The sides of the triangle are 150m, 200m and 250m.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Given: The sides of a triangle are in the ratio of 3:4:5. A man jogged around it 5 times and cover a distance of 3000m.
As man jogged around triangle 5 times and cover a distance of 3000m.
So, the distance for one round is 3000/5 = 600m.
The covered distance is nothing but the perimeter of the triangle.
So, the perimeter of the triangle is 600m.
Let, 3x, 4x, 5x are the sides of the triangle.
⇒ 3x + 4x + 5x = 600
12 x = 600
x = 50
Therefore,
3x = 3(50) = 150
4x = 4(50) = 200
5x = 5(50) = 250
Hence, the sides of the triangle are, 150m, 200m and 250m.
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asking help for a friend
Length of the line AB is 1.414 units and midpoint of AB is (3.5,5.5).
Given in the graph,
A(4,6) and B(3,5)
Distance formula = [tex]\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }[/tex]
AB = [tex]\sqrt{(4-3)^{2} +(6-5)^{2} }[/tex]
= [tex]\sqrt{1^{2} +1^{2} }[/tex]
= [tex]\sqrt{2}[/tex]
= 1.414 units
Midpoint = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
Let midpoint of AB be C(x,y)
C = (x,y) = [tex](\frac{4+3}{2},\frac{6+5}{2})[/tex]
= [tex](\frac{7}{2},\frac{11}{2})[/tex]
= (3.5,5.5)
Hence, length is 1.414 units and midpoint is (3.5,5.5).
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A line passes through points
(8, - 2) and
(-5, 7). Which ratio can be used to determine the slope of the line?
7+2/
8+5
7-2/
-5-8
8+5/
-2+7
7+2/
-5-8
Answer:
7+2/8+5
Step-by-step explanation:
the drying times for a certain type of cement are normally distributed with a standard deviation of 62 minutes. a researcher wishes to estimate the mean drying time for this type of cement. find the least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes.
The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.
What is normal distribution?A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.
Here,
The z value at the 90 percent confidence interval is 1.645.
t ≥ z*s/√n
5≥1.645*62/√n
√n≥20.398
√n≥20.4
n≥416.16
The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.
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Jackson buys 60 books at £3 each.
He sells 35 of these at £8 each and
the remainder at £4 each. What
percentage profit does he make
(give the answer to the nearest
whole number).
Answer:
111%
Step-by-step explanation:
£3 × 60 = £180
(35 × £8) + ( 25 × £4) = £380
£380 ‐ £180 = £200
200/180 × 100% = 111% (nearest whole number)
Jorge has 20 fish for his dog sled team that he wants to divide into smaller pieces. How many pieces of fish would there be if Jorge divided each fish into tenths?
2,000
200
2
0.2
Answer:
200
Step-by-step explanation:
20*10=200
the chief of police in statville wanted to estimate the number of people above the age of 181818 who are using illegal substances in town. he obtained 200200200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse. once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances. what type of statistical study did the chief of police use?
The chief of police use sample statistical study to estimate the number of people above the age of 18 who are using illegal substances in town.
In the given question,
The chief of police in statville wanted to estimate the number of people above the age of 18 who are using illegal substances in town.
He obtained 200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse.
Once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances.
We have to explain what type of statistical study the chief of police use.
In the given question chief of police wants to check number of people who using illegal substances in town above the age of 18. So he take 200 random names from a computer database. That means he take the sample of 200 random people.
As we know that a sample is a selection from a larger population of individuals, things, or things that are used for measurement. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.
So we can say that the chief of police use sample statistical study to estimate the number of people above the age of 18 who are using illegal substances in town.
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Answer: Sample Study
No because there’s a great risk of obtaining biased answers.
What is an equation of the line that passes through the points (4, −2) and (2, 3)?
The equation of the line, in slope-intercept form, that passes through
(4, 2) and (-2, -3) is y = 5/6 x - 4/3.
What is slope-intercept form?
