if an equilateral triangle has an altitude measuring 17 root 3 what is the measure of its sides?
Answers
The equilateral triangle has a side length of 34
Here, given the altitude of an equilateral triangle, we want to get the measure of its sides
Let the sides measure be x (all sides are equal)
The altitude divides the base length into two equal parts
So, one part of the base will measure x/2
So we have a right-angled triangle with hypotenuse x , while the two other sides are x/2 and 17 root 3
Using Pythagoras' theorem, we understand that the square of the hypotenuse equals the sum of the squares of the two other sides
Mathematically, we have this as follows;
\(\begin{gathered} x^2\text{ = (17}\sqrt[]{3})^2\text{ + (}\frac{x}{2})^2 \\ \\ x^2\text{ = 867 + }\frac{x^2}{4} \\ \\ \text{Multiply through by 4} \\ \\ 4x^2=3468+x^2 \\ \\ 4x^2-x^2\text{ = 3468} \\ \\ 3x^2\text{ = 3468} \\ \\ x^2\text{ = }\frac{3468}{3} \\ \\ x^2\text{ = 1156} \\ \\ x^2=34^2 \\ \\ x\text{ = 34} \end{gathered}\)Related Questions
Solve for b
10, b, 150degrees, 12degrees
Answers
Hello!
We have all angles of the triangle:
We will use the law of cosines. This relation is valid for all sides of any t
We have:
angle A = 12°
côté a = 10
angle B = 150°
This is therefore the first case of application of the sine law.
So:
\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)
\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)
b = 25cm
A comparison of two unrelated samples (n = 8 and n = 10) yield an estimated standard error of 2 points and a t statistic of t = 1.500. What is the difference between the sample means?
Answers
The difference between the sample means is A = ( 4√10/3 )
Given data ,
Difference between sample means A = (t-statistic) * (estimated standard error) / √(1/n1 + 1/n2)
On simplifying , we get
To find the difference between the sample means, we need to multiply the estimated standard error by the t-statistic and then divide by the square root of the sum of the reciprocals of the sample sizes.
Given that the estimated standard error is 2 points, the t-statistic is 1.500, and the sample sizes are n1 = 8 and n2 = 10, we can substitute these values into the formula:
Difference between sample means = (1.500) x (2) / √(1/8 + 1/10)
Calculating the sum of the reciprocals of the sample sizes:
1/8 + 1/10 = 5/40 + 4/40 = 9/40
Difference between sample means = (1.500) x (2) / √(9/40)
A √(9/40) = √(9) / √(40) = 3 / (2 x √(10))
Difference between sample means = 1.500 x 2 x (2 x √(10) / 3)
Difference between sample means ≈ 4√(10) / 3
Therefore, the difference between the sample means is ( 4√10/3 )
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You are selling pizzas to raise money for a school field trip. Cheese pizza cost $8 andpepperoni pizza cost $9. You need to sell at least two of each kind of pizza, and you want tosell at least $180 worth of pizza.a. Write and graph a system of linear inequalities that represent the information given.b. You sell 14 cheese pizzas and 10 pepperoni pizzas. Did you reach your sales goal? Explainhow you know.
Answers
We have the following:
Let x cheese pizza
Let y pepperoni pizza
\(\begin{gathered} x\ge2 \\ y\ge2 \\ 8\cdot x+9\cdot y\ge180 \end{gathered}\)therefore:
a.
b.
yes, because it is in our shaded region
7. The fastest ever Formula 1 qualifying lap at Silverstone is 1 minute, 29.6 seconds.
The fastest ever racing lap is 1 minute, 30.9 seconds.
How many tenths of a second quicker is the qualifying lap?
Answers
Answer:
1.3 seconds ; 13 tenth of a second
Step-by-step explanation:
Fastest ever qualifying lap = 1 minute 29.6 seconds
Fastest ever racing lap = 1 minute 30.9 seconds
The difference :
1 minute 30.9 seconds - 1 minute 29.6
30.9 seconds - 29.6 seconds = 1.3 seconds
1.3 seconds = 1.3/0. 1 = 13 tenth of a second
Find the volume of this sphere.
Use 3 for TT.
V =
8 cm
πr³
V =
π[?]³
Hint: Plug in the value of the
radius for r. The diameter is 8.
The radius is half this value.
Enter
4 is the radius
Answers
Answer:
16
Step-by-step explanation:
What is the value of ?
T
80°
25°
R
?
P
PLEASE
Answers
9514 1404 393
Answer:
105°
Step-by-step explanation:
The exterior angle marked "?" is equal to the sum of the remote interior angles:
? = 25° +80°
? = 105°
According to some sources, the African continent has about 170 million Internet users. According to the bar graph, which statement is true?
Africa has fewer users than the Middle East.
Africa has more users than Asia.
Africa has more users than Europe but fewer than Asia.
Africa has more users than the Middle East but fewer users than North America.
Answers
Answer:
The last answer choice
Step-by-step explanation:
Interpretation of internet users
Middle East - about 100 million
North America - about 250 million
Europe - about 500 million
Asia - over 1 billion
Now lets look back at the question.
If Africa has 170 million internet users, according to the graphs, which statement is true.
"Africa has fewer users than the middle east"
This is false as Africa has 170 million users whereas The middle east has about 100 million users
170 mil > 100 mil therefore the statement is false
"Africa has more users then Asia"
This is also false as Asia has the most internet users at 1 billion
Africa has no where near as many users at 170 million users therefore the statement is false
"Africa has more users than Europe but fewer than Asia."
We have already identified that Africa has fewer users than Europe so this one could be it if the other part is true.
"Africa has more users than Europe" This is false as Europe has 500 million internet users while Africa only has 170 million users
Therefore this statement is false
"Africa has more users than the Middle East but fewer users than North America."
Africa has more internet users than the Middle East ( 170 mil > 100 mil ) and fewer users than North America ( 250 mil > 170 mil )
therefore this is the correct statement
two way frequency table!! giving points!!
Answers
Answer:
see attached
Step-by-step explanation:
To fill in the relative frequency table, divide every number in the table by the total at lower right. For example, 7th (0-50) would be 72/250 = 28.8%.
This is conveniently done using a spreadsheet. The spreadsheet can do the rounding for you.
Triangle A B C is shown. The length of A C is 8 and the length of C B is a. Angle C A B is 45 degrees and angle A B C is 77 degrees.
Complete the work to determine the value of a.
Use the law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction.
Substitute: StartFraction sine (45 degrees) Over a EndFraction = StartFraction sine (77 degrees) Over 8 EndFraction .
Cross multiply: 8sin(45°) = asin(77°).
Solve for a and round to the nearest hundredth:
a ≈
.
Answers
Answer:
approximately 4.75 units
Step-by-step explanation:
Using the law of sines, we have:
sin(A)/a = sin(B)/b
Substituting the given values, we get:
sin(45°)/a = sin(77°)/8
Solving for 'a', we have:
a = sin(45°) * 8 / sin(77°)
a ≈ 4.75 (rounded to two decimal places)
Therefore, the length of CB is approximately 4.75 units
Answer:5.81
Step-by-step explanation: I'm doing the assignment rn and got it right.
What is the value of r
Answers
Step-by-step explanation:
Vertical angles are equal r = 70 degrees
Simplify the expression StartFraction a b Superscript 3 Baseline over a Superscript 4 Baseline b EndFraction plus left-parenthesis c Superscript 2 Baseline right-parenthesis Superscript 3 Baseline
Answers
The simplification of the expression ab³/a⁴b + (c²)³ is determined as b²/a³ + c⁶.
What is the simplification of the expression?The given expression is simplified as follows;
The given expression is written as;
ab³/a⁴b + (c²)³
To simplify the expression given above, we will divide the fraction with the common factor as follows;
From the numerator; ab³, we will factor out "ab"
From denominator; a⁴b, we will factor out "ab"
The resulting expression becomes;
ab³/a⁴b + (c²)³
= b²/a³ + c⁶
Note: for the power of c, we simplify by multiplying 2 and 3 = 6
Thus, the simplification of the expression ab³/a⁴b + (c²)³ is determined as b²/a³ + c⁶.
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Is this the graph of a function?
Answers
Answer:
function
Step-by-step explanation:
this graph is a function.
why?
if we draw a vertical line on all points of the function we can see that it only intersects ONCE. Therefore, it's a function. if it intersects more than once then it will not be a function
How do you solve -3(1-(-2))•2+3-12÷6
Answers
Answer:
-17
Step-by-step explanation:
-3(1-(-2))•2+3-12÷6 (first parenthesis)
-3(3)•2+3-12÷6 (Multiplication with parenthesis)
-9•2+3-12÷6 (them multiplication and division are on the same level)
-18+3-2 (adding and subtraction are on the same level)
-17
cises
1. Yesterday the Rockville Corporation instituted a 2-for-1 stock split. Before the split, the market
share price was $63.44 per share and the corporation had 2.3 billion shares outstanding.
a. What was the pre-split market cap for Rockville?
b. What was the post-split number of shares outstanding for Rockville?
c. What was the post-split market price per share for Rockville?
Answers
a: $145,912,000,000
b: 4.6 bn shares
c: $31.72/per share (divide in half)
Which of the following is false about the central limit theorem (CLT)? O If we take more samples from the original population, the sampling distribution is more likely to be nearly normal. O If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. O As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution. O The CLT states that the sampling distribution will be centered at the true population parameter.
Answers
Only the first statement is false. The rest are true statements about the Central Limit Theorem.
The Central Limit Theorem (CLT) is a fundamental theorem in probability and statistics which states that, given a sufficiently large sample size from a population with a given mean and standard deviation, the sampling distribution of the mean will be nearly normal, regardless of the shape of the original population distribution.
It is important to note that the first statement presented is false. Taking more samples from the population will not necessarily result in a more normal sampling distribution. The CLT does not guarantee that the sampling distribution will be normally distributed, only that it is more likely to be so as the sample size increases.
The second statement is true. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. The third statement is also true. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.
Finally, the fourth statement is also true. The CLT states that the sampling distribution will be centered at the true population parameter. This means that the mean of the sampling distribution will be equal to the mean of the population.
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help, hurry pleaseee.
Answers
Answer:
3.5 and -3.5
Step-by-step explanation:
The lines on the outside of n mean the absolute value (the distance from 0)
Answer:
3.5 and -3.5
Step-by-step explanation:
Sense n is absolute value it doesn't matter whether the integer/number is negative or positive.
7. Find the equation of the line joining the points (3, -6) and (-5, 6).
Answers
Answer:
y= -3/2x-3/2
Step-by-step explanation:
5 in
4 in
What is the length of the missing leg?
Answers
solved by following the rules of a 3 4 5 right triangle
pleaseee helpppppp!!!
Answers
The measure of a straight line is 180
125+30=155
180-155=25
x = 25
Answer:
x=25
the angles are ona straight line, so that means it's 180 degrees
125+30=155
180-155=x
180-155=25
hope it helps :)
2(2x - 4) = 3(x + 4)
Answers
Answer:
24
Step-by-step explanation:
i dont know if its correct
PLEASE HELP!! BEST ANSWER WILL BE MARKED BRAINIEST! The stadium is at (-2,3) and the high schools (1,8). What is the shortest driving distance (in blocks) between these two locations? Can you figure this out without looking a the grid
Answers
Answer:
Shortest distance is 5 blocks.
Answer:
5.8
Step-by-step explanation:
I'm not 100% on this as the decimal in the answer makes me doubt myself. Here's the explanation anyways
At a sale, dresses were sold for 36% of their original price. If the dresses originally cost $200 each, how much did a dress cost on sale?
Answers
Answer:
Each dress would cost 72
Step-by-step explanation:
36% of 200 is 72
An ion channel can be in either open (O) or closed (C) states. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. Calculate the probability of the ion channel going through the following sequence of states: COO. An individual can be either susceptible (S) or infected (I), the probability of infection for a susceptible person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day. Calculate the probability of a person going through the following string of states: SISI.
Answers
Answer:
a) P (COO) = 0,135
b) P ( SISI) = 0,00015
Step-by-step explanation:
a) the probability of an ion channel in open position is 50 % 0,5
the probability of an ion channel in close position is 50 % 0,5
probability for the following sequence of states COO
to be closed 0,5 (C)
from (C) to pass to open 0,3 (O)
and to stay O is 0,9
Then the probability of the sequence of states COO is
P (COO) = 0,5 * 0,3 * 0,9
P (COO) = 0,135
b) If people are either infected or susceptible, then
Probability of an individual infected is 0,5
Probability of an individual susceptible is 0,5
to pass from susceptible to infected is 0,05
to pass from infected to susceptible is 0,12
then
P ( SISI) = 0,5 * 0,05*0,12*0,05
P ( SISI) = 0,00015
probability for the following sequence of states COO
How many different passwords can be made if it is three letters, followed by two digits, followed by a letter? (Repetition is allowed.) Use the fundamental counting principle.
Answers
Answer:
There are 45,697,600 different passwords.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
In this question:
3 letters, each with 26 possible options(ways).
Two digits, each with 10 possible options.
One digit, with 26 possible options.
How many different passwords?
Each digit/letter is independent, so:
26*26*26*10*10*26 = 45,697,600
There are 45,697,600 different passwords.
A salesperson earns a commission of $418 for selling $2200 in merchandise.
Find the commission rate. Write your answer as a percentage.
Answers
Based on the information given the commission rate is 19%.
Commission rate:To determine the commission rate we would have to divide the sales commission by the merchandise using this formula
Commission rate=Sales commission/Merchandise×100
Where:
Sales commission=$418
Merchandise=$2,200
Let plug in the formula
Commission rate=$418/$2,200×100
Commission rate=19%
Inconclusion the commission rate is 19%.
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For what values of a are the following expressions true?
|a-5|=5-a
Answers
Answer:
this expression is true for all values of a.
Step-by-step explanation:
So if the expression is:
a - 5 = 5 - a
For this reason:
2a = 10
a = 5
a - 5 = -5 + a
0 = 0
PLEASE HELP! I WILL GIVE BRAINLIEST!! A worker at an animal shelter recorded data about the adoption of cats in the table shown below.
Based on the table, which of these statements are true? Choose all that are correct.
a
Of all the cats adopted, 34.9% are between 6 months and 1 year old
b
Of the cats 1 year or older, about 58% took more than 1 month to be adopted.
c
Of all the cats adopted, about 66% were adopted in a month or less.
d
Of the cats that took more than a month to adopt, 12.5% were younger than 6 months
e
Of the cats who took 1 to 7 days to be adopted, 25% were between 6 months and 1 year old.
Answers
The lengths of two sides of a triangle are 6cm and 8cm.Between what two measures should the length of the third side fall? PLEASE HELP !!!!!!!!
Answers
Answer: Search Results
Featured snippet from the web
In triangle sum of 2 sides must be greater than the 3rd side. So, the third > 8 - 6 = 2 and also the third < 8 + 6 = 14. So, the answer is 2 < third side < 14. The third side lies between(2,14).
Step-by-step explanation: Brainlyest please
At a carnival game, there is a 45% probability of winning a prize. What is the probability of not winning a prize?
Answers
Answer:
55%
Step-by-step explanation:
We know that probability must add up to 1 or 100%, so what you need to do is:
P(Not Winning) = 100% - P(Winning)
P(Not Winning) = 100% - 45%
P(Not Winning) = 55%
Answer:
The probability that you will win is9/10 .The probability that you won't win is 0.55.The probability that you won't win is 11/20
Step-by-step explanation:
Submit your answers to the following questions. Be sure to explain your reasoning for each; it is helpful to draw this out to get started to see any quantitative patterns that develop.
If you write the counting numbers in rows of 7 numbers each, like shown below (but you keep going), where all the number line up in seven vertical columns as you go. (Note in the example below, the number 13 is in the 2nd row and the 6th column.)
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
In which column would the number 100 land?
In which row?
Now write the counting numbers in rows of 6 numbers each. What’s the location of 100 in this array?
Write arrays with other length rows. Find a way to predict in which row and column 100 will land for any array of numbers.
Answers
The number 100 would land in column 2
The number 100 would land in row 14The location of 100 in rows of 6 numbers is row 16 and column 3The location of 100 in rows of n numbers is row q and column rIn which column would the number 100 land?Given that we have the array of numbers
The length of each row in the array is 7
Dividing 100 by 7, we have
100/7 = 14 Remainder 2
This means that
Column = 2
In which row would the number 100 land?In (a), we have
100/7 = 14 Remainder 2
This means that
Row = 14
The location of 100 in rows of 6 numbersHere, we have
The length of each row in the array is 6
Dividing 100 by 6, we have
100/6 = 16 Remainder 3
So, the location of 100 in rows of 6 numbers is row 16 and column 3
Predicting the row and column 100 will landLet the length of each row in the array be n
Dividing 100 by n, we have
100/n = q Remainder r
This means that the location of 100 in rows of n numbers is row q and column r
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