Warren flipped a coin and rolled a 20-sided number cube. What is the probability that his coin landed on tails and his number cube rolled a factor of 20? answer as a simplified fraction.
we have that
the probability that his coin landed on tails is
P=1/2
and
Factors of 20 are ----> 1,2,4,5,10,20
so
The probability that his number cube rolled a factor of 20 is
P=6/20=3/10
therefore
the probability that his coin landed on tails and his number cube rolled a factor of 20 is equal to
P=(1/2)*(3/10)
P=3/20What are the coordinates of vertex C'after rotating the figure 180° about theorigin?у6BID42A АEXo024 6A. (-6,4)B. (4.-6)C. (4,6)D. (-4,-6)
Vertex C (4, 6 ) Rotation 180º about the origin CCW c' (-4, -6)
C (x, y ) C ' (-x, -y )
________________
Answer
Option D
At store A, oranges are $3.99 for 5 apples. At store B oranges are $20 for 7 apples which is the better deal?
Answer:
Store A
Explanation:
To know which is the best deal, we need to find the price per apple for each store, so we need to divide the price by the number of apples.
For store A:
[tex]\frac{\text{ \$3.99}}{5\text{ Apples}}=0.798\text{ per apple}[/tex]For Store B:
[tex]\frac{\text{ \$20}}{7\text{ Apples}}=2.85\text{ per apple}[/tex]So, the best deal is Store A because the price per apple is less than the price of Store B.
find the surface area of a composite figure round to the nearest tenth if necessary to units
The composite image is that of a cuboid and a triangular prism
For the cuboid, the surface area will be
A = LB + 2BH + 2LH
L = 1.8
B= 1.1
H= 0.8
A = 1.8X1.1 + 2 X 1.1 X 0.8 + 2 X 1.8 X 0.8
A = 1.98 + 1.76 +2.88
Area of cuboid = 6.62
Complete the remainder of the table for the given rules
To complete the table you have to input each value of x in the given equation and solve for y:
Function:
[tex]y=-2x+9[/tex]For x= -2
[tex]\begin{gathered} y=-2\cdot(-2)+9 \\ y=4+9 \\ y=13 \end{gathered}[/tex]x= -2 → y=13
For x= 0
[tex]\begin{gathered} y=-2\cdot0+9 \\ y=0+9 \\ y=9 \end{gathered}[/tex]x=0 → y=9
For x= 2
[tex]\begin{gathered} y=-2\cdot2+9 \\ y=-4+9 \\ y=5 \end{gathered}[/tex]x=2 → y=5
For x= 4
[tex]\begin{gathered} y=-2\cdot4+9 \\ y=-8+9 \\ y=1 \end{gathered}[/tex]x=4 → y=1
Complete the general solution to [tex]y = arcsin - \frac{ \sqrt{3} }{2} [/tex]y=___+-2πkSelect all that apply.π/3(2π)/3(4π)/3(5π)/3
To find the general solution to y we need take the sine function in both sides of the equation given:
[tex]\begin{gathered} \sin y=\sin (\sin ^{-1}-\frac{\sqrt[]{3}}{2}) \\ \sin y=-\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Now, we have to find the value of y for which the sine function is equal to the right side. From the properties of the sine function and its definition we conclude that y has to be:
[tex]y=\frac{5\pi}{3}[/tex]Therefore the general solution is:
[tex]y=\frac{5\pi}{3}\pm2\pi k[/tex]Which of the following is equivalent to a rhombus? *O A rectangle with congruent diagonalsA parallelogram where opposite angles are congruentA parallelogram with two consecutive congruent sidesA quadrilateral where consecutive angles are supplementary
A parallelogram with two consecutive congruent sides.
1) Since a rhombus is a quadrilateral with 4 congruent sides. Then we can examine the options and state that
2) Given that a rhombus has congruent opposite angles, with four congruent sides.
3) The answer is
A parallelogram with two consecutive congruent sides.
With two consecutive sides, the whole polygon will have congruent sides.
The textbook isn't helping with the screenshot problem below.
