Answers
Answer:
[tex]\frac{\pi }{3}[/tex]
Step-by-step explanation:
[tex]sin^{-1}(\frac{\sqrt{3} }{2})[/tex]
In, 30-60-90 degree triangle ,
the sides are in the ratio [tex]1: \sqrt{3} :2[/tex]
[tex]sin(60)= \frac{opposite}{hypotenuse}[/tex]
for 60 degree, opposite side = square root (3)
hypotenuse = 2
So [tex]sin(60)= \frac{\sqrt{3}}{2}[/tex]
when we move sin to the other side then it becomes sin^-1
[tex]60= sin^{-1}\frac{\sqrt{3}}{2}[/tex]
angle 60 degree is [tex]\frac{\pi }{3}[/tex]
[tex]sin^{-1}(\frac{\sqrt{3} }{2})=\frac{\pi }{3}[/tex]
The expression that is equivalent to sin⁻¹(sqrt. 3/2) is π/3.
What is the equivalent expression?The expression that is equivalent to another is one that yields the same output no matter the arrangement of the figures and signs.
For the expression, sin⁻¹(sqrt. 3/2), the equivalent can be obtained thus;
sin 60 = opposite/hypotenuse
sin 60 = √3/2
60 = sine⁻¹√3/2
= π/3.
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Related Questions
Some students in a school were surveyed to determine how many hours they study per night and their grade-point averages. The results are shown in the table.
If the data are entered into a regression calculator, what is the approximate y-intercept of the resulting regression line?
–1.76
–0.63
0.63
1.76
Answers
The equation is in slope intercept form y = mx+b
m = slope = 0.628
b = y intercept = 1.759
The value 1.759 rounds to 1.76 which is the answer
:)
There are 16 pink jelly beans in a bag. The ratio of red to pink jelly beans in the bag is 3/4. Which proportion could NOT be used to find r, the number of red jelly beans in the bag
Answers
Let
r----------> the number of red jelly beans in the bag
p---------> the number of pink jelly beans in the bag
we know that
r/p=3/4
p=16
so
r/p=3/4--------> r/16=3/4-----> r=(3/4)*16-----> r=12
therefore
case A) 3/4=r/16-----> is correct, the proportion could be used to find r
case B) 16/r=4/3----> r=16/(4/3)----> r=16*3/4-----> r=12-----> is correct
the proportion could be used to find r
case C) 3/4=r/16-----> is correct, the proportion could be used to find r
case D) 3/4=r/16-----> is correct, the proportion could be used to find r
the answer is
All proportions could be used to find r
What’s the largest fraction in each group?
a. 5⁄6 and 29⁄36
b. 5⁄12 and 3⁄8
c. 2⁄5 and 19⁄45
d. 5⁄7, 13⁄14, and 19⁄21
e. 7⁄11 and 9⁄121
f. 1⁄2, 3⁄18, and 4⁄9
Answers
a) 5/6
b) 5/12
c) 19/45
d) 13/14
e) 7/11
f) 1/2
Hope this helps!
A circular plate has circumference 21.4 inches. What is the area of this plate? Use 3.14 for pi.
Answers
Given a circle with a circumference of 21.4 inches, first calculate the radius using the circumference formula, then use the radius to calculate the circle's area, which results in approximately 36.29 square inches.
Explanation:This question involves determining the area of a circle given its circumference. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference, r is the radius, and π is a constant (approximated to 3.14). Given that the circumference is 21.4 inches, we can rearrange this formula to find the radius (r = C/2π), giving us a radius of approximately 3.4 inches.
Now, knowing the radius, we can use it to find the area using the formula for the area of a circle, which is A = πr². Plugging in the values, we find that the area is approximately 36.29 square inches.
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Which of the following best describes the symmetry of a trapezoid? Select all that apply.
a) point
b) line
c) plane
d) rotational
Answers
Answer: A.) Point.
Step-by-step explanation:
Find the slope of the line that passes through each pair of points.
1. (5,2),(3,1)
2.(-7,4),(-5,0)
Answers
2. (0-4)/(-5-7) = (-4)/(-12) = 1/3
To find the slope you’d do the second y-value minus the first y-value over the second x-value minus the first x-value.
Determine the factors of ax + ab + 2by + 2xy.
Answers
=a(x+b) + 2y(x+b) =(x+b)(a+2y)
ax + ab + 2by + 2xy = (x+b)(a+2y)
Answer: (x+b) (a+2y)
Step-by-step explanation:
ax+ab+2by+2xy
split the equatuion in half
1. ax+ab 2. 2by+2xy
gcf=a gcf=2y
ax/a=x 2by/2y= b
ab/a=b 2xy/2y= x
a(x+b) 2y(x+b)
Answer :(x+b)(a+2y)
Anthony purchased 6 fruit bars and 3 chocolate-nut bars for a camping trip. He spent $4.12 on the bars. Anthony wrote the following equation: . What did he define as the variable x?
Answers
(price of FB)x+(price of CB)x=4.12
write an expression that represent the sum of r and 7
Answers
Final answer:
The expression that represents the sum of r and 7 is written simply as r + 7. This is a basic operation in algebra involving the addition of a variable and a constant.
Explanation:
To write an expression that represents the sum of r and 7, you simply add these two together. The mathematical expression for this is r + 7. This is a basic algebraic expression that demonstrates how to represent the addition of a variable, in this case r, with a constant number, which is 7.
Given the two expressions shown below:
square root of 64 plus square root of 5
square root of 64 plus square root of 4
Which statement best describes the two expressions?
Both are rational.
Both are irrational.
A is rational, but B is irrational.
A is irrational, but B is rational.
Answers
The answer is A is irrational, but B is rational.
An irrational number is a number that cannot be written as a fraction.
Expression A.
[tex] \sqrt{64} + \sqrt{5} = 64 + 2.23606...[/tex]
This cannot be written as a fraction and therefore the expression is irrational.
Expression B.
[tex] \sqrt{64} + \sqrt{4} = 8 + 2 = 10 = \frac{10}{1} [/tex]
This can be written as a fraction and therefore the expression is rational
Your answer:
A is irrational, but B is rational.
~ Hope this helps you!
MarkV
Answer:
A is rational, but B is irrational.
Step-by-step explanation:
PLESE HELP FAST!!!!!! WILL GIVE BRAINLIEST!!!! I NEED HELP ASAP!!
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r. Jones took a survey of college students and found that 60 out of 65 students are liberal arts majors. If a college has 8,943 students, what is the expected number of students who are liberal arts majors?
Answers
Here, we need to calculate the expected number of students who are liberal arts major.
It is given that, 60 out of 65 students are liberal arts major.
So, we will calculate the percentage of liberal arts major from the total.
Percentage of liberal arts major = [tex] \frac{Number of liberal arts major}{Total students} [/tex] X 100
Percentage of liberal arts major = [tex] \frac{60}{65} [/tex] X 100
Percentage of liberal arts major = 92.31 %
Now, we will calculate for 8,943 liberal arts majors -
In total students of 8,943, liberal arts majors = 92.31 % X 8,943
In total students of 8,943, liberal arts majors =8,256 students (approximately)
Written as a percent , what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5
Answers
The probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
To find the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5.
Since, From 1 to 5, there are three numbers 1, 3, 5 are odd numbers.
Hence, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is,
P = 3/5
Change into percent as;
P = 3/5 x 100%
P = 60%
Thus, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%
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William gave 4 football cards to each of the 6 friends.Suppose he had 54 cards left. Write and solve an equation to find how many cards each friend a initially had.
Answers
T = 6(4) + 54
William had 78 at the start
Reply if you need more help!
brainliest FOR WHO HELP ME a spherical mini donut hole has a diameter of 6 centimeters. A large spherical donut hole has a diameter of 9 centimeters. Approximately how much greater is the volume of a large donut hole than the volume of a mini donut hole?
86 cm³
113 cm³
226 cm³
268 cm³
Answers
4/3 *3.14*3^3-Mini Donut
Then Subtract the greater answer from the smaller one.
An equation is shown below:
5(2x − 3) = 5
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work.
Answers
10x = 20
x = 2
This equation has one solution.
The solution would be x = 2
A) This equation has only one solution. B) The solution would be x = 2.
How to find the solution to the given system of equation?For that ,we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.
If there comes a = a situation for any a, then there are infinite solutions.
Given equation is 5(2x − 3) = 5
By solving further,
10x -15 = 5
10x = 20
x = 2
A) This equation has only one solution.
B) The solution would be x = 2
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-1 ≥ -8; Multiply both sides by -2
Answers
Please answer the picture.
Answers
A bag contains a total of 25 marbles. Five of the marbles are blue, 3 are red, 8 are green, and 9 are white. If a marble is drawn from the bag and then replaced 50 times, about how many times would a green marble be drawn?
A. 4
B. 8
C. 16
D. 24
Answers
The Smith family has a two-and-a-half-foot-long sandwich to share. One-half foot of the sandwich will serve one person. How many one-half foot servings are in this sandwich?
Answers
2 1/2 / 1/2
This can simplify into:
5/2 / 1/2
Dividing a fraction is basically multiplying it's flipped side:
5/2 * 2
10/2 = 5
There are 5 servings in the sandwich
If the sum of three numbers is 144, what is the average of the three numbers?
Answers
Final answer:
The average of three numbers that sum to 144 is 48, found by dividing 144 by 3.
Explanation:
The average of three numbers is the sum of those numbers divided by three. In this case, if the sum of three numbers is 144, then the average can be found by dividing 144 by 3. Calculating this, we get the average, which is 48 (144 ÷ 3 = 48). Hence, the average of the three numbers is 48.
just say answer, no need to explain! Thanks!
Answers
f(x) = |x|
Moving 4 units to right means, subtracting the number from x. So moving |x| 4 units to right will give:
f(x) = |x-4|
Moving 2 units up means addition of a number to the function. So moving 2 units up will give:
f(x) = |x-4| + 2
Thus, the correct answer to the question is option B
at the pet shelter,for every 7 dogs there are 5 cats.what is the ratio of dogs to cats?
a.5:7
b.7:5
c.7:12
d.12:7
Answers
the greatest common factor gcf of 2 monomiald is 3x^2y. One of the monomials is 3x^4y . Which couod be the other monomial.
Answers
The reason this has to be is because of the GCF. Since 3 is part of the GCF, and the other monomial has a coefficient of 3, this means the missing monomial must be divisible by 3 as well.
Since x² is part of the GCF, the missing monomial must contain x². However, if it were to contain x³ or anything larger, the GCF would have x with a higher exponent.
The other monomial must have the factors of 3x^2y, with the possibility of having higher powers of y, but not lower, as this would change the GCF. An example of a compatible monomial with 3x^4y is 3x^2y^2.
Explanation:The question is asking for the other monomial given that the greatest common factor (GCF) of two monomials is 3x^2y and one of the monomials is 3x^4y. Since the GCF is the product of the lowest powers of common factors in the monomials, the other monomial must have at least the factors 3, x^2, and y to a certain power. It can have these factors to higher powers as well, but not to lower powers, since it would then alter the GCF.
An example of another monomial that could be paired with 3x^4y is 3x^2y^2, because it has the factors of the given GCF with potentially higher powers, without affecting the GCF. Therefore, any monomial of the form 3x^2y^n (where n is greater than or equal to 1) could be the other monomial.
Which substance traps pathogens and prevents them from entering the deeper tissue of the body? tears
Answers
Answer:
Mucus
Step-by-step explanation:
Jill has a balance of $5,000 on her credit card with an annual interest rate of 15%. To pay off the $5,000 in three years, Jill will have to make a minimum payment of $173.33 per month. To pay off the $5,000 in five years, Jill will have to make a minimum payment of $118.95 per month. How much more does Jill have to pay when the length of the loan changes from 3 years to 5 years? A) $1,239.88 B) $1,957.68 C) $2,137.00 D) $897.12
Answers
c is what it is
Answer:
The answer is D) $897.12
Step-by-step explanation:
3 years = 36 months
173.33 * 36 = 6239.88
5 years = 60 months
118.95 * 60 = 7137.00
7137.00 - 6239.88 = 897.12
Solve for x.
a) x=7.5 b) x=16 c) x=17.5 d) x=27.5
Answers
Note: This is done in the interior triangle as the angle will be equivalent to the other two angles.
Here's how you solve it:
You have to use the law of cosine for the interior triangle; the law of cosine is: c^2 = a^2 +b^2 - 2ab times cos (C)
Substitute each factor so that the equation now appears as so:
h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80)
This will give you: h = 11.67
Now, you have to apply this to the law of sin which is a over sin(A) = b over sin (B) = c over sin (C). (Lowercase letters are the opposite side of uppercase angles.)
This will then give you:
11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)
sin -1 ((8 times sin (80)) over 11.67) is equal to S
sin -1 ((10 times sin (80)0 over 11.67)) is equal to T
Because you now know the angles of S and T, you need to use the law of sin again.
t over sin (T) = s over sin (S)
t = 10 + x
s = 8 + 18 = 22
Thus, you need to substitute the variables to get this equation:
10 + x over sin (57.54) = 22 over sin (42.45)
x = 22 times sin (57.54) over sin (42.45) and next to this is -10
Thus, getting the answer of x = 17.50
Answer: x = 17.5
Step-by-step explanation:
You're using interior angles
Use the law of cosine: c^2 = a^2 +b^2 - 2ab times cos (C)
h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80) so h = 11.67
11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)
sin -1 ((8 times sin (80)) over 11.67) is equal to S
sin -1 ((10 times sin (80)0 over 11.67)) is equal to T
t over sin (T) = s over sin (S)
t = 10 + x
s = 8 + 18 = 22
10 + x over sin (57.54) = 22 over sin (42.45)
x = 22 times sin (57.54) over sin (42.45) and next to this is -10
the answer of x = 17.50
Hope this helps, have a BLESSED and wonderful day! :-)
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1) In a trapezoid ABCD with legs
AB
and
CD
, the diagonals intersect each other at point O. Compare the areas of: ΔABD and ΔACD
and then
2) In a trapezoid ABCD with legs
AB
and
CD
, the diagonals intersect each other at point O. Compare the areas of:
ΔABO and ΔCDO
pleassssee help
Answers
Answer:
1) Area of ΔABD = Area of ΔACD and
2) Area of ΔABO = Area of ΔCDO
Step-by-step explanation:
1) In the given trapezoid ABCD,
AD || BC
Triangles ΔABD and ΔACD lie on the same base AD and lie between the parallel lines AD and BC.
Hence, they are equal in area.
Therefore, Area of ΔABD = Area of ΔACD.
2) From 1), we have
Ar (ΔABD) = Ar(ΔACD)
Subtract Ar (ΔAOD) from both sides,
Ar (ΔABD) - Ar (ΔAOD) = Ar(ΔACD) - Ar (ΔAOD)
Ar (ΔABO) = Ar (ΔCDO)
Examine the system of equations. y = –3x – 2, y = 7 The value of x is . The solution to this system of equations is .
Answers
You can substitute y into the other equation
7 = -3x - 2
Add 2 to both sides
9 = -3x
Divide both sides by -3
-3 = x
The answer is -3
Hope this helps!
The value of x is -3 and the solution to this system of equations is (-3 , 7).
When a number of variables are involved, the system of equation is generated. The system of equation has been the set of simultaneous equations as well.
Given :
[tex]y = -3x-2[/tex] ---- (1)
[tex]y=7[/tex] ----- (2)
Solution :
From, equation (1) and (2) we get the value of x to be:
[tex]7=-3x-2[/tex]
[tex]9=-3x[/tex]
[tex]x=-3[/tex]
Therefore, the value of x is -3.
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In a recent fundraising campaign, Rise Over Run received 20 checks of various amounts to donate to their favorite charities. Olive uses this spinner to determine which charity will receive each check.
About how many of the 20 checks should arise Over Run expect to go to their TreeHuggers Campaign ?
Answers
Answer:
6 checks
Step-by-step explanation:
The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]
For this case, we're specified that:
The spinner has 10 parts.
3 belong to Treehuggers2 belong to Ameriteach5 belong to Paws of PeaceThus, the probability of getting the spinner fall on treehugger is 3/10 (three favorable parts of spinner to ten total parts, all parts assumingly equally probable and spinner assumingly not falling in the mid of two parts).
20 checks, all will be accompanied with 20 spins, all independent of each other.
Let X = total number of times the spinner falls on Treehuggers
And let Success for a spin = It landing on Treehugger
Failure for a spin = It not landing on Treehugger
Probability of success = p = 3/10 = 0.3Probability of faillure = 1-p = 7/10 = 0.7n = 20, so we get:
[tex]X \sim B(n=20,p=0.3)[/tex]
The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign = expected number of successes in those 20 spins = the expected number of values of X.
Since X follows a binomial distribution, we get:
[tex]E(X) = np = 20 \times 0.3 = 6[/tex]
Thus, the expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.
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A 25 foot ladder leans against a wall 7 feet from the base of the wall. How high does the ladder touch?
Answers
a² + 7² = 25²
a² = 25² - 7²
a² = 576
a = 24
Answer: The height is 24 feet.
The height formed by this 25 foot ladder that leans against a wall is 24 feet.
Given the following data:
Length of ladder (hypotenuse) = 25 foot.Adjacent = 7 feet.What is Pythagorean Theorem?Pythagorean theorem can be defined as a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right-angled triangle.
Mathematically, Pythagorean's Theorem is given by this formula:
[tex]h^2 = a^2 + b^2[/tex]
Where:
h is the hypotenuse.a is the adjacent side.b is the opposite side.Substituting the given parameters into the formula, we have;
[tex]h^2 = a^2 + b^2\\\\25^2 = 7^2 +b^2\\\\625=49+b^2\\\\b^2=625-49\\\\b=\sqrt{576}[/tex]
b = 24 feet.
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