If the measure of angle 1 is 78 degrees and the measure of angle 3 is (5x-2)degrees, what is the value of x ?
Answers
Answer:
16
Step-by-step explanation:
Vertical Angles are congruent (equal)
78 = 5x - 2
80 = 5x
16 = x
Related Questions
Please help solve for angles Q X and Z
Answers
Answer:
125
Step-by-step explanation:
Sum of Exterior Angles must add to 360 so
[tex]60 + 70 + 40 + 65 + x = 360[/tex]
[tex]235 + x = 360[/tex]
[tex]x = 125[/tex]
An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a yellow on your next toss of the die
Answers
Answer:
[tex]P(Yellow) = \frac{29}{147}[/tex]
Step-by-step explanation:
Given
[tex]Brown = 27\\Purple = 47\\Yellow = 29\\Green = 44[/tex]
Required
[tex]P(Yellow)[/tex] --- next roll to be yellow
This is calculated as:
[tex]P(Yellow) = \frac{Yellow}{Total}[/tex]
So, we have:
[tex]P(Yellow) = \frac{29}{27 + 47 + 29 + 44}[/tex]
[tex]P(Yellow) = \frac{29}{147}[/tex]
Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.L1: x / 1 = y - 1 / -1 = z - 2 / 3L2: x - 2 / 2 = y - 3 / -2 = z / 7
Answers
The lines are skew
Step-by-step explanation:
To make things clearer, rewrite the given lines as follows;
[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3}[/tex]
[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7}[/tex]
(i) Test if the lines are parallel.
Two lines are parallel if the cross product of their directional vectors is equal to the zero vector 0 (which is equal to <0, 0, 0>). For example, if their directional vectors are m and n, then;
m x n = 0
Where;
m, n and 0 are vectors
In the given lines, L₁ and L₂, their directional vectors are given by the denominators of their symmetric equation.
For L₁, the directional vector = <1, -1, 3>
For L₂, the directional vector = <2, -2, 7>
Let
m = <1, -1, 3> = i - j + 3k
n = <2, -2, 7> = 2i - 2j + 7k
Now, find the cross product of the vectors;
m x n = | i j k |
| 1 -1 3 |
| 2 -2 7 |
m x n = i(-7 + 6) -j(7 - 6) + k(-2 + 2)
m x n = i(-1) -j(1) + k(0)
m x n = -i -j + 0k
Since the cross product does not give a zero vector, then the lines are not parallel.
(ii) Test if the lines intersect
To do this:
(a) First, we express the lines in parametric form rather than the symmetric form. Therefore
[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3}[/tex] is equated to say a;
and
[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7}[/tex] is equated to say b;
We have;
[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3} = a[/tex]
[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7} = b[/tex]
Split the lines into system of three equations in terms of a and b
For L₁
=> [tex]\frac{x}{1}[/tex] = a which gives x = a
=> [tex]\frac{y-1}{-1}[/tex] = a which gives y = 1 - a
=> [tex]\frac{z-2}{3}[/tex] = a which gives z = 3a + 2
∴ L₁ has these three equations
x = a -------------------------(i)
y = 1 - a --------------------------(ii)
z = 3a + 2 --------------------------(iii)
For L₂
=> [tex]\frac{x-2}{2}[/tex] = b which gives x = 2b + 2
=> [tex]\frac{y-3}{-2}[/tex] = b which gives y = 3 - 2b
=> [tex]\frac{z}{7}[/tex] = b which gives z = 7b
∴ L₂ has these three equations
x = 2b + 2 --------------(iv)
y = 3 - 2b ---------------(v)
z = 7b ----------------(vi)
(b) Secondly, we combine the set of equations of the two lines.