From the frequency distribution, the measures are given as follows:
a) Total number of observations: 27.
b) The width of each class is of 5.
c) The midpoint of the second class if of 20.5.
d) The modal class is Class 12 - 17.
e) If another class was added, the limits would be 48 - 53.
What is represented by the frequency distribution?The frequency distribution gives the number of observations that is located in each class.
Hence the total number of observations is given by the sum of the frequencies, as follows:
Total = 9 + 1 + 3 + 8 + 6 = 27.
The modal class is class with the highest number of observations, hence it is of:
Class 12-17.
The width of a class is given by the subtraction of the limits, hence:
Width = 47 - 42 = ... = 23 - 18 = 17 - 12 = 5.
For an added class, the lower bound would be one more than the last class, while the upper bound would be five added to the lower bound, hence the limits are:
48 - 53.
The midpoint of each class is given by the mean of the coordinates, hence, for the second class, it is of:
Midpoint = (18 + 23)/2 = 41/2 = 20.5.
More can be learned about frequency distributions at https://brainly.com/question/24623209
#SPJ1
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials andthe probability of obtaining a success. Round your answer to four decimal places.P(X ≤ 4), n = 8, p = 0.4
Given:
n = 8, p = 0.4
To find:
P(X ≤ 4)
To determine the given probability, we will apply the binomial probability formula:
[tex]\begin{gathered} $$P(x=X)=^nC_x\times p^x\times q^{n-x}$$ \\ n\text{ = number of trials} \\ p\text{ = number of success} \\ q\text{ = number of failure} \end{gathered}[/tex][tex]P\left(X≤4\right)\text{ = P\lparen x = 0\rparen + P\lparen x = 1\rparen + P\lparen x =2 \rparen + P\lparen x = 3\rparen + P\lparen x = 4\rparen}[/tex][tex]\begin{gathered} p\text{ + q = 1} \\ q\text{ = 1- p} \\ q\text{ = 1 - 0.4} \\ q\text{ = 0.6} \\ \\ P(x=0)=\text{ }^8C_0\times(0.4)^0\times(0.6)^{8-0} \\ P(x\text{ = 0\rparen = 0.01679616} \\ \\ P(x=1)=\text{ }^8C_1\times(0.4)^1\times(0.6)^{8-1} \\ P(x\text{ = 1\rparen = 0.08957952} \end{gathered}[/tex][tex]\begin{gathered} P(x=2)=\text{ }^8C_2\times(0.4)^2\times(0.6)^{8-2} \\ P(x\text{ = 2\rparen = 0.20901888} \\ \\ P(x=3)=\text{ }^8C_3\times(0.4)^3\times(0.6)^{8-3} \\ P(x\text{ = 3\rparen = 0.27869184} \\ \\ P(x=4)=\text{ }^8C_4\times(0.4)^4\times(0.6)^{8-4} \\ P(x\text{ = 4\rparen = 0.2322432} \end{gathered}[/tex][tex]\begin{gathered} P(X≤4)\text{ = 0.01679616 + 0.08957952 + 0.20901888 + 0.27869184 + 0.2322432} \\ \\ P\left(X≤4\right)\text{ = 0.8263296} \\ \\ To\text{ 4 decimal place, P\lparen X \le4\rparen is 0.8263} \end{gathered}[/tex]What is the volume of this cube? 2 cm 2cm 2cm
Answer:
The volume is
[tex]8\operatorname{cm}^3[/tex]Explanation:
The volume of a cube with length l is given by the formula:
[tex]V=l^3[/tex]Given the length 2 cm
The volume is:
[tex]V=2^3=8\operatorname{cm}^3[/tex]2 multiplied by the square root of 8
Note that the square root of 8 is written as:
[tex]\sqrt[]{8}[/tex]2 multiplied by the square root of 8 will then be expressed as:
[tex]\begin{gathered} 2\sqrt[]{8} \\ 2\text{ }\times\sqrt[]{8} \\ 2\text{ }\times\text{ }\sqrt[]{4}\text{ }\times\text{ }\sqrt[]{2} \\ 2\text{ }\times\text{ 2 }\times\text{ }\sqrt[]{2} \\ 4\text{ }\times\text{ }\sqrt[]{2} \\ 4\sqrt[]{2} \end{gathered}[/tex]Garrick gets paid $4.70 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 46hours?a. $195.05b. $220.90c. $230.30d. $188
