Given there are 9 customers who have entered the drawing, 5 live in the town of Gaston, 2 live in Pike, and 2 live in wells. Two winners will be selected at random.
We have to find the probability that both winners live in Gaston.
The probability that the first winner selected is from Gaston is:
[tex]P(A)=\frac{5}{9}[/tex]The probability that the second winner selected is from Gaston is:
[tex]P(B|A)=\frac{4}{8}=\frac{1}{2}[/tex]The probability that both winners live in Gaston is:
[tex]\begin{gathered} P(A\cap B)=P(A)\cdot P(B|A) \\ =\frac{5}{9}\cdot\frac{1}{2} \\ =\frac{5}{18} \end{gathered}[/tex]Thus, the answer is 5/18.
15.A snack bar sells scoops of strawberry, chocolate, andvanilla ice cream. On Monday, the snack bar sold100 scoops in total of these flavors of ice cream. Thesnack bar sold 3 times as many scoops of chocolate asit did strawberry and 2 times as many scoops ofvanilla as it did chocolate. How many scoops ofchocolate ice cream did the snack bar sell onMonday?
54 scoops of chocolate.
1) Gathering the data from the question
Monday = 100 scoops in total
Snack bar sells 3x chocolate
x strawberry
1.5x Vanilla ( 3 : 1.5 = 2)
How many chocolate scoops?
2) Setting the expression:
3x+x+1.5x=100
4x +1.5x=100
5.5x=100
x=18.1 approximately then x = 18
Answer
3x = Chocolate
3*18 = 54 chocolate scoops
Find the value of x so that the ordered pair (x, 7) satisfies the equation y = 4x - 5. *
Answer:
x=3
Explanation:
Given the equation:
[tex]y=4x-5[/tex]In the ordered pair, (x,7): y=7
[tex]\begin{gathered} \implies7=4x-5 \\ 7+5=4x \\ 12=4x \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]The value of x so that the ordered pair (x, 7) satisfies the equation y=4x-5 is 3.
Question Help Which of the following expressions can be used to find the area of the polygon? 4cm 3 cm 3 cm 4 cm 3 cm Choose the correct answer below. 1 O A. (4x3) + z(9x4) 1 OB. 2 (3 x 4)+(9x4) Click to select your answer and then click Check Answer. All parts showing Clear All Check Ans Review progress Question 9 of 10 Back Next
The polygon is formed by a triangle and a rectangle:
Area of a rectangle = lenght x width
A1 = (4 x 3)
Area of a triangle = 1/2 x base length x heigth
A2 = 1/2 (9x4)
Add both areas
Area of the polygon = A1+ A2 = (4 x 3 ) + 1/2 (9 x 4)
answer : option A
if a flock of ducks is growing by 6 percent per year and starts with a population of 68 about how many ducks will be there in 10 years
We know that the next year the flock of ducks will have 6% more than the current year. If the current year the number of ducks is x, then
0.06 · x = the increase number
Then, the population of ducks next year will be
x + 0.06x = number of ducks next year
we can simplify the equation:
1.06x = number of ducks next year
Two years after, then number of ducks will be:
1.06 · number of ducks next year = number of ducks two years after
using the equation we found:
1.06 · (1.6x) = number of ducks two years after
1.06²x = number of ducks two years after
Similarly, three years after will be
1.06³x = number of ducks three years after
If we keep writing equations for every year, we will find a relation between the number of years that pass and the exponent...
n years after will be:
1.06ⁿx = number of ducks n years after
Since the current year the population is 68, then
1.06ⁿ · 68 = number of ducks n years after
We want to find the number of ducks after 10 years. This is n = 10:
[tex]1.06^{10}\cdot68=\text{ number of ducks 10 years after}[/tex]Since
[tex]\begin{gathered} 1.06^{10}=1.79 \\ 1.79\cdot68\approx121.78 \end{gathered}[/tex]Then, the equation we found says that:
number of ducks 10 years after = 121.78
But it is not possible because we cannor have 121.78 ducks, we always have an integer. Then we round it to the nearest integer: 122
Then
answer - the number of ducks 10 years after will be 122
Greatest common factor 12,30,72
The first step is to write the prime factors of each number. We have
12 = 2 x 2 x 3
30 = 2 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3
Looking at the factors, one 2 and one 3 are common to all three list of factors. Thus,
Greatest common factor = 2 x 3 = 6
20. f(x) = 6x2 – 3x2 + 4x - 4 and g(x) = 9x2 + x - 1. What is f(x) = g(x)? Show all of your steps and write your final answer in factored form.
