Find the GCF (greatest common factor) of 18 and 11.
Answers
Related Questions
Given the point with Cartesian coordinates, (3√3,−3), find the polar coordinates of the point.
Answers
Answer: (6,11π/6).
Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so
because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.
So the final answer is (6,11π6).
You spin the spinner with 5 possible outcomes and flip a coin find the probability of the compound event the probability of not spinning a five and flipping heads is _
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To answer this question we will use the following expression to compute the theoretical probability that an event occurs:
\(\frac{\text{favorable cases}}{total\text{ cases}}.\)Notice that the given spin has 5 cases: 1, 2, 3, 4, and 5, and flipping a coin has 2 possible cases: head and tails.
Notice that the events are independents, therefore the probability of the compounded event is equal to the product of each probability.
The theoretical probability of not spinning a five is:
\(\frac{4}{5}\text{.}\)The theoretical probability of flipping heads is:
\(\frac{1}{2}\text{.}\)Therefore, the theoretical probability of not spinning a five and flipping heads is:
\(\frac{4}{5}\times\frac{1}{2}\text{.}\)Answer:
\(\frac{2}{5}\text{.}\)place the following words in a binary search tree. add the words to the tree in the order given. lust gluttony greed sloth wrath envy pride
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The binary search tree for the given words (lust gluttony greed sloth wrath envy pride) can be seen as attached.
Running the Python code referenced the attached binary search tree will produce results as follows:
value: envy, count: 1
value: gluttony, count: 1
value: greed, count: 1
value: lust, count: 1
value: pride, count: 1
value: sloth, count: 1
value: wrath, count: 1
search lust, result: (1, 1)
search gluttony, result: (2, 1)
search greed, result: (3, 1)
search sloth, result: (2, 1)
search wrath, result: (3, 1)
search envy, result: (3, 1)
search pride, result: (3, 1)
What is the binary search tree?The binary search tree is an advanced algorithm used for analyzing the node, its left and right branches, which are modeled in a tree structure and returning the value. The binary search tree is devised on the architecture of a basic binary search algorithm; so, it enables faster lookups, insertions, and removals of nodes.
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Which equation shows how to rewrite the sum of 42 and 54 using their greatest common factor?
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Answer:69
Step-by-step explanation:
31+38=69
A parallelogram has sides measuring 10 and 18, and an angle measuring 100 degrees. What is its area?
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Answer:
180
Step-by-step explanation:
The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:
A=10×18
A=180
The area of the parallelogram is 180 square units
find the vertex and y intercept of the quadratic function
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Answer: 5) Vertex = (2, 28) y-intercept = 40 → (0, 40)
6) Vertex = (2, 11) y-intercept = 7 → (0, 7)
Step-by-step explanation:
The y-intercept of the equation is when x = 0. It is the c-value when given in standard form: y = ax² + bx + c
To find the vertex, use the Axis of Symmetry equation to find the x-value
x = -b/(2a). Then plug the x-value into the equation to find the y-value.
5) y = 3x² - 12x + 40
↓ ↓ ↓
a=3 b= -12 c=40
\(\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(-12)}{2(3)}\quad =\dfrac{12}{6}\quad =2\)
Min: y = 3(2)² - 12(2) + 40
= 3(4) - 24 + 40
= 12 - 24 + 40
= 28
Vertex: (2, 28) y-intercept = 40
*******************************************************************************************
6) y = -x² + 4x + 7
↓ ↓ ↓
a= -1 b=4 c=7
\(\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(4)}{2(-1)}\quad =\dfrac{-4}{-2}\quad =2\)
Max: y = -(2)² + 4(2) + 7
= -(4) + 8 + 7
= -4 + 8 + 7
= 11
Vertex: (2, 11) y-intercept = 7
HOW TO CHANGE THE PERCENT INTO DECIMAL?
57%= ?
Answers
Answer:
0.57
Step-by-step explanation:
57 / 100 = 0.57
You need to divide the percent by 100
Fred is standing at a point looking north. He walks on a bearing 056° for 9.8km before stopping. He then walks an additional 3.5 km on a bearing of 112° before stopping to rest. (a) Find out how far he is away from his start point using sine or cosine rule (b) Determine the area of the enclosed shape (c) Draw neat labeled scale diagram of the same
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The area of the enclosed shape is about 14.47 km^2.
