Use the drop-down menus to complete the solution to the equation cosine (start fraction pi over 2 end fraction minus x) = start fraction start root 3 end root over 2 end fraction for all possible values of x on the interval [0, 2pi].
Using trigonometric identities, the solution to the equation [tex]cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2}[/tex] for all possible values of x on the interval [0, 2π].
What are trigonometric identities?
Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
[tex]cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2} \\\\cos(x)cos\frac{\pi }{2}+sin(x)sin \frac{\pi }{2} = \frac{\sqrt{3} }{2}\\\\cos(x)(0)+sin(x)(1) = \frac{\sqrt{3} }{2}\\\\sin(x) = \frac{\sqrt{3} }{2}\\\\x = \frac{\pi }{3}, \frac{2\pi }{3}[/tex]
To learn more about trigonometric identities click here https://brainly.com/question/7331447
#SPJ4
a sphere is partially filled with air. if the volume of the sphere is increasing at a rate of 548 cubic feet per second, what is the rate, in feet per second, at which the radius of the sphere is changing when the radius is 6 feet?
1.2113 ft/s is the speed at which the radius of the sphere is changing when the radius is 6 feet .
What is mensuration ?Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures.
Mensuration is a subject of geometry. Mensuration deals with the size, region, and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.
CalculationThe rate of change of volume will be the product of the rate of change of radius and the area of the sphere. The area of the sphere is ...
A = 4πr² = 4π(6 ft)² = 144π ft²
Then the relationship above is ...
dV/dt = A·dr/dt
548 ft³/s = (144π ft²)·dr/dt
dr/dt = (548 ft³/s)/(144π ft²) = 137/(36π) ft/s ≈ 1.2113 ft/s
learn more about mensuration here :
brainly.com/question/14312097
#SPJ4
order these from lease to gratest, 1/3, 0.3, 33%,
8/25, 33.6%
Rearranging [1/3, 0.3, 33%, 8/25, 33.6%] in the ascending order of magnitude, we get, [33.6%, (1/3), 33%, (8/25), 0.3].
As per the question statement, we are provided with a set of values [1/3, 0.3, 33%, 8/25, 33.6%],
And we are required to rearrange the above mentioned set in the ascending order of magnitude.
To answer this question, we will have to convert all the values into fractions with a common denominator, and then arrange the fractions in an ascending order of magnitude of their numerators to obtain our desired answer, that is,
[(1/3) = 0.33333333...]
[(0.3) = (3/10) = (30/100)],
[(33%) = (33/100) = 0.330],
[(8/25) = (32/100) = 0.320]
And, [33.6% = (33.6/100) = 0.336]
Since (0.336 > 0.333 > 0.330 > 0.320 > 0.300),
Therefore, rearranging [1/3, 0.3, 33%, 8/25, 33.6%] in the ascending order of magnitude, we get, [33.6%, (1/3), 33%, (8/25), 0.3]
To learn more about Ascending Order, click on the link below.
https://brainly.com/question/15202532
#SPJ1
if a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can:
If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can increase the sample size.
The margin of error refers to the statistic measurement that expresses the level of random sampling error in the outcomes of a survey. If the margin of error of the result is high, the confidence level would be low that a result reflects the census of the entire population. It indicated the difference between the actual and estimated results in a random survey sample. The margin of error is generally used in non-survey contexts to show observational error in reporting measured quantities. In order to minimize the margin of error associated with a confidence interval estimate for a population mean, the researchers can increase the sample size to capture the actual trend of the population more accurately.
Learn more about Margin of error:
https://brainly.com/question/24289590
#SPJ4
Hsu-Mel wants to save $9,000 for a down payment on a car. To the nearest dollar, how much will she need to invest in an account now with 7.4% APR, compounded daily, in order to reach her goal in
3 years ?
The amount of money (principal) that Hsu-Mel would need to invest in an account now with 7.4% APR, compounded daily, in order to reach her goal in 3 years is $7206.24.
How to determine the principal amount?Mathematically, compound interest can be calculated by using this formula:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Note: The annual percentage interest (APR) rate would be divided by 365 since it is compounded daily.
Substituting the given parameters into the formula, we have;
9,000 = P(1 + 0.074/265)^{365 × 3}
9,000 = P(1.00023)^{1095}
9,000 = P(1.2489)
Principal, P = 9000/1.2489
Principal, P = $7206.24.
Read more on interest rate here: https://brainly.com/question/26343258
#SPJ1
Find the value of f(5) for the function.
f(a)=3(a+2)−8
Answer:
f(5) = 3(5+2) - 8
f(5) = 15+6 -8
f(5) = 21 - 8
f(5) = 13
Nadia i a tockbroker. She earn 13% commiion each week. Lat week, he old $7,500 worth of tock. How much did he make lat week in commiion? If he average that ame amount each week, how much did he make in commiion in 2011?
