Solution:
Given:
[tex]\begin{gathered} total=5000 \\ n_{online\text{ class}}=1200 \\ n_{basketball}=1700 \end{gathered}[/tex]Since both events are independent, then;
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence,
[tex]\begin{gathered} P(online)=\frac{1200}{5000} \\ P(basketball)=\frac{1700}{5000} \\ Hence,\text{ } \\ P(online\cap basketball)=\frac{1200}{5000}\times\frac{1700}{5000} \\ P(online\cap basketball)=\frac{51}{625} \\ P(online\cap basketball)=0.0816 \end{gathered}[/tex]The number of students taking an online course and prefer basketball to football is;
[tex]\begin{gathered} n(online\cap basketball)=0.0816\times5000 \\ n(online\cap basketball)=408 \end{gathered}[/tex]Therefore, the number of students taking an online course and prefer basketball to football is 408
What is the equivalent decimal of 16/52? Enter your answer, rounded to the nearest thousandth of a degree, in the box.
find the area of each Lister answer exact form and approximate form
In the given circle, The diameter of the circle is 8 in
Radius is the half of the diameter,
Radius = Diameter/2
Radius = 8/2
Radius = 4 in
Area of the circle with radius r is express as :
[tex]\text{ Area of Circle =}\Pi(radius)^2[/tex]Substitute the value of radius = 4in
[tex]\begin{gathered} \text{ Area of Circle =}\Pi(radius)^2 \\ \text{ Area of Circle =}\Pi\times4\times4 \\ \text{ Area of Circle = 50.27 in}^2 \end{gathered}[/tex]Area of the circle is 50.27 in²
Answer : Area of the circle is 50.27 in²
what is the missing factor in the following factoring problem
notice that we have one factor of the complete expression, then, we can make the following division:
therefore, the missing factor is 7y+4
Solve each system by substitution.8). -7x-2y=-13x-2y=11
We have the following:
[tex]\begin{gathered} -7x-2y=-13 \\ x-2y=11 \end{gathered}[/tex]solving by substitution:
[tex]\begin{gathered} x-2y=11\Rightarrow x=11+2y \\ \text{replacing} \\ -7\cdot(11+2y)-2y=-13 \\ -77-14y-2y=-13 \\ -16y=-13+77 \\ y=\frac{64}{-16} \\ y=-4 \end{gathered}[/tex]now, for x
[tex]\begin{gathered} x=11+2\cdot-4 \\ x=11-8 \\ x=3 \end{gathered}[/tex]The solution is
[tex](3,-4)[/tex]need help with this question please parts 2 and 3
Given:
[tex]p(x)=3(x+3)^3+2[/tex](a) The parent function of p(x) is the cubic function:
[tex]y=x^3[/tex](b) To produce p(x) from y, we need to perform the following transformations in order:
* Shift to the left 3 units. This gives the function:
[tex]y=(x+3)^3[/tex]* Stretch vertically by a factor of 3. This gives the function:
[tex]y=3(x+3)^3[/tex]* Shift upward 2 units. This gives the final function:
[tex]p(x)=3(x+3)^3+2[/tex](c) The graphs of the parent function (in blue) and the transformed function (in red) are shown below:
Tom wants to get to the playground at 2:30 p.m. It takes him 27 minutes to bike there.What time should Tom leave for the playground? Move numbers to the clock to show the time.0 1 2 3 4 5 6 7 8 9
SOLUTION
Tom wants to get to the playground at 2:30 p.m
if it take him 2
Evaluate the expression when x=5 and z=7.25z+ xSimplify your answer as much as possible.
We are given the expression
[tex]\frac{5z+x^2}{x}[/tex]and are asked to evaluate it when x=5 and z=7. For this, we simply replace the given values on the original expression, like this:
[tex]\frac{5(7)+(5)^2}{5}[/tex]And now we simplify it as much as possible:
[tex]\frac{35+25}{5}=\frac{60}{5}=12[/tex]Hello can you please help me out with this question please
Explanation: There are different ways to solve this problem but let's focus on just one. When we have a division multiplied by a number we can always consider the following
Step 1: Once we understand that we can solve by models as follows
First, let's solve the numerator (our multiplication)
Step 2: Once our numerator 3 x 12 = 36 now we have
[tex]\frac{36}{4}[/tex]Now we can solve our division as follows
As we can see above, we have 36 blue boxes divided into 4 red larger boxes equally which gives us 9 blue boxes for each of the red boxes. It means 36/4 = 9.
