Answer:
a. The railing is transversal to the posts
b. In order to make the posts parallel, the angle between the posts and the transversal should be = 78°
c. The angle between the post and the ramp is 102° as we reach the post from the bottom and 102° and 78° immediately after the post
d. 1) Alternate interior angles = 78° and 102°
2) Alternate exterior angles = 102°
3) Corresponding angles = 78° and 102° depending on the side of from which we approach the post
4) Consecutive interior = 78° and 102° depending on the side of from which we approach the post
e. The interior angles are supplementary
f. Horizontal spacing between posts = 2.93 ft.
Spacing between posts along the length of the railing = 3 ft. spacing
Step-by-step explanation:
a. A transversal is a line crossing two or more parallel lines which are in a plane at different points
Therefore, the railing is transversal to the posts
b. Whereby the ramp rises at an angle of 12°, the railing, which is the transversal is therefore inclined at 12° to the horizontal and the posts which will be vertical erect will be at 90° to the horizontal
Therefore, in order to make the posts parallel, the angle between the posts and the transversal should be 90° - 12° = 78° for each post to railing.
c. The angle between the post and the ramp before the post as we ascend the ramp is therefore, 180 - 78 = 102° and 78° after the post
d. The alternate interior angles lie on the opposite sides of the transversal = 78° on one side and 102° on the other (Sum of angles on a straight line) which are the angles on the transversal
The alternate exterior angles lie on the exterior opposite sides of the transversal = 102°
Corresponding angles are the angles located in the corresponding positions on the transversal = 78° on one side and 102°as we cross the post (Sum of angles on a straight line)
Consecutive interior angles are the angles that are located on the same part of the transversal = 78° and 102° (Sum of consecutive interior angles of parallelogram = 180°
e. For the posts to be parallel, the consecutive interior angles should be supplementary or equal to 180°
f. Whereby we have a 12-ft rail inclined at 12°, we have;
Horizontal distance covered by the rail = 12 × cos(12) = 11.74 ft
Since we have 5 posts, there 4 equal spaces between them which gives
Spaces between posts = 11.74/4 = 2.93 ft. horizontally and 3 ft. spacing between each post along the railing.
order the following values from least to greatest: 22.4, -28, 27, -17
Answer:
asDawas
Step-by-step explanation:
sadasda
Answer: -28, -17, 22.4, 27
hope this helps
Select the correct answer. Which pair of statements correctly compares the two data sets? A. The difference of the means is 1. This value is less than half of the mean absolute deviation of either data set. B. The difference of the means is 1. This value is more than half of the mean absolute deviation of either data set. C. The difference of the means is 1. This value is 1 times the mean absolute deviation of either data set. D. The difference of the means is 1. This value is 2 times the mean absolute deviation of either data set.
Answer:
For this case since the p value is higher than the significance level we can FAIL to reject the null hypothesis and we can conclude that the true means are NOT significantly different at 10% of significance.
Step-by-step explanation:
Information provided
represent the mean for sample 1
represent the mean for sample 2
represent the sample standard deviation for 1
represent the sample standard deviation for 2
sample size for the group 2
sample size for the group 2
Significance level provided
t would represent the statistic
Hypothesis to test
We want to verify if the true means for this case are significantly different, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
And the degrees of freedom are given by
Replacing the info given we got:
The degreess of freedom are given by:
Now we can calculate the p value with the following probability:
For this case since the p value is higher than the significance level we can FAIL to reject the null hypothesis and we can conclude that the true means are NOT significantly different at 10% of significance.
Step-by-step explanation:
Use the graph to find the value of y = sin q for the value of q.
Answer:
c
Step-by-step explanation:
The following table shows the number of animal crackers in each kid's lunch box. Find the median number of animal crackers.
Answer:
4
Step-by-step explanation:
2 2 3 5 7 7 (order from least to greatest)
3+5=8(find the most middle number,if there are two numbers you add both and then divide by 2)
8÷2
4
Hi there!! (✿◕‿◕)
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
First, you have to put the numbers from least to greatest.
