Probability formula:
[tex]\text{ P(E) = }\frac{\text{ N(Required outcome)}}{\text{N}(\text{Total outcome)}}\text{ }[/tex]Total number of months in a year = 12
[tex]\begin{gathered} \text{P(July) = }\frac{1}{12} \\ \text{P}(\text{October) =}\frac{1}{12} \end{gathered}[/tex][tex]\begin{gathered} \text{ P(July or October) = P(July) + P(October)} \\ =\frac{1}{12}+\frac{1}{12}=\frac{2}{12} \end{gathered}[/tex][tex]\frac{2}{12}=\frac{1}{6}[/tex]Therefore, the probability that it will be July or October is 1/6
Find the coterminal angles of 65ᵒ and 580ᵒ.425ᵒ and 220ᵒ are coterminal angles of 65ᵒ and 580ᵒ.225ᵒ and 120ᵒ are coterminal angles of 65ᵒ and 580ᵒ.65ᵒ and 210ᵒ are coterminal angles of 65ᵒ and 580ᵒ.85ᵒ and 20ᵒ are co-terminal angles of 65ᵒ and 580ᵒ.
Given:
The angles are 65ᵒ and 580ᵒ.
To find:
The coterminal angles
Explanation:
As we know,
Two angles are coterminal when the angles themselves are different, but their sides and vertices are identical.
The coterminal angles are found by adding or subtracting by 360 degrees with the given angle.
The coterminal angle of 65 degrees is,
[tex]65+360=425^{\circ}[/tex]The coterminal angle of 580 degrees is,
[tex]580-360=120^{\circ}[/tex]Therefore,
425ᵒ and 220ᵒ are the coterminal angles of 65ᵒ and 580ᵒ.
Final answer:
425ᵒ and 220ᵒ are coterminal angles of 65ᵒ and 580ᵒ
14. A jury pool consists of 27 people, 15 men and 12 women. Compute the probability that a randomly selected jury of 12 people is all male.
Given:
Total number of people (n)=27
men =15
women=12
[tex]^{}Totalnumberofwaystoselect12peoplefrom24=^{27}C_{12}[/tex][tex]=\frac{27!}{12!(15!)}[/tex][tex]=\frac{27\times26\times25\times24\times23\times22\times21\times20\times19\times18\times17\times16\times15!}{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1\times15!}[/tex][tex]=3\times13\times23\times3\times20\times19\times17[/tex][tex]=17383860[/tex][tex]NO\text{ of ways to select 12 male=}^{15}x_{12}[/tex][tex]=\frac{15!}{12!(3!)}[/tex][tex]=\frac{15\times14\times13\times12!}{12!3!}[/tex][tex]=5\times7\times13[/tex][tex]=455[/tex]Probability of selecting the 12 males is P(A)
[tex]P(A)=\frac{455}{17383860}[/tex][tex]P(A)=\frac{7}{267444}[/tex]Hi, can you help me answer this question please, thank you
Given that the interval of the widget width is
[tex]12.8<\mu<34.9[/tex]The correct statements out the once given are,
Option 2 which says;
There is 95% chance that the mean of a sample of 29 widgets will be between 12.8 and 34.9.
Option 3 which says;
With 95% confidence, the mean width of a randomly selected widget will be between 12.8 and 34.9
Therefore, the correct options are Option 2 and 3.
Find the perimeter of the polygon with the vertices 01 - 3, 2), R(1,2), (1, - 2), and 77 - 3. - 2).The perimeter isunits.
Approximately 30.47 units
To find the Perimeter of this polygon, we can find by calculating the distance between each point
Considering the points are:
1 (3,2) R (1,2) (7,7) and (-3,-2)
1) Let's calculate the distance between each of them, using the formula of the distance derived from the Pythagorean Theorem.
d1 = (3,2) and (1,2)
d_2 =(1,2) and (7,7)
d_3= (7,7) and (-3,-2)
d_4= (-3,-2) and (3,2)
[tex]\begin{gathered} d_{}=\sqrt{(x_{_2-}x_{1\text{ }})^2+(y_2-y_1)^2^{_{}}} \\ d_{_1=}\sqrt{(1-3)^2+(2-2)^2}=2 \\ d_2=\sqrt{(7-1)^2+(7-2)^2}=\sqrt{61} \\ d_3=\sqrt{(-3-7)^2+(-2-7)^2}=\sqrt{181} \\ d_4\text{ =}\sqrt{(3+3)^2+(2+2)^2}=2\sqrt{13} \end{gathered}[/tex]2) Since we have four points then let's consider them as our vertices, and add those line segments do calculate its Perimeter (2P)
[tex]2P\text{ = 2 +}\sqrt{61}+2\sqrt{13}+\sqrt{181}\text{ }\approx\text{ 30.47}[/tex]Notice that for those radicals are not perfect squares they are irrational so approximating these we have.
2) A number in the set {50, 51, 52, 53, ..., 999} is randomly selected. What is the probability that thenumber selected is a two-digit number? Express your answer as a common fraction.
To answer this questions we have to count how many numbers are in the set and how many of them are two digits numbers.
In the set given there are 950 numbers, of those numbers there are 49 two digits numbers, then the probability is:
[tex]P=\frac{49}{950}[/tex]find the area of the shaded regions in the figures below, whose measures of radius or diameters are given. take [tex]\pi 3.14[/tex]
a) The area is comprised of a semicircle and a rectangle so the combined area is given by:
[tex]\frac{\pi(10)^2}{2}+25\times20=657m^2[/tex]So the area is 657 square meters.
b) The area of required region is the difference between the area of large circle and small circle. The radius of large and small circles are 12 cm and 10 cm respectively.
So the area is given by:
[tex]\pi(12)^2-\pi(10)^2=144\pi-100\pi=44\pi=138.16cm^2[/tex]Hence the area is 138.16 square centimeters.
Tim earns $120 plus $30 for each lawn he mows. Write an inequality to represent how many lawns he needs to mow to make more than $310.how much he will make if he mows 9 lawns?
Let's use the variable x to represent the number of lawn Tim mows.
If he earns $120 plus $30 for each lawn, we can write the following equation for his earnings:
[tex]\text{Earning}=120+30x[/tex]Then, we want an earning greater than $310, so we have the following inequality:
[tex]\begin{gathered} \text{Earning}>310 \\ 120+30x>310 \end{gathered}[/tex]Now, to find the earning for 9 lawns, let's use x = 9 and calculate the total earning:
[tex]\begin{gathered} \text{Earning}=120+30\cdot9 \\ \text{Earning}=120+270 \\ \text{Earning}=390 \end{gathered}[/tex]Therefore his earning after mowing 9 lawns is $390.
Select the regression equation that best fits the following data
.Plot the points (x, f(x)) given by the table and the given functions.
Of all the given functions, the only one that models all the plotted points closely is the red curve.
The function that is given by the red curve is:
[tex]f\left(x\right)=-21.30x^{2}+231.22x+318.41[/tex]Therefore, the regression equation that best fits the given data is f(x) = -21.30x² + 231.22x + 318.41
A
On the basis of the graph, answers the following questions.
a) The factors have the form:
[tex](x-x_1)[/tex]where x1 is a zero of the function. A zero is a point at which the graph intercepts the x-axis. From the graph, the zeros are:
-6, -4, 2, and 3
Therefore, the factors are:
(x + 6)
(x + 4)
(x - 2)
(x - 3)
b) Multiplying all these factors we get a polynomial, p(x), with the zeros of the graph. That is:
p(x) = (x + 6)(x + 4)(x - 2)(x - 3)
c) Yes, it is possible to find other polynomials with the same zeros. To do that we have to multiply p(x) by a constant. For example, multiplying by 2:
f(x) = 2(x + 6)(x + 4)(x - 2)(x - 3)
and f(x) has the same zeros as p(x)
d) Every polynomial obtained in the previous way, multiplying p(x) by a constant, will have a different graph. In conclusion, it is not possible to find other polynomials with the same zeros and the same graph.
