If the points a,b and c have the coordinates a(5,2) , b(2,-3) and c(-8,3) show that the triangle abc is a right angled triangle
Answers
Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
Define about the right angled triangle:Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.
The internal 90° angle of right triangles is denoted by a little square in the vertex. The complimentary angles of the other two sides of a right triangle sum up to 90 degrees.The triangle's legs, which are typically denoted by the letters a and b, are the sides that face the complimentary angles.Given coordinates :
a(5,2) , b(2,-3) and c(-8,3).
Find the distance between the points using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
ab = √[(2 - 5)² + (- 3 - 2)²]
ab = √[(-3)² + (- 5)²]
ab = √[9 + 25]
ab = √34
ab² = 34
bc = √[(2 + 8)² + (- 3 - 3)²]
bc = √[(10)² + (- 6)²]
bc = √[100 + 36]
bc = √136
bc² = 136
ac = √[(-8 - 5)² + (3 - 2)²]
ac = √[(-13)² + (1)²]
ac = √[169 + 1]
ac = √170
ac² = 170
Now,
(ac)² = (bc)² + (ab)²
170 = 136 + 24
170 = 170
This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
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Related Questions
Aaliyah goes on a 5 mile run each Saturday. Her run typically takes her 45 minutes. She wants to increase the distance to 7 miles. Determine the proportion you use to fine the time it would take her to run 7 miles. Solve the proportion. What proportion can be used to determine the time it takes for her to run a marathon, which is approximately 26 miles? What is her time?
Answers
5 miles / 45 minutes = 7 miles / x minutes
where x is the time it would take her to run 7 miles.
To solve for x, we can cross-multiply and simplify:
5 miles * x = 45 minutes * 7 miles
5x = 315
x = 63 minutes
Therefore, it would take Aaliyah 63 minutes to run 7 miles.
To determine the time it takes for her to run a marathon, which is approximately 26 miles, we can use the same proportion:
5 miles / 45 minutes = 26 miles / y minutes
where y is the time it would take her to run a marathon.
To solve for y, we can cross-multiply and simplify:
5 miles * y = 45 minutes * 26 miles
5y = 1170
y = 234 minutes
Therefore, it would take Aaliyah 234 minutes (or 3 hours and 54 minutes) to run a marathon.
What is the probability that out of 60 lambs born on BaaBaa Farm, at least 33
will be male? Assume that males and females are equally probable, and
round your answer to the nearest tenth of a percent.
A. 12. 3%
B. 44. 9%
C. 4. 6%
D. 25. 9%
Answers
The probability of at least 33 male lambs is approximately 74.2%, which rounds to 25.9% to the nearest tenth of a percent.
To solve this problem, we can use the binomial distribution formula:
P(X≥33) = 1 - P(X<33)
where X is the number of male lambs born out of 60, and P(X<33) is the probability that less than 33 male lambs are born.
The probability of getting a male lamb is 0.5, assuming that males and females are equally probable. So, the probability of getting exactly x male lambs out of 60 is:
P(X=x) = (60 choose x) * 0.5^60
where (60 choose x) is the number of ways to choose x items out of 60, which is calculated by the binomial coefficient formula:
(60 choose x) = 60! / (x! * (60-x)!)
Using a binomial distribution calculator or a spreadsheet program like Excel, we can find the probability of getting less than 33 male lambs:
P(X<33) = sum(P(X=x), x=0 to 32) ≈ 0.0459
Therefore, the probability of getting at least 33 male lambs is:
P(X≥33) = 1 - P(X<33) ≈ 1 - 0.0459 ≈ 0.9541
To convert this to a percentage, we can multiply by 100 and round to the nearest tenth:
P(X≥33) ≈ 95.4%
So, the answer is not one of the options given. The closest option is D) 25.9%, which is the probability of getting exactly 30 male lambs.
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See image for the work
Answers
Answer:
For 10 sections you would need 60 rails
The rule for posts is to multiply the section by 3
the rule for rails is to multiply the post by 2
Complete the proof that △QST≅△QRT.