Final answer: So our final answer is
[tex]\frac{3}{4}\cdot12=9[/tex].
B Ε D A Ε Which two triangles are congruent? Ο ΔΑΒC ΔΕFD Ο ΔABC_ΔΕΡΕ Ο ΔΑΒC2 DEE Ο Ο ΔΑΒΟ ΔΕΡΕ
From the figure given;
Observe that, side AB is congruent to EF.
Side AC is congruenct ED
side BC is congruent to FD
From the above, we can deduce that Δ ABC ≅ Δ EFD
the arithmet mean of 20, 30, 45, x is 35 what is x?
Answer:
x is 45===================
The mean is:
(20 + 30 + 45 + x)/4 = 35Simplify and solve for x:
(95 + x)/4 = 3595 + x = 4*3595 + x = 140x = 140 - 95x = 45Answer:
x = 45
Step-by-step explanation:
Formula we use,
→ (Sum of numbers/Total numbers) = 35
Now the value of x will be,
→ (Sum of numbers/Total numbers) = 35
→ (20 + 30 + 45 + x)/4 = 35
→ (95 + x)/4 = 35
→ 95 + x = 35 × 4
→ x = 140 - 95
→ [ x = 45 ]
Hence, the value of x is 45.
two objects leave from point b at a right angle after ten seconds, object A has moved 12 meters and object C has moved 5 meters. what is the distance between points a and C
In order to calculate the distance between A and C, we can use the Pythagorean Theorem, since we have a right triangle:
[tex]\begin{gathered} AC^2=12^2+5^2 \\ AC^2=144+25 \\ AC^2=169 \\ AC=13 \end{gathered}[/tex]So the distance between A and C is 13 meters.
please help figure out if these are similar angles, AA,SAS,SSS
The two triangles are not similar
Here, we want to check the if the given triangles are similar
From the diagrams given, we can see that the only similarity between the two is the presence of an angle 100 at the top vertex
This does not give any other proof of similarity between the two triangles
Thus, we have it that the triangles cannot be similar based on the given point
Hence, we can conclude that the two triangles are not similar
A square box is being cut apart and has the measurements shown below. What is the area of the box ?
6 square box, each of length 3.5 inches:
Area of the original box = 6 x area of the smaller box = 6 x L x L
Area of the original box = 6 (3.5 x 3.5) = 6 (12.25) = 73.5 square inches
the table indicates the table indicates a man use data usage over the last 4 months positive values indicate the amount of data that went over his data package plan the negative values indicate the amount of data that was under the plan identify the amount of Emmanuel's use less least amount of data justify your response
Answer:
Febuary -2.25
Explanation:
We are told that the negative values indicate the amount of data that was under the plan. Therefore, the more negative the value, the less of the data Emmanuel used.
With this in mind, looking at the table we note that in the month of febuary Emmnuel used -2..25 of data (2.25 untis less than his plan ) which is the least amount of data used in any month.
In AVWX, XV W X and m_W = 27°. Find mZX.
We will solve as follows:
From the information given we can deduce that the triangle is Isosceles. We also have from theorem that angles that are opposite to congruent sides are also congruent, therefore angle
Using this, and the fact that the sum o all internal angles of a triangle add to 180°, the following is true:
[tex]V+W+X=180[/tex]Now, we replace the values we know:
[tex]27+27+X=180\Rightarrow X=126[/tex]So, the value of angle
Question 1 (Essay Worth 10 points)(03.03 MC)A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:f(d) = 11(1.01)dPart A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points) Source StylesFormat ◢ Question 2 (Essay Worth 10 points)(03.02, 03.03, 03.04 MC)The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.The amount f(x), in dollars, in account A after x years is represented by the function below:f(x) = 1,264(1.09)xPart A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:r (number of years)1234g(r) (amount in dollars)1,3751,512.501,663.751,830.13Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
A biologist studying the growth of a particular species of algae and later designed a model equation for the growth
F(d) = 11(1.01)d
Where, f(d) is in mm and d is days
QUESTION A
F(d) = 11(1.01)d
f(d) = 11.79 mm
Substitute f(d) = 11.79 mm into the model equation
11.79 = 11(1.01)d
11.79 = 11 * 1.01 * d
11 .79 = 11.11 x d
11.79 = 11.11d
Divide both sides by 11.11
11.79/11.11 = 11.11d/11.11
d = 11.79/11.11
d = 1.061
Thde reasonable domain to plot the growth function is 1.061 < d > 1.061
Create a real life word problem that represents a partial variation and has a constant of variation of 4
We and a problem with a constant of variation of 4.