The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Using two points and slope-intercept form we can find the equation of the line.
According to the given question:
The formula to find the slope of two points (x₁, y₁) and (x₂, y₂) is
m = (y₂ - y₁) / (x₂ - x₁)
The points given are (4, 2) and (-2, -3)
m = (-3 - 2) / (-2 - 4)
m = -5/ -6
m = 5/6
Now using the slope and the point (4, 2) the y intercept is
y = mx + b
2 = 5/6 (4) + b
2 = 10/3 + b
By further calculation,
b = 2 - 10/3
Taking LCM
b = (6 - 10)/3 = -4/3
By writing the equation in slope intercept form
y = mx + b
y = 5/6x - 4/3
Therefore, the equation of the line in slope intercept form is
y = 5/6 x - 4/3.
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Find m/ABD.
D
с
A
20°
B
The answer of this question can be given by using congruence
Answer is 20°
What is an example of congruence?
Congruent relates to anything that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.
Given That:
∡DBC = 20°
DC = AD
DB is common on both triangle
As we have hypotenuse common in both triangle and 1 side equal then we can sa it is a congruent triangle by RHS
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x^2-6x-3=(x-a)^2-b where a and b are constants.Find the values of a and b
Answer:
a = 3, b = 12
Step-by-step explanation:
x^2-6x-3=(x-a)^2-b
Lets expand the right side:
(x-a)^2-b = (x-a)(x-a)-b
(x-a)(x-a)-b = x^2 -2ax + a^2 - b
The left side is equal to the right, as per the original equation:
x^2-6x-3 = x^2 -2ax + (a^2 - b)
Compare each term:
1) x^2 = x^2 OK
2) -6x = -2ax; a = 3 so that -6x = -2(3)x
3) -3 = (a^2-b); a^2 = (b-3)
a = [tex]\sqrt{b-3}[/tex]
a is 3, from above
3 = [tex]\sqrt{b-3}[/tex]
9 = b-3
b = 12
Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
Answer:yes
Step-by-step explanation:
for every week he gets 3 cars so it can only incre ment by 3. (1,3) (2,6) (3,9) and so on.
Given mn, find the value of x.
(5x+2)®
(4x+6)°
m
The value of x in the angle illustrated as (5x + 2)° and (4x + 6)° is 4
How to calculate the value of x?It is important to note that line m and line n are parallel. In the diagram, they also intersect each other.
Therefore, it should be noted that according to angle rule, (5x + 2) and (4x + 6) are alternate angles. In this case, they're equal.
These will be illustrated as:
5x + 2 = 4x + 6
Collect like terms
5x - 4x = 6 - 2
x = 4
Therefore, x is 4°.
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Solve the following
2( x + 3 ) = x - 4
2x + 6 = x - 4
x ≈ -0,67
or
x = -2^3
use the figure to complete the following statements
Step-by-step explanation:
I don't see the options and how they are written, but I can tell you the right answer in numbers :
sin(F) = 3/5 = 0.6
cos(F) = 4/5 = 0.8
sin(G) = 4/5 = 0.8
cos(G) = 3/5 = 0.6
why ?
remember the norm circle (radius 1) with ask the trigonometric functions.
the sine of an angle is the vertical height from that point in the circle arc down to x-axis.
the cosine of an angle is the length on the x-axis from the center of the circle to the point, where the sine touches the x-axis.
in any case, sine and cosine enclose the right angle (90°).
each function is now defined for the norm circle with radius = 1.
for angles in larger circles we need to divide the find lengths by the actual radius (we formality do this in the norm circle too, but a division by 1 does not change anything).
for the angles at F and G the radius is the side with the length 5.
10 plus the difference of 6 and 2
Answer: 14
Step-by-step explanation: 10 + (6-2) = 14
What is the slope of the line below?
Answer:
1/2
Step-by-step explanation:
if you take the (2,2) and make it (6,10), you add 4 to the x and 8 to the y. putting this as rise over run (x/y) it comes out to four eighths (4/8). reducing that comes out to one half (4/8).