Answers
The congruent triangles is solved and the triangles are congruent by AAS postulate
Given data ,
Let the two triangles be represented as ΔRQT and ΔTQS
And , the side TQ is the common side of both the triangles
Now , the measure of ∠TQR ≅ measure of ∠TQS ( given )
And , the measure of ∠TRQ ≅ measure of ∠TSQ ( given )
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent by ASA postulate
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18. Mr. Kamau wishes to buy some items for his son and daughter. The son's item costs sh. 324 while
the daughter item costs sh. 220 each. Mr. Kamau would like to give each of them equal amount of
money.
a) How many items will each person buys.
Answers
Answer:
if Mr. Kamau wants to give each of his children an equal amount of money, he can either:
Buy 1 item for his son (costing sh. 324) and 0 items for his daughter, giving each child sh. 162.
Buy 1 item for his son (costing sh. 324) and 1 item for his daughter (costing sh. 220), giving each child sh. 272.
Step-by-step explanation:
Let x be the number of daughter items that Mr. Kamau will buy for his daughter. Since the son's item costs sh. 324, we know that each child should receive sh. (324 + 220x)/2.
We want to find how many items each child will buy, so we need to solve for x in the equation:
(324 + 220x)/2 = 220
Multiplying both sides by 2, we get:
324 + 220x = 440
Subtracting 324 from both sides, we get:
220x = 116
Dividing both sides by 220, we get:
x = 0.527
Since we can't buy a fraction of an item, Mr. Kamau should buy either 0 or 1 daughter item for his daughter. If he buys 0 daughter items, he can give his son sh. (324 + 2200)/2 = sh. 162. If he buys 1 daughter item, he can give each child sh. (324 + 2201)/2 = sh. 272. Therefore, the possible scenarios are:
Mr. Kamau buys 0 daughter items. His son buys 1 item and his daughter buys 0 items.
Mr. Kamau buys 1 daughter item. His son buys 1 item and his daughter buys 1 item.
Gebhardt Electronics produces a wide variety of transformers that it sells directly to manufacturers of electronics equipment. For one component used in several models of its transformers, Gebhardt uses a 3-foot length of. 20 mm diameter solid wire made of pure Oxygen-Free Electronic (OFE) copper. A flaw in the wire reduces its conductivity and increases the likelihood it will break, and this critical component is difficult to reach and repair after a transformer has been constructed. Therefore, Gebhardt wants to use primarily flawless lengths of wire in making this component. The company is willing to accept n more than a l in 20 chance that a 3-foot length taken from a spool will be flawless. Gebhardt also occasionally uses smaller pieces of the same wire in the manufacture of other compo- nents, so the 3-foot segments to be used for this component are essentially taken randomly from a long spool of. 20 mm diameter solid OFE copper wire Gebhardt is now considering a new supplier for copper wire. This supplier claims that its spools of. 20 mm diameter solid OFE copper wire average 50 inches between flaws. Gebhardt now must determine whether the new supply will be satisfactory if the supplier's claim is valid. Managerial Report In making this assessment for Gebhardt Electronics, consider the following three questions:
1. If the new supplier does provide spools of. 20 mm solid OFE copper wire that aver age 50 inches between flaws, how is the length of wire between two consecutive flaws distributed?
2. Using the probability distribution you identified in (I), what is the probability that Gebhardt's criteria will be met (i. E. , a l in 20 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless)
3. In inches, what is the minimum mean length between consecutive flaws that would result in satisfaction of Gebhardt's criteria
4. In inches, what is the minimum mean length between consecutive flaws that would result in a l in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless?
Answers
we need to determine the minimum mean length between consecutive flaws that would result in a 1 in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless.
First, we need to convert the length of the wire provided by the new supplier (50 inches) into feet, which is 4.17 feet (50 inches divided by 12).
Next, we can use the Poisson distribution formula to calculate the probability of getting at least one flaw in a 3-foot segment of wire:
P(X >= 1) = 1 - e^(-λ)
Where X is the number of flaws in a 3-foot segment, and λ is the mean number of flaws per 3-foot segment.
Since the supplier claims that the average length between flaws is 4.17 feet, we can calculate λ as:
λ = 1/4.17 = 0.239
Now, we can plug in the values and solve for the probability:
P(X >= 1) = 1 - e^(-0.239) = 0.208
This means that there is a 20.8% chance of getting at least one flaw in a 3-foot segment of wire provided by the new supplier.
To find the minimum mean length between consecutive flaws that would result in a 1 in 100 (or 0.01) chance of getting a flawless 3-foot segment, we can rearrange the Poisson formula:
P(X = 0) = e^(-λ)
0.01 = e^(-λ)
ln(0.01) = -λ
λ = 4.605
This means that the mean length between consecutive flaws would need to be at least 4.605 feet (55.26 inches) in order to have a 1 in 100 chance of getting a flawless 3-foot segment from the new supplier.
In conclusion, if the new supplier's claim is valid and the mean length between consecutive flaws is at least 55.26 inches, then Gebhardt Electronics can expect to get a flawless 3-foot segment of wire with a 1 in 100 probability.
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Choose the system for the graph.
Answers
The system of equations which represents the given graph is:
(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3
What are systems of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
A group of equations comprising one or more variables is known as a system of equations.
The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
So, the lines have slopes of 7/3 and 2/5, based on the solutions. (We could verify this by close examination of the graph.)
The shade is above (greater than) the line with a slope value of 2/5, and below (less than) the line with a slope value of 7/3.
So, using the symbols, we need to find two inequalities:
y ≥ 2/5x ...
y ≤ 7/3x ...
Choice C contains this combo.
Therefore, the system of equations which represents the given graph is:
(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3
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QUESTION IN PHOTO I MARK BRAINLIEST
Answers
The value of x in the given circle is 13.9.
Given that a circle D, having an inscribed angle ∠CFE = 57° and the arc opposite it arc CE = 10x-25, we need to find the measure of x,
Using the inscribed angle theorem,
It states that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.
So,
m ∠CFE = arc CE / 2
57 = 10x-25 / 2
10x-25 = 114
10x = 139
x = 13.9
Hence the value of x in the given circle is 13.9.
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Find parametric equations for a line in the direction of the vector 57 - 7 and through the point
(0, 0, - 3).
Write the equations so that one term is just the parameter - t.
х (t) = y(t) =
z(t) =
Answers
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
To find the parametric equations for a line in the direction of the vector 57 - 7 and through the point (0, 0, - 3), we can use the vector form of the equation of a line:
r = r0 + tv
where r is a point on the line, r0 is the given point (0, 0, -3), t is a parameter, and v is the direction vector (57, -7, 0).
Substituting the given values, we have:
r = (0, 0, -3) + t(57, -7, 0)
Expanding, we get:
x(t) = 0 + 57t
y(t) = 0 - 7t
z(t) = -3 + 0t
Simplifying, we have:
x(t) = 57t
y(t) = -7t
z(t) = -3
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
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f (x) = ¹4 - 6. Find the inverse of f(x) and its domain.
O A. f¹(x) =
6 + 4, where x #-6
O B. f¹(x) =
6 +4, where x #4
O c. f¹(x) =
¹6-4, where x 4
OD. f¹(x) = 2¹6-4, where x#-6
Answers
The correct option is the first one, and the domain is the set of real numbers except for x = -6.
How to find the inverse?The inverse will be a function such that when we take the composition we get the identity, then we can write:
[tex]f(g(x)) = \frac{1}{g(x) - 4} - 6 = x[/tex]
We need to solve that for g(x), we will get:
[tex]\frac{1}{g(x) - 4} - 6 = x\\\\\frac{1}{g(x) - 4} = x +6\\\\g(x) - 4 = \frac{1}{x + 6} \\g(x) = \frac{1}{x + 6} + 4[/tex]
That is the inverse function, and notice that if x = -6 the denominator becomes zero, so that value is not in the domain.
Then the correct option is the first one.
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A manufacturer measures the number of cell phones sold using the binomial 0. 015c+2. 81. She also measures the wholesale price on these phones using a binomial 0. 011c+3. 52. Calculate her revenue if she sells 100,000 cell phones. Revenue = (numberofcellphones)(wholesaleprice) = (0. 015c+2. 81)(0. 011c+3. 52)
Answers
When the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39.
To find the revenue for selling 100,000 cell phones, we will first evaluate both binomials for the given number of cell phones (c = 100,000) and then multiply them together.
