The lengths of the sides and angles of the triangles, obtained using Pythagorean Theorem and trigonometric ratios are;
D. 19.2
C. 5.3
F. 2·√5
G. √3
H. 8·√3
K. 18.9
O. 15.5
N. 14.5
M. 41.4°
I. 74.1°
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the triangle.
D. x = √(15² + 12²) ≈ 19.2
C. x = √(10² - 8.5²) ≈ 5.3
F. x = 2·√(5) (Special triangles)
G. tan (60°) = 30/x = √3
x = 30/√3 = 10·√3
H. x/16 = (√3)/2
x = 16 × (√3)/2 = 8·√3
x = 8·√3
K. tan(34°) = x/28
x = 28 × tan(34°) ≈ 18.9
O. cos(55°) = x/27
x = 27 × cos(55) ≈ 15.5
N. sin(16°) = 4/x
x = 4/(sin(16°) ≈ 14.5
M. x = arccos(9/12) ≈ 41.4°
I. x = arcsin(25/26) ≈ 74.1°
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A cylinder has a height of 18 cm and a diameter of 12 cm. Calculate the surface area of the cylinder. Give your answer to the nearest integer.
The surface area of the cylinder is 905 square centimeters
Finding the surface area of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Diameter, d = 12 cm
Height, h = 18 m
This means that
Radius, r = 12/2 = 6 cm
Using the above as a guide, we have the following:
Surface area = 2πr(r + h)
Substitute the known values in the above equation, so, we have the following representation
Surface area = 2π * 6 * (6 + 18)
Evaluate
Surface area = 905
Hence, the surface area is 905 square centimeters
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A rare increased in value 260% over the past 64 years. This was in increase of $300.l What was the value of the vase 65 years ago? What is the value of the vase now?
The value of the vase 65 years ago was $115.38
The value of the vase now is $415.38.
What is the value of the vase?Percentage is a measure of frequency. Percentage is the fraction of an amount that is expressed as a number out of 100. The sign that is used to represent percentage is %.
The equation that can be used to represent the increase in the value of the vase is:
Increase in the value of the vase = percentage increase x value of the vase 65 years ago
300 = 2.6v
In order to determine the value of v, divide both sides of the equation by 2.65.
v = 300 / 2.60
v = $115.38
Value of the vase now = value of the vase 65 years ago + increase
$115.38 + $300 = $415.38
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The elephants at the Norfolk Zoo are fed 1/2 of a barrel of corn each day. The buffalo are fed 7/10 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?
Addition
Subtraction
Multiplication
Division
If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.
How to solve word problems?
Recognize the issue, including all the terminology used to describe it. Recognize what we need to look for, Recognize the issue's context.
Convert the issue into an equation. Give the unknown a variable (or variables) to symbolize, Indicate exactly what the variable stands for.
Put the strategy into action and find a solution.
Given:
Elephants at the Norfolk zoo are fed = 1/2 of the barrel
Buffalo are fed 7/10 as much corn as the elephants = 7/10 * Elephants fed
= 7/10 * 1/2
= 7/20
Therefore, If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.
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NEED HELP ASAP
WILL MARK BEST ANSWER AS BRAINLEST
Answer:
The fourth one, I think
Step-by-step explanation:
math go brrr
For f(x) = 4x+1 and g(x) = x^2 -5, find (f-g)(x)
Answer:
(f-g)(x) is given by -x^2+4x+6
Step-by-step explanation:
√10 Multiple √15 is equal to
(a) 6√5
(b) √30
(c) √25
step by step
Solve :-
Answer:
Answer is 5√6 ( none of the objectives )
Step-by-step explanation:
\( \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = \sqrt{25} \times \sqrt{6} \\ = 5 \times \sqrt{6} \\ = 5 \sqrt{6} \)
Sketch BC intersecting KT at point F. F is the midpoint of BC but not KTp
The desired sketch is attached below.
To sketch the scenario where BC intersects KT at point F, with F being the midpoint of BC but not KT, you can follow these steps:
Take a blank sheet of paper or open a drawing application on your device.Draw a straight line segment BC anywhere on the paper, and label the endpoints as B and C.Draw another line segment KT, intersecting BC at some point. Make sure that KT does not pass through the midpoint of BC.Label the intersection point of BC and KT as F.Draw a small line segment perpendicular to BC from point F. This line segment represents the intersection between BC and KT.Add arrows or marks on BC and KT to indicate the directions in which the lines extend.Finally, write the labels B, C, K, and T next to their respective points on the sketch to make it clear which points correspond to each line segment.Learn more about midpoint here:
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what is the equation of a circle with center (-4,7) and radius 8?
The equation of the circle would be (x−(−4))2+(y)2=6or (x+4)2+(y−72=36.
Explanation:The equations of the circle is(−h)2+y−k)2=r2
where h is the x of the center of the circle and k is the y of the center of the circle, and r is the radius(-4,7) radus is 6h = -4k = 7r = 6plug in the values(x−(−4))2+(y−7)2=62simplify(x+4)2+(y−7)2=36.
encircle the number that are divisible by 2 a.4224 b.3012 c.8817 d. 10172
Answer:
a,b,c are divisible by 2
What are the vertex, focus, and directrix of the parabola with the equation x2+8x+4y+4=0
Simplify
10z-2 +9z-3-z
Answer:
18z-5
Step-by-step explanation:
For each line, determine whether the slope is positive, negative, zero, or undefined.
Answer:
1. Undefined
2. Negative
3. Zero
4. Positive
Step-by-step explanation:
1. Undefined, the line moves in both directions vertically. It's impossible to tell what the slope is.
2. Negative, the line is decreasing at a constant rate, the slope is negative.
3. Zero, the line doesn't increase or decrease, therefore the slope is 0. (No changes)
4. Positive, the line is increasing at a large rate, the slope is positive.
A bag is filled with an equal number of red, yellow, green, blue, and purple socks. The theoretical probability of a child drawing 2 yellow socks from the bag with replacement is one fifth. If the experiment is repeated 175 times, what is a reasonable prediction of the number of times he will select 2 yellow socks?
one fifth
10
25
35
35 is a reasonable prediction of the number of times he will select 2 yellow socks?
what is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
What is event?In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.
In the given question,
The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:
P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25
So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.
To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:
E(X) = n * p
where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.
In this case, n = 175 and p = 1/25. So,
E(X) = 175 * (1/25) = 7
Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.
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Bookwork code: A99
The table shows the hair colours of the
students in a sports team.
Hair colour
Black
Blonde
Brown
Frequency
1
< Back
a) What fraction of the students have brown
hair? Give your answer in its simplest form.
b) How many sections on this pie chart
would you shade to show the students with
brown hair?
4
2
Scroll down
Watch video
Answer >
A fraction of the students who have brown hair is equal to 1/7.
You should shade only one (1) section on the pie chart to show the number of students with brown hair.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.
Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;
Number of brown hair = 1 brown hair.
Number of blonde hair = 4 blonde hair.
Number of black hair = 2 black hair.
Therefore, the total number of hairs is equal to 7 hairs.
For the fraction of students with brown hair, we have;
Fraction = 1/7.
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hi loves is this correct?
Solve for X.
X^2 - 2x + 1 = 0
X= 1?
Answer:
yes x=1
Step-by-step explanation:
x\(x^{2} -2x+1=0\\(x-1)^{2}=0 x-1=0 \\x=1\)
Internet prices for glasses are often considerably lower than those at the brick and mortar stores but quality is another question. To address that issue, some optometrists ordered 154 adult pairs of spectacles from various online stores. Of the 154 pairs of spectacles, 44 pairs of eye wear contained at least one lens that did not pass optical analysis testing.
Required:
a. Conduct a test of hypotheses with the intent of establishing that the probability of not passing the optical analysis testing is greater than 0.20. Use level of significance 0.05.
b. Calculate the p-value and comment.
Help please When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
When writing a proof, we construct the first statement by copying the “given” statement(s) from the original problem. Hence, option D is correct.
When writing a proof, the first statement is typically either the "given" statement(s) or a previously proven result. Therefore, option D ("By copying the 'given' statement(s) from the original problem") is often the correct choice for constructing the first statement.
In some cases, option C ("By writing the next logical statement from the current one") may be a more appropriate choice. Regardless of which option is chosen, it is important to clearly justify each statement in the right column of the proof.
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Why does Paine use the example of
Massanello?
O to compare the situation to a man who insisted on
independence from Spain and then became king
O to illustrate the importance of protesting loudly in a public
place to get support for the fight for freedom
O to identify a hero that the American colonists can look up
to and model their fight after
O to prove that even simple fishermen have something
important to contribute to society
Answer: A
Step-by-step explanation: I just did it.
A quarter is tossed. How many total number of outcomes are there? total number of outcomes
Answer:
2
Step-by-step explanation:
Answer:
2 is the correct answer please mark brainliest
Step-by-step explanation:
Numerical Problems: a. From From the given figure, identify which path represents distance and displacement. Also, calculate the length of paths (distance travelled and displacement). h Hantra initial point A 9m 3m B 5m G 6m C C E
Path A-B-C-E represents the distance traveled, which is 18 meters.
Path A-G-C-E represents the displacement, which is 17 meters.
From the given figure, we can identify the paths and calculate the distance and displacement.
Path A-B-C-E represents the distance traveled, and path A-G-C-E represents the displacement.
Let's calculate the lengths of both paths:
Distance traveled (Path A-B-C-E):
Length of AB = 9m
Length of BC = 3m
Length of CE = 6m
Total distance traveled = Length of AB + Length of BC + Length of CE
= 9m + 3m + 6m
= 18m
Therefore, the distance traveled along path A-B-C-E is 18 meters.
Displacement (Path A-G-C-E):
Length of AG = 5m
Length of GC = 6m
Length of CE = 6m
Total displacement = Length of AG + Length of GC + Length of CE
= 5m + 6m + 6m
= 17m
Therefore, the displacement along path A-G-C-E is 17 meters.
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CAN ANYONE HELP ME PLEASE? Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.
Answer:
The adult ticket costs $18 and the children ticket costs $13.
Step-by-step explanation:
Let the price of the adult ticket be a.
Let the price of the children ticket be c.
Three adults and four children must pay $106. This implies that:
3a + 4c = 106 _______(1)
Two adults and three children must pay $75. This implies that:
2a + 3c = 75 ________(2)
We have two simultaneous equations:
3a + 4c = 106 _____(1)
2a + 3c = 75 ______(2)
Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):
6a + 9c = 225
- (6a + 8c = 212)
c = $13
Put this value of c in (2):
2a + 3*13 = 75
2a + 39 = 75
=> 2a = 75 - 39
2a = 36
a = 36/2 = $18
Therefore, the adult ticket costs $18 and the children ticket costs $13.
Jamie cut a rope into thirds. he used two of the pieces to make a swing. he use equal length of the leftover rope on four picture frames. what fractions of the original rope did he use for each picture frame
Answer:
1/12
Step-by-step explanation:
Since he divided the rope into 3 original pieces, and used two of them, he only had 1/3 of the rope left over. Then he divided the leftover 1/3 into 4 parts, so you would multiply 1/3 by 1/4 to get 1/12.
The rubber playground mulch is sold in packages that cover 300 square feet each. what expression represents the number of packages of mulch that will be needed to cover both rounded ends?
The expression represents the number of packages of mulch that will be needed to cover both rounded ends is 600/x
How to determine the expression represents the number of packages of mulch that will be needed to cover both rounded ends?The given parameters are:
Area covered = 300 square feet
Number of ends = 2
So, the total surface area is:
Total surface area = Area covered * Number of ends
This gives
Total surface area = 300 * 2
Total surface area = 600 square feet
Let the area covered by each package of mulch be x.
So, the number of mulch is
Number = Area covered/area covered by each
This gives
Number = 600/x
Hence, the expression represents the number of packages of mulch that will be needed to cover both rounded ends is 600/x
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AB is a radius of the circle. The circumference of the circle is 119.56. Find the
length of AB, rounding to the nearest tenth.
B
A
Answer:
19.0285
Step-by-step explanation:
For this, we have to work backwards.
First, the equation for the circumference of a circle is:
\(2\pi r\)
We already know the circumference, so we can solve for r:
\(119.56=2\pi r\)
divide both sides by 2
\(59.78=\pi r\)
divide both sides by pi
\(19.0285...=r\)
So, depending on the answer choices, the answer is 19.0285 rounded to the according decimal place.
Hope this helps! :)
Finde the value of x in the proportion ( 5x+ 1 ):3 =(2x +2): 7(6 x) = (4x) :7
In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.
In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.
To find the value of x in the given proportions, let's solve them one by one:
(5x + 1) : 3 = (2x + 2) : 7
To solve this proportion, we can cross-multiply:
7(5x + 1) = 3(2x + 2)
35x + 7 = 6x + 6
Subtracting 6x from both sides and subtracting 7 from both sides:
35x - 6x = 6 - 7
29x = -1
Dividing both sides by 29:
x = -1/29
Therefore, the value of x in the first proportion is -1/29.
(6x) : (4x) = 7
To solve this proportion, we can simplify the left side:
6x / 4x = 7
Dividing both sides by 2x:
3/2 = 7
This equation is not true, as 3/2 is not equal to 7.
Therefore, there is no value of x that satisfies the second proportion.
In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.
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Hilary is making lemonade.She uses 2 cups of lemon juice for every 6 cups of water to make the lemonade.The recipe below shown below will make one pitcher of lemonade.
Hilary makes 5 pitchers.How much of each ingredient does she use?
Answer:
she uses 10 cups of lemon juice and 30 cups of water for 5 pitchers
Step-by-step explanation:
you multiply the ingredients for one pitcher by 5 because they are making 5 pitchers
A grain is a measure of weight equal to 0.06 gram. An aspirin tablet
weighs 5 grains. How many milligrams
does the tablet weigh?
Answer:
300 milligrams
Step-by-step explanation:
You find the answer in grams which is 0.3 then you convert it to milligrams
Can y’all help me on question six?!
Answer:
The answer is C (2:1)
Step-by-step explanation:
1. The greatest common factor of 8 and 4, is 4. We need to divide both numbers by the GCM, 4.
8 / 4 = 2
4 / 4 = 1
Therefore, the answer is 2:1 (C)
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 10% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 10% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 13 customers buy a magazine?
Answer:
0.55% probability that exactly 5 out of the first 13 customers buy a magazine
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of other customers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
10% of his customers buy a magazine
This means that \(P = 0.1\)
What is the probability that exactly 5 out of the first 13 customers buy a magazine?
This is P(X = 5) when n = 13. So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 5) = C_{13,5}.(0.1)^{5}.(0.9)^{8} = 0.0055\)
0.55% probability that exactly 5 out of the first 13 customers buy a magazine
Answer:
\( P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554\)
So then he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554
Step-by-step explanation:
Let X the random variable of interest "number of customers that buy a magazine", on this case we can model the variable of interest with this distribution:
\(X \sim Binom(n=13, p=0.1)\)
The probability mass function for the Binomial distribution is given as:
\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)
Where (nCx) means combinatory and it's given by this formula:
\(nCx=\frac{n!}{(n-x)! x!}\)
We want to find this probability:
\( P(X=5)\)
And using the probability mass function we got:
\( P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554\)
So then he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554
What is the measure of one exterior angle of a 15-sided regular polygon?
O 12 degrees
O 168 degrees
O24 degrees
O 156 degrees
Answer:
24°
Step-by-step explanation:
For an n-sided regular polygon, the sum of internal angles = (n-2)×180°
Since all internal angles are equal, the internal angle can is given as:
Here, it is given that the polygon has 15 sides.
So n = 15
So each internal angle is 156°.
Internal and external angles are always supplementary. So the sum of the internal and external angles is 180°.
So external angle = 180° - 156° = 24°.
The measure of each external angle is 24°.