Solution
For this case we can calculate the total with the following formula:
Fixed amount= 40*4$.70= $188
And now for the remain hours we can do this:
Extra = 6* 1.5*$4.70= $42.3
Then the total amount is:
Fixed amount+ Extra = 188$ + 42.3$ = $230.3
Then the answer is:
c. $230.30
2500/10.5 please show work
The given expression is
2500/10.5
We would multiply the numerator and denominator by 10. We have
2500 x 10/10.5 x 10
= 25000/105
We would divide the numerator and denominator by common factors until they can't be simplified further. Dividing by 5, we have
5000/21
It can't be simplified further since there is no common factor of 5000 and 21. We would convert the fraction to mixed fraction
5000/21 = 238 remainder 2
Thus, if we write it as mixed fraction, we have
238 2/21
factorize 5m^3-10m^2+8m+2
The expression 5m³ - 10m² + 8m + 2 cannot be factorized
How to factorize the polynomial?From the question, the polynomial is given as
5m^3-10m^2+8m+2
Rewrite the polynomial properly
So, we have
5m³ - 10m² + 8m + 2
Next, we represent the above expression on a graph
From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -0.197
This implies that the expression cannot be factored
So, we cannot further rewrite the given expression
Read more about factorized expressions at
https://brainly.com/question/2750166
#SPJ1
units givenQuestion 2 (3 points)toUsing the Rectangular Prism in the picture, find the Lateral Area, the Area of a Single Base,and the TOTAL Surface Area:.12 cm825 cm10 cmUse the face with dimensions 10cm x 5cm as the base.Lateral Area =cm²Single Base Area =64188 in48cm²
Solution:
Given the rectangular prism;
Where;
[tex]\begin{gathered} length,l=10cm \\ \\ width,w=5cm \\ \\ height,h=2cm \end{gathered}[/tex]Thus, the lateral area, L is;
[tex]\begin{gathered} L=2(l+w)h \\ \\ L=2(10+5)2 \\ \\ L=4(15) \\ \\ L=60cm^2 \end{gathered}[/tex]ANSWER:
[tex]Lateral\text{ }Area=60cm^2[/tex]Also, the single base area, B, is;
[tex]\begin{gathered} B=l\times w \\ \\ B=10\times5 \\ \\ B=50cm^2 \end{gathered}[/tex]ANSWER:
[tex]Single\text{ }Base\text{ }Area=50cm^2[/tex]Then, the surface area, S, is;
[tex]\begin{gathered} S=L+2B \\ \\ S=60+2(50) \\ \\ S=60+100 \\ \\ S=160cm^2 \\ \\ \end{gathered}[/tex]ANSWER:
[tex]Surface\text{ }Area=160cm^2[/tex]Is 128 degrees plus 62 degrees supplementary or complimentary?
Let's begin by identifying key information given to us:
One angle = 128 degrees, Second angle = 62 degrees
Complementary angle are angles that sum up to 90 degrees
Supplementary angles are angles that sum up to 180 degrees
We will proceed to sum these two angles together. We have:
[tex]\begin{gathered} 128^{\circ}+62^{\circ}=180^{\circ} \\ \therefore These\text{ angles are supplementary angles since they sum up to 180 degr}ees \end{gathered}[/tex]Therefore, these angles are supplementary angles since they sum up to 180 degrees
Shaun estimated that the attendance at a college basketball game was 4,000. The actual attendance was 3,475. What is the percent error of Shaun's estimate? Round to the nearest whole percent.
Percentage = 100 * (4000 - 3475)/3475 = 100 * (525/3475) = 52500/3475 = 15.1 %
Answer:
15.1%
What should be true about the line of best fit? Check all that apply.
