The confidence interval for variance is (0.29,0.58)
A family of continuous probability distributions is known as the chi-square (X2) distribution. They are frequently employed in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.
The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.
The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for testing hypotheses rather than for modeling actual distributions.
Since we have given that the sample size n= 54,
variance = 0.44
we need to find a 98% confidence interval to estimate the variance.
So, we will use Chi-square distribution,
For this, we will find
df=n-1 = 54-1 = 53,
the interval would be,
[tex]\frac{(n-1)s^2}{X^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{X^2_{1-\alpha/2}}\\\\\alpha=1-0.98=0.02\\\\\alpha/2=0.02/2=0.01\\X^2_{0.01,53}=79.84\\Similarly\\\\1-\alpha/2=0.99\\\\X_{1-\alpha/2}^2,df=X^2_{0.99,53}=40.308\\\\So,\\\frac{53*0.44}{79.84} < \sigma^2 < \frac{53*0.44}{40.308}\\\\0.29 < \sigma^2 < 0.58[/tex]
Hence the confidence interval is (0.29,0.58)
learn more about chi-square distribution.
https://brainly.com/question/30259945
#SPJ4
the shortest side of a triangle with angles 50o, 60o, and 70ohas length of 9 furlongs. what is the approximate length, in furlongs, of the longest side?
The longest side of a triangle with angles of 50°, 60°, and 70° and a length of 9 furlongs on the shortest side is approximately 12.2 furlongs.
What is the Law of Cosines?The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle are known (SAS) or the lengths of the three sides (SSS) are known.
To calculate this, using the Law of Cosines formula,
which is:
[tex]c^2 = a^2 + b^2 - 2abcosC[/tex]
where c is the longest side, a is the shortest side, b is the other side of the triangle, and C is the angle
between a and b.
In this case, c = 12.2 furlongs,
a = 9 furlongs,
b is the side opposite the angle 70°, and C = 70°.
So the formula becomes:
[tex]c^2 = 92 + b^2 - 2(9)(b)cos70^{o}[/tex]
Solving for b gives us b = 12.2 furlongs, which is the length of the longest side.
Learn more about triangles with the angle and length, of the longest side at: https://brainly.com/question/11011280
#SPJ11
Please help i really need help due tomorrow
The area of the composite figure is 80ft².
Define area of composite figure?Composite shapes may have overlaps between their perimeter and area.
Although we frequently define any shape's area through its perimeter, these two ideas are distinct. The area determines how much room the shape can store, while the perimeter merely draws the object's exterior border. Hence, the space that a shape encloses within its perimeter or boundary is its area.
Calculating the areas of various fundamental shapes is necessary to determine the area of a composite shape.
Breaking the form down is the easiest method:
Separate the composite shape into its constituent parts.
Each fundamental shape's area should be determined separately.
Add these areas together to determine the composite shape's area.
Here, first the area of the triangle:
1/2 × b × h
=1/2 ×(18-7-7) × 4
= 1/2 × 4 × 4
= 8ft².
Now, area of the rectangle:
b × l
= 4× 18
= 74ft².
Area of the whole figure = 8 + 72 = 80ft².
To know more about area, visit:
https://brainly.com/question/16890298
#SPJ1
Determine whether it is possible to find values of L 0 so that the given boundary-value problem has precisely one nontrivial solution, more than one solution, no solution, and the trivial solution. (Let k represent an arbitrary integer. If an answer does not exist, enter DNE.) y" + 16y=0, y(0)= 1, y(L) = 1 (a) precisely one nontrivial solution (b) more than one solution (c) no solution (d) the trivial solution
There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
We are given the boundary-value problem:
y" + 16y = 0, y(0) = 1, y(L) = 1
The characteristic equation is r^2 + 16 = 0, which has roots r = ±4i.
The general solution to the differential equation is then y(x) = c1cos(4x) + c2sin(4x).
Using the boundary conditions, we get:
y(0) = c1 = 1
y(L) = c1cos(4L) + c2sin(4L) = 1
Substituting c1 = 1 into the second equation, we get:
cos(4L) + c2*sin(4L) = 1
Solving for c2, we get:
c2 = (1 - cos(4L))/sin(4L)
Thus, the general solution to the differential equation that satisfies the given boundary conditions is:
y(x) = cos(4x) + (1 - cos(4L))/sin(4L)*sin(4x)
Now, we can answer the questions:
(a) To have precisely one nontrivial solution, we need the coefficients c1 and c2 to be uniquely determined. From the above expression for c2, we see that this is only possible if sin(4L) is nonzero. Thus, if sin(4L) ≠ 0, there exists precisely one nontrivial solution.
