:
[tex]d(t)=20\sin (\frac{\pi}{30}t)+10[/tex]If we consider the position of the person at t = 0, which is:
[tex]d(0)=20\sin (\frac{\pi}{30}\cdot0)+10=20\cdot0+10=10[/tex]This position, for t = 0, will be the same position as when the argument of the sine function is equal to 2π, which is equivalent to one cycle of the wheel. Then, we can find the value of t:
[tex]\begin{gathered} \sin (\frac{\pi}{30}t)=\sin (2\pi) \\ \frac{\pi}{30}\cdot t=2\pi \\ t=2\pi\cdot\frac{30}{\pi} \\ t=60 \end{gathered}[/tex]Then, the wheel will repeat its position after t = 60 seconds.
Answer: 60 seconds.
Solve the system using algebraic methods.
y = x² + 4x
y = 2x² + 3x - 6
Solution x =
Two or more expressions with an Equal sign is called as Equation. x is -6 and 7 for equations y = x² + 4x and y = 2x² + 3x - 6
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given two equations are
y = x² + 4x
y = 2x² + 3x - 6
Let us simplify these equations as below.
x² + 4x-y=0..(1)
2x² + 3x -y= 6..(2)
subtract equations (2) from (1)
x² + 4x-y-2x² - 3x+y=-6
-x² +x=-6
x(-x+1)=-6
x=-6
and -x+1=-6
Subtract -1 from both sides
-x=-7
x=7
Hence solution of x is -6 and 7 for equations y = x² + 4x and y = 2x² + 3x - 6
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A museum curator counted the number of paintings in each exhibit at the art museum. Number of paintings Number of exhibits 9 2 21 1 40 1 1 46 3 52 1 67 2 X is the number of paintings that a randomly chosen exhibit has. What is the expected value of x Write your answer as a decimal.
Answer
Expected number of paintings that a randomly chosen exhibit has = 40.3
Explanation
The expected value of any distribution is calculated as the mean of that distribution.
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = (9 × 2) + (21 × 1) + (40 × 1) + (46 × 3) + (52 × 1) + (67 × 2)
Σx = 18 + 21 + 40 + 138 + 52 + 134
Σx = 403
N = 2 + 1 + 1 + 3 + 1 + 2 = 10
Mean = (Σx)/N
Mean = (403/10) = 40.3
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Answers asap please
x ≥ 1 or x ≥ 3 is inequality of equations .
What do you mean by inequality?
The allocation of opportunities and resources among the people who make up a society in an unequal and/or unfair manner is known as inequality. Different persons and contexts may interpret the word "inequality" differently.The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. It is an illustration of inequity. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.9 - 4x ≥ 5
4x ≥ 9 - 5
4x ≥ 4
x ≥ 1
4( - 1 + x) -6 ≥ 2
-4 + 4x - 6 ≥ 2
4x ≥ 2 + 8
4x ≥ 10
x ≥ 10/4
x ≥ 5/2
x ≥ 2.5
x ≥ 1 or x ≥ 3
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What is the equation for a line passing through (-2,5) perpendicular to y - 3x = 8
Consider that the equation of a line with slope 'm' and y-intercept 'c' is given by,
[tex]y=mx+c[/tex]Consider the given equation of line,
[tex]\begin{gathered} y-3x=8 \\ y=3x+8 \end{gathered}[/tex]Comparing the coefficient, it is found that the slope of the given line is 3,
[tex]m=3[/tex]Let 's' be the slope of the line which is perpendicular to this line.
Consider that two lines will be perpendicular if their product of slopes is -1,
[tex]\begin{gathered} m\times s=-1 \\ 3\times s=-1 \\ s=\frac{-1}{3} \end{gathered}[/tex]So the slope of the perpendicular line is given by,
[tex]y=\frac{-1}{3}x+c[/tex]Now, it is given that this line passes through the point (-2,5), so it must satisfy the equation of the line,
[tex]\begin{gathered} 5=\frac{-1}{3}(-2)+c_{} \\ 5=\frac{2}{3}+c \\ c=5-\frac{2}{3} \\ c=\frac{13}{3} \end{gathered}[/tex]Substitute the value of 'c' to get the final equation,
[tex]\begin{gathered} y=\frac{-1}{3}x+\frac{13}{3} \\ 3y=-x+13 \\ x+3y=13 \end{gathered}[/tex]Thus, the required equation of the perpendicular line is x + 3y = 13 .
i need help with this. for 2nd option, select only one sub-option
A matrix being in row echelon form means that Gaussian elimination has operated on the rows.