A. The line of best fit must have an equal number of points above and below the line.
B. The line must show the relationship between the two variables.
C. The line of best fit should minimize the distance between itself and the data points.
D. The line of best fit has to cross through at least 2 points in the scatter plot.
E. The line of best fit could be used as a prediction tool showing a trend in the data.
F. The line of best fit should be an exact representation of the data points.
The line of best fit could be used as a prediction tool showing a trend in the data and the line of best fit should minimize the distance between itself and the data points thus options (C) and (E) will be correct.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
A scatter point represents the relation or function.
If a line is used to predict the function then the distance between the points to the line must be minimized.
The line is useful for the representation of the data point.
Hence "The line of best fit could be used as a prediction tool showing a trend in the data and the line of best fit should minimize the distance between itself and the data points".
To learn more about graphs,
brainly.com/question/24861666
#SPJ1
A sample has a mean of M = 90 and a standard devia-tion of s 20.=a. Find the z-score for each of the following X values.X = 95X = 80X = 98X = 88X = 105X = 76
Answer:
[tex]\begin{gathered} X=95,z=0.25 \\ X=80,z=-0.5 \\ X=98,z=0.4 \\ X=88,z=-0.1 \\ X=105,z=0.75 \\ X=76,z=-0.7 \end{gathered}[/tex]Explanation:
Given a sample with the following:
• Mean,M = 90
,• Standard deviation, s = 20
To find the z-score for each of the given X values, we use the formula below:
[tex]\begin{equation*} z-score=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}{X=Raw\;Score} \\ {\mu=mean} \\ {\sigma=Standard\;Deviation}\end{cases} \end{equation*}[/tex]The z-scores are calculated below:
[tex]\begin{gathered} \text{When X=95, }z=\frac{95-90}{20}=\frac{5}{20}=0.25 \\ \text{When X=80, }z=\frac{80-90}{20}=\frac{-10}{20}=-0.5 \\ \text{When X=98, }z=\frac{98-90}{20}=\frac{8}{20}=0.4 \end{gathered}[/tex][tex]\begin{gathered} \text{When X=88,}z=\frac{88-90}{20}=\frac{-2}{20}=-0.1 \\ \text{When X=105, }z=\frac{105-90}{20}=\frac{15}{20}=0.75 \\ \text{When X=76, }z=\frac{76-90}{20}=\frac{-14}{20}=-0.7 \end{gathered}[/tex]14. Which points are on the graph by = 3x - 12? Select all that apply. (A) (B) (C) (D) (-2,0) (0,-2) (6,-3) (8,2) M 23 hp
6y=3x-127
Replace the values of x , y in the equation by the coordinates values given on each option, and check if the equality remains.
A. (x,y) = (-2,0)
6y=3x-127
6(0) =3(-2)-127
0 = -6-127
0= -133
zero is not equal to -133.
A. is not
B. (0,-2)
6(-2) = 3(0)-127
-12 = -127
B is not
C, (6,-3)
6(-3) = 3(6)-127
-18 = 18-127
-18 = -109
C is not
D (8,2)
6(2) = 3(8)-127
12 = 24-127
12=-103
D is not
None of the points are in the graph
Hi how are you today can you please help me with this question
$ 119.607
Explanation
we can easily solve this by using a rule of three
Step 1
Let
actual price(2020)=price of 2019 + 2%
so
actual price(2020)= 102 % and
price ( 2019)=100 %
let x represents the cost for 2019, so
[tex]\begin{gathered} \text{if} \\ 122\Rightarrow\text{ 102\%} \\ x\text{ }\Rightarrow\text{ 100 \%} \end{gathered}[/tex]the proportion would be
[tex]\begin{gathered} \frac{122}{102\text{ \%}}=\frac{x}{100\text{ \% }} \\ \text{ Multiply both sides by 100 \%} \\ \frac{122}{102\text{ \%}}\cdot100=\frac{x}{100\text{ \% }}\cdot100 \\ 119.607=x \end{gathered}[/tex]therefore, the cost in January of 2019 is
$ 119.607
I hope this helps you
solve2cos²x+3sin x=0
One of the most important trigonometric identities is the one below
[tex]\cos ^2x+\sin ^2x=1[/tex]Then,
[tex]\Rightarrow\cos ^2x=1-\sin ^2x[/tex]Use this result in the equation given by the problem
[tex]\begin{gathered} 2\cos ^2x+3\sin x=0 \\ \Rightarrow2(1-\sin ^2x)+3\sin x=0 \\ \Rightarrow2-2\sin ^2x+3\sin x=0 \end{gathered}[/tex]Furthermore,
[tex]\begin{gathered} \Rightarrow2\sin ^2x-3\sin x-2=0 \\ \Rightarrow2\sin ^2x-3\sin x=2 \\ \Rightarrow\sin x(2\sin x-3)=2 \end{gathered}[/tex]Set y=sinx
[tex]\begin{gathered} \Rightarrow y(2y-3)=2 \\ \Rightarrow y=-\frac{1}{2},y=2 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \sin x=-\frac{1}{2},\sin x=2 \\ \Rightarrow\sin x=-\frac{1}{2} \\ \text{if sinx=2, then x is not a real number} \end{gathered}[/tex]Finally,
[tex]\begin{gathered} \sin x=-\frac{1}{2} \\ \Rightarrow x=\sin ^{-1}(-\frac{1}{2})=-\frac{\pi}{6} \end{gathered}[/tex]Then, the answer is
[tex]x=-\frac{\pi}{6}+2n\pi,\text{ n is an integer}[/tex]The answer is x=-pi/6+2n*pi
if there are 36 successful outcomes in a sample size of 80 what is the sample proportion
The sample proportion is the number of successes over the sample size. That is:
36/80 = 9/20
A county is planning to expand its train service. To better understand the current service, the county planner looked at which train stations are along or not along various train lines
Solution
(a)
5 stations are along the orange line
(b)
8 stations
Find the largest angle of △TUV. Assume that s is a positive number.
Remember that
In any triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle
so
In this problem
the largest interior angle is opposite to the longest side (TU)
that means
the largest interior angle isA pyramid has a square base with sides of length s. The height of the pyramid is equal to of the length of a side on the base. Which formularepresents the volume of the pyramid?OA. V = ¹8³OB. V=¹8³OC. V=8³OD. V=35³OE V=65³
Given,
The measure of the length of the side of square is s.
The height of the pyramid is 1/2 of the length of the side.
Required
The volume of the square pyramid.
The formula for the volume of the square pyramid is,
[tex]Volume\text{ =}\frac{side\times side\times height}{3}[/tex]Substituting the values then,
[tex]\begin{gathered} Volume\text{ =}\frac{s\times s\times s}{3\times2} \\ =\frac{s^3}{6} \end{gathered}[/tex]Hence, the volume of the pyramid is s^3/6.
The number of fish in a fish tank doubles each week. The function y=equals 3 (2)^x represents the population, where X is the number of one week periodsa. Describe the domains and range of the function. Then graph the functionb. Find and interpret the y intercept c. How many fish are in the tank at the end of first week?d. How many fish are in the tank after 4 weeks?
a. The domain of the function is the set of values of the independent variable (x) on which the function acts, in this case, the independent variable is time, since the time can only take positive values, the domain would be [0,∞) or x≥0.
The range is all the possible values that the dependent variable can take, in this case, the dependent variable is the population of fish, then it can't be a negative number, since you can't have for example -1 fish, then, again, the interval would be [0,∞) or y≥0
A graph of the function looks like this:
b. We can find the y-intercept by making x equals 0 in the formula of the function, like this:
y= 3*(2)^x
y= 3*(2)^0
y= 3*1, since any number raised to zero equals 1
y=3
Since x equals zero represents the initial time, the y-intercept represents the initial population of fish, then at the beginning, there were 3 fish.
c. We just have to replace 1 for x, and then calculate y, like this:
y= 3*(2)^x
y= 3*(2)^1
y= 3*(2)
y=6
At the end of the first week, there will be 6 fish.
d. Now, we just have to replace 4 for x, like this:
y= 3*(2)^4
y= 3*16
y=48
Then, after 4 weeks, there will be 48 fish
I need help with this question please1) Picture2) In(2x) + ln(7) = 4
1) We must solve for x the following equation:
[tex]e^{5x}=25.[/tex]To solve this equation, we take the natural logarithm to both sides of the equation:
[tex]\begin{gathered} \ln (e^{5x})=\ln (25), \\ 5x\cdot\ln e=\ln 25. \end{gathered}[/tex]Now, we use the following results:
[tex]\begin{gathered} \ln e=1, \\ \ln (25)=\ln (5^2)=2\cdot\ln 5. \end{gathered}[/tex]Replacing these results in the equation above, we have:
[tex]5x=2\cdot\ln 5.[/tex]Solving for x, we get:
[tex]x=\frac{2}{5}\cdot\ln 5\cong0.64.[/tex]2) We must solve for x the following equation:
[tex]\ln (2x)+\ln (7)=4.[/tex]To solve this problem, we isolate the part that involves the x:
[tex]\ln (2x)=4-\ln (7)\text{.}[/tex]Now, using the following property:
[tex]\ln y=z\rightarrow y=e^z\text{.}[/tex]with:
[tex]\begin{gathered} y=2x, \\ z=4-\ln 7. \end{gathered}[/tex]we have:
[tex]\ln (2x)=4-\ln 7\rightarrow2x=e^{4-\ln 7}.[/tex]Solving the last equation for x, we get:
[tex]x=\frac{1}{2}\cdot e^{4-\ln 7}\cong3.90.[/tex]Answers
1) The value of x that solves the first equation is 0.64 to two decimal places.
2) The value of x that solves the second equation is 3.90 to two decimal places.
Review of the base of a logarithm
We can define the logarithm in base a through the following equations:
[tex]\begin{gathered} \log _aa=1, \\ \log _aa^x=x\cdot\log _aa=x\cdot1=x\text{.} \end{gathered}[/tex]When we use as a base the Euler number e ≅ 2.718, the logarithm is called "natural" and we use the following notation for it:
[tex]_{}\log _e=\ln .[/tex]With this notation, we have the following properties:
[tex]\begin{gathered} \ln e=1, \\ \ln e^x=x\cdot\ln e=x\cdot1=x\text{.} \end{gathered}[/tex]Ronald was 1.5 times olderthan Megan. If Ronald was 27years old, how old is Megan?Write an equation to solve.
Solution:
Let x represent Ronald's age, and y represent Megan's age.
Thus,
[tex]\begin{gathered} x\Rightarrow Ronald^{\prime}s\text{ age} \\ y\Rightarrow Megan^{\prime}s\text{ age} \end{gathered}[/tex]Given that Ronald was 1.5 times older than Megan, we have the equation to be represented
[tex]x=1.5y\text{ ---- equation 1}[/tex]If Ronald was 27 years old, we have
[tex]x=27[/tex]Substituting the value of 27 for x into equation 1, we have
[tex]\begin{gathered} 27=1.5y \\ solve\text{ for y by dividing both sides by the coefficient of y,} \\ \frac{27}{1.5}=\frac{1.5y}{1.5} \\ \Rightarrow y=18 \end{gathered}[/tex]This implies that Megan's age is
[tex]18\text{ years}[/tex]The lowest airport in the world is Atyrau Airport in Kazakhstan at 72 feet below sea level. How would we represent this elevation using negative numbers? 6.NS.5
ANSWER
-72 ft
EXPLANATION
We can draw a number line:
If the 0 of the number line is sea level, we would normally say that all positive numbers are those that are above sea level and negative numbers those that are below sea level.
Therefore, to represent an elevation that is below sea level, we'd write it as a negative number: -72 ft
21. The table below shows the frequency of chirps for the striped ground cricket compared to the ambient temperature, in degrees Fahrenheit.Chirps per SecondTemperature208916722093188417811675157017821569Draw a scatterplot for this data, using x to represent the chirping frequency and y to represent temperature.131415161718192021226768697071727374757677787980818283848586878889909192939495
Using a graphing calculator :
The scatter plot will look thus: