Explanation:
The probability of getting a head when you flip a coin = 50% = 1/2
If the coin is flipped three times :
= 1/2 in three places
= 1/2 × 1/2 × 1/2
= 1/8
If the probability is in f percent
AWS Managemer Consider the equation 4x – 3y = 9. Write the equation in slope-intercept form, y = mx + b, and then determine the slope. The slope i I don't 4/3 -(4/3) -3 4
Given the equation :
[tex]4x-3y=9[/tex]we need to write the given equation in slope - intercept form
The general slope intercept form is :
[tex]y=m\cdot x+b[/tex]So, we need to convert the 4x - 3y = 9 to the previous form
So, solve the given equation for y ( make y alone on the left side )
So,
[tex]4x-3y=9[/tex]Subtract (4x) from both sides
[tex]\begin{gathered} 4x-3y-4x=9-4x \\ \\ -3y=-4x+9 \end{gathered}[/tex]Divide all terms by -3
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-4x}{-3}+\frac{9}{-3} \\ \\ y=\frac{4}{3}x-3 \end{gathered}[/tex]So, the slope will be the coefficient of x = 4/3
Slope = 4/3
Consider the following functions: f(x) = sqrt(x - 3) and g(x) = 4 . Step 2 of 3: Find four ordered pairs that satisfy the function, g(x) = 4
Given the function below:
[tex]g(x)=4[/tex]This equation is an equation of a horizontal line. This means that for a horizontal line, the y-coordinates will be constant for any point on the line while the x-coordinates will take any value.
Using our x-coordinate values to be -1, 1, 2 and 3, the required coordinate pairs for the function g(x) = 4 will be;
[tex](-1,4),(1,4),(2,4),(3,4)[/tex]Note that any values can be used as the x-coordinates since they all lies on the horizontal line
Fill in the missing reasons to correctly complete the proof.
For the first question, how do you know that
[tex]\begin{gathered} \bar{AB}\parallel\bar{CD}; \\ \bar{AD}\parallel\bar{BC} \\ \text{ and these segments are crossed by cross-segment }BD \\ \end{gathered}[/tex]Then, then angles
[tex]\begin{gathered} \angle ABD \\ \text{and} \\ \angle CDB \end{gathered}[/tex]satisfy the definition of alternate interior angles
The same goes for angles
[tex]\begin{gathered} \angle ADB \\ \text{and} \\ \angle CBD \end{gathered}[/tex]Therefore, for the first question, the correct answer is Alternate interior angles are congruent.
For the second question, you know that
[tex]\begin{gathered} \angle ABD\cong\angle CDB \\ \angle ADB\cong\angle CBD \\ \text{and} \\ BD\cong BD \end{gathered}[/tex]And this satisfies the triangle congruence theorem ASA (Angle-side-Angle).
Therefore, for the second question, the correct answer is ASA Triangle Congruence Theorem.
For the third question, since you already know that the triangles ABD and CDB are congruent, then the respective segments that make up the triangles will also be congruent.
Therefore, for the third question, the correct answer is Corresponding parts of congruent triangles are congruent.
−7m+4<−45 Solve the inequality by entering the correct answer
So, given:
[tex]-7m+4<-45[/tex]We're going to solve this inequality as follows:
[tex]\begin{gathered} -7m<-49 \\ m>-\frac{49}{-7} \\ m>7 \end{gathered}[/tex]Then, the answer is m>7.
Answer:
m>7
Step-by-step explanation:
Without graphing, decide whether the system of equations has one solution, no solution, or infinitely many solutions.How many solutions does the system of equations have?y=4x+5y=-4x+5One solutionNo solutionInfinitely many solutions
Answer:
One solution
Explanation:
Given the system of equations:
[tex]\begin{gathered} y=4x+5 \\ y=-4x+5 \end{gathered}[/tex]If you compare the two lines, the slopes are different.
Thus, the system of equations has only one solution.