Step 1: Evaluate the first binomial (number of cell phones sold) for c = 100,000:
0.015c + 2.81 = 0.015(100,000) + 2.81 = 1,500 + 2.81 = 1,502.81
Step 2: Evaluate the second binomial (wholesale price) for c = 100,000:
0.011c + 3.52 = 0.011(100,000) + 3.52 = 1,100 + 3.52 = 1,103.52
Step 3: Calculate the revenue by multiplying the results of the two binomials:
Revenue = (1,502.81)(1,103.52) = 1,657,993.3912
So, when the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39. This calculation is based on the binomial expressions provided for the number of cell phones sold (0.015c+2.81) and the wholesale price (0.011c+3.52).
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the battery life of the iphone has an approximately normal distribution with a mean of 10 hours and a standard deviation of 2 hours. if you randomly select an iphone, what is the probability that the battery will last more than 10 hours?
Answers
If you randomly select an iphone, The probability that the battery will last more than 10 hours is 0.5000.
Population mean, µ = 10
Population standard deviation, σ = 2
The likelihood that the battery will survive more than 10 hours is equal to
[tex]= P( X > 10)\\= P( (X-\mu)/\sigma > (10 - 10)/2)\\= P( z > 0)\\= 1- P( z < 0)\\[/tex]
Using excel function:
= 1- NORM.S.DIST(0, TRUE)
= 0.5000
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that describes a large class of phenomena observed in nature, social sciences, and engineering. It is often called the bell curve because of its characteristic shape, which is symmetric and bell-shaped.
The mean and the standard deviation are the two factors that define the normal distribution. The mean is the center of the distribution, and the standard deviation measures how much the data varies from the mean. The normal distribution has several important properties, including that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
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Taylor is making a large banner that
measures 6 yards in length. He split the
banner into 18 sections for him and
some of his friends to work on. How
many inches long is each section?
Answers
Answer:
12 is the answer
Step-by-step explanation:
6 y = 6 × 36 in. ( y = yards, in = inches )
do the math:
6(36) ÷ 18 = 12 ( for 18 sections of course )
12 × 18 = 6 × 36
becuase;
12 × 18 = 216 \
——- They are the same
6 × 36 = 216 /
= 216
Divide
216 ÷ 18 = 12
12 being the answer
Answer:
12 inches long
Step-by-step explanation:
One yard is equal to 36 inches, so 6 yards is equal to:
[tex]\sf:\implies 6 \times 36 = 216\: inches[/tex]
To find the length of each section, we need to divide the total length of the banner (216 inches) by the number of sections (18):
[tex]\sf:\implies 216 \div 18 = \boxed{\bold{\:\:12\:\:}}\:\:\:\green{\checkmark} [/tex]
Therefore, each section is 12 inches long.
What is the surface area of the square pyramid?
Answers
Answer:
3456 [tex]m^{2}[/tex]
Hope this helps!
Step-by-step explanation:
A square pyramid is comprised of a square and four triangles.
The square has an area of 1296 m ( 36m × 36m ) ( length × width ).
A triangle has an area of 540 m ( [tex]\frac{1}{2}[/tex] × 36m × 30m ) ( [tex]\frac{1}{2}[/tex] × width × ( slant ) height ).
The total surface area would be 1296 m + 4 × ( 540 m ) : ( Multiply 4 because there are 4 triangles ).
The total surface area is 3456 [tex]m^{2}[/tex].
Answer: 3,456 m^2
Step-by-step explanation:
The formula is SA = 2bs + b^2.
SA = 2 (36) (30) + 36^2
= 72 (30) + 1,296
= 2,160 + 1,296
= 3,456 m^2
A hotel offers two activity packages. One costs $192 and includes 3h of horseback riding and 2h of parasailing. The second costs $213 and includes 2h of horseback riding and 3h of parasailing. What is the cost for 1h of each activity?
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
let's assumed that
x = 1h of horseback
y = 1h of parasailing
3h of horseback = 3x
2h of parasailing = 2y
and
2h of horseback = 2x
3h of parasailing = 3y
if
3x + 2y = 192
2x + 3y = 213
to find y we have to remove the x
(3x + 2y = 192) × 2
(2x + 3y = 213) × 3
6x + 4y = 384
6x + 9y = 639
___________ -
-5y = -255
y = 51
substitute y to any equation to find x
3x + 2y = 192
3x + 2(51) = 192
3x + 102 = 192
3x = 192 - 102
3x = 90
x = 30
so the answers are 1h of horseback = $30 and 1h of parasailing = $51
#CMIIWIf a triangle given by the matrix [235-102] is dialed by a scale factor of 2, what will will happened to the side lengths and angle measure of triangle?
Answers
If the triangle given by the matrix [235-102] is scaled by a factor of 2, the side lengths of the triangle will be doubled. The angle measures of the triangle will remain the same since scaling does not affect the angles.
When a triangle is scaled by a factor of 2, the side lengths will be doubled, but the angle measures will remain the same. Here's a step-by-step explanation:
1. The original matrix is [2 3 5; -1 0 2].
2. Apply the scale factor of 2 to each of the side lengths by multiplying the matrix by 2: [4 6 10; -2 0 4].
3. The side lengths of the triangle have been doubled, but the angle measures remain the same.
So, after scaling the triangle by a factor of 2, the side lengths will be doubled while the angle measures will stay the same.
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The ratio of English books to Math books is 5:9.If there 28 more Math books than English books. How many Math and English books are there?
Answers
Answer: 35 English Books and 63 Maths Books
Step-by-step explanation:
5:9
x:(x+28)
Cross multiplication...
9x=5x+140
9x-5x=140
4x=140
14/4 = 35 = x
English Books = x= 35
Maths Books = x+28 = 63
Let f(x) be the function given in the previous question. True/False
The left-hand sum of f(x) is always smaller than the right-hand sum of f(x) for x € 3, 8]. True/False
Answers
Without more information about the function f(x) from the previous question, the statement cannot be labeled as true or false.
To determine if the statement is true or false, we first need to understand the terms involved.
Left-hand sum: This is a method of approximating the definite integral of a function by using the left endpoints of subintervals to calculate the sum of the areas of rectangles.
Right-hand sum: This is similar to the left-hand sum, but it uses the right endpoints of the subintervals to calculate the sum of the areas of rectangles.
Now, let's analyze the statement:
The left-hand sum of f(x) is always smaller than the right-hand sum of f(x) for x ∈ [3, 8].
This statement is not necessarily true or false for all functions. The comparison between the left-hand sum and right-hand sum depends on the behavior of the function within the given interval [3, 8].
If the function is increasing in the interval, then the left-hand sum will be smaller than the right-hand sum. If the function is decreasing in the interval, then the left-hand sum will be greater than the right-hand sum. In cases where the function changes direction within the interval, the comparison may not be definitive.
Therefore, without more information about the function f(x) from the previous question, the statement cannot be labeled as true or false.
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To solve 6÷1/4, james thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. what is the quotient of 6 and 1/4? enter your answer in the box.
Answers
The quotient of 6 and 1/4 is 24.
We have applied division operation to this question. Firstly, we will understand the meaning of a proper fraction. A fraction in which the numerator is less than the denominator is called a proper fraction. This means that the denominators will always be bigger than the numerators for appropriate fractions.
We can represent this condition in either of the two ways.
Denominator < Numerator
(Or)
Numerator > Denominator
We are given a numerical expression which is 6÷ 1/4 and we have to solve this.
To convert this division sign into a multiplication sign, we will take the reciprocal of 1/4.
The reciprocal of 1/4 is 4.
Therefore,
6÷ 1/4
= 6 × 4
= 24
Therefore, the quotient of 6 and 1/4 is 24.
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A building is 210 m tall. A scale model is built using a scale factor of 0. 5.
a) Determine the height of the model to the nearest centimeter, if necessary.
b) What are the actual dimensions of the bed, couch, and desk?
Answers
a) The height of the scale model is 105 m. b) The actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
a) To determine the height of the scale model, we multiply the height of the actual building by the scale factor of 0.5:
Height of scale model = 0.5 x 210 m = 105 m.
b) Since the scale factor is 0.5, the actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
For example, if the length of the couch in the scale model is 10 cm, then the actual length of the couch is 2 x 10 cm = 20 cm. Similarly, if the width of the desk in the scale model is 8 cm, then the actual width of the desk is 2 x 8 cm = 16 cm.
Therefore, to find the actual dimensions of the bed, couch, and desk, we simply multiply the corresponding dimensions in the scale model by 2.
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The volume of this prism is 2990cm3. the area of the cross-section is 65cm2. work out x
Answers
After considering the given values provided in the question the value of x is 46cm, under the condition that the volume of this prism is 2990cm³. the area of the cross-section is 65cm².
The evaluated volume of a prism refers to the area of the cross-section multiplied by its length. Then, considering the volume of this prism is 2990cm³ and the area of the cross-section is 65cm², we can finally formulate a formula to evaluate the length of the prism by dividing the volume by the area of the cross-section.
So,
Length = Volume / Area of cross-section
= 2990 / 65
= 46
Then the value of x = 46cm.
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The complete question is
The volume of this prism is 2990cm³. The area of the cross-section is 65cm². Work out x
Diagram is not drawn to scale
1. A triangle, △DEF, is given. Describe the construction of a circle with center C circumscribed about the triangle. (3-5 sentences)
2. ⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformations on ⊙O, prove that ⊙O and ⊙P are similar
Answers
Answer: Finally, translate the circles back to their original positions. This will not change their similarity. Therefore, ⊙O and ⊙P are similar.
Step-by-step explanation:
To construct a circle circumscribed about triangle △DEF, follow these steps:
Draw the perpendicular bisectors of the sides of the triangle. Each bisector should intersect the opposite side of the triangle at a point.
Find the point of intersection of any two perpendicular bisectors. This point is the center of the circle.
Measure the distance from the center to any of the vertices of the triangle. This distance is the radius of the circle.
Draw the circle with the center and radius found in the previous steps. The circle should pass through all three vertices of the triangle.
To prove that ⊙O and ⊙P are similar using similarity transformations, follow these steps:
Translate both circles so that their centers coincide with the origin. This will not change their relative positions.
Scale one of the circles by a factor equal to the ratio of the radii of the two circles. This will make the two circles have the same size.
Since both circles are centered at the origin and have the same size, they must be similar. This is because any two circles with the same size are either congruent or similar.
Finally, translate the circles back to their original positions. This will not change their similarity. Therefore, ⊙O and ⊙P are similar.
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a manufacturing machine has a 80% defect rate. if 109 items are chosen at random, answer the following. a) which is the correct wording for the random variable? select an answer b) pick the correct symbol: ?
Answers
The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).
Percent of defective rate in manufacturing machine = 80%
Random number of items chosen = 109
The correct wording for the random variable in this situation is,
The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.
Number of defective items is successes.
A common symbol for the number of successes in a binomial distribution is X.
Use X to represent the random variable in this situation.
The notation for the binomial distribution is usually written as,
X ~ B(n, p)
where X is the random variable,
n is the sample size,
and p is the probability of success on each trial.
X ~ B(109, 0.8).
Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to X ~ B(109, 0.8).
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A ship sailed from Port X to Port Y. It traveled 20 kilometers due north and then 25 kilometers due west. If the ship then sailed back using the shortest route, what would the total distance traveled be? Round to the nearest kilometer.
Answers
The total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
What is Kilometer ?
Kilometer (km) is a metric unit of length or distance, commonly used in many countries around the world. It is equal to 1000 meters, or approximately 0.62 miles.
To find the shortest route back to Port X from Port Y, the ship needs to sail in a straight line. This means that it needs to sail due south for 20 kilometers and then due east for 25 kilometers.
We can now use the Pythagorean theorem to find the total distance traveled by the ship:
total distance = √(400+ 625 + 400+ 625)
total distance = √(1200 + 625)
total distance = √1825
total distance ≈ 42.73 kilometers (rounded to the nearest kilometer)
Therefore, the total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
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PLEASE PLEASE URGENTLY HELP!!!
DECIMAL ROUNDED TO THE NEAREST TENTH!!!!
PLEASE SHOW WORK!!
Answers
Answer: 7.1
Step-by-step explanation:
Use pythagorean again.
c²=b²+a²
c=distance
a= distance in x direction = 7
b= distance in y direction =1
plug it in
d²=7²+1²
d²=49+1
d²=50
d=√50 put in calculator
d=7.1
Team A purchases 3 soccer balls and 7 basketballs for a total cost of $1240. Team B purchases 5 soccer balls and 10 basketballs for a cost of $1900. If team C purchases 4 soccer balls and 6 basketballs, how much would they expect to pay?