(b) If sin(4L) = 0, then c2 is undefined and we have a family of solutions that differ by a constant multiple of sin(4x). Hence, there are infinitely many solutions.
(c) There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
To learn more about nontrivial solution visit: https://brainly.com/question/30452276
#SPJ11
What is the equation of the line of reflection that reflects shape P into shape Q
The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.
To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:
Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.
Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.
Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.
The slope formula is given by m = (y2 − y1) / (x2 − x1).
Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.
Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.
for such more question on reflection
https://brainly.com/question/26642069
#SPJ11
Compare using <, >, or =.
3 yards
10 feet
Answer: 10 feet > 3 yards
Step-by-step explanation:
if 1 yard = 3 feet
then 3 yards = 9 feet
so 10 feet > 3yards
when we make inferences about one population proportion, what assumptions do we need to make? mark all that apply.
The data should come from a binomial distribution. There should be no non-response or other forms of bias. The sample size should not be more than 10% of the population size, and the sample should be independent of one another.
When making inferences about one population proportion, the following assumptions need to be made:
Option 1: The sample is a simple random sample from the population.
Option 2: The sample size should be large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
Option 3: The data comes from a binomial distribution.
Option 4: There is no non-response or other forms of bias.
Option 5: The sample size is no more than 10% of the population size.
Option 6: The sample is independent of one another.In order to make inferences about one population proportion, the assumptions mentioned above need to be made. It is vital to make sure that the sample is a simple random sample from the population, and that the sample size is large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
for such more question on population
https://brainly.com/question/25896797
#SPJ11
A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation
The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25
Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.
The amount of medicine in the 10 grams of 15% solution is
0.15 × 10 = 1.5 grams
The amount of medicine in the 25 grams of 10% solution is
0.10 × 25 = 2.5 grams
So the total amount of medicine in the original mixture is,
1.5 + 2.5 = 4 grams
Now let x be the amount of pure medicine added.
The total amount of medicine in the final mixture is,
4 + x
The total amount of solution in the final mixture is,
10 + 25 + x
So the concentration of the final mixture is,
(4 + x) / (10 + 25 + x)
We know that this concentration is 25%, so we can write:
(4 + x) / (10 + 25 + x) = 0.25
This is the equation that represents the situation.
Learn more about equation here
brainly.com/question/14603452
#SPJ4
The given question is incomplete, the complete question is:
A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation
he square quilt block shown is made from nine unit squares, some of which have been divided in half to form triangles. what fraction of the square quilt is shaded? express your answer as a common fraction.
To find the fraction of the square quilt block that is shaded, we need to count the number of shaded unit squares and divide it by the total number of unit squares in the quilt block. Let us begin by counting the number of shaded unit squares.
We notice that there are a total of 6 unit squares that are shaded. The unit squares that are shaded are the 2 squares that are completely shaded and the 4 squares that are half shaded due to the presence of triangles.
Next, we need to count the total number of unit squares in the quilt block. We notice that the quilt block is made up of 9 unit squares, each of which can be divided into 4 smaller unit squares. Thus, the total number of unit squares in the quilt block is 9 x 4 = 36.
Therefore, the fraction of the square quilt block that is shaded is 6/36 or 1/6.
To summarize, the shaded portion of the quilt block consists of 6 unit squares out of a total of 36 unit squares. Thus, the fraction of the square quilt block that is shaded is 1/6.
For more details about fraction click here:
https://brainly.com/question/10354322#
#SPJ11
the process mean can be adjusted through calibration. to what value should the mean be adjusted so that 99% of the cans will contain 12 oz or more?
The value of mean should be adjusted to 12 + 2.576σ so that 99% of the cans will contain 12 oz or more.
The process mean can be adjusted through calibration. The mean is a measure of central tendency in a dataset that represents the average value of a group of data. The population standard deviation is denoted by σ. The formula for the population mean is as follows: μ = (Σ xi) / n, where xi represents the data values and n represents the total number of data values.
Here we can use the formula of confidence interval as,μ±z σ/√n, Where μ is the mean, z is the z-score, σ is the standard deviation is the sample size. Given,The required confidence level is 99%. So,α = 1-0.99α = 0.01. We can find z from the z-score table at α/2 = 0.005 as, z = 2.576.
Now, we need to find out the value of μ when the mean will be 12 ounces so that 99% of cans will contain 12 ounces or more. So,μ ± z σ/√n = 12. We know that, P(X > 12) = 0.99. The formula for standardization is, Z = (X - μ) / σHere, X = 12, σ is given and we need to find the value of μ.z = (X - μ) / σ2.576 = (12 - μ) / σμ - 12 = 2.576 × σμ = 12 + 2.576 × σ.
Now, the value of μ should be adjusted to 12 + 2.576σ so that 99% of the cans will contain 12 oz or more.
To know more about mean refer here:
https://brainly.com/question/30546599
#SPJ11
for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
Company A will charge less than Company B for any mileage greater than 70 miles. For mileages less than 70 miles, Company B will be cheaper. The inequality solved is m > 70.
To determine for what mileages Company A will charge less than Company B, we can set up an inequality with m representing the number of miles driven.
Let's start by finding the total cost for each company based on the number of miles driven:
Company A: $138 (unlimited mileage)
Company B: $75 + $0.90m (where m is the number of miles driven)
To find the mileage for which Company A will charge less than Company B, we need to set up an inequality by equating the total cost for Company A to the total cost for Company B and then solving for m:
138 < 75 + 0.90m
Subtracting 75 from both sides, we get:
63 < 0.90m
Dividing both sides by 0.90, we get:
m > 70
To learn more about inequality click on,
https://brainly.com/question/31083568
#SPJ4
Complete question is:
Latoya is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $138 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
Find the area of the shaded region.
11 yd
22 yd
5 yd
The shaded region of the provided number is 214.5 yards, according to the given statement.
Rectangle: What does that mean?A rectangular shape is an illustration of a trapezoid with proportionate and matched opposite sides. It has four sides, four 90-degree borders, and is shaped like a rectangular. Any shape with only two sides is said to be rectangular.
Calculating Area by Subtracting Area from Two as well as More Regions: To determine the area for combined figures consisting of basic forms that overlap, deduct the area of the unshaded figure from the total area to obtain the area of the shaded region.
For illustration, let's calculate the size of the shaded section in the provided picture.
It is clear from the provided picture that a triangular and a rectangle have overlapped. We must deduct the triangular area from the size of the parallelogram in order to determine the area about the shaded figure. Area of the shaded figure =
Area of the rectangle −
Area of triangle
=l×b−12×b×h
=22×11−12×11×5
=214.5yd2
Hence, the area of the shaded figure is 214.5yd2
To know more about Rectangle visit:
https://brainly.com/question/2607596
#SPJ1
A 90 digit number 9999. Is divided by 89, what is the remainder?
The remainder when a 90-digit number 9999 is divided by 89 is 0, as the result of applying the divisibility rule of 89, which involves reversing the digits of the number and subtracting the smaller from the larger.
To find the remainder when a 90-digit number 9999 is divided by 89, we can use the divisibility rule of 89. The rule states that for any integer n, the number obtained by reversing the digits of n and subtracting the smaller from the larger is divisible by 89.
In this case, we reverse the digits of 9999 to get 9999 again, and subtract the smaller from the larger to get 0. Since 0 is divisible by any number, including 89, the remainder when 9999 is divided by 89 is 0.
To know more about divisibility:
https://brainly.com/question/11323048
#SPJ4
Can someone pls help me with this
A. The equation of the line is expressed as: y = (-5/2)x + 13.
B. The x-intercept of the equation is calculated as: 26/5.
How to Find the Equation of a Line?A. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, to find the equation of a line passing through the point (4,3) with a slope of -5/2.
Substituting the values, we get y - 3 = (-5/2)(x - 4), which simplifies to y = (-5/2)x + 13 by expanding and adding 3 to both sides.
B. To find the x-intercept of the equation y = (-5/2)x + 13, we set y to 0 and solve for x. 0 = (-5/2)x + 13, which simplifies to x = 26/5 by multiplying both sides by -2/5 and adding (26/5) to both sides.
Learn more about the equation of a line on:
https://brainly.com/question/13763238
#SPJ1
A store sells boxes of juice is equal size packs. Garth bought 18 boxes, Rico bought 36 boxes and Mia bought 45 boxes. What is the greatest number of boxes in each pack? How many packs did each person buy if each box contained the greatest number of boxes?
Answer:29160
Step-by-step explanation:
what is the 1ooth digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 ?
The 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
First, let's convert the number (1 .fi.)3000 into its decimal representation. This is done by dividing 3000 by 10 raised to the power of the number of digits following the decimal point, which in this case is 3. We get the answer 1000, or 1.000.
Now, we can look at the 100th digit to the right of the decimal point. This will be the 0th digit from the right of the decimal point, which is 0. Therefore, the 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
Learn more about decimal representation:
brainly.com/question/12342812
#SPJ11
16. A savings account was worth $1250 at the end of 2010 and worth $1306 at the end of 2011. The linear model
for the worth of the account is w = 56t+1250, where t is the number of years since the end of 2010.
Find an exponential model, in the form of w= a(b)', for the worth of the savings account. Round b to the
nearest thousandth.
How much greater is the worth predicted by the exponential model than predicted by the linear model at the
end of 2020? Round to the nearest cent.
An exponential model for the worth of the savings account is [tex]W = 1250(1.045)^t[/tex]
The worth predicted by the exponential model is greater than predicted by the linear model at the end of 2020 by $131.2.
What is an exponential function?In Mathematics, an exponential function can be modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.Based on the information provided about the savings account, we would determine the growth rate as follows;
[tex]W = P_{0}e^{rt}[/tex]
Growth rate, r = 1/(1 - 0)ln(1250/1306)
Growth rate, r = ln(1250/1306)
Growth rate, r = 0.0438
In the form [tex]W = a(b)^t[/tex], the required exponential function is given by;[tex]W = 1250(1.045)^t[/tex]
Years = 2020 -2010 = 10 years.
From the linear function, we have:
W = 56t + 1250
W = 56(10) + 1250
W = $1,810.
From the exponential function, we have:
[tex]W = 1250(1.045)^t\\\\W = 1250(1.045)^{10}[/tex]
W = $1,941.2
Difference = $1,941.2 - $1,810
Difference = $131.2.
Read more on exponential functions here: https://brainly.com/question/30241796
#SPJ1
The third term of a sequence is 14. Term to term rule is square, then subtract 11. Find the first term of the sequence
The third term of a sequence is 14. Term to term rule is square, then subtract 11. The first term of the sequence is 6.
The given information is about the third term of a sequence which is 14, and the term to term rule is square, then subtract 11.
We have to find the first term of the sequence. The sequence can be calculated using the following formula:
An = A1 + (n-1)d
Where, An is the nth term of the sequence A1 is the first term of the sequence d is the common difference between the terms of the sequence. Let's solve the problem by finding the value of the common difference between the terms of the sequence.
Using the given information, we can write: A3 = 14=> A1 + (3 - 1)d = 14=> A1 + 2d = 14 ----- (i)
Also, the term to term rule is square, then subtract 11.So, we can write, A2 = A1 + d = (A1)² - 11 ---- (ii)
Substituting the value of d from equation (ii) in equation (i),
we get: A1 + 2 [(A1)² - 11] = 14 Simplifying this equation, we get: A1² - 2A1 - 12 = 0 On solving this quadratic equation
we get: A1 = -2 or A1 = 6 Ignoring the negative value of A1, we get the first term of the sequence to be 6.
for such more question on sequence
https://brainly.com/question/7882626
#SPJ11
. Calculate the slope of the line that passes through (3, 2) and (-7, 4).
Answer:
-0.2
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
^This here is how I calculated the slope^
Y2=4
Y1= 2
4-2= 2
X2=-7
x1=3
-7-3=-10
2/-10
or -2/10
how much of a 12% 12 % salt solution must combined with a 26% 26 % salt solution to make 2 2 gallons of a 20% 20 % salt solution?
To make 2 gallons of a 20% salt solution, combine 0.86 gallons of the 12% salt solution and 1.14 gallons of the 26% salt solution.
Let x be the amount of the 12% salt solution needed in gallons, and y be the amount of the 26% salt solution needed in gallons to make 2 gallons of a 20% salt solution.
Based on the provided data, we can construct the following system of two equations:
X + y = 2 (total volume of the mixture is 2 gallons)
0.12x + 0.26y = 0.2(2) (total salt content of the mixture is 20% of 2 gallons)
Simplifying the second equation, we get:
0.12x + 0.26y = 0.4
Multiplying the first equation by 0.12 and subtracting it from the second equation, we get:
0.14y = 0.16
Y = 1.14
Substituting y = 1.14 into the first equation, we get:
X + 1.14 = 2
X = 0.86
In order to create 2 gallons of a 20% salt solution, 0.86 gallons of the 12% salt solution and 1.14 gallons of the 26% salt solution must be combined.
The complete question is:-
How much of a 12% salt solution must combined with a 26% salt solution to make 2 gallons of a 20% salt solution?
To learn more about solution, refer:-
https://brainly.com/question/30665317
#SPJ4
Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Responses
3×9
0×5√
2√ ×8√
2√×3√
Step-by-step explanation:
Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Responses
option c
a bond is worth 100$ and grows in value by 4 percent each year. f(x) =
To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).
Jessica went deep sea diving. She make the first stop on her descent at 25 meters below the surface of the water. From that point she dives down further, stopping every 5 meters. If she makes 4 additional stops, which number represents her position, relative to the surface of the water?
*
A 45
B 20
C -20
D -45
Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.Option(A) is correct.
What is sea diving?Divers who engage in scuba diving use breathing apparatus that is entirely independent of a surface air source. Christian J. Lambert-sen came up with the moniker "scuba," which stands for "Self-Contained Underwater Breathing Apparatus," in a 1952 trademark application.
According to question:Jessica's position relative to the surface of the water can be represented by the following arithmetic sequence:
[tex]$$25, 30, 35, 40, 45$$[/tex]
where the first term is 25 and the common difference is 5 (the distance between each stop).
To find the fifth term (her position after making 4 additional stops), we can use the formula for the nth term of an arithmetic sequence:
[tex]$$a_n = a_1 + (n-1)d$$[/tex]
where [tex]$a_1$[/tex] is the first term, d is the common difference, and n is the term number.
Plugging in the values we know, we get:
[tex]$$a_5 = 25 + (5-1)5 = 45$$[/tex]
Therefore, Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.
To know more about Meter visit:
brainly.com/question/22552981
#SPJ1
Find the value of x in a triangle, 142 degrees and 112 degrees
The value of x in the triangle can be found by using the fact that the sum of all angles in a triangle is 180 degrees. Simplifying the equation 142 degrees + 112 degrees + x = 180 degrees, we get x = 26 degrees.
To find the value of x in the triangle, we use the fact that the sum of all angles in a triangle is 180 degrees.
Let's call the third angle of the triangle "x".
Then, we have:
142 degrees + 112 degrees + x = 180 degrees
Simplifying this equation, we get:
x = 180 degrees - 142 degrees - 112 degrees
x = 26 degrees
Therefore, the value of x in the triangle is 26 degrees.
Learn more about triangle here: brainly.com/question/2773823
#SPJ4
Make a graph of kinetic energy versus mass for the bikers. Label each biker on your
graph. (4 points)
See Below
HAVE A NICE DAY !
in the number 240.149, how does the value of the 4 in the hundredths place compare to the value of the 4 in the tens place?
The 4 in the hundredths place has a smaller value than the 4 in the tens place.
In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.
In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.
Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.
To know more about the decimal number system, refer here:
https://brainly.com/question/30477589#
#SPJ11
sin 30° = 0.5 Using the equality above, copy and complete the following: sin-¹ (0.5) =
However, sin⁻¹ is defined to return an angle between -90° and 90°, so it returns the angle that is closest to 30° (which is 30° in this case).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.
Here,
If sin 30° = 0.5, then sin⁻¹(0.5) is the angle whose sine is 0.5. In other words, we are looking for the angle whose sine is 0.5. Since sin 30° = 0.5, we know that one possible answer is 30 degrees. However, there are other angles that also have a sine of 0.5. One way to find the other angles is to use the inverse sine function, denoted as sin⁻¹. This function takes a value between -1 and 1 as its input and returns an angle between -90° and 90° as its output. So, if we want to find sin⁻¹(0.5), we are asking: what angle has a sine of 0.5?
The answer is: sin⁻¹(0.5) = 30°.
Note that there are other angles that also have a sine of 0.5, such as 150°, 390°, etc.
To know more about trigonometry,
https://brainly.com/question/26719838
#SPJ1
Complete question:
Using the equality above, copy and complete the following:
The value of sin⁻¹ (0.5) when sin 30° = 0.5.
What is the measure of each interior angle of a regular 20-gon?
Answer:
162°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 20 , then
sum = 180° × (20 - 2) = 180° × 18 = 3240°
The interior angles of a regular polygon are congruent
then each interior angle = 3240° ÷ 20 = 162°
a local county has an unemployment rate of 4%. a random sample of 19 employable people are picked at random from the county and are asked if they are employed. round answers to 4 decimal places.
The probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
We need to calculate the probability that exactly 8 of the 19 people in the random sample are employed. The probability of a single person being employed is 4%, or 0.04.
To calculate the probability of 8 people being employed out of the 19, we can use the binomial distribution formula:
P(X=8) = nCx * (p^x) * (1-p)^(n-x) Where n = 19, x = 8, p = 0.04, and 1-p = 0.96
So, P(X=8) = 19C8 * (0.04^8) * (0.96^11) = 0.2793 or 27.93%.
Therefore, the probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
For more such questions on Probability.
https://brainly.com/question/11234923#
#SPJ11
the admission fee at an amusement park is $4.25 for children and $7.00 for adults. on a certain day, 303 people entered the park, and the admission fees collected totaled 1824 dollars. how many children and how many adults were admitted?
The admission fee at an amusement park is $4.25 for children and $7.00 for adults. on a certain day, 303 people entered the park, and the admission fees collected totaled 1824 dollars. There are 108 children and 195 adults were admitted
Let the number of children admitted = C and the number of adults admitted = A
Total number of people admitted = 303
We can form two equations from the given information.
The first equation is to represent the number of people admitted in terms of children and adults.
So, the equation will be
C + A = 303 ------(1)
The second equation represents the total amount collected from admission fees.
So, the equation will be
4.25C + 7A = 1824 ------(2)
Multiplying equation (1) by 4.25, we get
4.25C + 4.25A = 1289.25 ------(3)
Subtracting equation (3) from equation (2), we get:
7A - 4.25A = 1824 - 1289.25
Simplifying, we get:
2.75A = 534.75
Dividing by 2.75, we get:
A = 195
Putting A = 195 in equation (1), we get:
C + 195 = 303
Simplifying, we get:
C = 108
So, there were 108 children and 195 adults admitted on that day.
For similar question on Simplification,
https://brainly.com/question/28008382
#SPJ11
given the following exponential function, identify whether the change represents growth or decay and determine the percentage rate of increase or decrease y=620(0.941)x
the function represents exponential decay with a rate of decrease of 5.9% per unit increase in x.
In the exponential function y = [tex]620(0.941)^x:[/tex]
The base of the exponent is 0.941, which is between 0 and 1.
As x increases, the value of [tex](0.941)^x[/tex]gets smaller and smaller, approaching 0 but never reaching it.
Therefore, the function represents exponential decay.
To determine the percentage rate of decrease, we can use the formula:
rate of decrease = (1 - base) x 100%
In this case, the base is 0.941, so the rate of decrease is:
rate of decrease = (1 - 0.941) x 100% = 5.9%
The exponential function is y = 620(0.941)^x.
To determine whether the function represents growth or decay, we need to look at the base of the exponential function, which is 0.941. Since this base is less than 1, the function represents decay.
To determine the percentage rate of decrease, we can use the formula:
r = (1 - b) x 100%
where r is the percentage rate of decrease, and b is the base of the exponential function.
In this case, b = 0.941, so we have:
r = (1 - 0.941) x 100%
= 0.059 x 100%
= 5.9%
Therefore, the exponential function y = 620(0.941)^x represents decay with a rate of 5.9% per unit of x.
A sort of mathematical function called exponential decay can be used to explain a quantity's decline across time or space. The quantity at any given time will change at a pace that is proportionate to the quantity itself, which is characterised by a decreasing rate of change. In other words, the amount of reduction decreases as time or space grows, but it never decreases to zero.
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=620(0.941)^x y=620(0.941) x
Learn more about exponential decay here:
https://brainly.com/question/2193799
#SPJ1