Nadia made $975 last week and $50, 700 in 2011.
The amount earned last week = Percentage of comission × earnings
The amount earned last week = 13% × 7500
The amount earned last week = 13 × 75
Performing multiplication on Right Hand Side of the equation
The amount earned last week = $975
As per the known fact, 1 year has 52 weeks. So, the commission earned in 2011 = 52 × 975
Performing multiplication on Right Hand Side of the equation
The commission earned in 2011 = $50, 700
Thus, the amount earned last week is $975 and comission earned in 2011 is $50, 700.
Learn more about percentage -
https://brainly.com/question/24877689
#SPJ4
How much pure acid is in 780 milliliters of a 18% solution?
The amount of pure acid present in 780 milliliters of a 18% solution is 140.4 milliliter .
In the question ,
it is given that
the amount of solution = 780 milliliter
we need to find the amount of pure acid in the solution .
amount of pure acid in the solution can be calculated using the formula ,
amount of pure acid = 18% of 780 milliliter
the term of represents, multiplication ,
So , the amount of pure acid = 18% × 780
= 0.18 × 780
= 140.4 milliliter
Therefore , The amount of pure acid present in 780 milliliters of a 18% solution is 140.4 milliliter .
Learn more about Percent here
https://brainly.com/question/16733361
#SPJ1
BY SELLING AN ARTICLE FOR $10.80, A SHOPKEEPER MAKES A PROFIT OF 8%. WHAT SHOULD BE THE SELLING PRICE FOR A PROFIT OF 20%?
Answer:
$27.00
Step-by-step explanation:
8 : 20 = 10.80 : x
x = 20 * 10.80 / 8
x = 5 * 10.80 / 2
x = 5 * 5.40
x = $27.00
Simplify the expression to a + bi form:
(-4+9i)²
Explain in layman's terms for brainiest please
The simplified form of the expression ( -4 + 9i )² such that it takes the form a + bi is; -65 - 72i.
What is the simplified form of the expression?It follows from the task content that the simplified form of the expression is to be determined.
Hence, since the given expression is; ( -4 + 9i )², we have;
( -4 + 9i ) ( -4 + 9i )
= 16 -36i - 36i + 81i²
However, recall that the i² = -1 which follows from the fact that i = √-1.
On this note, the expression can be written as;
= 16 - 72i + 81 (-1)
= 16 - 72i - 81
= -65 - 72i.
Hence, the required simplified form of the expression is; -65 - 72i.
Read more on complex numbers;
https://brainly.com/question/10662770
#SPJ1
For each direct variation, find the constant of variation. Then find the value of y when x = -0.5.
21. y =4 when x = 0.5
22. y =2 when x = 3
When x = -0.5, the value of y is -0.33. When y varies directly with respect to x, the equation y = kx is used. where k is the constant of proportionality
What is meant by variation?A variation is a relationship between one set of values for one variable and another set of values for another variable. Variation in direct. If m is a nonzero constant and b = 0, then the function y = mx (often written y = kx) is a direct variation of the equation y = mx + b. Variation is defined as differences in an individual's genetic constituents that result in differences in the physical appearance of individuals living in a population. Individuals differ in their physical appearance, fertility, metabolism, and mode of reproduction.The average of the squared deviations from the mean is defined as variance.Therefore,
When X equals 3, Y equals 2.
We solve for k by plugging in 3 for x and 2 for y.
y = kx \s 2 = k(3) (3)
Subtract 3 from both sides.
2/3 = k
Now we plug in 2/3 for k
y = 2/3 x
Given x = -0.5 simplifying we get,
y = 2/3 (-0.5)
y = -0.33
Hence, the value of y is -0.33 when x = -0.5
To learn more about 'variation' refer to
brainly.com/question/11578472
#SPJ13
13. (03. 02 LC)Wren earns an average weekly net pay of $896. 0. Which compound inequality correctly shows the amount of money she can spend with a monthly budget for housing between 25% and 354701point)O $970. 67 shs $1,358. 93O $970. 67 2h $1,358. 93O $224. 00<<$313. 60O $224. 00 >h> $313. 60
The correct compound inequality to the amount of money Wren can spend with a monthly budget for housing between 25% and 35% will be:
224.0< h< 313.60
Given that:
wren own an average weekly net pay $ 896.00
and, Wren can spend with a monthly budget for housing between 25% and 35%.