A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions:
- It is in row echelon form.
-The leading entry in each nonzero row is a 1 (called a leading 1).
-Each column containing a leading 1 has zeros in all its other entries.
The matrix presented on the problem satisfies all conditions, therefore, the matrix is indeed in reduced row-echelon form.
The ratio of boys to girls in a school is 5:4. if there are 500 girls , how many boys are there in the school?
Answer:
The number of boys in the school is;
[tex]625[/tex]Explanation:
Given that the ratio of boys to girls in a school is 5:4;
[tex]5\colon4[/tex]And there are 500 girls in the school.
The number of boys in the school will be;
[tex]\begin{gathered} \frac{B}{G}=\frac{5}{4} \\ G=500 \\ B=\frac{5\times G}{4}=\frac{5\times500}{4} \\ B=625 \end{gathered}[/tex]Therefore, the number of boys in the school is;
[tex]625[/tex]Transform AABC by the following transformations:• Reflect across the line y = -X• Translate 1 unit to the right and 2 units down.87BА )5421-B-7-6-5-4-301245678- 1-2.-3-5-6-7-8Identify the final coordinates of each vertex after both transformations:A"B"(C"
SOLUTION
A reflection on the line y = -x is gotten as
[tex]y=-x\colon(x,y)\rightarrow(-y,-x)[/tex]So, the coordinates of points A, B and C are
A(3, 6)
B(-2, 6)
C(3, -3)
Traslating this becomes
[tex]\begin{gathered} A\mleft(3,6\mright)\rightarrow A^{\prime}(-6,-3) \\ B(-2,6)\rightarrow B^{\prime}(-6,2) \\ C(3,-3)\rightarrow C^{\prime}(3,-3 \end{gathered}[/tex]Now translate 1 unit to the right and 2 units down becomes
[tex]\begin{gathered} A^{\prime}(-6,-3)\rightarrow A^{\doubleprime}(-5,-5) \\ B^{\prime}(-6,2)\rightarrow B^{\doubleprime}(-5,0) \\ C^{\prime}(3,-3\rightarrow C^{\doubleprime}(4,-5) \end{gathered}[/tex]So, I will attach an image now to show you the final translation.
Find the probability and odds of winning the two-number bet (split) in roulette. Then find expected value of a $1 bet in roulette for the two-number bet.P.S Might not have enough information
We have to find the probaiblity of winning a split bet in roulette.
Then, we will have 2 numbers that will make us wind the bet out of 37 numbers that make the sample space.
We can then calculate the probability of winning the split bet as the quotient between the number of success outcomes (2) and the number of possible otucomes (37):
[tex]P(w)=\frac{2}{37}\approx0.054[/tex]We can transform this into the odds of winning by taking into account that if 2 are the success outcomes, then 37-2 = 35 are the failure outcomes.
Then, the odds of winning are 2:35.
We now have to calculate the expected value for a $1 bet.
We know the probabilities of winning and losing, but we don't know the value or prize for winning.
The payout for a split bet is 17:1, meaning that winning a split bet of $1 has a prize of $17.
Then, we can use this to calculate the expected value as:
[tex]\begin{gathered} E(x)=P(w)*w+P(l)*l \\ E(x)=\frac{2}{37}*17+\frac{35}{37}*0 \\ E(x)=\frac{34}{37} \\ E(x)\approx0.9189 \end{gathered}[/tex]This means that is expected to win $0.9189 per $1 split bet.
Answer:
Probability of winning: 2/37 ≈ 0.054
Odds of winning: 2:35
Expected value of $1 split bet (17:1 payout): $0.9189