Equations of x : (i) and (iv)
a = 2b + 2
=> a - 2b = 2 --------------------------------------(vii)
Equations of y: (ii) and (v)
1 - a = 3 - 2b
=> - a + 2b = 2 --------------------------------------(viii)
Equations of z: (iii) and (vi)
3a + 2 = 7b
=> 3a - 7b = -2 -------------------------------------(ix)
(c) Thirdly, solve equations (vii), (viii) and (ix) simultaneously to find the values of a and b
Add equations (vii) and (viii)
a - 2b = 2
+
-a + 2b = 2
0 + 0 = 4
Since 0 + 0 ≠ 4, then the values of s and t cannot be determined from the system of equations due to inconsistency. Therefore, the lines L₁ and L₂ do not intersect.
(iii) Test if the lines are skew
Two lines are said to be skew if they are neither parallel nor intersecting.
Since the lines L₁ and L₂ are neither parallel nor intersecting, the lines are skew.
Below is a frequency distribution for our RCCC sample of men's heights.
Class Class Frequency Midpoint (inches)
64-65 4
66-67 4
68-69 4
70-71 5
72-73 10
74-75 4
a. Fill in the midpoint of each class in the column provided.
b. Enter the midpoints in L, and the frequencies in L2, and use 1- VarStats to calculate the mean and standard deviation of the frequency distribution. Using the frequency distribution, I found the mean height to be ___________with a standard deviation of____________
c. Now, let's compare the mean of the frequency distribution you just found in part (b), which is an estimate of the actual sample mean, to the actual sample mean you found in (#1).
Using the frequency distribution in (a), I found the mean height to be___________ inches, while using the actual data in #1, I found the mean height to be___________ inches. The true sample mean (using all the data) and the sample mean estimated from a frequency distribution can be fairly close to each other or very different. In this case, do you think the two means were close___________ Using complete sentences, explain why you think the two means came out so close, or why they came out so different, whichever the case may be.
Answers
Answer:
[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { 64.5} & {64-65} & {4} & {66.5 } & {66-67} & {4} & {68.5 } & {68-69} & {4} &{70.5 } & {70-71} & {5} & {72.5 } & {72-73} & {10} & {74.5 } & {74-75} & {4}\ \end{array}[/tex]
Using the frequency distribution, I found the mean height to be 70.1129 with a standard deviation of 3.2831
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { } & {64-65} & {4} & { } & {66-67} & {4} & { } & {68-69} & {4} &{ } & {70-71} & {5} & { } & {72-73} & {10} & { } & {74-75} & {4}\ \end{array}[/tex]
Solving (a): Fill the midpoint of each class.
Midpoint (M) is calculated as:
[tex]M = \frac{1}{2}(Lower + Upper)[/tex]
Where
[tex]Lower \to[/tex] Lower class interval
[tex]Upper \to[/tex] Upper class interval
So, we have:
Class 64-65:
[tex]M = \frac{1}{2}(64 + 65) = 64.5[/tex]
Class 66 - 67:
[tex]M = \frac{1}{2}(66 + 67) = 66.5[/tex]
When the computation is completed, the frequency distribution will be:
[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { 64.5} & {64-65} & {4} & {66.5 } & {66-67} & {4} & {68.5 } & {68-69} & {4} &{70.5 } & {70-71} & {5} & {72.5 } & {72-73} & {10} & {74.5 } & {74-75} & {4}\ \end{array}[/tex]
Solving (b): Mean and standard deviation using 1-VarStats
Using 1-VarStats, the solution is:
[tex]\bar x = 70.1129[/tex]
[tex]\sigma = 3.2831[/tex]
See attachment for result of 1-VarStats
Solving (c): Compare the calculated mean to the actual mean
The actual mean is missing from the question, so I will make assumptions in this part
Assume they are close
This means that the selected sample is a reflection of the actual population where the samples are selected.
Assume they are not close
This means that the selected sample does not reflect the actual population where the samples are selected.
PLEASE HELP ASAP Find f(-2) for f(x)=3•2^x
Answers
Answer:
3/4
Step-by-step explanation:
f(x)=3•2^x
Let x = -2
f(-2)=3•2^-2
Exponents first ( We know a^-b = 1/ a^b)
f(-2)=3• 1/2^2
=3 * 1/4
= 3/4
Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.91 with a standard deviation of $0.13. Using Chebyshev's Theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.65 and $4.17
Answers
Answer:
The minimum percentage of stores that sell a gallon of milk for between $3.65 and $4.17 is of 75%.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
We have a mean of $3.91 and a standard deviation of $0.13.
Using Chebyshev's Theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.65 and $4.17?
3.65 = 3.91 - 2*0.13
4.17 = 3.91 + 2*0.13
Within 2 standard deviations of the mean, so, by the Chebyshev's Theorem, the minimum percentage of stores that sell a gallon of milk for between $3.65 and $4.17 is of 75%.
The square ABCD is divided into eight equal parts. The shaded area is 25 cm². What is the area of the square ABCD
Answers
Answer:
I think the answer is 200cm^2
Step-by-step explanation:
since the square is divided into eight equal parts
and one shaded part is =25cm^2
multiply the area of the shaded part by the number of equal parts
= 25cm^2 ×8
= 200cm^2
25% of 6430
thank you in advance
Answers
Answer:
25% of 6430 is 1607.5
Calculate the geometric mean return for the following data set:
-3% 2% -5% 2.7% 3.1%
Answers
Answer:
none Geometric mean cannot be calculated for negative values
Step-by-step explanation:
Please help! 35 points
Answers
Answer:
10.A
11.A
12.A
Step-by-step explanation:
thank me later
Now go to diagonals of parallelograms. You'll see two line segments, and marked with their midpoints, E and F. Verify that E and F divide the line segments equally by measuring and recording the length of the four line segments that you see.
Answers
Answer:
AE=4
EC=4
BF=2.24
FD=2.24
Step-by-step explanation:
here we go honey
Can someone please simplify this??
Answers
Answer:
0
Step-by-step explanation:
=>sec A cosec A - tan A - cot A
=>(1/sinAcosA)-(sinA/cosA)-(cosA/sinA)
You get the LCM as sinAcosA then it becomes
=>(1-sin^2(A)-cos^2(A)) /sinAcosA [1-sin^2(A)=cos^2(A)]
=>(cos^2(A)-cos^2(A))/sinAcosA
=>0/sinAcosA
=>0
Choose the greatest fraction.
OA) 1/2
OB) 1/3
C) 1/4
OD) 1/5
Answers
Explanation:
1/2= 30/60
1/3= 20/60
1/4= 15/60
1/5= 12/60
(Remember, these I made each fraction another fraction that is equivalent to the point where they all have same denominators)
We can see that 1/2 is the greates out of all of them.
Shorter explanation, i think we all know that 1/2 is greater because if u have fractions with the same numerator, the fraction with the smallest denominator is the greatest fraction.
Brainliest please
Alice has a total of 12 dimes and nickels. She has 2 more nickels than dimes.
Which equation represents the given problem situation?
c+(c + 2) = 12, where c is the number of dimes
c+2c= 12, where c is the number of dimes
C+(c+ 2) = 12, where c is the number of nickels
c+2c =12, where c is the number of nickels
Answers
Answer:
c + (C+2) = 12
Step-by-step explanation:
Assume C is the no of dimes
So there are C+2 no of nickels
Guven that C + (C+ 2) = 12
What is the mode and the median?
1.2.6.6.7.8.9.9
Cual es la moda y la mediana
Answers
For the data set 1, 1, 2, 5, 6, 6, 9 the median is 5.
For the data set 1, 1, 2, 6, 6, 9 the median is 4.
This is Algebra btw.
For the functions defined above, fill in the table of values.
Explain how we can find the solution to the system of equations using the table.