We are given that;
056° for 9.8km and 3.5 km on a bearing of 112°
Now,
We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:
y = 180° - 56° - 112°
y = 12°
Now we can use the cosine rule to find z:
z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)
z^2 ≈ 101.87
z ≈ 10.09
Therefore, Fred is about 10.09 km away from his start point.
To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:
sin(56°) = x/9.8
x = 9.8 sin(56°)
x ≈ 8.27
The area of a triangle is given by half the base times the height, so:
A = (1/2)(3.5)(8.27)
A ≈ 14.47
Therefore, by trigonometric ratios the answer will be 14.47 km^2.
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How do we know where to label base and where to label height on a trapezium. does it matter where they are on the trapezium or does it have to be in rectangular please help on question
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The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.
In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.
Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.
Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.
It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.
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Suppose a die has been loaded so that a six is scored three times more often than any other score, while all the other scores are equally likely. Express your answers to three decimals.
Part a)
What is the probability of scoring a one?
Part b)
What is the probability of scoring a six?
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a) The probability of scoring a one is 1/7, since a one is not the loaded number six and all other scores are equally likely.
b) The probability of scoring a six is 3/7, since a six is the loaded number and occurs three times as often as any other score.
Let p be the probability of scoring any number except six. Then the probability of scoring a six is 3p, since a six is scored three times more often than any other score. Since there are six equally likely possible scores on a die, we have:
p + 3p + p + p + p + p = 1
Simplifying, we get:
7p = 1
Dividing both sides by 7, we get:
p = 1/7
Therefore, the probability of scoring any number except six is 1/7, and the probability of scoring a six is 3/7. We can now answer the questions:
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A of apples has a mass of 4 kg. The average mass of each apple is 1/8 . How many apples are in the bag?
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Answer:
There are 32 apples in the bag.
Step-by-step explanation:
To find the number of apples in the bag, we can use the formula:
number of apples = total mass of apples / average mass of each apple
Given that the bag of apples has a mass of 4 kg, and the average mass of each apple is 1/8 kg, we can substitute these values into the formula to get:
number of apples = 4 kg / (1/8) kg/apple
Simplifying the right-hand side by dividing 4 kg by (1/8) kg/apple, we get:
number of apples = 4 kg * 8/apple = 32 apples
Therefore, there are 32 apples in the bag.
Answer:
Step-by-step explanation:
It is simple by averaging formula as follows
Total mass/average mass = Total apples
4/(1/8)= 32 Apples
Several expressions are shown below. Which expressions are equal to 18?
5x (9 x 2)
(9 X 2) X (4-3)
(9 X 2) + 3
22 - (9 X 2)
(9x2 + 7
4x x (9x2)
1 X 9 X 2)
3X (9x2)
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A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
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Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.
1. Find extrema and intervals of increasing and decreasing the function
\(y = \frac{ {e }^ { - (x + 2)} }{x + 2} \)
2. Find inflection points and intervals of concavity and convexity of the function:
\(y = \frac{2x - 1}{(x - 1) ^{2} } \)
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The function y = (e⁻⁽ˣ⁺²⁾) / x + 2 increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but concave downwards along (-∞, 1) ∪ (1 ,∞)
Extrema and Intervals of a FunctionAn extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
The function given;
y = (e⁻⁽ˣ⁺²⁾) / x + 2
The extrema and intervals of increase or decrease of this function are
(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)
2. The inflection points and intervals of concavity and convexity of the function
y = 2x - 1 / (x - 1)² are
The function has no inflection pointsIt's concave downwards along (-∞, 1) ∪ (1 ,∞)Learn more on intervals of a function here;
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Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes
Point
Slopes
(1, 1)
(a) 3 (b) -3 (c) -5/2 (d) Undefined
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The sketch for slope is attached below.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Point Slopes
(1, 1) (a) 3
_ (b) -3
_ (c) -5/2
_ (d) Undefined
a) Now, using slope intercept form
y - 1= 3 (x-1)
y- 1= 3x- 3
y= 3x - 2
(b) Equation of a line has a slope -3 is given by
y - 1= (-3) (x-1)
y-1 = 3- 3x
y = -3x + 4
(c) Equation of a line has a slope -5/2 is given by
y - 1= (-5/2) (x-1)
y-1 = -5/2x + 5/2
y= -5/2x + 7/2
(d) The line parallel to y axis and passes through given point : x=1
"undefined" means the line is vertical.
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Which of the following relations has a range of {-8, -6, 4}?
A. {(-8,2), (-6,2), (4,2)}
B. {(-8,2), (-6,4), (2,4)}
C. {(1, -8), (4, -6), (1, -6) (4, -4)}
D. {(1, -8), (4, -6), (1, -6) (5,4)}
Answers
Answer:
D. {(1, -8), (4, -6), (1, -6) (5,4)}
Step-by-step explanation:
The Range of a Relation
Is the set of all second elements of ordered pairs (y-coordinates). Only the elements used by the relation or function constitute the range.
For example, for the ordered pair of a relation (5,2), 5 belongs to the domain and 2 belongs to the range.
Given the range {-8,-6,4} we only have to go through the options and check which one has these values as the second element of the ordered pairs.
Note option D has y-coordinates -8, -6, -6, and 4. Those values correspond to the given range, thus the answer is
D. {(1, -8), (4, -6), (1, -6) (5,4)}
Help!!! Which of the following situations dose not have the same unit rate as the graph shown
Answers
Answer:
the answer is F
Step-by-step explanation:
one of the point is 2,10 and the costant would be 5 so g would be 30/6 which is 5 h would be 45/9 which is 5 and j would be 10/2 which is 5 so f is the correct answer because it foesnt have the same unit ratr
What is 5/6 plus 7/8?
Answers
Answer:
1 17/24
Step-by-step explanation:
Answer:
41/24 or 1 17/24
Step-by-step explanation:
A to D is an example of _____________?
A. reflection across the line y = 1
B. reflection across the line y = x
C. y-axis symmetry
D. x-axis symmetry
Answers
Answer:
D
Step-by-step explanation:
A and D are both equidistant from the x- axis, that is
A is 3 units above the x- axis and D is 3 units below the x- axis
then the x- axis is the line of symmetry
Graph the equation x^3 = 8 to find its solution.A. 2B. 1C. 8D. 4
Answers
Solution
We are given the equation
\(x^3=8\)Note:
\(\begin{gathered} 2^3=2\times2\times2=8 \\ so\text{ therefore,} \\ 8=2^3 \end{gathered}\)Come back to the equation
\(\begin{gathered} x^3=8 \\ x^3=2^3 \\ taking\text{ the cube root of both sides} \\ \sqrt[3]{x^3}=\sqrt[3]{2^3} \\ \\ x=2 \end{gathered}\)Correct Option A
x = 2
Angles are not necessarily drawn to scale.
X=?
Answers
Answer:
x = 76
Step-by-step explanation:
A line has an angle measurement of 180 degrees.
Knowing that, let's first find the angle measurement of DIJ:
180 - 107 = 73
Angle DIJ has an angle measurement of 73
To find the angle measurement of DJI, we have to apply knowledge of angles in a triangle. When you add all the angles in a triangle, they ALWAYS equal to 180 degrees.
Using that knowledge, we can add 73 and 31 and subtract that value from 180:
73 + 31 = 104
180 - 104 = 76
The angle measurement of Angle DJI is 76.
Because vertical angles are ALWAYS going to have the same angle measurement, Angle AJF is going to have an angle measurement of 76 as well.
So x = 76
Hope that helps (●'◡'●)
The value of a piece of equipment is decreasing at a rate of 7,5% yearly. If the equipment
was valued at $930 when it was purchased, which function represents the value of the
equipment x years after it was purchased? Explain,
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Answer:
y=930 x 075^x
Step-by-step explanation:
y is the price after the amount of years x being plugged into the equation. 930 is what you started with. 7.5 is what is being decreased so divide that by 100 and you get 0.075 plug in the amount of years into x and you have your equation
Suppose a sample of 879 new car buyers is drawn. Of those sampled, 288 preferred foreign over domestic cars. Using the data construct a 95% confidence interval for the population proportion of new car buyers who prefer for foreign cars over domestic cars. Round your answers to three decimal places
Answers
To find the confidence interval for a proportion, we use the following formula:
\(Confidence\text{ }interval=p\pm z\cdot\sqrt{\frac{p(p-1)}{n}}\)Where:
p is the sample proportion
z the chosen z-value
n sample size
Since we want to make a confidence interval of 95%, we need to use z = 1.96. The sample size is n = 879.
We can use cross multiplication to find p, which is the percentage of the total sample size that preferred foreign cars:
\(\begin{gathered} \frac{879}{288}=\frac{100\%}{x} \\ . \\ x=100\%\cdot\frac{288}{879} \\ . \\ x=32.765\% \end{gathered}\)p is the proportion in decimal, we need to divide by 100:
\(p=\frac{32.765}{100}=0.32765\)Now, we can use the formula:
\(Confidence\text{ }interval=0.32765\pm1.96\sqrt{\frac{0.32765(1-0.32765)}{879}}=0.32765\pm0.031028\)\(\begin{gathered} Lower\text{ }endpoint=0.32765-0.031028=0.296616 \\ Upper\text{ }endpoint=0.32765+0.031028=0.35867 \end{gathered}\)Thus, the answer is:
Lower endpoint: 0.297
Upper endpoint: 0.359
Members of the store's loyalty club get an additional %20 off their computer purchases. How much do club members pay for the computer with their discount?
thanks for the support :)
Answers
Let (1=1,2,3, 4, 5, 6, 7, 8, 9, 10
Answers
The list of elements in the sets are as follows:
A. A ∩ B = {2, 9}
B. B ∩ C = {2, 3}
C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D. B ∪ C = {2, 3, 5, 7, 9, 10}
How to find the elements in a set?Set are defined as the collection of objects whose elements are fixed and can not be changed.
Therefore,
universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 7, 8, 9}
B = {2, 3, 5, 9}
C = {2, 3, 7, 10}
Therefore,
A.
A ∩ B = {2, 9}
B.
B ∩ C = {2, 3}
C.
A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D.
B ∪ C = {2, 3, 5, 7, 9, 10}
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The maximum capacity on a school bus is 48 students . If there are 36 students on the bus , what percent of the bus is full ?
Answers
Answer:
75%
Step-by-step explanation:
75% of 3/4 of 48 is 36
Hope this helps :D
AnsWER
Step-by-step explanation:
is %## because ## happens ## be #### we #### to ###### so ## divided ## 36 ## %13
Commitment to goals can be promoted in which of the following ways?
Answers
Commitment to goals can be promoted in through:
by imagining how you will feel when you achieve themby identifying who or what might keep you from achieving themWhat is goal commitment?Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain outcomes, are significant. Commitment helps you stick to your goals in both good and bad times, when obstacles arise. Commitment is influenced by two factors: importance and
Goal commitment is generally defined as an individual's determination to devote time and effort to achieving a goal.
Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain.
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What is the y-intercept of the line that passes
through the points (1,-13) and (-10,31) ?
F.
G.
H.
J.
K.
-9
-4
0
9
Answers
The slope is
\(\frac{-13-31}{1-(-10)}=-4 \)
So, the equation is
\(y+13=-4(x-1)
\)
The y-intercept is when x=0, so
\(y+13=-4(0-1) \\ \\ y+13=4 \\ \\ \boxed{y=-9}\)
Solve if you want cookie!
Answers
Step-by-step explanation:
\(y = 2x \: \: \: \: x + y = 6 \\ y = 2x \: \: \: \: x = 6 - y \\ y = 2(6 - y) \: \: \: \: x = 6 - y \\ 3y = 12 \: \: \: \: x = 6 - y \\ y = 4 \: \: \: \: x = 2\)
Gimme tha cookie
Determine whether the sample is biased or unbiased. Explain how you know. If the sample is biased, give an example of an unbiased sample for the situation. You want to estimate the number of students in your school who play a musical instrument. You survey the first 15 students who arrive at a band class.
Answers
Answer: This is a biased sample.
Step-by-step explanation:
A biased sample is when there is some kind of "selection" in your sampling process, where in order to avoid this we should have the most random selection that we can make
Here, the sample is "the first 15 students who arrive at a band class"
Here is obviously a bias, because you could think that these students may be more "dedicated" students than the ones that will arrive later to the class, and we also have the fact that all the students in our sample are in the same class, so there is another bias.
Then we can conclude that this is a biased sample.