Is this rat correct tell me tell me NOWWWW teehee
Answer:
No , x = -2
Step-by-step explanation:
When Dividing the Equation by a Constant , all terms in both sides must be divided by this Constant.
So here we divided both sides by 2 , but -6 is not divided , so this step is incorrect
The correct Answer is
[tex]\frac{-6}{2}+\frac{2x}{2} =\frac{-10}{2} \\-3+x=-5\\x=-5+3=-2[/tex]
8x + 24 I was solutions
Step-by-step explanation:
8x + 24 is a simplified expression.
It is not an equation, so it can't be solved.
There are two terms in 8x + 24, 8x and 24.
The two terms are unlike terms, so they cannot be combined together.
g(x) = x-2
What is the Parent function and transformation
The parent function is y = x ; shift 2 units downwards.
Given,
In the question:
The function is :
g(x) = x - 2
Now, According to the question ;
Let's know
What is the Parent function and transformation?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
According to the above statement is;
g(x) = x -2
Hence, The parent function is y = x ; shift 2 units downwards.
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Can you help me create a polynomial function from the diagram displayed below? My teacher never went over this in class.
Thanks!
Considering the dimensions of the rectangular prism and it's volume, it is found that:
The expression is: V(x) = 4x³ - 22x² + 30x.The degree is of 3, the number of terms is of 3, and the leading coefficient is of 4.How to obtain the volume of a rectangular prism?The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:
V = l x w x h.
In the context of this problem, from the image, the dimensions are given as follows:
Length: l = 2x - 5.Width: w = x - 3.Height: h = 2x.Then the polynomial expression regarding the volume of the prism is obtained as follows:
V(x) = 2x(x - 3)(2x - 5)
V(x)= 2x(2x² - 11x + 15)
V(x) = 4x³ - 22x² + 30x.
The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:
Degree of 3, which is the highest exponent of the function V(x).Number of terms of 3, which are 4x³, 22x² and 30x.The leading coefficient is of 3, as it is the term that multiplies the term with the highest exponent x³.A similar problem, also about the volume of a rectangular prism, is presented at brainly.com/question/22070273
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Triangles geometry . PLS
Step-by-step explanation:
Angle BAC = angle BCA
as sum of angles in triangle = 180
49 + 49 + ABC = 180
180 - 49 - 49 = ABC
ABC = 82°
let 0 < a < b < 1,
a) is a^x < b^x, for x>0
b) is a^x < b^x, for x<0
For 0 < a < b < 1, a^x < b^x, for x < 0.
What are inequalities and their types?
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, 0 < a < b < 1.
Assuming a = 0.25 and b = 0.5.
∴ (0.25)^x < (0.5)^x for x > 0, again assuming x to be 2.
∴ (0.25)^2 = 0.625 and (0.5)^2 = 0.25.
Now, 0.625 > 0.25 which is not satisfying a^x < b^x, for x > 0.
Therefore, if 0 < a < b < 1, then a^x < b^x, for x < 0.
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pls help ASAP
just fill the blank
Answer:
Use the formula to find distance
consider this confidence interval interpretation: we are 95% confident the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg. what needs to be done to fix this statement?
"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.
The true parameter must be properly and contextually stated.
We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.
Thus the correct statement is as mentioned above.
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In a pack of Skittles, 20% are red. If 13 are red, how many skittles were in the entire bag?
The total number of skittles in the bag will be 65.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,
N = ( 13 / 20 ) x 100
N = 130 / 2
N = 65
Therefore, the total number of skittles in the bag will be 65.
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What is the slope of the line created by this equation?
Round your answer out to two decimal places
6x + 7y = 5
Answer:
-0.86
Step-by-step explanation:
What is the slope of the line created by this equation? Round your answer out to two decimal places. 6x + 7y = 5
_____________________________________________
Slope intercept form solves for y:
y = mx + b when m = slope and b = y-intercept
First, solve for y:
6x + 7y = 5
subtract 6x from both sides:
6x + 7y - 6x = 5 - 6x
7y = 5 - 6x
divide both sides by 7:
7y/7 = (5 - 6x)/7
y = 5/7 - 6/7x
rearrange right side:
y = - 6/7x + 5/7
Back to the equation: y = mx + b when m = slope and b = y-intercept
your slope is -6/7
in decimal form, rounded to two digits: -0.86
In triangle ABC, what is the measure of angle C if A = 120°, a = 25, and b = 20? Round the answer to the nearest hundredth.
The angle C = 103.85° using the sine rule and rounded to the nearest hundredth.
What is the sine rule?In trigonometry, the sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
Considering the ∆ABC, the sine rule states that;
(a/sinA) = (b/sinB) = (c/sinC)
so
25/sin120° = 20/sinB
sinB = (20 × sin120°)/25 {cross multiplication}
sinB = 0.6928
B = sin^(-1)[0.6928)] {sine inverse}
B = 43. 85°
Sum of interior angles in ∆ABC is 180° so;
C = 180° - (120° + 43.85°)
C = 180° - 76.15°
C = 103.85°
With the application of the sine rule, we can conclude that the value of the angle C is 103.85° rounded to the nearest hundredth.
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What is the value of the following numerical expression?
-23 +-15+|-17| + -35
A. -56
B.-26
C. 1-261
D. 56
The value of expression -23 +-15+|-17| + -35 is -56
In this question, we have been given a numerical expression.
-23 +-15+|-17| + -35
We need to find the value of given numerical expression.
Consider given numerical expression,
-23 +-15+|-17| + -35
= -23 + (-15) + |-17| + (-35)
= -23 - 15 + |-17| - 35
We know that for any real number a, |±a| = a
So, |-17| = 17
= -38 + 17 - 35
= -56
Therefore, the value of expression -23 +-15+|-17| + -35 is -56
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you are flying a kite and the angle of elevation from the horizon is 36 if your kite string is 15 feet long, how high are you flying the kite ?
By using a trigonometric relation we will see that the height of the kite is 8.82 feet above the point where you hold the line.
how high are you flying the kite?We can view this as a right triangle, where the hypotenuse has a measure of 15 feet, we know one angle that measures 36°, and the opposite cathetus to that angle is x, the height we want to find.
We want to get the value of x, which is the opposite cathetus to the given angle, then we can use the trigonometric relation:
sin(a) = (opposite cathetus)/(hypotenuse)
Replacing what we know we will get:
sin(36°) = x/15ft
Solving this for x we get:
x = sin(36°)*15ft = 8.82ft
The height of the kite is 8.82 feet.
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Three people each have a tendency to lie 1/3 of the time. There is a coin flip that they all see. They all say it's Heads. What's the probability it is actually Heads
The probability is 8/9.
From the question, we have
probability = (1/3)*(1/3)*(1/3) = 1/27 chance (all of them lie)
probability = (2/3)*(2/3)*(2/3) = 8/27 chance (all of them true).
Since, they all say it's heads.
Thus, the probability of it being heads = (8/27)/ ((8/27)+(1/27)) = 8/9.
Probability:
Chance is referred to as probability. This branch of mathematics studies the probability of a random event. The value is between 0 and 1. Probability is a concept that mathematics has adopted to predict the likelihood of particular events. Probability is just the measure of how likely something is to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will be able to comprehend the possible results for a random experiment. How likely something is to occur can be determined using probability. It might be challenging to predict many things with complete certainty. We can only predict whether an event will occur or how likely it is using it, not if it will actually occur.
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Find the geometric mean between 2 and 19. Write your answer in radical form or round to the nearest tenth, if
necessary.
Answer: 6.2
Step-by-step explanation:
Geometric Mean = √( 2 x 19 ) = 2√38 = 6.1644