We can think as following:
Kate wants to make a party and make candies for her guests. She intent to make at least 15 candies and an additional of 4 candies for each guest. Thetermine the total number of candies, c, that Kate must make according to the total numer of guests, g.
Answer: c = 4g + 15
There are two bags containing only white and blue marbles.BagA has 11 white marbles and 9 blue marbles.Bag B has 6 white marbles and 2 blue marbles
from Least likely to Most likely
Event 3,
Event 1,
Event 4,
Event 2
STEP-BY-STEP EXPLANATION
BAG A contains:
no of white marbles = 11
no of blue marbles = 9
Total marbles in Bag A
= 11 + 9 = 20
Prob. of choosing a white marble in Bag A
= 11 / 20
Prob. of choosing a blue marble in Bag A
= 9 / 20
BAG B contains:
no of white marbles = 6
no of blue marbles = 2
Total marbles in Bag B
= 6 + 2 = 8
Prob. of choosing a white marble in Bag B
= 6 / 8
Prob. of choosing a blue marble in Bag B
= 2 / 8.
Event 1: Choosing blue marble from Bag B
= 2 / 8 = 0.25
Event 2: Choosing white marble from Bag B
= 6 / 8 = 0.75
Event 3: Choosing purple marble from Bag A
= 0 / 20 = 0
Event 4: Choosing white marble from Bag A
= 11 / 20 = 0.55.
Hence, from Least likely to Most likely we have Event 3, Event 1, Event 4, Event 2.
Question 6 Clare volunteers at a local library during the summer. Her work includes putting labels on 750 books. How many minutes will she need to finish labeling all books if she takes no breaks and labels 15 books a minute Question 7 Suppose Clare labels the books at a constant speed of x books per minute. Write an equation that represents the relationship between her labeling speed and the number of minutes it would take her to finish labeling.
Clare is going to need 50 minutes to label 750 books
1) Gathering the data
750 books
15 books per minute
2) Let's set a proportion for that, considering the fact that her speed is constant
15 books ----------------------1 minute
750 -------------------------------x
15x = 750
x= 50 books
3) Clare is going to need 50 minutes to label 750 books.
This is a graph of the relationship between millimeters of rainfall and umbrella sales. In your own words, explain what happens to umbrella sales as the amount of rainfall changes.
On the graph, the x axis represents rainfall while the y axis represents number of umbrella sold. We can see that as the amount of rainfall is increasing, the number of umbrellas sold is increasing. This is shown by the line moving upwards in the positive direction. the relationship between the amount of rainfall and the number of a umbrellas sold is a positive association.
Show that the function g(x)=x-2/5 is the inverse of f(x)=5x+2Step 1: the function notation f(x) can be written as a variable in an equation. Is that variable x or y?Write f(x)=5x+2 as an equation with the variable you chose above.Step 2: switch the variables in the equation from Step 1. Then solve for y. Show your work.Step 3: Find the inverse of g(x)= x-2/5. What does this tell you about the relationship between f(x)=5x+2 and g(x)? Show your work.
Given that :
[tex]f(x)\text{ = 5x + 2}[/tex]We can prove that :
[tex]g(x)\text{ = }\frac{x\text{ -2}}{5}[/tex]is it's inverse doing the following:
Step 1. Set y = f(x):
[tex]y\text{ = 5x + 2}[/tex]Step 2. Switch the variables:
[tex]x\text{ = 5y + 2}[/tex]Then we solve for y:
[tex]\begin{gathered} 5y\text{ = x - 2} \\ \text{Divide both sides by 5} \\ y\text{ = }\frac{x\text{ -2}}{5} \end{gathered}[/tex]Step 3. The inverse of :
[tex]g(x)\text{ = }\frac{x-2}{5}[/tex]can be found in a similar way.