Here, we want to subtract g(x) from f(x)
We have this as follows;
[tex]\begin{gathered} f(x)-g(x)=6x^3-3x^2+4x-4-(9x^2+x-1) \\ =6x^3-3x^2+4x-4-9x^2-x+1 \\ =6x^3-3x^2-9x^2+4x-x-4+1 \\ =6x^3-12x^2+3x-3 \\ =3(2x^3-4x^2+x-1)_{} \end{gathered}[/tex]what is the inverseof f(x)=x/5+6
Let's begin by listing out the information given to us:
[tex]\begin{gathered} f\mleft(x\mright)=\frac{1}{5}x+6 \\ f(x)=y \\ y=\frac{1}{5}x+6 \end{gathered}[/tex]To find the inverse, of this equation, we have to interchange the two variables (x for y). We have:
[tex]\begin{gathered} y=\frac{1}{5}x+6\Rightarrow x=\frac{1}{5}y+6 \\ x=\frac{1}{5}y+6 \\ \text{Multiply through each element by 5, we have:} \\ 5\cdot x=\frac{1}{5}y\cdot5+6\cdot5 \\ 5x=y+30 \\ \text{Subtract 30 from both side, we have:} \\ 5x-30=y+30-30 \\ 5x-30=y\Rightarrow y=5x-30 \\ y=5x-30 \\ f(^{-1})=5x-30 \end{gathered}[/tex]Determine whether the system of equations below has one solution, infinitely many solutions, or no solution. 10x +9y = 25 20x + 6y = - 10 [classify]show work too please and will give brainliest for the right answer with work shown
Let's try to solve the system:
Taking the first equation and solving for x, we get:
[tex]\begin{gathered} 10x+9y=25 \\ 10x=25-9y \\ x=\frac{25-9y}{10} \\ x=2.5-0.9y \end{gathered}[/tex]Replacing it on the second and solving for y, we get:
[tex]\begin{gathered} 20x+6y=-10 \\ 20(2.5-0.9y)+6y=-10 \\ 50-18y+6y=-10 \\ 50-12y=-10 \\ -12y=-10-50 \\ -12y=-60 \\ y=\frac{-60}{-12} \\ y=5 \end{gathered}[/tex]Now, we can calculate x, replacing y by 5 as follows:
[tex]\begin{gathered} x=2.5-0.9y \\ x=2.5-0.9(5) \\ x=2.5-4.5 \\ x=-2 \end{gathered}[/tex]It means that x = -2 and y = 5 is the solution for the system.
Answer: The system has one solution and it is x = -2 and y = 5
If a car travels for 0 hours, it will travel enter your response here mile(s). This means it will pass through the point enter your response here. Use the slope to move 3 units to the right of the origin and enter your response here unit(s) up to find the point enter your response here that can be used to graph the relationship.
If the car travels for 0 hours, it will travel 0 miles. This means that it will pass through the point (0,0). Use the slope to move 3 units to the right of the origin and 186 units up to find the point (3,186) that can be used to graph the relationship.
What is the proportional relationship?The proportional relationship that models this situation is that the distance is obtained as the multiplied of the time and of the velocity, as follows:
d = vt.
The time is the input of the relationship, hence the constant of proportionality of the relation is given by:
The velocity.
The car travels 186 miles in 3 hours, hence the point is of:
(3,186).
As the format of the point is of:
(Input, output) = (Time, Distance).
Then the velocity is of:
v = 186/3 = 62 miles per hour.
Missing InformationThe car travels 186 miles in 3 hours.
More can be learned about proportional relationships at https://brainly.com/question/10424180
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Write a function that represents the sequences 7,14,21,28
Given:-
[tex]7,14,21,28,\ldots[/tex]To find the sequence inside the pattern.
Since the number are the numbers in 7th table the function can be,
[tex]f(n)=7n[/tex]So the required function is f(n)=7n
Find the x-intercepts and the vertex of the parabola y = (x − 4)(x + 2). Find the x-intercepts of the parabola and write them as ordered pairs. Write the equation y = (x − 4)(x + 2) in standard form. With the standard form of the equation from Part II, use the quadratic formula to identify the x-value of the vertex. Substitute the x-value of the vertex from Part III into the original equation to find the y-value of the vertex. Then, write the coordinates of the vertex.
Given:
The eyuation of the parabola.
[tex]y=(x-4)(x+2)[/tex]Required:
We need to find the x-intercepts, vertex, and standard form of the equation.
Explanation:
Set y =0 and solve for x to find the x-intercepts of the parabola.
[tex](x-4)(x+2)=0[/tex][tex](x-4)=0,(x+2)=0[/tex][tex]x=4,x=-2[/tex]The x-intercepts are 4 and -2.
Multipy (x-4) and (x+2) to find the stansdad form of the equation.
[tex]y=x\left(x+2\right)-4\left(x+2\right)[/tex][tex]y=(x)x+2(x)+(-4)x+(-4)2[/tex][tex]y=x^2+2x-4x-8[/tex][tex]y=x^2-2x-8[/tex]The standard form of the equation is
[tex]y=x^2-2x-8.[/tex]which is of the fom
[tex]y=ax^2+bx+c[/tex]where a =1, b =-2 and c =-8.
[tex]\text{ The x- coordinate of the vertex is }h=-\frac{b}{2a}.[/tex]Substitute b =-2 and a =1 in the equation.
[tex]\text{ The x- coordinate of the vertex is }h=-\frac{(-2)}{2(1)}=1[/tex][tex]substitute\text{ x =1 in the equation }y=x^2-2x-8\text{ to find the y-coordinate of the vertex.}[/tex][tex]y=1^2-2(1)-8=-9[/tex]The vertex of the given parabola is (1,-9).
Final answer:
1)
The x-intercepts are 4 and -2.
2)
The standard form of the equation is
[tex]y=x^2-2x-8.[/tex]3)
The vertex of the given parabola is (1,-9).
Logan opened a savings account 6 years ago the account earns 5% interest compounded annually. if the current balance is $300.00 how much did he deposit initially
Each year, the initial deposit gets multiplied by a factor of:
[tex](1+\frac{5}{100})[/tex]Let L be the initial deposit. 6 years later, the balance of the account will be equal to:
[tex]L\cdot(1+\frac{5}{100})^6[/tex]On the other hand, the current balance is $300. Therefore:
[tex]L\cdot(1+\frac{5}{100})^6=300[/tex]Solve for L:
[tex]\begin{gathered} L=\frac{300}{(1+\frac{5}{100})^6} \\ =\frac{300}{1.05^6} \\ =223.8646\ldots \\ \cong223.86 \end{gathered}[/tex]Therefore, the initial amount of money in the account 6 years ago, was:
[tex]223.86[/tex]1) A ferris wheel can accommodate 40 people in the 20 minutes. How many people could ride the ferris wheel in 3 hours? What was that rate per hour?
3 hours = 3 x 60 = 180 min, then
40 people ---> 20 min
x ----------------> 180 min
[tex]\begin{gathered} x\times20=40\times180 \\ 20x=7200 \\ \frac{20x}{20}=\frac{7200}{20} \\ x=360 \end{gathered}[/tex]answer 1: 360 people in 3 hours
[tex]\frac{360}{3}=120[/tex]answer 2: 120 people per hour
How much money do they make by selling the house ?
ANSWER
$16,200
EXPLANATION
First, they bought the house for $186,700, and then, they sold it for $202,900, which is a greater amount than what they paid for the house. The amount of money they made by selling the house is the difference between the selling prince and the price they paid for,
[tex]202,900-186,700=16,200[/tex]Hence, they made $16,200 selling the house.
2+32 + 3 + 5 + 5 + 5
Solution
We have the following expression:
2+32+3+5+5+5
And we can do this:
34 +3+5+5+5
37 + 5 +5 +5
42 +5+5
42+10 =52
Finala answer : 52
Find the surface area of a parallelogram with adjacent sides u= <4,7, -8> and v= <-2, 5, 11>
Given:
The adjacent sides of parallelogram are u = <4,7,-8> and v = <-2,5,11>
Find:
we have to find the surface area of the parallelogram.
Explanation:
Formula:
Conclusion:
Therefore the surface area of the parallelogram is 125.01.
Estimate the product. Round each factor to the nearest whole number, and then mult 4.6 x 4.1 The product is approximately Submit O
We need to multiply:
[tex]4.6\cdot4.1=\text{???}[/tex]But first, we will round each term to the nearest whole number
so,
4.6 will be rounded to 5 ( because 0.6 > 0.5 )
4.1 will be rounded to 4 ( because 0.1 < 0.5 )
so,
4.6 x 4.1 ( approximately ) = 5 * 4 = 20
Line A (y= 5x - 7) is transformed into Line B (y= 2x+3). which best describes the new slope and y-intercept? the slope is ___, and the line is shifted ____. a) steeper b) flatter ----a) upward b) downward
The graphs of both lines is shown below;
Note that the red line represents y = 5x - 7 and
The blue line represents y = 2x + 3
The slope changes from +5 to +2 and therefore is becoming flatter
The y-intercept has also chabged from -7 to +3 and therefore the line has shifted upward.
The a
The fox population in a certain region has an annual growth rate of 9% per year. In the year 2012 there were 23,900 fox counted in the area. What is the fox population predicted to be in year 2020?What calculations and thinking did you use to find the answer?
Given:
The initial population is P(i) = 23,900.
The annual growth rate is r = 9% = 0.09.
The number of year is t = 2020-2012 = 8 years.
The objective is to find the population in the year 2020.
Explanation:
The growth formula to find the final population is,
[tex]P=P(i)\times(1+r)^t\ldots\text{ . . . (1)}[/tex]On plugging the given values in equation (1),
[tex]P=23900(1+0.09)^8[/tex]On further solving the above equation,
[tex]\begin{gathered} P=23900(1.09)^8 \\ =47622.2471\ldots\text{.} \\ \approx47622 \end{gathered}[/tex]Hence, the final population using the exponential growth formula is 47622.
Complete the equation describe how x and y are related
From the given equation and the given table, let the missing are m and b
[tex]y=mx+b[/tex]To find them use two points from the table
Let us use point (0, -2)
[tex]\begin{gathered} x=0,y=-2 \\ -2=m(0)+b \\ -2=0+b \\ -2=b \end{gathered}[/tex]Substitute b in the equation by -2
[tex]\begin{gathered} y=mx+(-2) \\ y=mx-2 \end{gathered}[/tex]Now, use the point (1, 1) to find m
[tex]\begin{gathered} 1=m(1)-2 \\ 1=m-2 \end{gathered}[/tex]Add 2 to both sides
[tex]\begin{gathered} 1+2=m-2+2 \\ 3=m \end{gathered}[/tex]Substitute m by 3 in the equation, then
The equation is
[tex]\begin{gathered} y=3x-2 \\ y=3x+(-2) \end{gathered}[/tex]The answer is y = 3x + (-2)
The missings are 3
Find the measure of the arc.А1460EB.MABC = [ ? ]°
The measure of the arc m ABC is given by the central angles:
mBC = 360 - (146 + 90) (We have a right angle in the figure).
mBC = 360 - (236)
mBC = 124
The total length of the circle is the circumference:
C = 2*pi * r
If we use for pi = 22/7 (approximation)
Then the arc is given by the fraction that multiplies C:
(2 * pi * r) (mBC+m/360) =
Because 2/360 = 180, we have:
( pi * r) * (124/180)
(22/7) * r * (124/180)
Simplifying the fraction 124/180 by 4 (this is the greatest common divisor), we have:
22/7 * r * 31/45
Then, the measure for the arc is given by (a function of r):
m
22/7 * r * 31/45
For instance, if r = 3, then
Р(А) = 1/2 P(В) = 1/3 If A and B are independent, what is P(A n B)?1/6 5/61/21/3
Given that events A and B are independent.
It follows that the probability of the occurrence of both events is equal to the product of occurrence of each event independently,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]According to the given problem,
[tex]\begin{gathered} P(A)=\frac{1}{2} \\ P(B)=\frac{1}{3} \end{gathered}[/tex]Substitute the values,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]6. In deciding whether to set up a new manufacturing plant, company analysts have established that a reasonable function for the total cost to produce x items is C(x) = 500,000 + 4.75x. (a) Find the total cost to produce 100,000 items. (b) Find the marginal cost of the items to be produced in this plant.
1)
a) Let's find out the total Cost to Produce 100,00 items considering x to stand for "items", so we can write out:
[tex]\begin{gathered} C(x)=500,000+4.75x \\ C(100,000)=500,000+4.75(100,000) \\ C(100,000)=\$975,000 \end{gathered}[/tex]Note that we just had to plug into x, the number of items.
b) The Marginal Cost
On the other hand, the Marginal Cost can be found by taking the first derivative of the Total Cost function, so we can write out:
[tex]\begin{gathered} C(x)=500,000+4.75x \\ C^{\prime}(x)=4.75 \end{gathered}[/tex]The basic idea of the marginal cost is the cost per unit $4.75
3) Hence, the answer is:
a) $975,000
b) $4.75 per unit
Ben has a basket of 5 red socks, 3 yellow socks, and 2 green socks. What is the theoretical probability that if he randomly selects a sock from the basket it will be red?
the probability of pen being red is,
[tex]p=\frac{^5C_1}{10C_1}[/tex][tex]p=\frac{5}{10}=\frac{1}{2}=0.5[/tex]so the answer is 0.5
In △WXY, m∠W = (10x + 17), m∠X = (2x – 9), and m∠Y = (3x + 7)º. Find m∠Y.
Answer:
m∠Y = 40º
Explanation:
The sum of the angles in a triangle is 180 degrees. In △WXY:
[tex]m\angle W+m\angle X+m\angle Y=180\degree[/tex]Substitute the given values:
[tex](10x+17)\degree+(2x-9)\degree+(3x+7)\degree=180\degree[/tex]First, solve for x:
[tex]\begin{gathered} 10x+2x+3x+17-9+7=180\degree \\ 15x+15=180\degree \\ 15x=180-15 \\ 15x=165 \\ x=\frac{165}{15} \\ x=11 \end{gathered}[/tex]Next, solve for the measure of angle Y:
[tex]\begin{gathered} m\angle Y=(3x+7)º \\ =3(11)+7 \\ =33+7 \\ m\angle Y=40\degree \end{gathered}[/tex]What is the appropriate domain and range of the line segment below?
Solution
The domain of a function is the set of all possible inputs for the function.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
From the graph, we can easily see that;
solve for x 8/9x +4=12
hello
to solve for x, we have to simplify this equation
step one
collect like terms
[tex]\begin{gathered} \frac{8}{9}x+4=12 \\ \frac{8}{9}x=12-4 \\ \frac{8}{9}x=8 \\ \end{gathered}[/tex]step two
cross multipy both sides
[tex]\begin{gathered} \frac{8}{9}x=8 \\ 8x=8\times9 \\ 8x=72 \end{gathered}[/tex]step three
divide both sides by the coefficient of x
[tex]\begin{gathered} 8x=72 \\ \frac{8x}{8}=\frac{72}{8} \\ x=9 \end{gathered}[/tex]from the calculation above, the value of x is equal to 9
In business, you may encounter situations that require you to set up equations with more than just parentheses. For practice, solve the following equation.X = 6{2 + 3[2(8 − 3) + (7 + 1) − 3]}
Given:
[tex]x=6\lbrace2+3[2(8-3)+(7+1)-3]\rbrace[/tex]Required:
To solve the given equation.
Explanation:
Consider
[tex]x=6\lbrace2+3[2(8-3)+(7+1)-3]\rbrace[/tex][tex]\begin{gathered} =6\lbrace2+3[2(5)+8-3]\rbrace \\ \\ =6\lbrace2+3[10+8-3]\rbrace \\ \\ =6\lbrace2+3[15]\rbrace \\ \\ =6\lbrace2+45\rbrace \\ \\ =6\lbrace47\rbrace \\ \\ =282 \end{gathered}[/tex]Final Answer:
[tex]x=282[/tex]what is the maximum profit
Total Profit=Total Revenue - Total Cost
P(x) = R(x)-C(x)
where x is the number of unit sold
From the question,
R(x) = 20x - 0.1x² and c(x) =4x + 2
P(x) = R(x) - c(x) = 20x - 0.1x² - 4x - 2
= -0.1x² + 16x - 2
Profit = -0.1x² + 16x - 2
We have a quadratic equation;
a=-0.1 b= 16
Maximum occurs when x = -b/2a
substitute the values of a and b in the above
x = -16/2(-0.1) = -16/-0.2 = 80
To find the maximum profit, we will substitute x=80 in our profit function
Profit = -0.1(80)² + 16(80) - 2
= -640 + 1280 - 2
= 638
Hence, the maximum profit is $638
On March 8, 2017, one South African rand was worth 0.08 U.S. dollars.(a) On that date, how many dollars was 168.18 rand worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many rand was 59.09 dollars worth?Round your answer to the nearest hundredth of a rand.I need help with these two problems.
Given: The conversion rate below
[tex]1(rand)=0.08(dollars)[/tex]To Deteremine: The worth of 168.18 rand in dollars
Solution
[tex]\begin{gathered} 1(rand)=0.08(dollars) \\ 168.18(rand)=x(dollars) \end{gathered}[/tex]Let us cross multiply
[tex]\begin{gathered} x\times1=0.08\times168.18 \\ x=13.4544 \\ x\approx13.45(nearest-hundredth) \end{gathered}[/tex]Hence, worth of 168.18 rand in dollars is approximately 13.45 U.S. dollars
(b) To Determine: How many rand was 59.09 dollars
[tex]\begin{gathered} Recollect \\ 1(rand)=0.08(dollars) \\ y(rand)=59.09(dollars) \end{gathered}[/tex]Let us cross-multiply
[tex]\begin{gathered} 0.08\times y=1\times59.09 \\ 0.08y=59.09 \\ y=\frac{59.09}{0.08} \\ y=738.625 \\ y\approx738.63(rand) \end{gathered}[/tex]Hence, 59.09 dollars is worth approximately 738.63 rands