Answers
Answer:
6.1, 13.7, 8.2: Cannot be side lengths of a triangle
10, 15, 27: Cannot be side lengths of a triangle
15, 8, 14: Cannot be side lengths of a triangle
13, 12, 14: Can be side lengths of a triangle
Step-by-step explanation:
According to the Triangle Inequality Theorem, three lengths are able to form a triangle if the sum of the squares of any two lengths is greater than the square of the third length.
Because there are three lengths, we have to repeat the process unless we find a violation of the theorem, as one violation automatically disqualifies three lengths from forming a triangle.
'll refer to the three lengths as a, b, and c for the sake of clarity.
Checking 6.1 (a), 13.7 (b), and 8.2 (c):
a^2 + b^2 > c^2
6.1^2 + 13.7^2 > 8.2^2
37.21 + 187.69 > 67.24
224.9 > 67.24
b^2 + c^2 > a^2
13.7^2 + 8.2^2 > 6.1^2
187.69 + 67.24 > 37.21
254.93 > 37.21
c^2 + a^2 > b^2
8.2^2 + 6.1^2 > 13.7^2
67.24 + 37.21 > 187.69
104.56 < 187.69.
Because the sum of the squares of 8.2 and 6.2 is less than the square of 13.7, these three lengths can't form a triangle.
Checking 10 (a), 15 (b), and 27 (c):
a^2 + b^2 > c^2
10^2 + 15^2 > 27^2
100 + 225 > 729
325 < 729
Because the sum of the squares of 10 and 15 is less than the square of 27, these three lengths can't form a triangle:
Checking 15 (a), 8 (b), and 14 (c):
a^2 + b^2 > c^2
15^2 + 8^2 > 14^2
225 + 64 > 196
289 > 196
b^2 + c^2 > a^2
8^2 + 14^2 > 15^2
64 + 196 > 225
260 > 225
c^2 + a^2 > b^2
14^2 + 15^2 > 8^2
196 + 225 > 64
421 < 64
Because the sum of the squares of 14 and 15 is less than the square of 8, these three lengths can't form a triangle.
Checking 13 (a), 12 (b), and 14 (c):
a^2 + b^2 > c^2
13^2 + 12^2 > 14^2
169 + 144 > 196
313 > 196
b^2 + c^2 > a^2
12^2 + 14^2 > 13^2
144 + 196 > 169
340 > 169
c^2 + a^2 > b^2
14^2 + 13^2 > 12^2
196 + 169 > 144
365 > 144
Because all three lengths satisfy the Triangle Inequality Theorem, 13, 12, and 14 can form a triangle.
Related Questions
in the fig given below .AB║DC find x
helpplzzz
Answers
Answer:
x = 150°
Step-by-step explanation:
The given parameters are;
AB ║ DC
∠BAE = 105°
∠AEC = 25°
We construct a line CF from C parallel to the line AE as presented in the included diagram created with Microsoft Visio
We have;
∠DCF ≅ ∠BAE = 105° by similar angles formed by two pairs of parallel lines
∠AEC = ∠ECF = 25° by alternate interior angles formed by two parallel lines and a common transversal
x = 125° + 25° = 150° By angle addition postulate
x = 150°.
equation of the circle centered at the origin and passing through the point equation of the circle centered at the origin and passing through the point (-4,0)
Answers
The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).
Equation of a circle
A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.
We know that,
Equation of the circle passing through the origin is given by:-
\(x^2+y^2=r^2\)
Where,
r is the radius of the circle, and
(x,y) are the coordinates of each point of the circle.
Hence, we can write,
The radius of the circle will be :-
\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)
Hence, r = 4 units.
Hence, the equation of the circle is given by:-
\(x^2+y^2=16\)
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which of these random samples represents a representative sample of the systolic blood pressure of all patients in a hospital?
Answers
A representative sample based on the hospital scenario is option A
What is representative sample?A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.
Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.
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Given that QM = 15 units, SM = 10 units, and RM = 18 units, what is the length of segment PM?
R
18
M
10
15
Q
OA 13 units
OB.
7 units
Ос.
8 units
OD
12 units
Answers
The length of segment PM would be 12 units
I won't proceed based on your circle's association with any specific segments; instead, I'll use the illustration below.
We can determine QM = 15, SM = 10, and RM = 18 from the image. We apply the formula for determining segment lengths when there are two chords in a circle to determine the length of segment PM.
Our equation QM = (SM)(RM) (PM)
We now enter the information and resolve: (10)(18) = (15)(x) (x)
(10)(18) = 180
(15)(x) = 15x
180 = 15x → 180 ÷ 15 = 12 & 15x ÷ 15 = x
x = 12
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There were 12 stray cats in a town the first year. The next year, there were 21 stray cats in the town. What is the percent increase?
Answers
Answer: 75% increase
Step-by-step explanation:
Percentage Increase=(Final Value−Starting Value/Starting Value)×100
Percentage Increase=(21-12/12) ×100
Percentage Increase=(9/12) ×100
Percentage Increase=0.75 ×100
Percentage Increase=75%
Answer:
75 percent
Step-by-step explanation:
21-12=9
9=x%*12
/ /
12 12
3/4 = x
0.75 =x
75% = x
Find the factorial form
3x2x1
Answers
Answer:
3x2x1=3!
Step-by-step explanation:
using nx(n-1)x_x1=n
3x2x1=3!
hence,3x2x1=3!
the length of a rectangle is three times the width. Determine the dimensions that will give a total area of 27 meters
Answers
Answer:
A width of 3 and a length of 9
Step-by-step explanation:
To solve this problem, we're going to have to create an equation. So, let's call the width w. The length of the rectangle is three times the width, so the length will be 3w. The total area is 27, and the length times the width must equal the area, so this gives us the following equation:
w(3w) = 27
Let's simplify and start solving.
3w² = 27
3w²/3 = 27/3
w² = 9
√w² = √9
w = 3
Remember, we defined w as the width. So, the width of the rectangle is 3. The length is 3w, or three times the width, so the length must be 9. And these are our dimensions: 3 × 9.
PLSSSSSS HELPPPP MEEE WITHH THISS QUESTION ASAP NO GUESSING AND ANSWER CORRECTLY!!!!!!
Which of the following can be used to describe the crowds who attended Jackson's inauguration ceremony?
A. very crowded
B. violent
C. rowdy
D. not crowded
WILL BE MARKING BRAINIEST!!!!! SO PLEASEE SHOW, EXPLAIN, AND PUT EFFORT PLSSSSSSS!!!!!!
Answers
Answer:
A
Step-by-step explanation:
Answer: C-rowdy
- Rowdy is being noisy and the question is asking you to describe Jackson's crowds who attended the ceremony.
help me plz i need the answer ? :)
Answers
Answer:
D
Step-by-step explanation:
I am not sure if this is right can someone check it ASAP please
Answers
Answer:
x=10
Step-by-step explanation:
3(4x-12) = 84
Divide each side by 3
3/3(4x-12) = 84/3
4x-12 =28
Add 12 to each side
4x-12+12 = 28+12
4x= 40
Divide each side by 4
4x/4 = 40/4
x = 10
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 4
11 7 2.5
9.5 3 5
Perks A Lot
10 3.5 3
5 2.5 7
8 5.5 9.5
6 9 4.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Perks A Lot, with a mean value of 6.125 gallons
Perks A Lot, with a median value of 6.125 gallons
Coffee Ground, with a mean value of 6.75 gallons
Coffee Ground, with a median value of 6.75 gallons
Answers
Generally, the correct average measure for identifying stores with the highest hourly coffee sales is C. Coffee grounds, averaging about 6.75 gallons.
How to explain the measure of center?
The average is calculated by adding all data points and dividing by the number of data points.
The average for Coffee Ground is \(\frac{(1.5+20+3.5+12+2+4+11+7+2.5+9.5+3+5)}{12} = 6.75\) gallons per hour. If the data are sorted sequentially, the median is the mean. The sorted list in this situation is: 1.5, 2, 2.5, 3, 3.5, 4, 5, 7, 9.5, 11, 12, 20. 5 + 7 / 2 = 6 gallons per hour is the median.
The mean for Perks A Lot is \((10+3.5+3+5+2.5+7+8+5.5+9.5+6+9+4.5)/12 = 6.125\) gallons per hour. The ordered list in this example is 2.5, 3, 3.5, 4.5, 5, 6, 7, 8, 9, 9.5, 10. The average flow rate is 6.125 gallons per hour.
When comparing the averages of the two stores, Coffee Ground scores higher than the Perks A Lot average. This suggests that Coffee Ground on average sells more coffee per hour than he does.
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example: determine a basis and the dimension of the subspace s in v4 over z2 consisting of vectors: (0 0 0 0) (1 1 0 0) (1 0 1 0) (0 0 0 1) (0 1 1 0) (1 1 0 1) (1 0 1 1) (0 1 1 1)
Answers
The basis of the subspace S in V4 over Z2 consists of the vectors: (1 1 0 0), (0 1 1 0), (1 0 1 1). The dimension of the subspace S is 3.
To determine a basis for the subspace S, we need to find a set of vectors that are linearly independent and span the subspace. The given vectors in the subspace S are: (0 0 0 0), (1 1 0 0), (1 0 1 0), (0 0 0 1), (0 1 1 0), (1 1 0 1), (1 0 1 1), (0 1 1 1).
We can observe that the first vector (0 0 0 0) is the zero vector, which is not useful for spanning the subspace. However, the other seven vectors are linearly independent and span the subspace S. By removing the redundant vectors and keeping only the linearly independent ones, we obtain the basis for S: (1 1 0 0), (0 1 1 0), (1 0 1 1).
The dimension of a subspace is defined as the number of vectors in its basis. In this case, the basis for S consists of three vectors, so the dimension of S is 3.
Therefore, the basis of the subspace S is {(1 1 0 0), (0 1 1 0), (1 0 1 1)}, and the dimension of S is 3.
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In a study of commuting patterns of people in a large metropolitan area, respondents are asked to report the time it took them to travel to their work on a specific day of the week. What is the variable of interest
Answers
The population of a certain town this year is 12480. If the rate of increase of the population is 4%, what was previous year's population?
Answers
Answer:
The previous year's population was 12000.
Step-by-step explanation:
Let the previous year's population be P. Then:
P + 0.04P = 1.04P = 12480.
Solving 1.04P = 12480 results in P = 12000
The previous year's population was 12000.
Step-by-step explanation:
12480*4/100
= 1248* 0.4
=499.2 is 4% of 1280
:. 1280 - 499.2
780.8 is previous year's population
Thang decided to borrow $2000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 7%
Answers
Answer:
Thang will pay $300 as interest
Step-by-step explanation:
T = 3 years
P = $2000
R = 5%
Therefore
I = (2000 × 5 × 3)/100
I = 30000/100
I = $300
What is the y-intercept of a line that has a slope of -3 and passes through point (0, -7)?
-7
3
0
4
Answers
Answer:
-7
Step-by-step explanation:
The y intercept of a line is the y value of the line when the x value = 0
In this case we are given the coordinates (0, -7)
so when x =0 y= -7
Therefore, the y- intercept is -7
Answer:
-7
Step-by-step explanation:
The y intercept of a line is the y value of the line when the x value = 0
In this case we are given the coordinates (0, -7)
so when x =0 y= -7
Therefore, the y- intercept is -7
QUICK!!!
The total arm and blade of a windshield wiper is 12 in. long and rotates back and forth through an angle of 90 degrees. The shaded region in the figure is the portion of the windshield cleaned by the 9-in. wiper blade. What is the area of the region cleaned?
answer with the last three decimal places (no rounding)
Answers
The area of the region is: 63.585 square inches.
What is the area of the region cleaned?If we have a circle of radius R, the area of said circle is:
A = pi*R^2
Particularly, if we have a section of the circle defined by an angle θ, the area of that region is:
A = (θ/2pi)*pi*R^2 = (θ/2)*R^2
In this case we have:
θ = 90° = pi/2
R = 9in
Replacing that we get:
A = (pi/4)*(9in)^2 = (3.14/4)*(9in)^2 = 63.585 in^2
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The lengths of the 2 diagonal of a rhombus are 24cm and 32cm what is the length of one side of the rhombus.
Answers
Answer:
\(height = \frac{24}{2} = 12 \: cm \\ adjacent = \frac{32}{2} = 16 \: cm\)
We get a triangle of height 12 cm and adjacent 16 cm
\(side = \sqrt{ {12}^{2} + {16}^{2} } \\ = \sqrt{400} \\ = 20 \: cm\)
Answer:
side=√(24/2)²+(32/2)²
=√12²+16²
=√400
= 20
chase ran 36 3/4 miles over 6 days he ran the same distance each day how many miles did he run each day
Answers
Therefore, Chase ran 49/8 miles each day.
To find out how many miles Chase ran each day, we need to divide the total distance he ran (36 3/4 miles) by the number of days (6 days).
First, let's convert the mixed number into an improper fraction. 36 3/4 is equal to (4 * 36 + 3)/4 = 147/4.
Now, we can divide 147/4 by 6 to find the distance he ran each day:
(147/4) / 6 = 147/4 * 1/6 = (147 * 1) / (4 * 6) = 147/24.
Therefore, Chase ran 147/24 miles each day.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 147 and 24 is 3.
So, dividing 147 and 24 by 3, we get:
147/3 / 24/3 = 49/8.
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Chase ran a total of 36 3/4 miles over six days. To find out how many miles he ran each day, simply divide the total distance (36.75 miles) by the number of days (6). The result is approximately 6.125 miles per day.
Explanation:To solve this problem, you simply need to divide the total number of miles Chase ran by the total number of days. In this case, Chase ran 36 3/4 miles over six days. To express 36 3/4 as a decimal, convert 3/4 to .75. So, 36 3/4 becomes 36.75 miles.
Now, we can divide the total distance by the total number of days:
36.75 miles ÷ 6 days = 6.125 miles per day. So, Chase ran about 6.125 miles each day.
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3. Morgan almost never writes checks anymore, but she recently used Check
301 to pay a $30 fee at her school and then sent Check 302 to her niece as a
$25 birthday gift. Have both checks cleared? If not, how much will come out
of her account soon for the missing check(s)?
Answers
If both checks have not cleared yet, $55 will come out of Morgan's account soon for the missing check(s).
To determine if both checks have cleared, we need to know the current status of Morgan's account. Without that information, we cannot definitively say whether the checks have cleared or not.
However, based on the information provided, we can calculate the total amount that will come out of Morgan's account soon for the missing check(s).
The total amount that will come out of Morgan's account soon can be calculated as the sum of the $30 fee and the $25 birthday gift, which is $55 in total.
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a researcher counted the hours a brand of batteries could power different devices. the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. what percentage of devices ran on the batteries for fewer than
Answers
the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So 10.2% of gadgets were powered by batteries for fewer than 63 hours.
Given that,
Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.
The standard deviation is defined as ?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
\(p(X\leq 63) = p(Z\leq 63-74.6/9.1)\)
From standard deviation,
\(p(X\leq 63) = p(Z\leq -1.279)= 0.1061\)
a certain percentage of gadgets have battery life of less than 63 hours.
X= 63 hours
Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%
Therefore, 10.2% of electronic devices had battery life of less than 63 hours
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reposting again
i will give brainliest to best answer
Answers
Answer:
the answer is c plz trust
Step-by-step explanation:
The dogs in an animal parade are grouped by size. There are 18 small dogs, 12 medium-sized dogs, and 10 large dogs. If one dog is randomly chosen to lead the parade, what is the probability that a medium-sized dog will be chosen
Answers
Answer:
0.3
Step-by-step explanation:
Given:
Number of small dogs = 18
Number of medium-sized dogs = 12
Number of large dogs = 10
To find: probability that a medium-sized dog will be chosen
Solution:
Probability refers to chances of occurrence of some event.
Probability = number of favourable outcomes/total number of outcomes
Total number of dogs = 18 + 12 + 10 = 40
Number of medium-sized dogs = 12
So,
probability that a medium-sized dog will be chosen = Number of medium-sized dogs/Total number of dogs = \(\frac{12}{40}=0.3\)
Answer:
0.3
Step-by-step explanation:
There are only 7 blue pens,4 green pens and 6 red pens in a box.
One pen is taken at random from the box.
Write down the probability that the pen is blue
Answers
asap
"If two random variables are independent, then their covariance is o" True False
Answers
"If two random variables are independent, then their covariance is 0" is true.
Random variables are considered as a numerical value assigned to an outcome of a random event or a random process. A couple of random variables are autonomous if learning the value of one variable doesn't provide any details about the other variable.
The covariance between two arbitrary random variables X and Y, both of which have finite second moments, is defined by the formula:
Cov(X,Y) = E[XY] - E[X]E[Y]
However, if two arbitrary random variables X and Y are autonomous, then their covariance is equal to 0. It follows that if two random variables are independent, then their covariance is 0. The reason for this is that the expected value of a product of independent random variables is equal to the product of their expected values.
Therefore, we have:
Cov(X,Y) = E[XY] - E[X]E[Y]
Cov(X,Y) = E[X]E[Y] - E[X]E[Y]
Cov(X,Y) = 0.
The above statement is true.
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What is NOT a way to write 52 + 80? 50 + 2 + 80 (50 + 80) + 2 50 + 80 + 2 + 8 50 + 2 + 80 + 0
Answers
Answer: 52-80
Step-by-step explanation:
Answer:
52-80
Step-by-step explanation:
A study of child care enrolled 1364 infants and followed them through their sixth year in school. Later, the researchers published an article in which they stated that "the more time children spent in child care from birth to age four-and-a-half, the more adults tended to rate them, both at age four-and-a-half and at kindergarten, as less likely to get along with others, as more assertive, as disobedient, and as aggressive." $^{31}$ (a) Is this an observational study or an experiment? Justify your answer. (b) What are the explanatory and response variables? (c) Does this study show that child care causes children to be more aggressive? Explain.
Answers
(a) Is this an observational study or an experiment?
ans=Observational study – no treatment was imposed
(b) What are the explanatory and response variables?
ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior
d) Does this study show that child care causes children to be more aggressive? Explain.
No. Observational studies cannot show cause-and-effect
Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.
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Whats a Factor tree?
Answers
find slope of the altitude on each side of triangle ABC (d) A(-2,-3), B(3,6), C(-5,5)letter d) question 3)
Answers
Graphing the points that make up the triangle you have
Now, to obtain the slope of each side of the triangle you can use the slope formula, that is,
\(\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}\)So, the slope of segment AB will be
\(\begin{gathered} A=(x_1,y_1)=(-2,-3) \\ B=(x_2,y_2)=(3,6) \end{gathered}\)\(\begin{gathered} m=\frac{6-(-3)}{3-(-2)} \\ m=\frac{6+3}{3+2} \\ m=\frac{9}{5} \end{gathered}\)The slope of segment BC will be
\(\begin{gathered} B=(x_1,y_1)=(3,6) \\ C=(x_2,y_2)=(-5,5) \\ m=\frac{5-6}{-5-3} \\ m=\frac{-1}{-8} \\ m=\frac{1}{8} \end{gathered}\)The slope of segment AC will be
\(\begin{gathered} A=(x_1,y_1)=(-2,-3) \\ C=(x_2,y_2)=(-5,5) \\ m=\frac{5-(-3)}{-5-(-2)} \\ m=\frac{5+3}{-5+2} \\ m=\frac{8}{-3} \\ m=-\frac{8}{3} \end{gathered}\)Therefore, the slope of each side of the triangle ABC is
\(\begin{gathered} \text{ The slope of segment AB is }\frac{9}{5} \\ \text{ The slope of segment BC is }\frac{1}{8} \\ \text{ The slope of segment AC is }\frac{-8}{3} \end{gathered}\)
An activity on a pert network has these time estimates: optimistic = 2, most likely = 5, and pessimistic = 10. what is its expected activity time?
Answers
The expected activity time for the given statement is = 5.33
What time is the PERT network expected to be active?The average amount of time required for an activity when it is repeatedly performed is known as the expected time. The weighted average of the three estimated times, i.e., the optimistic time, the most probable time, and the pessimistic time, is used in project management analysis to determine the expected time of activity.
The PERT system:A network model called the Program Evaluation and Review Technique (PERT) allows for randomness in the timing of activity completion. PERT was created in the late 1950s again for a massively labor-intensive Polaris project for the US Navy. It might shorten a lot of time and cost needed to finish a project.
According to the given information:optimistic = 2
most likely = 5
pessimistic = 10.
We will use the following formula to calculate the anticipated time for each activity in order to solve this problem:
Expected Time = (Optimistic Time + (4 x Most likely) + Pessimistic Time) / 6
Putting the values into formula:
= (2 + (4 x 5) + 10)/ 6
= (2 + 20 + 10) / 6
= 5.33
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