the statement say us the rate of winning is 3/4 then the probability is the same
but performance it on decimals
[tex]\frac{3}{4}=0.75[/tex]probability is 0.75
write an equation of the line in the point- slope form that passes through the given points in the table. Then write the equation in slope-intercept form. (10,80) (15,95)
We know that the line passes through the points (10,130) and (20,200).
First, we have to find the slope with the following formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=10 \\ ^{}x_2=15^{} \\ y_1=80 \\ y_2=95 \end{gathered}[/tex]Replacing these coordinates, we have
[tex]m=\frac{95-80}{15-10}=\frac{15}{5}=3[/tex]The slope is 7.
Now, we use one point, the slope, and the point-slope formula to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-80=3(x-10) \end{gathered}[/tex]Therefore, the point-slope form of the line is[tex]y-80=3(x-10)[/tex]1. Reasons quantitatively. AB lies on the number line. The coordinate of point A is -6. Given thay AB = 20, what are two possible coordinates for point B?2. Given: Point K is between points H and J, HK = x - 5, KJ = 5x - 12, and HJ = 25. Find the value of x.
The distance in a coordinate line is given by:
[tex]d(A,B)=\lvert B-A\rvert[/tex]in this case we know that A=-6 and we would like to know the value of B so that the distance is 20. Plugging this values in the equation we have:
[tex]\begin{gathered} \lvert B-(-6)\rvert=20 \\ \lvert B+6\rvert=20 \end{gathered}[/tex]Now we need to remember the property:
[tex]\begin{gathered} \lvert x\rvert=a \\ \text{implies} \\ x=\pm a \end{gathered}[/tex]Using this we have:
[tex]\begin{gathered} \lvert B+6\rvert=20 \\ B+6=\pm20 \\ B=-6\pm20 \end{gathered}[/tex]Then:
[tex]\begin{gathered} B=-6+20=14 \\ B=-6-20=-26 \end{gathered}[/tex]Therefore the two possible coordinates for B are 14 and -26.
A passcode to enter a building is a sequence of 4 single digit numbers (0-9), and repeated digits aren'tallowed.Suppose someone doesn't know the passcode and randomly guesses a sequence of 4 digits.What is the probability that they guess the correct sequence?
ANSWER
0.0001984
EXPLANATION
There are 10 possible values for each digit of the passcode to enter the building.
These include: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
So, there are:10 x 10 x 10 x 10 = 10^4 = 10,000 total possible passcodes.
For no repeat passcode
We have: 10 x 9x 8 x7 = 5040 total possible passcodes without repetition.
Probability of guessing correct sequence
Since there is only 1 correct sequence of 4 digits passcode (without repetition) to enter the building
[tex]\begin{gathered} Prob\text{ = }\frac{1}{5040} \\ Prob\text{ = 0.0001984} \end{gathered}[/tex]Hence, the probability that they guess the correct sequence is 0.0001984
Graph ABCD with vertices B(2, 1), C(4,4) and D(4,0) and its image after the reflection in the line n: x=0.
We have a triangle BCD with vertices
[tex]\lbrace(2,1),(4,4),(4,0)\rbrace[/tex]The transformation is a reflection in the line x = 0(also know as the y-axis). A reflection on the y-axis is given by the following transformation:
[tex](x,y)\rightarrow(-x,y)[/tex]Doing this transformation on each one of our vertices, we can find the transformed figure.
[tex]\begin{gathered} (2,1)\rightarrow(-2,1) \\ (4,4)\rightarrow(-4,4) \\ (4,0)\rightarrow(-4,0) \end{gathered}[/tex]Then, the image is
[tex]\lbrace(-2,1),(-4,4),(-4,0)\rbrace[/tex]The option that fits this transformation is option b.
The male and female guests attending Patricia's party were surveyed to see if they drove to the party or did not drive. The data is displayed in the table below: MaleFemale 26 24 drove to the party 34 116 did not drive to the partyIf a guest is chosen at random from this group, what are the chances of choosing a guest who is male and did not drive to the party? 12%13%17%58%
The given table is
Male Female Total
Drive 26 24 50
Did not drive 34 116 150
Total 60 140 200
From the table, total number of males and females = 200
number of guests that are males and did not drive = 34
Recall, Probability is expressed as
number of favorable outcomes/number of total outcomes
Therefore, the chances of choosing a guest who is male and did not drive to the party is
34/200 = 0.17
By converting to percentage, it is
0.17 x 100 = 17%
1. Do you the following side lengths form a right triangle?2. Which measurement is closest to the value of X in centimeters?
Answer:
Part 1:
Yes, the side lengths form a right triangle.
Part 2:
Option d 37.1 cm
Explanation:
We need to use the pythagorean theorem.
In part 1, if the 3 side lengths are a right triangle, then, they must verify:
[tex]7.5^2=4.5^2+6^2[/tex]By the theorem. Then:
[tex]\begin{gathered} 7.5^2=56.25 \\ 4.5^2+6^2=20.25+36=56.25 \end{gathered}[/tex]They're equal, then the lengths correspond to a right triangle.
For part 2, we need to use again the theorem. In this case:
[tex]\begin{gathered} 12^2+x^2=39^2 \\ x=\sqrt{1521-144} \\ x=\sqrt{1377} \\ x\approx37.1cm \end{gathered}[/tex](4a²b) ?Simplify:(2a3b4)32a5710AB.4ab63с225510D4ab53
We would apply the following laws of exponents
(x^y)^z = x^(yz)
a^c * a^d = a^(c + d)
a^c / a^d = a^(c - d)
The given expression is
(4a^2b)^2/(2a^3b^4)^3
By applying the first law above, it becomes
[4^2a^(2*2)b^2]/[2^3a^(3*3)b^(4*3)]
= [16a^4b^2]/[8a^9b^12]
by applying the second and third laws, we have
16/8 * a^(4 - 9) * b^(2 - 12)
= 2a^-5b^-10
Also, x^-1 = 1/x
Thus, the final expression would be
2/a^5b^10
Option C is correct
Given the circle below with radius 5y centimeters, find its area. Do not approximate [tex]\pi[/tex]. ( A = [tex]\pi r^{2}[/tex] )
The area of the given circle as represented in the image attached in the task content is; 550y² / 7.
What is the area of the given circle as in the task content?It follows from the task content that the area of the given circle is to be determined without approximating π.
Since the area of a circle is given by the formula;
A = π r²
where the radius, r = 5y.
The area of the circle is therefore;
A = π ( 5 y )²
The area of the circle is therefore;
A = 25 π y².
Hence, by substitution of 22 / 7 for π;
Area, A = 550y² / 7.
Ultimately, it can be inferred from the solution above that the area of the circle which is as described is; 550y² / 7.
Read more on area of a circle;
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1 foot= 12 inches 2 feet= inches
Solution
We are given that
[tex]1\text{ foot = 12 inches}[/tex]To find
[tex]\begin{gathered} \text{2 f}eet\text{ = 2}\times12\text{ inches} \\ \text{2 f}eet\text{ =}24\text{ inches} \end{gathered}[/tex]Please help me if you can! in the image it shows a problem I need guidance on.
We can use trigonometric functions to determine how far it is across the lake.
Here, use tangent of angle A:
[tex]\begin{gathered} \tan 40^o=\frac{a}{630} \\ 0.839=\frac{a}{630} \\ 0.839\times630=a \\ 528.632=a \end{gathered}[/tex]Thus, the lake is 529 yards across.
Question 12Which equation contains a perfect square trinomial?O x2 - 6x + 72 = 0O x2 + 2x - 4 = 0O2? + 14x + 49 = 0O x2 – 5x + 64 = 0
A perfect square trinomial has a general structure which is
[tex]a^2\pm2ab+b^2[/tex]The one that meets this structure is
[tex]x^2+14x+49[/tex]We know it because it can be re written as
[tex]x^2+2\cdot7\cdot x+7^2[/tex]Which shows in a more explicit way the estructure of a perfect square trinomial. The right answer is c
x - 51Solve for x:42
Answer : x = 7
[tex]\begin{gathered} \text{Solve for x: }\frac{x\text{ - 5}}{4}\text{ = }\frac{1}{2} \\ \text{Firstly, introduce cross multiplication} \\ 2(x\text{ - 5) = 4 x 1} \\ \text{Open the parenthesis} \\ 2\cdot x\text{ - 2}\cdot5\text{ = 4} \\ 2x\text{ - 10 = 4} \\ \text{Make 2x the subject of the formula} \\ 2x\text{ = 4 + 10} \\ 2x\text{ = 14} \\ \text{Divide both sides by 2} \\ \frac{2x}{2}\text{ = }\frac{14}{2} \\ x\text{ = 7} \end{gathered}[/tex]Graph the functions f ( x ) = x 2 , g ( x ) = x 2 + 7 , and h ( x ) = x 2 − 7 on the same rectangular coordinate system. Then describe what effect adding a constant, k , to the function has on the vertex of the basic parabola.
ANSWER :
EXPLANATION :
a juice box has a volume approximately 60in3 with a height of 5 in. The box is cut in half to a height of 2.5 in. How does the new volume compare to the original?
Height of the box = 5 in
which set of angle measures will not be the three interior angles of a triangle?A. 78°, 2°, 100°B. 52°, 52°, 52°C. 60°, 30°, 90°D. 13°, 37°, 130°
The sum of an interior angle of a triangle is 180 degrees.
[tex]\begin{gathered} A.78^{\circ}+2^{\circ}+100^{\circ}=180^{\circ} \\ B.52^{\circ}+52^{\circ}+52^{\circ}=156^{\circ} \\ C.60^{\circ}+30^{\circ}+90^{\circ}=180^{\circ} \\ D.13^{\circ}+37^{\circ}+130^{\circ}=180^{\circ} \\ \text{Hence, (B) is the right option.} \end{gathered}[/tex]Answer:
Step-by-step explanation:
"B" could not be angles of a triangle. It forms a straight line. So the answer is "B"
The graph shows which quadratic equation?A)y = (x + 4)2 - 3B)y = (x - 4)2 + 3C)y = (x - 4)2 - 3D)y = -(x - 3)2 + 4
The answer is
[tex]y=-(x-3)^2+4[/tex]3x+2y=10 table of ordered pair
Answer:
Step-by-step explanation:
for sure
please help me with 168÷45
please help me with 168÷45
we know that
168=(2^3)(3)(7)
45=(3^2)(5)
so
[tex]\frac{168}{45}=\frac{2^3\cdot3\cdot7}{3^2\cdot5}=\frac{2^3\cdot7}{3\cdot5}=\frac{56}{15}[/tex]therefore
Convert to mixed number
56/15=45/15+11/15=3+11/15=3 11/15
therefore
the answer is
3 11/15 or 56/15
Part 2
Estimate te quotient using compatible numbers
so
168:45------------> 180:45=4do
Remember that
Compatible numbers are numbers that are easy to compute mentally
Translate each graph as specified below.(a) The graph of =yfx is shown. Translate it to get the graph of =y+fx2.(b) The graph of =ygx is shown. Translate it to get the graph of =yg−x5.
See graphs below
Explanation:[tex]\begin{gathered} a)\text{ y = f(x)} \\ f(x)\text{ + 2 is a translation of 2 units upward} \\ To\text{ get }y\text{ = f(x )+ 2, we will assign values to x and add 2 to its y coordinates in order to get } \\ \text{the coordinates of the new one} \end{gathered}[/tex]let x = -2, -1, 0, 1, 2
on the original
when x = -2, y = -3
new y coordinate = -3 + 2 = -1
when x = -1, y = 0.5
new y -coordinate = 0.5 + 2 = 2.5
when x = 0, y = 1
new y coordinate = 1 + 2 = 3
when x = 1, y = 1.5
new y oordinate = 1.5 +2 = 3.5
when x = 2, y = 5
new y-coordinate = 5 + 2 = 7
plotting the new points against x:
b) y = g(x)
y = g(x - 5)
subtract 5 from the x coordinate of the previous line
We will assign values for x, in order to get values of y
let x = 0, 1, 3
when x = 0, y = 0
new x coordinate = 0 - 5 = -5
when x = 1, y = 4
new x coordinate = 1 - 5 = -4
when x = 3, y = 7
new x coordinate = 3 - 5 = -2
plotting the points on the graph:
An 8-sided die with numbers from 1 to 8 is rolled. What is the probability that a 4 is rolled? Write your answer as an exact fraction which is reduced as much as possible.