2, 2, 3, 5, 7, 7
Then, you have to find the middle number.
2, 2, 3, 5, 7, 7
3 and 5 and both in the middle so, you add them both and divide them by 2.
3+5 = 8
8/2 = 4
4 is the median.
Hope this helped!! ٩(◕‿◕｡)۶
When you simplify,
10!/(10 - 3)!-3
is equal to:?
Answer:
120
Step-by-step explanation:
expand and calculate
10x9x8x7!/(10-3)!x3!
10x9x8x7!/7!x3!
reduce
10x9x8x7!/7!x3!
10x9x8/3!
Calculate the product
10x9x8/3!
Now Cacluate the factorial
720/3!
720/6
reduce
120
Answer: 120
Step-by-step explanation:
A =3x2+4x+1,B=5x2−3x+8,C=4x2−7x−3, find the value of B + C –A.
Answer:
6x^2 - 14x + 4.
Step-by-step explanation:
5x^2 - 3x + 8 + 4x^2 - 7x - 3 - (3x^2 + 4x + 1)
= 5x^2 - 3x + 8 + 4x^2 - 7x - 3 - 3x^2 - 4x - 1
= 6x^2 - 14x + 4.
Leah wants to carpet a room that is 12 feet wide and 15 feet long. Carpeting is sold by the square yard. Find the length and width of the room in yards. Then find the number of square yards needed to carpet the room.
Answer:
length: 5 yd
width: 4 yd
area: 20 yd^2
Step-by-step explanation:
1 yd = 3 ft
15 ft * (1 yd)/(3 ft) = 5 yd
12 ft * (1 yd)/(3 ft) = 4 yd
A = LW
A = 5 yd * 4 yd = 20 yd^2
Answer:
20 yd²
Step-by-step explanation:
1 yd = 3 ft =>
=>w = 12ft×yd/3ft = 4 yd
=> l = 15ft×yd/3ft = 5 yd
A = l × w
= 5yd × 4yd
= 20 yd²
simplify the expression
[tex]8p + 10 + - 2p - 1 + 10[/tex]
Answer:
6p+19
Step-by-step explanation:
combine like terms:
8p+10+-2p+-1+10
(8p+-2p)+(10+-1+10)
6p+19
HOPE THIS HELPS!!!!!!:)
If the variance of a variable is 16, what is the standard deviation?
Answer:
Standard deviation=4
Step-by-step explanation:
Standard deviation = square root of variance
Standard deviation=√variance
Variance=standard deviation square
Variance=standard deviation^2
From the question
Variance=16
Standard deviation=?
Standard deviation=√variance
=√16
=4
Standard deviation=4
check:
If standard deviation=4
Variance=standard deviation^2
=4^2
=16
Therefore,
Standard deviation=√variance
[tex]4[/tex]
VarianceThe variance is a measure of how much each point deviates from the mean on average.The standard deviation of a set of numbers is the distance between them and the mean. (The mean is the arithmetic average of a given group of integers.)To compute the standard deviation, take the square root of the variance.Variance of the variable [tex]=16[/tex]
Standard deviation [tex]=\sqrt{16}[/tex]
[tex]=\boldsymbol{4}[/tex]
Find out more information about the variance here:
https://brainly.com/question/24304293?referrer=searchResults
Need help plz, i will give brainliest and 20 points. Thank you
Answer:
1/2
Step-by-step explanation:
helppp plzzzzzz help me right now plz i need help
Answer:
the third one is the correct answer
ASAP its not 36 do RSM way Find the number of rectangles in 6×6 chessboard.
Answer:
441 rectangles
Step-by-step explanation:
Formula for the number of rectangles in a chessboard=
n²(n + 1)²/ 4
We are told in the question that is a 6×6 chessboard
Hence, n = 6
= 6²(6 + 1) ²/ 4
= 6²× 7²/4
= 36 × 49/4
= 1761/4
= 441 rectangles
Therefore, the number of rectangles in 6×6 chessboard is 441 rectangles.