Pretest: Coordinate Geometry4Line segment PQ is a directed line segment beginning at P(6,-5) and ending at Q(-2,4).Find point R on The line segment PQ that partition it into the segments PR and RQ in the ratio 3:2
Given:
The point is that P and Q
[tex]\begin{gathered} P(6,-5) \\ \\ Q(-2,4) \end{gathered}[/tex]The point of ratio is:
[tex]m:n=3:2[/tex]Find-:
The point of "R"
Explanation-:
If the line ratio is m:n is:
[tex]\begin{gathered} A=(x_1,y_1) \\ \\ B=(x_2,y_2) \end{gathered}[/tex]Point "C" is:
[tex]C=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]The given point and ratio is:
[tex]\begin{gathered} m:n=3:2 \\ \\ P=(x_1,y_1)=(6,-5) \\ \\ Q=(x_2,y_2)=(-2,4) \end{gathered}[/tex][tex]R=(\frac{3(-2)+2(6)}{3+2},\frac{3(4)+2(-5)}{3+2})[/tex]The point so,
[tex]\begin{gathered} R=(\frac{-6+12}{5},\frac{12-10}{5}) \\ \\ \\ R=(\frac{6}{5},\frac{2}{5}) \\ \\ \end{gathered}[/tex]The point of R is (6/5, 2/5)
- Area & perime... Sina wants to paint two walls on her bedroom. One wall has the dimensions 2.7 mx 4 m and the other 2.7 mx 3 m. If a door with dimensions of 1 mx 2.3 m is in one of the walls, what is the total area of the wall that Sina needs to paint? m2 ........
In order to determine the area tota that Sina needs to paint, first, calculate the area of both walls
[tex]\begin{gathered} \text{Wall}_1=2.7\cdot4 \\ \text{Wall}_1=10.8m^2 \\ \text{Wall}_2=2.7\cdot3 \\ \text{Wall}_2=8.1m^2 \end{gathered}[/tex]then, calculate the area of the door
[tex]\begin{gathered} \text{Door}=1\cdot2.3 \\ \text{Door}=2.3m^2 \end{gathered}[/tex]Finally, add the area of both walls and subtract the area of the door
[tex]\begin{gathered} 10.8+8.1-2.3 \\ 16.6m^2 \end{gathered}[/tex]Sina needs to paint 16.6 square meters.
Help me out please I don’t understand what I’m foing
We are given the equation, y= 2x
The graph can be obtained by finding at least two points.
First point:
when x = 0,
[tex]\begin{gathered} y\text{ = 2}\times\text{ 0 } \\ =\text{ 0} \end{gathered}[/tex]The first point (0,0)
Second point:
when x = 1,
[tex]\begin{gathered} y\text{ = 2}\times\text{ 1} \\ =\text{ 2} \end{gathered}[/tex]Second point (1, 2)
The graph of the line is shown below:
Help please! Answer both, it's all one question.2 0 C H A R E C T E R S
Pocahontas has a container with 4/5 of a quart of lemonade. She pours an equal amount into 2 cups. There’s still 1/2 of a quart of lemonade remaining in the container. How much lemonade, and quartz, is poured into each cup?
Given
Container has 4/5 of a quart
She use 2 cups and there’s still 1/2 of a quart
Then, we have the following expressions:
Let x amount of a quart into 2 cups.
[tex]\begin{gathered} x+\frac{1}{2}=\frac{4}{5} \\ \end{gathered}[/tex]So, solve for x:
[tex]undefined[/tex]find the slope, starting point and equation of each of the graphs
From the graph
The line passing through points (-1, 4) and (4, -4)
We will use these points to find the slope of the line
The rule of the slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=-1 \\ y_1=4 \\ x_2=4 \\ y_2=-4 \end{gathered}[/tex]Let us substitute these values in the rule
[tex]m=\frac{-4-4}{4-(-1)}=\frac{-8}{5}=-1.6[/tex]The form of the equation is
y = m x + b
m is the slope
b is the y-intercept
Substitute m by -1.6
y = -1.6 x + b
To find b substitute x and y by the coordinates of a point on the line
x = -1 , y = 4
4 = -1.6(-1) + b
4 = 1.6 + b
Subtract 1.6 from both sides
4 - 1.6 = 1.6 - 1.6 + b
2.4 = b
Substitute the value of b in the equation
y = -1.6 x + 2.4
The slope = -1.6
y-intercept = 2.4
Equation : y = -1.6 x + 2.4
Graph a 4th degree or higher polynomial function whose graph never cross the horizontal axis more than once
Answer:
[tex]f\mleft(x\mright)=x^4[/tex]Step-by-step explanation:
The Fundamental Theorem of Algebra states that the degree of a polynomial is the maximum number of roots the polynomial has.
