Answer: 18º
Step-by-step explanation:
a + 126º = 180º (adj. ∠s on st. line)
a = 54º
Let the adjacent angle next to b be c.
a + c = 180º (int. ∠, AB//CD)
54º + c = 180º
c = 126º
108º + x = 126º (ext. ∠ of Δ)
x = 18º
write in rectangular form
The rectangular form of the complex number z = 2.5(cos(3.6) + isin(3.6)) is given as follows:
B. z = -2.25 - 1.1i.
What is a complex number?A complex number is a number that is composed by a real part and an imaginary part, as follows:
z = a + bi.
In which:
a is the real part.b is the imaginary part.The number for this problem is given as follows:
z = 2.5(cos(3.6) + isin(3.6))
Hence the real and the imaginary part are given as follows:
a = 2.5 x cos(3.6) = -2.25.b = 2.5 x sin(3.6) = -1.1.Hence the rectangular form of the number is:
B. z = -2.25 - 1.1i.
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HELP read the picture
You would have an open circle. A way to remember it is that < and > is open and ≥ and ≤ mean closed circle. A way to also remember which way to go is remembering this cool strategy.
<ess than
>greater than
Less means left. Greater means right. So your graph would look like something along the lines of:
P(A)=.60, P(B)=.30, and P(A and B)=.10. What is P9A or B)?
The probability of events A or B occurring is 0.80 or 80%.
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
Probability can be calculated by dividing the number of favourable outcomes by the total number of possible outcomes.
To find P(A or B), we need to use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the given values, we get:
P(A or B) = 0.60 + 0.30 - 0.10
= 0.80
Therefore, the probability of events A or B occurring is 0.80 or 80%.
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PLS ANSWER WILL GIVE BRAINLIEST IF ANSWER IS RIGHT(NO LINKS)
∆ UVW ~ ∆ XYZ. Identity the perimeter and area of ∆ UVW to the nearest tenth.
Please help me!!! quick and right answer only
Answer:
average rate of change = (16 - 1)/(4 - 1)
= 15/3 = 5
Find the sun of the polynomial expression shown
The sum of the given two polynomials (x²-7x+14) + (x²+10x-4) is 2x² + 3x + 10
To find the sum of the polynomial expression, we need to add the like terms of the two polynomials.
The first polynomial is x²-7x+14 and the second polynomial is x²+10x-4. We can combine the terms with x² to get 2x².
Then, we can combine the x terms to get 3x.
Finally, we can combine the constant terms to get 10.
Therefore, the sum of the two polynomials is:
2x² + 3x + 10
In summary, we can find the sum of two polynomials by adding the like terms of the polynomials. We group the terms with the same degree of x, add them up and simplify the expression by combining the like terms.
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Given the graph below, find the average rate of change between the points x=2 and x=6
The average rate of change between the points x=2 and x=6 is 1
Finding the average rate of change between the points x=2 and x=6From the question, we have the following parameters that can be used in our computation:
The graph
From the graph, we have
f(2) = 6 and f(6) = 10
So, we have
Rate = Change in function values/change in x values
This gives
Rate = (10 - 6)/(6 - 2)
Evaluate
Rate = 1
Hence, the average rate of change between the points x=2 and x=6 is 1
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Try It
Answer the questions to help choose the best data display.
1 Five teams are competing in a variety of events. The table shows the number of darts that hit
the bullseye for team results.
Team
Sharks
Tigers
Bananas
Stem-and-Leaf Plot frequency with
Eagles
Rubies
Number of
Bullseyes
12
2
7
1
10
What type of information is given?
What does the organizer want the display to show?
How will the display be analyzed?
Which type of display would be most appropriate? Explain your
answer.
The given information shows the number of bullseyes hit by five different teams in a variety of events.
What is the best way to display and analyze these team results?To display & analyze these results, the organizer would want a clear and concise visualization that highlights the performance of each team in which bar graph or a horizontal bar chart would be the most appropriate display to use in this scenario.
On the chart, x-axis would represent the team names and the y-axis would represent the number of bullseyes hit, so, the display would allow for easy comparison of the performance of each team, as well as highlighting any significant differences in performance.
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In the figure below, points X, Z, Q, R, and S lie in plane P. Points T and Y do not lie in plane P.
For each part below, fill in the blanks to write a true statement.
The blank spaces in the statements area. S, R, and Q are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.
What are Colinear Points?Points that lie on the same straight line are collinear points.
If two lines are lie on the same plane, they are referred to as coplanar lines.
(a.) S, R, and Q are on a straight line. Therefore S, R, and Q are distinct points that are collinear.
b. TX and QS are distinct lines that intersect.
c. Point Y and line QS are on the same plane. Therefore:
Point Y and line QS are coplanar.
d. Another name for plane P is: plane QSY.