Now, Spend money for housing by 25% = 25% of $896.00
= 25÷100 × 896
= 0.25 ×896
= $ 224.00
Again, spend money for housing by
35%= 35% of 896
=35÷100 × 896
= 0.35 × 896
= $ 313.60
Learn more about Inequality here:
https://brainly.com/question/19003099
#SPJ4
What is the average of first 50 numbers?.
The average of first 50 numbers is 25.5 because average is computed by adding a set of numbers and then dividing by the total number of those numbers.
Why do you use the word "average"?The average of a list of data is a mathematical expression for the central value of a set of data. The ratio of all the data points to all the units in the list is how it is mathematically defined. The average of a specific set of numerical data is also referred to as the "mean" in statistics.
Which four sorts of averages are there?The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.
The first 50 natural numbers are 1,2,3,...,50
The sum of first n natural numbers = n(n+1)/2
Sum of first 50 natural numbers is 50(51)/2
=25(51)/2=1275
Hence, average of first 50 natural numbers is
1275/50
=25.5
To know more about Average visit:
https://brainly.com/question/13185935
#SPJ4
∠A and \angle B∠B are supplementary angles. If \text{m}\angle A=(4x-16)^{\circ}m∠A=(4x−16) ∘ and \text{m}\angle B=(x+1)^{\circ}m∠B=(x+1) ∘ , then find the measure of \angle B∠B.
The measure of angle B is 40 degrees.
In this question, we have been given angle A and angle B are supplementary angles.
m∠A=(4x−16)°
and m∠B=(x+1)°
since angle A and angle B are supplementary angles,
angle A + angle B = 180°
So we get an equation,
(4x − 16)° + (x + 1)° = 180°
5x - 16 + 1 = 180
5x = 180 + 15
5x = 195
x = 39
So, x + 1 = 39 + 1
= 40°
Therefore, the measure of angle B is 40 degrees.
Learn more about the supplementary angles here:
https://brainly.com/question/13045673
#SPJ1
I need help on question 1 and 2. I really am stuck on it and it will be a lot of help if you help me. Thank you! :)
Three runners are training for a marathon. one day, they all run about ten miles, each at their own constant speed. which of the three runners has the fastest pace?
You did not post enough information.
a rectangle has one side of 8 cm. how fast is the area of the rectangle changing at the instant when the other side is 13 cm and increasing at 2 cm per minute?
30 is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute.
Area of a Rectangle is what?Rectangle's area is equal to its length times its width.
Given,
A rectangle has a 10 cm side.
We must determine how quickly the rectangle's area changes while one side is 12 cm and growing at a rate of 3 cm per minute.The formula for this is A=10x.Now make a distinction based on t.10 dx/dt = dA/dtat a rate of 3 centimeters per minutedx/dt=3dA/dt=10 (3) (3)dA/dt=30Consequently, 30 is the area of the rectangle that changes at the instant when the other side is 12 cm and growing at a rate of 3 cm per minute.
To learn more on Rectangle click here:
brainly.com/question/20693059
#SPJ4
Given f (x) = 5x - 12, find the value of x when f (x) = 13.
Answer:
53
Step-by-step explanation:
if x is 13, you would simply do the following:
multiply 5 by 13 which is 65.
then subtract 65 by 12 which is your final answer, 53!
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the largest angle.
(6x+17)°
105°
(5X+14)°
Answer:
56
Step-by-step explanation:
What is the probability that a standard normal random variable will be between. 3 and 3. 2?.
Using the z table, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.
In the given question,
We have to find that the probability that a standard normal random variable will be between 0.3 and 3.2 .
We firstly learn about a standard normal random variable which is expressed with a mean and standard deviation.
Since we have to find the probability that a standard normal random variable will be between 0.3 and 3.2 .
So The probability should be
P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)
From the standard value of z
P(0.3<z<3.2)=0.9993−0.6179
Simplifying
P(0.3<z<3.2)=0.3814
Hence, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.
To learn more about standard normal random variable link is here
brainly.com/question/14782203
#SPJ4
true or false, we can compare a model to before using a transformation on x or y to a model after using a transformation by using the corresponding values of sse.
True, we can compare a model before using a transformation on x or y to a mode before using a transformation by using the corresponding values of the sum of squares error SSE.
For example, to compare two models, one of which has a transformation on the outcome of the variable, that is:
First model[tex]y=x+z[/tex]
Second model:[tex]y^{1/k} =x+z[/tex]
The best logical approach might be to look at the comparative performance obviously with predicted transformed values back-transformed and then look at the models sum of squares error of these predictions. It has to be random predictions and comparisons because the error distributions are also transformed.
To know more about SSE sum of squares error:
https://brainly.com/question/28318354
#SPJ4
The distance of 2 laps around a park is 2.5 miles. Walking 5 laps around the same park is 6.25 miles.