Answers
Given equations;
y₁ = 3x - 8 -------------------(i)
y₂ = 0.5x + 7 --------------------(ii)
To fill the table, substitute the values of x into equations (i) and (ii)
=> At x = 0
y₁ = 3(0) - 8 = -8
y₂ = 0.5(0) + 7 = 7
=> At x = 1
y₁ = 3(1) - 8 = -5
y₂ = 0.5(1) + 7 = 7.5
=> At x = 2
y₁ = 3(2) - 8 = -2
y₂ = 0.5(2) + 7 = 8
=> At x = 3
y₁ = 3(3) - 8 = 1
y₂ = 0.5(3) + 7 = 8.5
=> At x = 4
y₁ = 3(4) - 8 = 4
y₂ = 0.5(4) + 7 = 9
=> At x = 5
y₁ = 3(5) - 8 = 7
y₂ = 0.5(5) + 7 = 9.5
=> At x = 6
y₁ = 3(6) - 8 = 10
y₂ = 0.5(6) + 7 = 10
=> At x = 7
y₁ = 3(7) - 8 = 13
y₂ = 0.5(7) + 7 = 10.5
=> At x = 8
y₁ = 3(8) - 8 = 16
y₂ = 0.5(8) + 7 = 11
=> At x = 9
y₁ = 3(9) - 8 = 19
y₂ = 0.5(9) + 7 = 11.5
=> At x = 10
y₁ = 3(10) - 8 = 22
y₂ = 0.5(10) + 7 = 12
The complete table is attached to this response.
(ii) To find the solution of the system of equations using the table, we find the value of x for which y₁ and y₂ are the same.
As shown in the table, that value of x = 6. At this value of x, the values of y₁ and y₂ are both 10.
HELPPP WHICH KNE DO I PICKK LEASE I NEED TO FO THIS JOW
Answers
Answer:
first and third option are correct.
Step-by-step explanation:
6(x+3)
=6*x + 6*3
=6x + 18
An aeroplane takes 4 hours to travel a distance of 440 0km. Another aeroplane travels at a speed which is 100km per hour less than the first aeroplane. How long will take the second aeroplane to travel he same distance as the first?
Answers
Answer:
7480 hours
Step-by-step explanation:
440 - 100 = 340
LCM of 440 and 340
440 = 2 × 2 × 2 × 5 × 11
340 = 2 × 2 × 5 × 17
LCM = 2 × 2 × 2 × 5 × 11 × 17
LCM = 7480
help plz ???????????????????????????
Answers
Answer
1. 4am to 6am and 12 midnight
2. 8am and 10 pm
3. 12 noon and 6pm
4. 10 am 8 pm
5. 2pm
6. 1pm and 4pm
7. 2pm (22C)
8. 4am to 6am and 12 midnight (10 C)
9. 8 am to 1 pm
You need to find the temperature on the y axis, then move right in the same line, and when the line touches the line graph, turn 90 degrees down. Then you get the time.
Please give brainliest if it helps
The table shows how many male and female students attended two different movies. What is the probability that a randomly chosen person from this group is mail and attended an action movie? Round your answer to two decimal places.
Answers
Answer -0.43
Just because I took the quiz
Answer:
the answer is d trust me 0.22
Step-by-step explanation:
3. Antoinette is building a rectangular pen with 78 feet of fencing. If the length of the pen is 5
feet longer than its width, what are the dimensions of the pen?
Width
Length
NUMBER 3
Answers
Answer:
length = 22
Width = 17
Step-by-step explanation:
78 = 2(w+5) + 2(w)
78 = 2w + 10 + 2w
78 = 4w + 10
68 = 4w
w = 17
l = 17 + 5 = 22
A 640-ounce bag of dog food contains 75 equal-sized portions. How big will each portion be? Use compatible numbers to solve. A. Between 7 and 8 ounces B. Between 8 and 9 ounces C. Between 9 and 10 ounces D. Between 10 and 11 ounces
Answers
Answer:
B
Step-by-step explanation:
If you do 640/75 that equals 8.5333 etc. That is between 8 and 9!
Hope that helps!
If you spoke 200 minutes per month, what would your monthly bill be for each plan?