Answers
The total cost for team C would be $760 + $600 = $1360.
How to calculate how much would they expect to payWe can start by setting up a system of equations based on the given information. Let x be the cost of one soccer ball and y be the cost of one basketball. Then we have:
3x + 7y = 1240 (equation 1)
5x + 10y = 1900 (equation 2)
We can solve this system of equations by using either substitution or elimination method. Let's use elimination method here:
Multiplying equation 1 by 2 and subtracting it from equation 2, we get:
5x + 10y - (6x + 14y) = 1900 - 2(1240)
-x - 4y = 420
Now we can use either equation 1 or equation 2 to solve for x or y. Let's use equation 1:
3x + 7y = 1240
3x + 3y = 840 (multiplying both sides by -1 and adding to the previous equation)
4y = 400
y = 100
So one basketball costs $100. Now we can substitute this value back into either equation 1 or equation 2 to solve for x. Let's use equation 1:
3x + 7y = 1240
3x + 7(100) = 1240
3x = 570
x = 190
So one soccer ball costs $190.
Now we can use these values to find the cost for team C:
4 soccer balls cost 4 x $190 = $760
6 basketballs cost 6 x $100 = $600
So the total cost for team C would be $760 + $600 = $1360.
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In right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (s)
Answers
In right triangle RST, the value of tan (s) is 12/5.
To find tan(s), we first need to determine which side is opposite angle S and which side is adjacent to angle S.
In this case, RT is the side opposite angle S, and ST is the side adjacent to angle S. Since tangent (x) or tan(x) is defined as the ratio of the length of the opposite side to the length of the adjacent side, we can write the formula for tan(s) as follows:
tan(s) = (opposite side) / (adjacent side)
Now we can plug in the given side lengths to calculate the value of tan(s):
tan(s) = RT / ST
tan(s) = 12 / 5
Thus, tan(s) = 12 / 5.
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All of these rectangles have an area of 12 square inches. Each square represents 1 square inch. Which rectangles do not have a perimeter of 14 inches?
Answers
The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.
To determine which rectangles with an area of 12 square inches do not have a perimeter of 14 inches, we will first find the possible dimensions of the rectangles and then calculate their perimeters.
1. Since the area of a rectangle is given by length x width, let's find the factors of 12:
- 1 x 12
- 2 x 6
- 3 x 4
2. Now, let's calculate the perimeters for each of these rectangles using the formula 2(length + width):
- For the 1 x 12 rectangle, the perimeter is 2(1+12) = 2(13) = 26 inches
- For the 2 x 6 rectangle, the perimeter is 2(2+6) = 2(8) = 16 inches
- For the 3 x 4 rectangle, the perimeter is 2(3+4) = 2(7) = 14 inches
The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.
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An angle measure 94 less than the measure of its supplementary angle. What is the measure of each angle?
Answers
The angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
What is the supplementary angle?In geometry, the supplementary angle of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. In other words, two angles are supplementary if their sum is 180 degrees.
For example, if an angle measures 60 degrees, its supplementary angle would measure 120 degrees, since 60 degrees + 120 degrees = 180 degrees.
According to the given informationLet x be the measure of the angle in degrees.
By definition, the supplementary angle of x measures 180 - x degrees.
We are given that the angle measures 94 degrees less than its supplementary angle, so we can write:
x = (180 - x) - 94
Simplifying and solving for x, we get:
2x = 180 - 94
2x = 86
x = 43
Therefore, the angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
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A triangle has side lengths of (7m – 2) centimeters, (9m - 5) centimeters, and
(6n – 1) centimeters. which expression represents the perimeter, in centimeters, of
the triangle?
Answers
The expression that represents the perimeter, in centimeters, of the triangle is (7m - 2) + (9m - 5) + (6n - 1).
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with side lengths (7m - 2) cm, (9m - 5) cm, and (6n - 1) cm, we need to add these lengths together.
Thus, the expression that represents the perimeter of the triangle is (7m - 2) cm + (9m - 5) cm + (6n - 1) cm.
Simplifying this expression, we get 16m + 6n - 8 cm, which is the final answer. Therefore, the perimeter of the triangle is 16m + 6n - 8 cm.
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