How many houses have an area less than 100^2m?
Answer:
4
Step-by-step explanation:
Each bar represents a range in area. The first bar represents the number of houses with an area of more than 50 but less than 100. It's height is 4, so there are 4 of those houses.
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer:
3 > x
Step-by-step explanation:
–2(5 – 4x) < 6x – 4
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: divide each side by by -2, remembering to flip the inequality
-6/-2 > -2/-2
3 > x
Answer:
x < 3
Step-by-step explanation:
−2(5−4x)<6x−4
Use the distributive property to multiply −2 by 5−4x.
−10+8x<6x−4
Subtract 6x from both sides.
−10+8x−6x<−4
Combine 8x and −6x to get 2x.
−10+2x<−4
Add 10 to both sides.
2x<−4+10
Add −4 and 10 to get 6.
2x<6
Divide both sides by 2. Since 2 is >0, the inequality direction remains the same.
x= 6/2
Divide 6 by 2 to get 3.
x= 3
X< 3
Mark me as brainliest
Solve the following equations and inequalities showing all work.
18.1/2(x - 5) + 1 = 2x +4
19.3-x>-3
20. - x = 12
21. -2 = 8
22. –1 + 3 = 3 +
5
23.4 - (5x + 6) = 18 - 3x
24.-6x + 24 = 4x - 15(x-3)
25.4(x – 3) 12 =(x-3)
26. (15x 2) (-2) = x + 4
Answer:
See the answers in the pics
Step-by-step explanation:
Srry, I didn't quite understood the last two equations
but I hope that from now on you will know how to solve equations and inequalities like this ;]
Answer:
LLLLLLLLLLLLLl
Step-by-step explanation:
Question 8 of 10
What is the value of X?
50°
100"
O.
A. 50°
B. 150°
ОО
C. 1000
D. 30°
Answer:
30 degrees
Step-by-step explanation:
100+50=150
180-150=30
All triangles equal 180 degrees, so if the other angles equal 150 than the third angle equals 30 degrees.
QUICK!! 18x^2+21x-60=0 pls give me the steps as well
Answer:
[tex]x1 = - \frac{5}{2} [/tex][tex]x2 = \frac{4}{3} [/tex]
Step-by-step explanation:
[tex]18 {x}^{2} + 21x - 60 = 0[/tex]
Divide both sides of the equation by 3
[tex]6 {x}^{2} + 7x - 20 = 0[/tex]
Write 7x as a difference
[tex]6 {x}^{2} + 15x - 8x - 20 = 0[/tex]
Factor out 3x from the expression
[tex]3x(2x + 5) - 8x - 20 = 0[/tex]
Factor out -4 from the expression
[tex]3x(2x + 5) - 4(2x + 5) = 0[/tex]
Factor out 2x + 5 from the expression
[tex](2x + 5)(3x - 4) = 0[/tex]
When the product of factors equals 0 , at least one factor is 0
[tex]2x + 5 = 0[/tex]
[tex]3x - 4 = 0[/tex]
Solve the equation for X
[tex]2x + 5 = 0[/tex]
Move constant to R.H.S and change its sign
[tex]2x = 0 - 5[/tex]
Calculate the difference
[tex]2x = - 5[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{ - 5}{2} [/tex]
Calculate
[tex]x 1= - \frac{5}{2} [/tex]
Again,
[tex]3x - 4 = 0[/tex]
Move constant to RHS and change its sign
[tex]3x = 0 + 4[/tex]
Calculate the sum
[tex]3x = 4[/tex]
divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{4}{3} [/tex]
Calculate
[tex]x 2= \frac{4}{3} [/tex]
Hope this helps..
Best regards!!
Answer:
39x+58
Step-by-step explanation:
18x 2+21x-60=0
pick the like terms together
18x+21x=39x
60-2=58
=39x+58
20 points repost because no one answered. Geomertry question
Answer:
x=2.25
Step-by-step explanation:
ΔABC and ΔADE are similar.
∴ sides are proportional.
[tex]\frac{5}{1} =\frac{x+9}{x} \\5=\frac{x}{x} +\frac{9}{x} \\5=1+\frac{9}{x}\\\frac{9}{x}=5-1\\\frac{9}{x}=4\\x=\frac{9}{4}=2.25[/tex]
Answer:
x = 9/4
Step-by-step explanation:
We know that the triangles are similar
We can use ratios to solve
x x+9
----- = ----------------
1 5
Using cross products
5x = 1(x+9)
5x = x+9
Subtract x
5x-x = x+9-x
4x= 9
Divide by 4
4x/4 = 9/4
x = 9/4
Please hurry!!!
The fraction bars represent which equation?
A fraction bar is labeled 1. Underneath the bar, 4 boxes are labeled 1/4. Underneath the 4 boxes, boxes are labeled 1/8. 6 of those boxes are circled.
A. 1/4 ÷ 1/8 = 6
B. 3/4 ÷ 1/8 = 6/8
C. 1/4 ÷ 1/8 = 6/8
D. 3/4 ÷ 1/8 = 6
Answer:
Answer- 3/4 divided by 1/8 = 6/8
What is the degree measure of an interior angle of a regular pentagon?
Answer:
it is 540 degrees.
Step-by-step explanation:
Answer:
108°
Step-by-step explanation:
Sum of interior angle of any polygon = (n - 2 )*180
Here, n = number of sides
Sum of interior angle of regular pentagon = ( 5 - 2)*180 = 3*180 = 540°
In regular pentagon all the angles are congruent.
Interior angle of regular pentagon = 540/5
= 108°
Find the amplitude of the sine curve shown below. a. 3 b. p c. 1.5 d. 6
Answer:
Amplitude = 3
Step-by-step explanation:
Given
The sine curve above
Required
Determine the amplitude
To determine the amplitude of a sine curve, we have to calculate the distance between the horizontal line of the curve and the top or bottom of the function
Using the top of the curve as a point of reference;
Amplitude = Top of curve - Horizontal Line.
The horizontal line is always at point 0
From the graph above, the top of the curve is at point 3
Hence,
Amplitude = 3 - 0
Amplitude = 3
How can you determine whether a rational number will have a terminating or a repeating decimal
form? Provide an example of both a terminating and repeating rational number when converted to
decimal form.
Answer:
You can determine this by putting the rational numbers in decimal form.
Step-by-step explanation:
A rational number like 1/2 will have a terminating decimal answer = 0.5
A rational number like 7/11 will have a terminating decimal answer = 0.636 where 36 is repeating.
solve each equation for 0 x 360 sqrt 2 cosx+1=0 please hurry
Answer:
[tex]120\º \text{ and } 240\º[/tex]
or in radians:
[tex]$\frac{2\pi }{3} \text{ and } \frac{4\pi }{3}$[/tex]
Step-by-step explanation:
From the way you wrote, you want to solve the equation
[tex]\sqrt {2 \cos(x)+1}=0[/tex] for [tex]0 \leq x < 360\º[/tex], or in radians [tex][0, 2\pi)[/tex]
[tex]\sqrt {2 \cos(x)+1}=0[/tex]
Square both sides
[tex]2 \cos(x) +1= 0[/tex]
[tex]2\cos(x)=-1[/tex]
[tex]$\cos(x)=-\frac{1}{2} $[/tex]
In the Unit Circle, considering one revolution (interval [tex][0, 2\pi)[/tex]),
the values where [tex]$\cos(x)=-\frac{1}{2} $[/tex] are in Quadrant II and III.
Once
[tex]$\cos(x)= \frac{1}{2} \text{ for } x = 60\º \text{ in the Quadrant I}$[/tex]
The values where
[tex]$\cos(x)=-\frac{1}{2} $[/tex] are 120º and 240º.
Answer:
C on edge
Step-by-step explanation:
What is 10^4 in standard notation
Answer:
10,000
Step-by-step explanation:
Standard notation is just the normal way of writing things. 10 x 10 x 10 x 10 = 10,000.
please help me immediately
Answer:
112 m³
Step-by-step explanation:
Let's calculate first the voulume of the tank
the volume of thi tank is given by :
V = l*w*h l is the length w is the width h is the heightso the volume is :
V = 4*12*3.5V=168 m³Multiply by 2/3 to get the volume of the water
V' = 168*(2/3) V' = 112 m³Answer:
112 m^3
Step-by-step explanation:
V = l x w x h
V = 4 x 12 x 3.5
V = 168 m^3
V = 168 x (2/3)
V = 112 m^3
rest text yeah cry GC Ci
What do you mean?? .-.
The time it takes to drive from Orangeville to the Vaughan Mills Mall is normally distributed with a mean of 52 minutes and standard deviation of 5 minutes. What intervals could you estimate, using the knowledge from this activity that do not include the mean as a max or min? For example, is an interval we could estimate? However, it includes the mean as the maximum of the interval. Another example is as an example of a probability interval that we know from this activity, but it includes the mean as the minimum.
Given:
Mean of 52 minutes and a standard deviation of 5 minutes.
Solution:
According to the empirical rule: For the normal distribution, all of the data will fall within three standard deviations of the mean.
1: 68% of the data will fall within the first standard deviation from the mean.
2: 95% of the data fall within two standard deviations.
3: 99.7% of the data fall within three standard deviations.
[tex]3SD =99.7\%=\mu\pm3\sigma\\[/tex]
Therefore, the 7 intervals and their probabilities are:
1. [tex]1SD=0.68=P(47<x<57)[/tex]
2. [tex]0.95=P(42<x<62)[/tex]
3. [tex]0.997=P(37<x<67)[/tex]
4.[tex]13.5\%=P(42<x<47)[/tex]
5.[tex]13.5\%=P(57<x<62)[/tex]
6. [tex]2.35\%=P(37<x<42)[/tex]
7.[tex]2.35\%=P(62<x<67)[/tex]
A five question multiple choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers, and 1’s representing correct answers to answer the following question: What is the experimental probability of correctly guessing at random exaclty three correct answers? PLS HELP ME
Answer:
9/20 (or) 45% (or) .45 (however your teacher wants it expressed)
Step-by-step explanation:
There are 20 experiments and 9 of them have three ones and two zeros.
9/20
Write h(x) = x2 - 6x + 3 in vertex form by following these
steps:
Step 1: Model x2 - 6x + 3 by placing tiles in the Product
section. First place the x2 and -x tiles along the left
and top borders to form two sides of a square. Then
place the + tiles along the ends of the -x tiles.
The vertex form of the quadratic equation is:
[tex]h(x) = (x - 3)^2 - 6[/tex]
How to write the quadratic equation in vertex form?
For a quadratic equation:
[tex]y = a*x^2 + b*x +c[/tex]
With vertex (h, k), the vertex form is:
[tex]y = a*(x - h)^2 + k[/tex]
In this case, we have the equation:
[tex]h(x) = x^2 - 6x + 3[/tex]
To get the x-value of the vertex we use the general formula:
[tex]h = -(-6)/(2*1) = 6/2 = 3[/tex]
To get the y-value, we evaluate the function in x = 3, so we get:
[tex]h(3) = k = (3)^2 - 6*3 + 3 = -6[/tex]
So the vertex is (3, -6).
Then the vertex form is:
[tex]h(x) = (x - 3)^2 - 6[/tex]
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
PLEASE HELP!! 20 POINTS
Answer:
5/12
Step-by-step explanation:
take the number of students who read under6 books (5) and divide by total amount of students (12)
5/12
Answer:
5/12
Step-by-step explanation:
there are a total of 12 books read and a frequency of 5 books read that is fewer than 6 books