Answers
Answer:
it will have 2be 408,99 cent plan so tht u can be able 2 speak the whole month
help me plz
this is very important for me
Answers
Step-by-step explanation:
A line with the specific numbers plotted on it, numerical order
Answer:
1- Put the letter A on positive 7
2- Put the letter B on positive 5
3- Put the letter C on 0
4- Put the letter D on negative 4
5- Put the letter E on negative 9
Under ideal conditions a certain bacteria population is known to double every three hours. Suppose that there are initially 40 bacteria. (a) What is the size of the population after 15 hours
Answers
What is the slope of the line that contains the points in the table?
A. -6
B. 2
C.-3
D. 3
Answers
Answer:
-3
Step-by-step explanation:
change in y over the change in x
pick to points and use slope formula
9-3
0-2
that's 6/-2 = -3
Solve this system of linear equations. Separat
the x- and y-values with a comma.
9x - 10y = -34
3x - 4y = -16
Answers
Answer:
[tex]9x - 10y = - 34 - - - (a) \\ 3x - 4y = - 16 - - - (b) \\ (a) - 3 \times (b) : \\ 0x + 2y = 14 \\ y = 7 \\ 3x - (4 \times 7) = - 16 \\ 3x = 12 \\ x = 4[/tex]
answer: ( 4, 7 )
Hi there!
»»————- ★ ————-««
I believe your answer is:
(4,7)
»»————- ★ ————-««
Here’s why:
I have graphed the system on a program. The two lines intercept at the point (4,7). This means that it is the solution to the system. See the graph attached.»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Three coins are tossed. Let the event H = all Heads and the event K = at least one Heads. (match like 1-a, etc)
1. 7/8
2. 1/7
3. 1/8
a. The probability that the outcome is all heads if at least one coin shows a heads
b. P(K) =
c. P(H∩K) =
Answers
Given:
Three coins are tossed.
Let the event H represents all Heads and the event K represents at least one Heads.
To find:
a. The probability that the outcome is all heads if at least one coin shows a heads.
b. P(K) = ?
c. P(H∩K) = ?
Solution:
If three coins are tossed, then the total possible outcomes are:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Total outcomes = 8
Possible outcomes for all Heads = 1
Possible outcomes for at least one Heads = 7
Let the following events:
H = all Heads
K = at least one Heads.
Then,
[tex]H=\{HHH\}[/tex]
[tex]K=\{HHH, HHT, HTH, HTT, THH, THT, TTH\}[/tex]
[tex]H\cap K=\{HHH\}[/tex]
Now,
[tex]P(K)=\dfrac{7}{8}[/tex]
[tex]P(H\cap K)=\dfrac{1}{8}[/tex]
a. The probability that the outcome is all heads if at least one coin shows a heads is:
[tex]P(H|K)=\dfrac{P(H\cap K)}{P(K)}[/tex]
[tex]P(H|K)=\dfrac{\dfrac{1}{8}}{\dfrac{7}{8}}[/tex]
[tex]P(H|K)=\dfrac{1}{7}[/tex]
Therefore, the probability that the outcome is all heads if at least one coin shows a heads is [tex]\dfrac{1}{7}[/tex].
b. [tex]P(K)=\dfrac{7}{8}[/tex]
c. [tex]P(H\cap K)=\dfrac{1}{8}[/tex]
Rosa went out to dinner with her three friends. The bill at the restaurant totaled $95.50. They wanted to give a tip of 20%. How much money did they pay altogether?
Answers
Answer: $108.60
Step-by-step explanation:
Initial cost: $95.50
Tip is an additional cost. They want to give a tip of 20%, so they will give additional 20% of the initial cost.
$90.50 + (90.50 * 0.2)
= $90.50 + $18.10
= $108.60
change the following into mixed fraction 19/6
Answers
Explanation:
1. divide the numerator by the denominator
2. write down the whole number result
3. use the remainder as the new numerator
Answer:
6 1/6
Step-by-step explanation:
Divide the numerator (19) by the denominator (6)
Write down the whole number result which in this case would be 3
Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number. which in this case is 1/6
therefore the answer is 6 1/6