For polynomials, the degree of the polynomial represents how many times the function crosses the x-axis or the zeros it has. Then if we want to graph a 4th degree or higher polynomial that crosses the horizontal axis no more than once:
[tex]f\mleft(x\mright)=x^4[/tex]First year students of Harvard university embarked on an excursion to Paris and travelled half the distance at 45km per hour and the other half at 55km per hour. Find the average speed for the whole journey
SOLUTION:
Step 1:
In this question, we are given the following:
First year students of Harvard university embarked on an excursion to Paris and travelled half the distance at 45km per hour and the other half at 55km per hour. Find the average speed for the whole journey.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} We\text{ can see that the total distance = 45 km + 55 km = 100 km} \\ Average\text{ distance = }\frac{45\text{ km + 55km}}{2}=\frac{100\text{ km }}{2}=\text{ 50 km} \end{gathered}[/tex][tex]\begin{gathered} Time\text{ spent in the first half of the journey = }\frac{Average\text{ Distance}}{speed_1} \\ =\text{ }\frac{50}{45}\text{ hours} \end{gathered}[/tex][tex]Time\text{ spent in the second part of the journey = }\frac{Average\text{ Distance}}{speed_2}[/tex][tex]=\frac{50\text{ }}{55}\text{ hour}[/tex]Then, the average speed for the whole journey will be:
[tex]\frac{Total\text{ Distance}}{Time\text{ spent in the first journey + Time spent in the second journey}}[/tex][tex]=\frac{100\text{ }}{(\frac{50}{45})\text{ + \lparen}\frac{50}{55})}[/tex][tex]=\text{ }\frac{100}{\frac{200}{99}}\text{ = 100 x }\frac{99}{200}=\text{ }\frac{99}{2}=\text{ 49.5 km per hour}[/tex]CONCLUSION:
The average speed for the whole journey =
[tex]49.\text{ 5 km per hour}[/tex]stion 1 OT 5A researcher recorded the number of swans and the number of ducks in a lake every month. Function s represents the number ofswans and function d represents the number of ducks in a lake after n months.s(n) = 2(1.1)" + 5d(n) = 4(1.08)" + 3Which function can be used to determine the total number of ducks and swans in the lake after n months?o++t(n) = 2 (1.1)” + + 2(1.0R)" + 4Ot(n) = 2[2(1.1)" + (1.08)" + 4t(n) = 4 (1.1)” + 2(1.08)” + 2)ot(n) = 2 (1.1)”. + 2(1.08)" + 2]++SubmitReset
Given functions are
[tex]s(n)=2(1.1)^n+5_{}[/tex][tex]d(n)=4(1.08)^n+3[/tex]The total number of ducks and swans in the lake after n months can be determined by adding the functions s(n) and d(n).
[tex]t(n)=s(n)+d(n)[/tex][tex]t(n)=(2(1.1)^n^{}+5)+(4(1.08)^n+3)[/tex][tex]t(n)=2(1.1)^n+5+4(1.08)^n+3[/tex][tex]t(n)=2(1.1)^n+4(1.08)^n+5+3[/tex][tex]t(n)=2(1.1)^n+4(1.08)^n+8[/tex]Taking 2 as common, we get
[tex]t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack[/tex]Hence The total number of ducks and swans in the lake after n months is
[tex]t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack[/tex]Use the triangle to find the tan o. Write answer as an unsimplified fraction and as a decimal rounded to 3 decimal places.a = 2.4' b = 3.2' C= 4.0'
Given:
[tex]\begin{gathered} a=2.4^{\prime} \\ b=3.2^{\prime} \\ c=4.0^{\prime} \end{gathered}[/tex]To find:
[tex]tan\theta[/tex]Explanation:
Using the trigonometric ratio for tangent,
[tex]\begin{gathered} tan\theta=\frac{Opp}{Adj} \\ tan\theta=\frac{b}{a} \\ tan\theta=\frac{3.2}{2.4} \end{gathered}[/tex]In decimal, we get
[tex]tan\theta=1.333[/tex]Finalanswer:
[tex]\begin{gathered} tan\theta=\frac{3.2^{\prime}}{2.4^{\prime}} \\ (or) \\ tan\theta=1.333 \end{gathered}[/tex]Let U = (x|= € 2), A = {x|x is an integer greater than 30| . and B = (32, 33, 34, 35). Select the Venn diagram that represents U, A, and B.
Based on the question, here are the given sets:
1. U is a set of all number x where x is an integer.
2. A is a set of all number x where x is an integer greater than 30.
3. B is set that contains the integers 32, 33, 34, and 35.
From this, we can imagine that the set U contains Set A and B since all are integers in both sets while Set Set A contains Set B since Set B contains integers that are greater than 30.
The venn diagram that represents this is:
I need to know which the flip transaction is I just need to know the answer
We have two trapezoids: A and B.
B is the image of A after at least two transformations.