Since it is an 8 sided dice
We have a sample space of 8 possible results 1,2,3,4,5,6,7,8
Just 4 is our favorable event, i.e. 1 possibility
Then we can write
P (4) = 1/8
I need help on question 6 and simple explanation please (8th grade algebra)
ANSWER
Linear function
EXPLANATION
6) To solve this, we have to observe the given data.
Notice that as each term comes, the circles are dropped by a specific factor:
Term 1: 16
Term 2: 8
Term 3: 4
Term 4: 2
Therefore, we see that the number of circles reduces by a certain factor which is ¹/ ₂.
Hence, there is a proportional relationship between the term and the number of circles.
Therefore, a proportional function will be used to model the pattern:
[tex]y=\frac{1}{2}x[/tex]This is also the form of a linear function without the constant. Hence, the answer is a linear function.
Will someone explain to me how I get this done?
The Solution:
The given system of equations are:
[tex]\begin{gathered} x-2y=4\ldots eqn(1) \\ 2x+y=-2\ldots eqn(2) \end{gathered}[/tex]We are asked to solve using the Substitution Method.
Step 1:
From eqn(1), we shall find x in terms of y.
[tex]\begin{gathered} x-2y=4 \\ \text{Adding 2y to both sides, we get} \\ x-2y+2y=4+2y \\ x=4+2y\ldots eqn(3) \end{gathered}[/tex]Putting eqn(3) into eqn(2), we get
[tex]\begin{gathered} 2x+y=-2 \\ \text{Putting 4+2y for x, we get} \\ 2(4+2y)+y=-2 \end{gathered}[/tex]Clearing the brackets, we get
[tex]\begin{gathered} 8+4y+y=-2 \\ \text{Subtracting 8 from both sides, we get} \\ 8-8+4y+y=-2-8 \\ 4y+y=-10 \\ 5y=-10 \end{gathered}[/tex]Dividing both sides by 5, we get
[tex]\begin{gathered} \frac{5y}{5}=\frac{-10}{5} \\ \\ y=-2 \end{gathered}[/tex]Substituting -2 for y in eqn(3), we have
[tex]\begin{gathered} x=4+2y \\ x=4+2(-2) \\ x=4-4=0 \\ \text{ So, the solution is (0,-2)} \end{gathered}[/tex]Therefore, the correct answer is x=0, y= -2
it was recently estimated that females outnumber males by about seven to three. if there are 2230 people in a county how many of them are females
Given:
7 out of 10 will be females.
[tex]No\text{ of females in country =}\frac{7}{10}\times2230[/tex][tex]No\text{ of females in country =}1561[/tex]When solving the system below algebraically using the substitution method, which of the following could be an equation you could create to solve for y?A. -4(2y - 20) + 3y = 30B. -4(-2y + 20) + 3y = 30C. -2y + 20 = -3y + 30D. 4(x + 2y = 20
The goal of the substitution method is to eliminate one of the variables using one of the equations of the systems. We are told that we want to solve for y, that is, we should use one equation to eliminate the variable x.