What does slope mean in context?Answer Choices: A. For every 1% increase in 4th grade pass rate, the predicted 8th grade pass rate will increase by 25.6%B. For every 1% increase in 8th grade pass rate, the predicted 4th grade pass rate will increase by 1.1%C. For every 1% increase in 4th grade pass rate, the predicted 8th grade pass rate will increase by 1.1%D. For every 1% increase in 8th grade pass rate, the predicted 4th grade pass rate will increase by 25.6%
Answer: The mathematical meaning of the slope in the following context is as described below:
(A):
[tex]\begin{gathered} S=\frac{\text{ 8th grade pass rate}}{\text{ 4th grade pass rate}} \\ \\ S=\frac{25.6\%}{1\%} \\ \end{gathered}[/tex](B):
[tex]\begin{gathered} S=\frac{\text{ 4th grade pass rate}}{\text{ 8th grade pass rate}} \\ \\ S=\frac{1.1\%}{1\%} \end{gathered}[/tex](C):
[tex]\begin{gathered} S=\frac{\text{ 8th grade pass rate}}{\text{ 4th grade pass rate}} \\ \\ S=\frac{1.1\%}{1\%} \end{gathered}[/tex](D): Finally the answer for the last part is:
[tex]\begin{gathered} S=\frac{\text{ 4th grade pass rate}}{\text{ 8th grade pass rate}} \\ \\ S=\frac{25.6\%}{1\%} \end{gathered}[/tex]If the sum of the interior angle measures of a polygon is 2340, then what kind of polygon is it?
Given:
The sum of interior angle measures of a polygon is 2340.
Required:
To find the type of polygon.
Explanation:
The formula for calculating the sum of interior angles is
[tex](n-2)\times180\degree[/tex]Here,
[tex]\begin{gathered} (n-2)\times180=2340 \\ \\ n-2=\frac{2340}{180} \\ \\ n-2=13 \\ \\ n=13+2 \\ \\ n=15 \end{gathered}[/tex]Therefore, the polygon is 15 sided.
Final Answer:
The polygone is 15 sided.
Subtract — 7x^2 + 4x + 2 from x^2 – 3.
We are required to subtract -7x^2+4x+2 from x^2-3.
This is written as:
[tex](x^2-3)-(-7x^2+4x+2)[/tex]First, we open the brackets
[tex]=x^2-3+7x^2-4x-2[/tex]Next, we collect like terms and simplify:
[tex]\begin{gathered} =x^2+7x^2-4x-3-2 \\ =8x^2-4x-5 \end{gathered}[/tex]Therefore:
[tex](x^2-3)-(-7x^2+4x+2)=8x^2-4x-5[/tex]Suppose the domain of f is restricted to {1,2}.State the domain of the inverse function.Separate your answers with a comma.
The domain of f is restricted to {1, 2}
The domain of the inverse function
Bob got a raise and he's hourly wage increased from $10 to $18 what is the percent increase?
In order to find the percent increase, let's first find the absolute increase, by subtracting the new value and the old value:
[tex]18-10=8[/tex]Now we just need to divide the absolute increase by the old value, then we will find the percent increase:
[tex]\frac{8}{10}=0.8=80\text{\%}[/tex]So the percent increase is 80%.
When preparing a fresh one, my mother used 3 L of Water, .0.5 L of fruit pulp, 0.5 L of orange juice and 0.5 L of Syrup, so how many liters of soda did she prepare?
As it is a soft drink, for this you can add the amounts given that the mother used in the preparation, that is,
[tex]3+0.5+0.5+0.5=4.5[/tex]Therefore, the mother prepared 4.5 liters of soda.
all you need is in the photo please show your work step by step and fast
Answer:
Kim is younger than 5 years. Kim could 1, 2, 3 or 4 years old.
Explanation:
Let Kim's age be z.
From the question, Josh's age can be as represented below;
[tex]Josh^{\prime}s\text{ age =}4z+6[/tex]We're also told that the sum of their ages is less than 31, we can express this as per below;
[tex]z+(4z+6)<31[/tex]So let's go ahead and find Kim's age, z;
[tex]\begin{gathered} 5z<31-6 \\ z<\frac{25}{5} \\ z<5 \end{gathered}[/tex]So Kim is younger than 5 years. Kim could 1, 2, 3 0r 4 years old.
what is the slope of this question because i don't really get slope
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Case A:
Line A :
Two points : ( -3, 4) and (-1,0)
[tex]\text{slope,m = }\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{0-4}{-1-(-3)\text{ }}\text{ =}\frac{-4}{-1+3}=\frac{-4}{2}=-2\text{ (COR}\R ECT)[/tex]Case B:
Line B:
Two points: ( -1, 4 ) and ( 1, 0 )
[tex]\text{slope, m = }\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{0-4}{1\text{ - (-1)}}=\frac{-4}{1+1}=\frac{-4}{2}=\text{ -2 (COR}\R ECT)[/tex]
Case C:
Line C:
Two points: ( 1, 4 ) and ( -1, 0 )
[tex]\text{slope, m = }\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{0-4}{-1-1}=\frac{-4}{-2}=\text{ 2 ( NOT COR}\R ECT)[/tex]Case D:
Line D:
Two points : ( 3,4 ) and ( 1,0)
[tex]\text{slope, m =}\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{1-3}=\frac{-4}{-2}=2\text{ (NOT COR}\R ECT)[/tex]CONCLUSION:
We have seen clearly that:
Line A and Line B have a slope of -2
6Drag each label to the correct location on the image Alan is converting large and small numbers from Standard notation. group the numbers according to the power of 10.
if the number is big the esponent must be positive, if the numbr is smal the exponent must be negative
so
example:
[tex]2.930.000\longrightarrow2.93\times10^6[/tex]Given: f(x) = -3x³ + x² - 3, find f(1). -1 1 -5 5
Answer:
f(1) = - 5
Step-by-step explanation:
substitute x = 1 into f(x)
f(1) = - 3(1)³ + (1)² - 3 = - 3(1) + 1 - 3 = - 3 + 1 - 3 = - 5
Find the derivatives of the following using increment method.1. y= 4x - 12
Given:
y= 4x - 12
Required:
Find the derivatives of the following using increment method.
Explanation:
x=4y-12
just simply switchx and y is the inverse
Required answer:
x=4y-12
How do the lower quartiles of the two sets of data compare?
Step 1
The first quartile is the value separating the lower quarter and the higher three-quarters of the data set.
The first quartile is sorted by taking the median of the lower of a sorted set.
Find the lower quartile of Milton
Arrange the data in ascending order
[tex]0,\: 54,\: 73,\: 85,\: 86,\: 89,\: 90,\: 91,\: 94,\: 95,\: 97[/tex]Take the lower half of the ascending set
[tex]0,54,73,85,86[/tex]Hence, the lower quartile of Milton is 73
Step 2
Find the lower quartile of Makenzie
Arrange the data in ascending order
[tex]84,\: 91,\: 92,\: 92,\: 93,\: 95,\: 97,\: 98,\: 98,\: 100,\: 100[/tex]Take the lower half of the ascending set
[tex]81,91,92,92,93[/tex]Hence the lower quartile of Makenzie = 92
The lower quartile of Milton is 73 and the lower quartile of Makenzie is 92. This means that the lower quartile of Makenzie is higher than the lower quartile of Milton and this is by (92-73)=19
Ahmad buys candy that costs $8 per pound. He will spend at least $56 on candy. What are the possible numbers of pounds he will buy?Use p for the number of pounds Ahmad will buy.Write your answer as an inequality solved for p.
Solution
Step 1
Cost of candy per pound = $8
Step 2
[tex]\begin{gathered} 8p\text{ }\ge\text{ 56} \\ \\ p\text{ }\ge\text{ }\frac{56}{8} \\ \\ p\text{ }\ge\text{ 7} \end{gathered}[/tex]Final answer
error analysis: describe and correct the error in solving the equation. 1) the only solution of the equation x^2+6x+9=0 is x=9
Answer:
[tex]x^2-8x-9=0\rightarrow\text{ Error-free equation}[/tex]Explanation: The only solution to the equation is x =9, we need to see if we can fix our equation such that the solution is indeed x = 9:
[tex]\begin{gathered} x^2+6x+9=0\rightarrow\cdot(1)_{} \\ \end{gathered}[/tex]Plugging in x = 9 gives us:
[tex]\begin{gathered} (9)^2+6(9)+9=0\rightarrow81+54+9=0 \\ 81+63=0\rightarrow\text{ False} \\ \therefore\rightarrow \\ 144\ne0 \end{gathered}[/tex]Fixing (1) gives us:
[tex]\begin{gathered} x^2-8x-9=0\rightarrow(2)^{}^{} \\ \therefore\rightarrow \\ (9)^2-8(9)-9=0 \\ \therefore\rightarrow \\ 81--72-9=0\rightarrow81-81=0 \\ \therefore\rightarrow \\ 81-81=0\rightarrow\text{ True} \\ \end{gathered}[/tex]Therefore (2) is the new error-free equation, and the error is corrected by replacing + to - as a sign and replacing a coefficient.
Darren went shopping and spent $19 on scarves. If he spent $.75 total, what percentage did he spend on scarves? Round your answer to the nearest percent.
The amonunt spent on scarves is $19.
The total amount spent is $75
To determine the percentage he spend on scarves .
amount spent/total amount×100
[tex]\frac{19}{75}\times100=25.34[/tex]The percentage he spent on scarves is 25.34 %.
Given v = 9i + 5j and w=i+j,a. Find projwvb. Decompose v into two vectors V, and V2, where V, is parallel to w and V2 is orthogonal to w..
We have two vectors, v and w.
a) We have to find the projection of v on w (projv w).
We can draw a projection of a vector over another as:
We can calculate the projection as:
[tex]\begin{gathered} \bar{p}=v_1\cdot\hat{w} \\ \bar{p}=|v|\cdot\cos \theta\cdot\hat{w} \end{gathered}[/tex]This means that the projection of a vector v over w is equal to the scalar projection of v over w, equal to the modulus of v times the cosine of the angle between the two vectors, times the unitary vector in the direction of w.
We can rearrange the expression as:
[tex]\begin{gathered} \bar{p}=|v|\cdot\cos \theta\cdot\hat{w} \\ \bar{p}=\frac{\bar{v}\cdot\bar{w}}{|w|}\cdot\frac{\bar{w}}{|w|} \\ \bar{p}=\frac{\bar{v}\cdot\bar{w}}{\bar{w}\cdot\bar{w}}\cdot\bar{w} \end{gathered}[/tex]This expression let us calculate the projection from the coordinates given as:
[tex]\begin{gathered} \bar{v}=(9,5) \\ \bar{w}=(1,1) \end{gathered}[/tex][tex]\begin{gathered} \bar{p}=\frac{\bar{v}\cdot\bar{w}}{\bar{w}\cdot\bar{w}}\cdot\bar{w} \\ \bar{p}=\frac{9\cdot1+5\cdot1}{1\cdot1+1\cdot1}\cdot(1,1) \\ \bar{p}=\frac{9+5}{1}\cdot(1,1) \\ \bar{p}=14\cdot(1,1) \\ \bar{p}=(14,14) \end{gathered}[/tex]The projection is (14,14) which can be decomposed as 14i + 14j.
b) We have to decompose v into two vectors: one parallel to w and the other orthogonal to w.
The vector parallel to w is the projection of v onto w, so we already know that it is 14i + 14j.
An orthogonal vector will be the projection of v onto an orthogonal vector to w.
We then have to find an orthogonal vector to w in the plane. We know that the dot product of orthogonal vectors is equal to 0.
So if we know a vector u = (a,b) it will be ortogonal if u * v = 0:
[tex]\begin{gathered} \bar{u}\cdot\bar{v}=0 \\ (a,b)\cdot(1,1)=0 \\ a+b=0 \\ a=-b \end{gathered}[/tex]Then, if we define a = -1 we will get b = 1, and u = (-1,1) that is orthogonal to vector w.
Now, we can calculate q, the projection of v onto u:
[tex]undefined[/tex]Alejandra has basketball practice two days a week. eighty- two percent of the time she attends both practices. Nine percent of the time she attends one practice. Nine percent of the times she does not attend either practice how many practices should expect alejandra to attend any given week
Answer:
1.73
Explanation:
The expected value can be calculated as:
[tex]E(x)=x_1P(x_1)+x_2P(x_2)+x_3P(x_3)[/tex]Where x1, x2, and x3 are the possible values that the variable can take and P(x1), P(x2), and P(x3) are their respective probabilities.
So, in this case, the expected value is:
[tex]\begin{gathered} E(x)=2(0.82)+1(0.09)+0(0.09) \\ E(x)=1.64+0.09+0 \\ E(x)=1.73 \end{gathered}[/tex]So, we should expect that Alejandra attends to 1.73 days of practice on a given week,
Given that R is between A and X on a segment, draw a picture and write an equationusing the Segment Addition Postulate. Then find AR and RX if AR = 5x - 15,RX = 3x + 1, and AX = 58.
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC
if and only if the distances between the points meet the requirements of the equation AB + BC = AC.
The picture can look roughly like this:
We can see that "R" is in-between "A" and "X".
From the postulate, we can write:
AR + RX = AX
Now,
Given
AR = 5x - 15
RX = 3x + 1
AX = 58,
We put it into the equation and find x first. Shown below:
[tex]\begin{gathered} AR+RX=AX \\ (5x-15)+(3x+1)=58 \\ 5x+3x-15+1=58 \\ 8x-14=58 \\ 8x=58+14 \\ 8x=72 \\ x=\frac{72}{8} \\ x=9 \end{gathered}[/tex]Since, we got x, we can easily find AR and RX. Shown below:
AR = 5x - 15
AR = 5(9) - 15
AR = 45 - 15
AR = 30and
RX = 3x + 1
RX = 3(9) + 1
RX = 27 + 1
RX = 28Find the area of the shaded region in the figure. Use the pi key for pi.The area of the shaded region in the figure is approximately: ft or ft^2(Type an integer or decimal rounded to the nearest tenth as needed.)
The area of the shaded region is equal to the area of the circle minus the area of the square, let's rember the formula to calculate the area of these figures:
[tex]\begin{gathered} A_{\bigcirc}=\frac{\pi d^{2^{}}}{4} \\ \\ A_{\square}=l^2 \end{gathered}[/tex]Remember that d is the diameter and l is the square length, then, let's apply these formulas:
[tex]\begin{gathered} A_T=A_{\bigcirc}-A_{\square} \\ \\ A_T=\frac{\pi d^2}{4}-l^2 \end{gathered}[/tex]The diameter is 3.1 ft and the length is 2.5 ft, then
[tex]\begin{gathered} A_T=\frac{\pi(3.1)^2}{4}-(2.5)^2 \\ \\ A_T=1.3\text{ ft}^2 \end{gathered}[/tex]Therefore, the area of the shaded region is 1.3 ft^2.
the equation (x+2)(2x+3)=0 has two solutions. one is an integer, the other is a fraction
Given the following euqation:
[tex]\text{ (x + 3)(2x + 3)}[/tex]Let's determine the integer solution, we'll use (x + 3).
[tex]\text{ x + 2 = 0}[/tex][tex]\text{ x + 2 - 2 = 0 - 2}[/tex][tex]\text{ x = -2}[/tex]Therefore, the integer solution is -2.
Next, let's determine the fraction solution, we'll use (2x + 3).
[tex]\text{ 2x + 3 = 0}[/tex][tex]\text{ 2x + 3 - 3 = 0 - 3}[/tex][tex]\text{ 2x = - 3}[/tex][tex]\text{ }\frac{\text{2x}}{2}\text{ = }\frac{\text{-3}}{2}[/tex][tex]\text{ x = -}\frac{3}{2}[/tex]Therefore, the fraction solution is -3/2.
In Summary,
The integer solution is : -2
The fraction solution is : -3/2
During a holiday sale, a department store offered a 25% discount on a blender that had an original price of $200. After the sale was over, the discounted price of the blender was increased by 50%. What was the price of the blender after the increase?
Answer: 100$
Step-by-step explanation:
I think it is at least :D