One of the transformations is a reflection. We can find what type of reflection by looking at how two of the vertices or the sides are transformed.
We can see that if we take the longest base and the shortest base, they have their image on the other side of the horizontal axis. Then, we can conclude, as there is no change in the shape, that this transformation is a reflection across the horizontal axis (x-axis).
The other transformation is a translation along the horizontal axis.
We can calculate how many units it is translated by identifying one vertex and its image. We can see it in the graph like this:
We can see that, after the reflection, the point is translated 9 units to the right. This will happens for all the points in the pre-image, but we use one point to find the distance.
Then, we can list the transformations:
0. Reflection across the x-axis.
,1. Translation 9 units to the right.
Answer:
reflection across the x-axis, then translation 9 unit squares to the right [Option B]
V 4 What is the length of x in this 45-45-90 triangle? 45 X 4/2 453 4 8
asdasdasdasdasdasdasdasdasdsasdasd
Answer:
are you just trying to say asda or an actual question???
7) The population of a city that is 200 square miles is 2.5 million. What is the population density per square mile of the city?
+Express the formula for population density.
[tex]\text{Population density=}\frac{Number\text{ of people}}{\text{Land Area}}[/tex]Calculate the population density.
[tex]\begin{gathered} \text{Popuylation density=}\frac{2.5\times10^6}{200} \\ =12500 \end{gathered}[/tex]Hence, Option D is right.
5. Draw 2 line segment of different lengths that both have M as a midpoint.
Step 1: Write out the coordinate of the midpoint
[tex]M(-2,-3)[/tex]Step 2: Find the coordinates of the two line segments by testing for values that will yeild the midpoint coordinates
[tex]\begin{gathered} \text{ Since the midpoint M is at (-2,-3), then} \\ M(-2,-3)\Rightarrow(x_m,y_m) \\ x_m=\frac{x_1+x_2}{2}=-2 \\ y_m=\frac{y_1+y_2}{2}=-3 \end{gathered}[/tex][tex]\begin{gathered} \text{Thus,} \\ x_1+x_2=-2(2)=-4 \\ y_1+y_2=-3(2)=-6 \end{gathered}[/tex]From the above, we can deduce to four values that will give -4 for the x-values and -6 for the y-values.
[tex]\begin{gathered} \text{For the first line segment},\text{ say line AB} \\ x_1+x_2=-6+2=-4,x_1=-6,x_2=2 \\ y_1+y_2=-9+3=-6,y_1=-9,y_2=3 \\ \text{Therefore, line AB coordinate is } \\ A(-6,-9),B(2,3) \end{gathered}[/tex][tex]\begin{gathered} \text{For the first line segment},\text{ say line CD} \\ x_1+x_2=-10+6=-4,x_1=-10,x_2=6 \\ y_1+y_2=-14+8=-6,y_1=-14,y_2=8 \\ \text{Therefore, line AB coordinate is } \\ C(-10,-14),D(6,8) \end{gathered}[/tex]Step 3: Draw the two lines segment on a cartesian plane showing M as the common midpoint.
X<0 need interval notation with steps to complete
Part a
we have the inequality
[tex]x\leq4[/tex]The solution in interval notation is equal to
(-infinite, 4]
because the number 4 is included, is a closed interval
Part b
we have the values of x [0,1,2,3,4,5,6,7,8]
the solutions for the given inequality are
[0,1,2,3,4]
we have
x< 0
the solution is the interval
(-infinite, 0)
In a number line, the solution is the shaded area at the left of x=0 (open circle)
x< 3
the solution is the interval
(-infinite, 3)
In a number line, the solution is the shaded area at the left of x=3 (open circle)
How can you use 3 X5 = 15 to help find 6 X 5 ?3rd grade subject
Given,
The expression is 3 X 5 = 15
The value of 6 X 5 is,
Taking the given expression as,
[tex]6\times5=(3+3)\times5[/tex]By distributive property,
[tex]\begin{gathered} 6\times5=3\times5+3\times5 \\ =15+15 \\ =30 \end{gathered}[/tex]Hence, the value of 6 X 5 is 30.
if i multiplied 3.625 x 10^-8 by 500, then reported my product in scientific notation what was the exponent in my product
From the given question,
There are given that exponent form is:
[tex]3.625\times10^{-8}[/tex]Now,
Multiply 500 with given form
[tex]3.625\times10^{-8}[/tex]So,
[tex]500\times3.625\times10^{-8}=1812.25\times10^{-8}[/tex]Then the reprted this answer in scientific notation.