Since the coefficient of x in the first equation is 1, we will use the first equation to eliminate x in the second equation. So, we have the first equation
[tex]x+2y=20[/tex]So, by subtracting 2y on both sides, we get
[tex]x=20-2y[/tex]which is equivalent to
[tex]x=-2y+20[/tex]So, if we replace this value of x in the second equation,w e get
[tex]-4\cdot(-2y+20)+3y=30[/tex]which corresponds to option B
Identify the constant term in this expression. 0.25 + 2× + 4z +0.75y
the constant term is the term without any variable so the answer is 0.25
Part A Mrs. Finney is making slime with her kids. They find a recipe that calls for 1 part borax solution to 3 parts glue. What is the value of the ratio of borax solution to glue? 1/3 What is the value of the ratio of glue to borax solution? < 1/3 Part B Complete the ratio table for the slime recipe. 1 Glue 3 Borax Solution (B) (G) 1 3 2 3 9 12
Answer
Ratio of borax solution to glue = (1/3)
Ratio of glue to borax solution = (3/1)
Part B
The ratio table
B - Borax solution
G - Glue
B | G
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
Explanation
The recipe calls for
1 part borax solution to 3 parts glue
Ratio of borax solution to glue = (1/3)
Ratio of glue to borax solution = (3/1)
Part B
Since we know that 1 part of borax solution = 3 parts of glue, we just need to multiply the amounts of borax solution by 3 to obtain the amount of glue.
The ratio table
B - Borax solution
G - Glue
B | G
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
Hope this Helps!!!
Question 20>Solve the given linear system of equations:- 1212ySy8Enter your answer in the form of an ordered pair(x, y).One solution:O No solutionO Infinite number of solutions
the equation given was
[tex]\begin{gathered} 9x-12y=-12 \\ -6x+8y=8 \end{gathered}[/tex]now to solve this equation, we should solve the simultaneous equation and get the values of x and y
now, let's take equation 1 and solve for x
[tex]\begin{gathered} 9x-12y=-12 \\ \text{make y the subject of formula} \\ 9x=-12+12y \\ \text{divide both sides by 9} \\ \frac{9x}{9}=\frac{-12+12y}{9} \\ x=\frac{-12+12y}{9} \end{gathered}[/tex]put x into equation 2
[tex]\begin{gathered} -6x+8y=8 \\ x=\frac{-12+12y}{9} \\ \text{put x into the equation} \\ -6(\frac{-12+12y}{9})+8y=8 \\ \frac{72-72y}{9}+8y=8 \\ 8-8y+8y=8 \\ 0=0 \end{gathered}[/tex]from the solution, y = 0
put y = 0 into either equation 1 or 2
from equation 1
[tex]\begin{gathered} 9x-12y=-12 \\ \text{put y = 0} \\ 9x-12(0)=-12 \\ 9x-0=-12 \\ 9x=-12 \\ \text{divide both sides by 9} \\ \frac{9x}{9}=-\frac{12}{9} \\ x=-\frac{4}{3} \end{gathered}[/tex]from the above calculation, the above equation has only one solution.
the ordered pair is
[tex](x,y)=(-\frac{4}{3},0)[/tex]Factoring the expression 24a63 – 20a%b2 + 4a3b2 gives a new expression of the formUa" by (Wa? + Vb+ 2), where U > 0.What is the value of U?1What is the value of W?What is the value of V?What is the value of Z?What is the value of c?What is the value of y?
Given the expression:
[tex]24a^3b^{3\text{ }}-20a^5b^2+4a^3b^2[/tex]Let's first re-arrange the expression:
[tex]-20a^5b^2+24a^3b^{3\text{ }}+4a^3b^2[/tex]Now factorize:
[tex]-4a^3b^2(5a^2\text{ + (-6b) + (-1))}[/tex]Now let's compare with this equation:
[tex]Ua^xb^y(Wa^2+Vb\text{ + Z)}[/tex]We can see that:
The value of U = -4
The value of V = -6
The value of W = 5
The value of Z = -1
The value of x = 3
I'm checking my son's homework Tina Nguyen help me with this
The amount of money Lilianna has is: 68
The least amount of money she needs is: y
The amont of money for the phone is: 194.
The above situation can be expressed as,
[tex]68+y\ge194[/tex]From the above expression the minimum value of y is,
[tex]\begin{gathered} y\ge194-68 \\ y\ge126 \end{gathered}[/tex]Thus, Lilianna needs at least 126 dollars more to buy the phone, and the correct option is option A.
identify the y-intercept from the table:answer as an ordered pair (x,y)
We can see that the y-intercept is located at (0, 6).
[Remember that the y-intercept is where the line cuts the y-axis when x = 0.]