[tex]\begin{gathered} y\text{ = }\frac{x-2}{5} \\ x\text{ = }\frac{y-2}{5} \\ \text{Cross}-\text{Multiply} \\ 5x\text{ = y -2} \\ y\text{ = 5x + 2} \end{gathered}[/tex]This tells us that f(x) and g(x) are one to one functions are f(x) is the mirror image of g(x)
R's sleep log: 8.5 8 9.5 9 7.5 8.5B's sleep log 6.5 7 7.5 6.5 12 7.5which statement is NOT true about the data provided?a. both sets of data have an interquartile range of 1b. both measures of center for R's data have a value of 8.5c. the shape of both data distributions are non-symmetricd. the IQR of B's data is best used to describe the spread because of the outlierR's sleep log: 8.5 8 9.5 9 7.5 8.5B's sleep log 6.5 7 7.5 6.5 12 7.5
Answer
C. The shape of both data distributions are non-symmetric
Step-by-step explanation
Ordering both data sets from least to greatest, we get:
R's sleep log:7.5 8 8.58.5 99.5
B's sleep log: 6.5 6.577.57.512
We can see that B's data is concentrated at the lower values (12, the maximum, is an outlier). Then, the shape of B's data distribution is non-symmetric. But, in R's data every value is equidistant from the other ones, in consequence, the shape of R's data distribution is symmetric.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65 % salt and Solution B is 90 % salt She wants to obtain 140 ounces of a mixture that is 85 % salt How many ounces of each solution should she use?
Given:
a.) Solution A is 65% salt
b.) Solution B is 90% salt
c.) She wants to obtain 140 ounces of a mixture that is 85% salt.
Let x = the number of ounces of Solution A
Let y = the number of ounces of Solution B
x + y = 140
y = 140 - x (Eq. 1)
0.65x + 0.90y = 0.85(140)
0.65x + 0.90y = 119
(0.65x + 0.90y = 119) x 100
65x + 90y = 11,900 (Eq. 2)
Substitute Eq. 1 to Eq. 2
65x + 90y = 11,900
65x + 90(140 - x) = 11,900
65x + 12,600 - 90x = 11,900
65x - 90x = 11,900 - 12,600
-25x = -700
-25x/-25 = -700/-25
x = 28 ounces
y = 140 - x
y = 140 - 28
y = 112 ounces
Therefore, you will be needing 28 ounces of Solution A and 112 ounces of Solution B.
find the annual percentage yield apyA bank offers an apr of 2.5% compounded semiannually
Apr = 2.5% every 6 months
Use formula
N = N1 ( 1+ 2.5/100)^ 2
APY= (1 + r/2) ^2 - 1
. = ( 1 + 2.5/2) ^2 - 1
. = (2.25)^2 - 1
. = 4.0625
Then answer is
Annual percentage yield
APY = 4.06 %
find the lettered side e cm
Answer:
[tex]\sqrt{122}\approx{11.05}[/tex]
Step-by-step explanation:
In any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This is commonly represented by the equation [tex]a^2+b^2=c^2[/tex].
In the triangle on the left:
[tex]a^2+b^2=c^2[/tex]
[tex]5^2+9^2=c^2[/tex]
[tex]25+81=c^2[/tex]
[tex]106=c^2[/tex]
[tex]\sqrt{106}=c[/tex]
The hypotenuse of the triangle on the left becomes a leg of the triangle on the right, so we repeat the process:
[tex]a^2+b^2=c^2[/tex]
[tex]4^2+(\sqrt{106})^2=c^2[/tex]
[tex]16+106=c^2[/tex]
[tex]122=c^2[/tex]
[tex]\sqrt{122}=c[/tex]
[tex]c\approx{11.05}[/tex]
On election day the polls open at 7:30 am and closes at 9pm. Marlene worked all day exceptfor a break at lunch 10:30 am to 12 pm and dthen break for dinner at 5:30 pm to 7 pm. Marleneworked What fraction of the time that the polls were open?(a) 4/7(b) *(C) ?(d)?(e) ?
ANSWER;
The fraction of the time she worked was 7/9 of the time the polls were opened
EXPLANATION;
Here, we want to get the fraction of the time in which Marlene worked
What we have to do here is to calculate the total time the pool was opened, then calculate the total time in which she went for break. Then we divide the break time by the total opening time
We proceed as follows;
From 7 : 30 am to 9pm
7:30 am to 9:30 pm is 14 hours
Kindly note that we are to subtract 30 minutes, so we have the total time as 13 hours and 30 minutes
For ease of calculations, we shall have all the time in minute
Recall, 60 minutes are in an hour
So, in 13 hours, we have 13(60) = 780 minutes
Added to the 30, we have a total of 780 minutes + 30 minutes = 810 minutes
Break Times
The first break is 10; 30 am to 12 pm; that is a total time of 1 hour 30 minutes
The second break is from 5:30 pm to 7 pm; that is another 1 hour 30 minutes
Total time spent on breaks is 3 hours
Converting to minutes, we simply multiply by 60 and that will give 3(60) = 180 minutes
Thus, we can now proceed to divide;
[tex]\frac{180}{810}\text{ = }\frac{6}{27}\text{ = }\frac{2}{9}[/tex]The above is the fraction spent on breaks. To get the farction worked, we simply subtract the above fraction from 1
We have this as;
[tex]1\text{ - }\frac{2}{9}\text{ = }\frac{7}{9}[/tex]What are the domain and range of the function f(x)=2x+1?domain: (0.00)range: (-0.00domain: (-0.00)range: (0.co)domain: (-0.00)range: (2.00)domain: (0.00)range: (2.0)
The given function is expressed as
f(x) = 2^(x + 1)
The domain of a function is the set of all the possible values of x that would satisfy the function.
The range of a function is the set of all the possible values of y that would satisfy the function.
Since the fuction has no denominator or even root, the values of can be all real numbers. This means that the domain would be between - infinity and infinity
For the range, no matter how small the value of x that we input into the function, the value of f(x) or y would never be lesser than zero. Also, there is no limit to the value of f(x) even if we input very large values of x. Thus, the range is between 0 and infinity. Thus,
the correct option is the second one
according to the synthetic division problem below, which of the statements are true?
Looking at the Algorithm
We can see that
A) True
2 is one of the roots and the divisor of that Divison
B) False
When we plug into the function (x) the root the result is going to be zero
Since f(-2) = 5(-2)² -16(-2) +12 f(-2) = 20 +32 +12 f(-2) = 64 not equal to zero, then x = -2 is not the root
f(x) = -5x² -16x +12 has x_1= 2 and x_2= 6/5
C) False
Factoring f(x) = -5x² -16x +12 we'll have f(x) = (5x -6)(x-2)
D) True
For the previous explanation
E) True
Rewriting as a factored form we'll have f(x) = (5x -6)(x-2)/(x-2) = 5x -6
F) False
We can't find the same result as the previous one. by dividing by (x+2)
find all of the zeros of p (x) = x^3-x^2+2, given that 1-i is a zero. (if there is more than one zero, separate them with commas.)
We have the next polynomial function
[tex]P(x)=x^3-x^2+2[/tex]In order to find the zero we punt the function equal to zero
[tex]x^3-x^2+2=0[/tex]We have a given zero that is 1-i
x=1-i
than means that we need the conjugate of the zero given is also a zero
x=1+i
and then we need a third zero because the polynomial has third-degree it can be calculated if we factorize the polynomial given
[tex]\mleft(x-1-i\mright)\mleft(x-1+i\mright)\mleft(x+1\mright)=0[/tex]Therefore the zeros are
x=-1
x=1-i
x=1+i
the answer to a multiplication problem is 3 /5 select to see if each statement is true or false
Part (A):
The value of 3/5 in the decimal form is 0.6 which is less than 1.
Thus, one of the factors of the should be less than 3/5 and other greater than 3/5.
Part (B):
For example take,
2 and 3/10.
The product of 2 and 3/10 is 3/5.
2 is greater than 3/5 and 3/10 is smaller than 3/5.