According to scientific notation is way of representing between 1 and 10 including 1 and excluding 10 multiplied by appropriate power of 10.
Now,
In given result , we move the decimal 3 times to left side.
Since, the decimal is moved left side, we multiply by
[tex]10^3[/tex]Then,
[tex]\begin{gathered} 1812.5\times10^{-8}=1.8125\times10^3\times10^{-8} \\ =1.8125\times10^{-5} \end{gathered}[/tex]So,
The exponent is quantity represent the power to which a given number or expression is to be raised.
Then,
[tex]1.8125\times10^{-5}[/tex]Hence, the exponent is -5.
Sophia and Emily are twin sisters and best friends. They're saving up for concert tickets and agreed to pay for the tickets together when they have enough money. They both created equations to see how fast they were making money and came up with the following expressions: Sophia: 35w + 55 - 10w where w is the number of weeks they have been saving Emily: 28w +75 - 5w + 12 (a) Combine their expressions to see how much they are making together. (b) Using the expressions see if they will have above $350 in four weeks. If not how much will they be short?can I show you the image
ANSWER
a) 48w + 142
b) No; $16 short
EXPLANATION
Sophia's equation is:
35w + 55 - 10w
Emily's equation is:
28w + 75 - 5w + 12
a) Combining their equations we have that, they money they would make together is:
35w + 55 - 10w + 28w + 75 - 5w + 12
Collect like terms:
35w - 10w + 28w - 5w + 55 + 75 + 12
48w + 142
That is the combined equation.
b) We want to see if they will make $350 after 4 weeks.
We will make w = 4 and then find the money they have made.
=> Money made = 48(4) + 142
Mm = 192 + 142
Money made = $334
They will not have above $350.
The difference in their money made and $350 is:
350 - 334
= $16
They will be $16 short.
What is the sum of the geometric series in which a1 = 2, r = 3, and an = 486?
In order to determine the sum of the geometric series, proceed as follow:
Use the following expression for an:
[tex]a_n=a_1r^{n-1}[/tex]where,
a1 = 2
r = 3
an = 486
Replace the previous values into the expression for an, solve for n and simplify:
[tex]\begin{gathered} 486=2\cdot3^{n-1} \\ \frac{486}{2}=3^{n-1} \\ 243=3^{n-1} \\ 3^5=3^{n-1} \end{gathered}[/tex]Then, it is necessary that n = 6, because n - 1 = 6 - 1 = 5 and the previous equation is consistent.
Now, consider that the sum of the geometric series is given by:
[tex]S_n=a_1(\frac{1-r^n}{1-r})[/tex]Replace the values of the parameters and simplify:
[tex]S_6=2(\frac{1-3^6}{1-3})=2(\frac{1-729}{-2})=728[/tex]Hence, the result is 728
which term best deacribes the statment given below if a = b and b= c then a=c
Answer:
Transitive property of numbers
Explanation:
Given three integers a, b and c. If the intergers are expressed as a = b, b = c and a =c, the term that explains the statement is the Transitive property of numbers
A brand of pen claims that it lasts twice as long as a normal pen. Janemeasures how long the pen lasts and puts that information in a chart. What isJane recording?A. ClaimsB. DataO C. ExplanationD. Hypothesis
Since the information is recorded in a chart, Then jane is recording a data.
[tex] - 4y ^{3 } - 16y^{2} - 12 - 4[/tex]divide the polynomiala. simplify the answer as much as possible
The given polynomial :
[tex]\frac{-4y^3-16y^2-12}{-4}[/tex]Divide each term of the numerator by 4:
[tex]\begin{gathered} \frac{-4y^3-16y^2-12}{-4}=\frac{-4y^3}{-4}-\frac{16y^2}{-4}-\frac{12}{-4} \\ \frac{-4y^3-16y^2-12}{-4}=y^3+4y^2+3 \end{gathered}[/tex]Answer : y³ + 4y² + 3
Formula SheetCalculator RefeAn artist is designing a sculpture for a park. A drawing of the sculpture uses a scale of 2 inches = 3 feet. Thesculpture will have a height of 7.5 feet. What is the height, in inches, of the sculpture in the scale drawing?11.25O2.53.755.0
Solution:
Given:
[tex]2inches=3feet[/tex][tex]\begin{gathered} 2inches=3feet \\ x=7.5feet \\ \\ Cross\text{ multiplying;} \\ 3x=2\times7.5 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5inches \end{gathered}[/tex]Therefore, the height in inches of the sculpture in the scale drawing is 5.0