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The graph shows the number of soda bottles a machine can make over time use the two points shown to find the number of soda bottles the machine can make per minute
The number of soda bottles the machine can make per minute is 25
Calculating he number of soda bottles the machine can make per minute.From the question, we have the following parameters that can be used in our computation:
The linear relation
Where we have the points
(2, 50) (6, 150)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
m = unit rate i.e the required slope
So, we have
2m + c = 50
6m + c = 150
Next, we have
4m = 100
Evaluate
m = 25
So, we have
2 * 25 + c = 50
Evaluate
c 0
So, we have
y = 25x
Hence, the equation of the line in fully simplified slope-intercept form is y = 25x
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solve for x image attched please help
Answer:
x/4 = 36/x
Step-by-step explanation:
You want the proportion relating the altitude of the right triangle to the segments of the hypotenuse.
Similar trianglesAll the triangles in this figure are similar, so the ratios of corresponding sides are the same:
long leg/short leg = x/4 = 36/x
The proportion of interest is ...
[tex]\boxed{\dfrac{x}{4}=\dfrac{36}{x}}[/tex]
__
Additional comment
The solution is ...
x² = 4·36
x = 2·6 = 12
<95141404393>
If P = (-4, 6), find the image
of P under the following rotation.
90° counterclockwise about the
origin
([?],
Enter the number that belongs in
the green box.
The image of the given point P = (-4, 6) as required to be determined in the task content is; (-6, -4).
What is the image of the point P under the given rotation?It follows from the task content that the image point of P = (-4, 6) after a 90° counterclockwise rotation is to be determined.
Recall, for a point (x, y) , the image point after a 90° counterclockwise rotation is; (-y, x).
Ultimately, since the point P is; P = (-4, 6).
The image point is; (-6, -4).
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can someone help me with this?
A movie theater can seat a maximum of 25 people. Let p represent the total number of people. Which inequality represents p, the number of people the theater can seat?
The inequality that represents p, the number of people the theater can seat is p ≤ 25
Which inequality represents p, the number of people the theater can seat?From the question, we have the following parameters that can be used in our computation:
A movie theater can seat a maximum of 25 people
This means that
Maximum = 25 people
In other words, the movie theatre can allow 25 or less people to attend a movie
In inequality, 25 or less means less than or equal to 25
When represented as an inequality expression, we have
≤ 25
Using the variable p, we have
p ≤ 25
Hence, the inequality is p ≤ 25
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i need help on this
The value of y on the diagram of the image is given as follows:
23 + 5y.
How to obtain the value of y?The value of y on the context of the given problem is obtained applying the proportions of the problem.
The bars represent an addition operation, with 23 added to 5 times y being equals to 38, hence the expression is given as follows:
23 + 5y = 38.
The value of y is then obtained isolating the variable y as follows:
5y = 15
y = 3.
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Which distribution is positively skewed?
O A.
О в.
0000
0000
::.
18
22 24 26
02 4 6 8 10 12 14 16 18 20 22 24 26 28 30
which is it
From the four options the positively skewed distribution is fourth one.
Hence the correct option is given by (D).
Positively skewed distribution is a distribution with its tail is more pronounced on the right side than it is on the left. Since the distribution is positively skewed, then the value is positive.
The median, mode and other statistical observation data are on left side of the arithmetic mean.
The graph for positively skewed distribution is given by,
Clearly from the given four graphs, fourth graph that is option (D) is looking like positively skewed distribution.
Hence the correct option will be (D).
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Declan invested an amount of money in a savings account that pays compound interest at a rate of 8% per annum.
After 14 years there is £14,685.97 in the savings account (rounded to the nearest 1p).
How much money did Declan initially invest?
Give your answer to the nearest £1.
The amount that Declan initially invested (present value) in a savings account that pays compound interest at a rate of 8% per annum and that had a balance of £14,685.97 after 14 years was £5,000.
How the present value is determined:The present value represents the future value discounted to the present or current date at an interest rate.
We can determine the present value using the PV formula or an online finance calculator as follows:
N (# of periods) = 14 years
I/Y (Interest per year) = 8%
PMT (Periodic Payment) = £0
FV (Future Value) = £14,685.97
Results:
Present Value (PV) = £5,000.00
Total Interest = £9,685.97
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a random sample from the 6th and 7th-grade student population was taken to determine which clubs were most popular. If there are 280 6th graders and 200 7th graders then how many more 7th graders are involved in the yearbook
The percentage of 6th graders involved in the yearbook club is 25%.
From the sample data given, we know that there are 10 6th graders in the yearbook club, and the total number of 6th graders in the sample is 40 (10 in yearbook + 24 in student council + 6 in jump rope). Therefore, to find the percentage of 6th graders involved in the yearbook club, we can use the following formula:
percentage = (number of 6th graders in yearbook club / total number of 6th graders in sample) x 100
Plugging in the values, we get:
percentage = (10 / 40) x 100
percentage = 0.25 x 100
percentage = 25
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Complete Question:
A random sample from the 6th and 7th grade student population was taken to determine which clubs were the most popular.
6th Grade: Yearbook 10; Student Council 24; Jump Rope 6
7th Grade: Yearbook 18; Student Council 20; Jump Rope 2
What percent of 6th graders are involved in the yearbook club?
Petra is making a batch of extra large donuts by stamping circles in dough using a pastry stamp with a diameter of 5 inches. For the donut hole, she stamps out a circle using a pastry stamp that has a diameter of 2 inches.
How many square inches of dough are left in the donut after the hole has been removed?
Answer:
π(5^2 - 2^2) = 21π square inches, or about 65.97 square inches
The expression 1125t approximates the distance, in feet, that sound travels in air in t seconds. What does the 1125 represent in the context of this situation? OA. the approximate number of feet that sound travels in air in 1 second OB. the approximate number of feet that sound travels in air in 1125 seconds OC. the approximate number of seconds it takes sound to travel 1 foot in air OD. the approximate number of seconds it takes sound to travel 1125 feet in air
The meaning of the number 1125 in the context of this problem is given as follows:
A. the approximate number of feet that sound travels in air in 1 second.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The input and the output variables for this problem are given as follows:
Input: time.Output: distance traveled by the sound.Hence the constant of 1125 represents the distance traveled by the sound each second.
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An artist has completed 1/4 of a painting in 2 weeks. At what rate is she working?
Answer:
completed I/8 of a panting in a week
Step-by-step explanation:
A rectangular hotel room is 4 yards by 6 yards. The owner of the hotel wants to recarpet the room with carpet which costs $73.00 per square yard. How much will it cost to recarpet the room?
The amount of money it would cost to recarpet the rectangular hotel room is equal to $1,752.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangular hotel room = 4 × 6
Area of rectangular hotel room = 24 yd²
Now, we can determine the cost as follows;
Cost of recarpet = $73.00 × 24 yd²
Cost of recarpet = $1,752.
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Y=(0,3) slope=4
What’s the equation
An equation of the line in slope-intercept form include the following: y = 4x + 3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (0, 3) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 4(x - 0)
y - 3 = 4x
y = 4x + 3
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ASSAAPP NEEDD HELLPPP
The measure of two angles are 22 and 85 degrees find the measure of the third angle
The triangle's third angle has a measure of 73 degrees.
The sum of the angles in a triangle is always 180 degrees. Let's call the third angle x.
So we have:
22 + 85 + x = 180
107 + x = 180
Subtracting 107 from both sides:
x = 73
Therefore, the measure of the third angle of the triangle is 73 degrees.
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please answer me a whole question
The two different statements are π times radius and π times diameter.
What is the circumference of the circle?
The circumference of a circle is the distance round the circle.
Mathematically, the formula for the circumference of a circle is given as;
C = 2πr, or
C = πD
where;
r is the radius of the circleD is the diameter of the circleFor this circle, the circumference is calculated as follows;
C = 2π x 6 in
C = 12π in
Thus, the distance round the circle and the circumference are the same.
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Please calculate this....
Answer:
it is 3/3 3/6 I hope this helped
CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
v(t) = 38 -9.8th(t) = -4.9t² +38t +1.8Step-by-step explanation:
You want functions for the velocity v(t) and height h(t) of a ball thrown upward at 38 m/s from a height of 1.8 m. The acceleration is -9.8 m/s².
RelationsThis sort of problem is usually discussed in a physics course. The relation between acceleration, velocity, and position is ...
velocity is the rate of change of position
acceleration is the rate of change of velocity
Then the inverse relations are ...
h(t) = ∫v(t)dt +h(0)
v(t) = ∫a(t)dt +v(0)
ApplicationWhen position is measured in one dimension (up = positive), these have the standard formulas:
v(t) = g·t + v(0)
h(t) = 1/2g·t² +v(0)·t +h(0)
Filling in the given values (g = -9.8, v(0) = 38, h(0) = 1.8), we have ...
v(t) = -9.8t +38 . . . . . . . . . . . . meters per second
h(t) = -4.9t² +38t +1.8 . . . . . . meters
The members of a recreation class were asked to name their
favorite sports. The table shows the numbers who responded in
various ways. If a member of this class is selected at random,
what is the probability that the favorite sport of the person
selected is bicycling?
The probability is
(Do not simplify.)
2
Sport
Sailing
Archery
Snowboarding
Bicycling
Rock climbing
Rafting
Number of Class Members
2
11
6
20
7
14
n
The probability is given as 7 / 60 for the favorite sport of the person being bicycling
How to solve the probabilityThe frequency of bicycling in the table is goven as 7
We have tp add the total of all of the values in order to get the given probability
Hence we would have
2 + 11 + 6 +20 + 7 + 14
= 60
The probability is given as 7 / 60
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A. 25 C. 32 21, 22, 24, 20, 25, 32 What is the mean?
Answer: All you have to do is add all of the numbers together, then divide them by how many there are. In this case, adding the numbers together equals 201; since there are 8 numbers, we divide 201 by 8. That gives us 25.125.
Hope this helps! :)
Answer:
The mean of the numbers 21, 22, 24, 20, 25, and 32 is 25.
To find the mean, we add all of the numbers together and then divide by the number of numbers. In this case, we have 6 numbers, so we add them together and then divide by 6.
```
(21 + 22 + 24 + 20 + 25 + 32) / 6 = 25
```
Therefore, the mean of the numbers 21, 22, 24, 20, 25, and 32 is 25.
Step-by-step explanation: