To find the area of a triangle, multiply the base area by the height and then divide by 2. Dividing by 2 comes from being able to divide a parallelogram into two triangles. For example, in the illustration on the left, the area of each triangle is equal to half the area of the parallelogram.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane.The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h.This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, To find the area of a triangle, multiply the base area by the height and then divide by 2. Dividing by 2 comes from being able to divide a parallelogram into two triangles. For example, in the illustration on the left, the area of each triangle is equal to half the area of the parallelogram.
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What is the bare minimum needed to write the equation of a line?
Answer:
Two points A(x,y) B(x₂,y₂) or One point A(x,y) and gradient(slope).
Step-by-step explanation:
a study is conducted to show that college women, on average, gain more weight than college men during their first year of college. the study is completed and reports a p-value of 0.001 what conclusion can be drawn?
From given report, on average college women gain more weight than college men during their first year of college.
In this question, we ahve been given a study is conducted to show that college women, on average, gain more weight than college men during their first year of college.
The study is completed and reports a p-value of 0.001
We need to write the conclusion for above situation.
We can see that the results are statistically significant.
And from given p-value, we can say that on average college women gain more weight than college men during their first year of college.
Therefore, on average college women gain more weight than college men.
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A knife i three time the cot of a poon 9 poon and 12 knive cot £82. 80 work out the cot of one knife
The cost of one knife is £ 5.52.
Given, one knife is equal to three times spoon.
Let the cost of knife be x, and cost of spoon be y.
x=3y. ------(1)
9 spoons and 12 knives costs £82. 80, which can be written as
9(spoons)+12(knife)=£82. 80
9y+12x=£82. 80
9y+12(3y)=£82. 80
9y+36y=£82. 80
45y=£82. 80
y=£82. 80/45
y=£ 1.84
The cost of one spoon is £1.84.
We have to find the cost of one knife, we can substitute the value of y in equation 1 to get the cost of one knife.
x=3(1.84)
x=5.52.
Therefore, the cost of one knife is £5.52.
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Corrected Question
A knife is three times the cost of a spoon. 9 spoon and 12 knives cost £82. 80 work out the cost of one knife.
Bo fell asleep 84% if the total length was 600 miles how many miles had they travel when bo fell asleep
The total distance traveled when Bo fell asleep is 504 miles.
What is the distance traveled?
The path taken by an object to move from a starting point to an ending location in a specified amount of time with a specific velocity is known as the distance traveled.
Given, the total length of distance = 600 miles
Bo fell asleep = 84%
Let 'x' be the distance traveled.
Then, according to the question
x = 84% of 600 miles
or, x = [tex]\frac{84}{100} * 600[/tex]
or, x = 84*6
or, x = 504 miles
Hence, the total distance traveled when Bo fell asleep is 504 miles.
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Dan is 12 4/5 years old. Karina is 1 1/6 years older than Dan and Jane is 1 1/3 years older than Karina. How old is Jane?
The age of Jane based on the information is 10 3/10 years.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
In this case, Dan is 12 4/5 years old, Karina is 1 1/6 years younger than Sarah and Jane is 1 1/3 years younger than Greg
The age of Jane will be:
= 12 4/5 - 1 1/6 - 1 1/3
= 12 24/30 - 1 5/30 - 1 10/30
= 12 24/30 - 2 15/30
= 10 9/30
= 10 3/10
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Find the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0).
The points on the ellipse 5x² + y² = 5 that are farthest away from (1, 0) are (-0.25, ±√4.6875).
The square of the distance from a point on the ellipse to the point (1, 0) is ...
d^2 = (x -1)^2 +y^2
Using the equation of the ellipse to write an expression for y^2, we have ...
d^2 = (x -1)^2 +5 -5x^2
d^2 = -4x^2 -2x +6
The expression on the right is that of a downward-opening parabola with ...
a = -4, b = -2, c = 6
The maximum is located at ...
x = -b/(2a) = -(-2)/(2(-4)) = -1/4
The value of y there is ...
y^2 = 5 -5(-1/4)^2 = 4 11/16
y = √4.6875
Hence the points on the ellipse farthest from (1, 0) are (-0.25,±√4.6875).
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Triangles acd and bcd are isosceles. Angle bac has a measure of 18 degrees and angle bdc has a measure of 48 degrees. Find the measure of angle abd.
The measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees
What are isosceles triangles?
Isosceles triangles are triangles that have two sides equal in measurement.
Main Body:
From the given diagram;
∠BAC = 18 degrees
∠BDC = 48 degrees
Required angle : ∠ABD
From the diagram, ∠DAB = ∠BAC = 18 degrees
Also, ∠ADC + ∠ACD + ∠DAC = 180
Since triangles ACD is isosceles, hence ∠ADC = ∠ACD. The expression above becomes
∠ADC + ∠ADC + ∠DAC = 180
2∠ADC + ∠DAC = 180
2∠ADC = 180 - 36
2∠ADC = 144
∠ADC = 144/2
∠ADC = 72 degrees
This means that ∠ADB = 72 - ∠BDC
∠ADB = 72 - 48
∠ADB = 24 degrees
Get the required angle ABD
From triangle ADB, ∠ABD + ∠ADB + ∠DAB = 180
∠ABD + 24 + 18 = 180
∠ABD + 42 = 180
∠ABD = 180 - 42
∠ABD = 138 degrees
Hence the measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees.
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1. Which definition best describes an insurance premium?
a.
The amount you must pay out-of-pocket before your insurance company will begin to pay
b. The maximum amount the insurance company will pay for your injury
C. An extra level of coverage offered only to VIPS
d.
The monthly amount you pay in order to purchase insurance coverage
Answer:
D
Step-by-step explanation:
D the premium you pay is your bill for insurance
mr. patrick teaches math to 15 students. he was grading tests and found that when he graded everyone's test except payton's, the average grade for the class was 80. after he graded payton's test, the class average became 81. what was payton's score on the test?
Mr. Patrick instructs 15 students in math. He discovered that Payton had received a 95 on the test while grading them from average.
There are 15 kids in Mr. Patrick's class. The average score on his most recent exam was 80 for 14 candidates (not including Payton).
I'm going to use x to represent the unknowable sum of the 14 test scores. Average is computed by adding all the numbers in the set (whose average you're trying to get) together, then dividing by the total number of numbers in that set.
This was the total of their scores: x=1120.
Adding Payton's score now (I'll use the letter p to stand in for her score):
1120+p /15=81→ Her test score was included in the fifteen students' average, which was 81 1120+p=1215
P=95.
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Find the 7th term in the
sequence
-4,-8, -16, ...
Answer:
The answer is -256
Step-by-step explanation:
-4+-4=-8
-8+-8=-16
-16+-16=-32
-32+-32=-64
-64+-64=-128
-128+-128=-256
Hope this helps :)
consolidated builders has bid on two large construction projects. the company president believes that the probability of winning the first contract (event a) is 0.6, that the probability of winning the second (event b) is 0.5, and that the joint probability of winning both jobs (event {a and b}) is 0.4. what is the probability of the event {a or b} that consolidated will win at least one of the jobs?
The probability of an event {a or b} is 0.7
Probability: It is the branch of mathematics concerning numerical, descriptions of how likely an event is to occur or how likely it is that a proposition is true. the probability of an event is a number between
0 and 1.
if the two events a and b are mutually exclusive then the addition rule of probability is:
P( a or b) = P(a) + P(b) - P(a∩ b)
Given that,
P(a) = 0.6 P(b) = 0.5
P(a ∩ b)= 0.4
According to probability methods, if two events are mutually exclusive, then the probability of either occurring is denoted as P (a ∪ b).
Now, we know that,
P( a ∪ b) = P(a) + P(b) - P( a ∩ b)
= 0.6 + 0.5 - 0.4
= 0.7
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What has the greater magnitude -41.5 47 -51 or 49
Answer:
The vector which has a greater magnitude.
Solution:
We know that, magnitude of a vector represents the length of it.
The first vector that is 2 meters long has a magnitude 2.
The second vector that is 4 meters long has a magnitude 4.
Clearly, 4 is greater that 2, i.e., 4 > 2. So, magnitude of second vector is greater.
Therefore, the vector that is 4 meters long has greater magnitude.
Step-by-step explanation:
Find the exact value of the trigonometric function given that in u = − 8 17 and co v = − 9 41. (Both u and v are in Quadrant III. ) ec(v − u)
Answer:
343
Step-by-step explanation:
A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $ each. She must deliver all the tee-shirts in days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).
The equation to represent total amount of money that she receives for the tee shirts in terms of number of machines is 2800*n*(200 - n) .
In the question ,
it is given that
the cost of 1 tee - shirt = $14
total days required to deliver the tee shirt = 20
number of tee - shirts that a machine can produce = 200 per day
let the number of machines = n
so the number of days require to set up the machines = n
hence all the machine will work for = (20 - n) days
1 machines will produce 200(200 - n) tee shirts
n machines will produce = 200n(200 - n) tee shirts in the remaining (20 - n) days .
the selling price of 1 tee shirt is = $14
So, the total money M that she will receive is = 14*200*n*(200 - n)
= 2800*n*(200 - n)
Therefore , The equation to represent total amount of money that she receives for the shirts in terms of number of machines is 2800*n*(200 - n) .
The given question is incomplete , the complete question is
A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $14 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money( M ) she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).
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hank needs to pack 100 golf balls into 8 boxes. each box must contain an equal number of golf balls. how many golf balls does he have left over?
Answer: 4
Step-by-step explanation:
100/8 = 12 golf balls in each box
8*12 = 96 golf balls are used
100-96= 4 gold balls left
Rajiv wihe to make a cube without a lid with cardboard. The amount of cardboard available i 245 q. Cm. What hould be the length of the ide chooen in order to make the cardboard box?
Rajiv chose to make a cardboard box of length 7 cm from the given cardboard available.
It is given that the amount of cardboard available is 245 cm. Therefore, the box's surface area will be less than or equal to 245 cm².
We are given that the box does not have any lid. Hence, the box is made up of 5 squares.
Let the length of one side of the box be x cm.
We know, that the surface of the area of a regular cube is
6a².
That means,
no. of squares X square of the length.
Hence, the surface area of the box is 5x².
Therefore from the given problem, we get that
5x² ≤ 245
or, x² ≤ 245/5
or, x² ≤ 49
49 is a perfect square of 7. Hence assuming Rajiv makes the largest possible box,
the length of the side he chose is 7 cm.
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By first finding tan 0, calculate the size of angle 0
Give your answer in degrees to the nearest integer.
[tex]\tan \theta=\frac{7}{16} \\ \\ \theta=\arctan(7/16) \approx 24^{\circ}[/tex]
why would you want to transform a set of raw scores into a set of z-scores? check all that apply. to make all the transformed scores greater than 0 to make sure the z-scores are normally distributed to be able to describe the location of a raw score in the distribution of raw scores to make a distribution with a mean of 0 and a standard deviation of 1
When you transform row score into a set of z- score, you are able to compare the score of both distribution. When you compare the scores you can allow one to have a mean of 0 and standard deviation 01. A z- score let us see how many standard deviation away from the mean an element lies.
Z- score: It is a numerical measurement that describes a value's relationship to the mean of a group of values and is measured in terms of standard deviation from mean.
Raw score: A raw score is unaltered measured. For example:- if there is a test in a class and someone for 75 out of 100, 75 would be there raw score.
Transform a set a raw scores into a set of z score:
Lets understand the importance of transforming raw scores into a set of z score with the help of an example.
For admission in PG program students need to appear in the entrance exam which held in two batches. John appeared in both the exams and he scored 160 out of 200 in paper A and 145 out of 185 on paper B.
Solution: we needs to find the z score corresponding to each paper in order to compare them.
paper A: Score obtained : 160
Average score: 155
Standard Deviation: 10
Paper B: Score obtained: 145
Average obtained: 135
Standard deviation: 08
Using the Z- score formula:
Z = (x - μ) /α
Using the above Z score formula to calculate z score for given raw score values:
z score for Paper A = ( 160-155)÷ 10
Z score for paper B = ( 145 - 135 ) ÷ 1.25
While Evaluating based on z score, we can say that John performed relatively better in paper B as compared to paper A.
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In a toy store the ratio of legos to board games is
9:6. If the store has 24 legos, how many board games
are in the store?
The store has 16 board games
What are equivalent ratios?
The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.
Let x = number of legos
Let y = number of board games
Given ratio: 9:6= 9/6
x/y = 9/6
substitute x=24
24/y=9/6
Do cross multiplication
(6*24)/9=y
16=y
or
y=16
So, the store has 16 board games
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a sociologist develops a test designed to measure attitudes about disabled people and gives the test to 16 randomly selected subjects. their mean score is 71.2 with a standard deviation of 10.5. construct the 99 percent confidence interval for the mean score of all subjects.
The 99 percent confidence interval for the mean score of all subjects lies greater than 63.464 and less than 78.936.
Given:
No. of samples (n)= 16
df = n-1 = 16 -1 = 15
The mean score is 71.2
The standard deviation = 10.5.
So, from the t-distribution of critical values table through the above-mentioned details. We get the values:
Alpha / 2 = 0.005
z = 99/100 + 0.005 = .99 + .005 = .995
Sample mean = xbar = 76.2
t = 2.947
The formula for standard error = E = value of t (at z, and df) / S.D./sqrt(n)
i.e. E = 2.947 x 10.5 / sqrt 16 = 7.736
I = 71.2 +/- E = 71.2 +/- 7.736
99 percent confidence interval - 71.2 +/- 7.736
Adding both sides 7.736 for range. We get,
63.464 < u < 78.936
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Solve for the indicated letter.
b = 4c, for c
The solution is c = ____.
Answer:
1/4b
Step-by-step explanation:
1. If a circle is centered at (5, -7) and goes through the point (-3, -1), what is the radius?
2. Why do we prefer the standard form for the equation of a circle over the general form?
Answer: r = 11.3
Step-by-step explanation:
Standard form : (x-h)2 + (y-k)2 = r2
(h,k) = (5,7)
(x,y) = (-3,-1)
r2 = (-3-5)2 + (-1-7)2
r2 = [tex]-8^{2} + -8^{2} = 64 + 64 = 128\\r = \sqrt{128} = 11.3[/tex]
When coordinates of the center of the circle and a point on the circle are known, Standard form is the one to use.
line L is a reflection in the Y-axis of line K. Write an equation that represents line k
The required line is y = 1.5·x + 2 which represents line K.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The given coordinate of two points on the line are;
(-2, 5) and (0, 2)
Line K is the line about which line L is reflected.
The coordinates of the point's image (x, y) after a reflection about
the y-axis is the point (-x, y).
Therefore, the coordinates of the points on the line K are;
(-2, 5) → (2, 5)
(0, 2) → (0, 2)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 2, y₁ = 5
x₂ = 0, y₂ = 2
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 5 = (5 - 2)/(0 -2)[x -2]
⇒ y - 5 = -3/2(x-2)
⇒ y = 1.5·x + 2
Therefore, the required line is y = 1.5·x + 2 which represents line K.
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How many solutions does 5(3x+2)-2=4(4x-3) have ?
Answer:
One Solution
Step-by-step explanation:
5(3x+2)-2=4(4x-3)
15x + 10 - 2 = 16x - 12
15x + 8 = 16x - 12
15x = 16x - 20
-x = -20
x = 20
3) What is the slope of the line from the following points (-3, -2) and (1, -7) ? (Please show your work for your full points)
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}} \implies \cfrac{-7 +2}{1 +3} \implies \cfrac{ -5 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{5 }{ 4 } \end{array}}[/tex]
Consider the equation.
12 - 4x
3
Choose the correct option from each box to make the sentence true.
y =
The range of the function is
The domain of the function is
The y-intercept of the function is
The rate of change of the function is
Y in the expression represents the range of the function. Option A is correct.
Given that,
In the expression y = 12- 4x, what y = 3 represents in the function, is to be determined.
Range, it is the set of values that come out to an outcome for a certain mathematical operation.
here,
y = 12 - 4x
where, 12 = intercept , -4 = rate,
when y = 3 implies that, at the value of x, the outcome of the equation is 3 or it is said to be range.
Thus, Y in the expression represents the range of the function. Option A is correct.
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Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of. 5. How many subscribers must they sample to obtain this interval?.
If Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. The number of subscribers they must sample to obtain this interval is: b) 385.
How to find the sample?Using this formula to find the number of subscribers they must sample to obtain this interval
n≥ (zσ/2 ÷ 2ME)²
Where:
n= Sample =?
zσ = Z-score for 95% confidence interval = 1.96
ME = margin of error = 0.05
Let plug in the formula
n≥ [1.96 / 2(0.05)]²
n≥ [1.96 / 0.1]²
= (19.6)²
= 384.16
=385 (Rounded)
Therefore the correct option is B.
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The complete question is:
Netflix would like to estimate the proportion of their current subscribers who would pay
extra for a premium membership including access to more movies and TV shows. To do
this, they plan to calculate a 95% confidence interval to estimate the proportion. They
would like a margin of error of .05. How many subscribers must they sample to obtain this
interval?
a) 1537
b) 385
c) 192
d) 10
The amount of money Jason earns working at his job is directly proportional to the
number of hours he works. If Jason works 12 hours he earns $186. How many hours
would he need to work to earn $294.50?
The number of hours Jason needs to work to earn $294.50 is 19 days which was found by using the given data.
In mathematics, what is a proportion?A proportion is an equation that sets two ratios equal to each other. For example, if there is one guy and three girls, the ratio may be written as 1: 3. (for every one boy there are 3 girls) One-quarter are males and three-quarters are girls. 0.25 are males (by dividing 1 by 4)What is the formula for calculating proportion?By dividing the supplied numbers, we can discover the missing value. A proportion formula is as follows a:b::c:d = a/b = c/d, where a and d are extreme terms and b and c are medium terms.Given: Jason's pay is directly proportionate to the number of hours he works at his job. Jason works 12 hours a day and makes $186.
Number of hours he needs to work to earn $294.50 is given as
= (12 × 294.50)/186
= 19
Therefore, the number of hours Jason needs to work to earn $294.50 is 19 days.
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Under her cell phone plan, Meena pays a flat cost of $38 per month and $3 per gigabyte. She wants to keep her bill under $55 per month. Which inequality can be used to determine xx, the maximum number of gigabytes Meena can use while staying within her budget?
The.maximum number of gigabytes Meena can use while staying within her budget is 5 gigabytes
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.
They are denoted by the symbols ≥ < > ≤.
Let the maximum gigabytes be x.
The inequality to illustrate the information will be:
38 + 3x < 55
Collect like terms
3x < 55 - 38
3x < 17
Divide
x < 17/3
x < 5 2/3
The maximum gigabytes is 5.
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According to the who monica project the mean blood pressure for people in china is 128 mmhg with a standard deviation of 23 mmhg. assume that blood pressure is normally distributed.
The answer to the question probability of randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.
What is standard deviation?
A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.
The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.
The mean blood pressure for people in china is 128 mmHg.
The standard deviation of 23 mmHg.
For blood pressure of 182.6 mmHg
=p(x> 182.6)
=p(z> 182.6-128/23)
=p(z> 2.37)
=0.0088
Hence the probability of a randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.
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