Complete the table to show the relationship between the number of laps and the number of miles. Enter the answers in the boxes.
Hence the complete table is ,
=> laps Miles
3 3.75
7 8.75
8 10
13 16.25
What is miles ?
A mile is a unit of length that is exactly equal to 5280 feet, or 1760 yards, and was standardised as exactly 1609.344 metres by an International agreement in 1959. It is the largest unit commonly used to measure the distance between distant locations.
Here the distance 2 laps = 2.5 miles. Then ,
=> 1 laps = 2.5/2 = 1.25 miles.
Now 3 laps = 3*1.25 = 3.75 miles
Here n laps = 8.75 miles .
=> n* 1.25 = 8.75
=> n = 7 laps .
Now 8 laps = 8*1.25 = 10 miles.
And n laps = 16.25
=> n = 16.25/1.25 = 13 laps. miles
Hence the complete table is ,
=> laps Miles
3 3.75
7 8.75
8 10
13 16.25
To learn more about miles
https://brainly.com/question/25631156
#SPJ13
Jude deposited 550$ into an account that earns simple interest, and after 11 years, the interest in the account was 484. What was the simple interest rate? Pls give proper explanation and not just answer, Thank u!
Answer: 8%
Step-by-step explanation: Rate = Interest 484 ÷ Principle (550) x Time (11), with this formula the answer is 8%.
Find the equation (in terms of x) of the line through the points (-4,3) and (2,-4)
The equation of the line (-4,3) and (2,-4) is y = -7/6x -5/3.
What is equation of line?
The equation of a line is the algebraic representation of a line using cartesian coordinates. The general form of the equation of a straight line is written as y = mx + c. Where m is the gradient of the straight line and c is the y y-intercept of the straight line.
Given, the points are (-4,3) and (2,-4)
m = -4-3/2+4
m = -7/6
The equation we get
y = -7/6x +b
the point (-4,3), we get
3 = -7/6(-4) +b
3 = 14/3 +b
3-14/3 = b
b = -5/3
Hence, the equation of line is y = -7/6x -5/3.
To know more about equation of line, visit:
https://brainly.com/question/9446123
#SPJ13
363 out of the 550 books at the library are fiction books. What percentage of the books at the
library are fiction books?
Answer:
72.6%
Step-by-step explanation:
Percentages are simple
(Number given / Total given ) × 100 = ?%
(363 / 550 ) × 100 =
0.726 × 100 = 72.6
This should be our final answer of 72.6%
Hope this helped and have a good day
Suppose that shoe sizes of american women have a bell shaped distribution with a mean of 8.21 and a standard deviation of 1.49. using the empirical rule what percentage of american women have shoe sizes that are less than 11.19
97.5% of American women have shoe sized less than 11.19 according to standard deviation of 1.49 .
What is standard deviation?
It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
Main Body:
Here, we want to use the empirical rule to find the percentage of women with shoe sizes less than 11.19
The first thing we shall do here is to find the z-score
Mathematically, that will be calculated using the formula;
z = (x-mean)/SD
z = (11.19-8.21)/1.49
z = 2
We can see that the given value is 2 standard deviation away to the right of mean
So, we want to get the percentage that is between the mean and two standard deviations away from it using the empirical rule
So according to the empirical rule
The percentage will be
= 100-2.35-0.15
= 100-2.5 = 97.5%
To learn more about standard deviation click on the link below
https://brainly.com/question/475676
#SPJ4
If P = (-1,-1) and Q = (5, 3) are the
endpoints of the diameter of a circle,
find the equation of the circle.
(x - 2)² + (y - [?])² = [ ]
Answer:
The equation of the circle is (x-2)^2+(y-1)^2=13
Step-by-step explanation:
Look at the graph of a function below.
Which set builder notation represents the domain of the function in the graph?
The domain of the function in the graph is {yl1≤y≤9}. Option b is the correct answer.
Graph:
The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables.
A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.
To learn more about graph visit: https://brainly.com/question/17267403
#SPJ1
Select the correct answer.
Solve the following compound inequality.
2x − 2 > -8 or -4x ≤ -36
The solution to the compound inequality is x > -3. The correct option is the third option x > -3
Solving compound inequalitiesFrom the question, we are to solve the given compound inequality
2x - 2 > -8 or -4x ≤ -36
Solving the first inequality
2x - 2 > -8
Add 2 to both sides of the inequality
2x -2 + 2 > -8 + 2
2x > -6
Divide both sides by 2
2x/2 > -6/2
x > -3
Solving the second inequality
-4x ≤ -36
Divide both sides of the inequality
-4x/-4 ≤ -36/-4
x ≥ 9
From the two solutions, we can conclude that x > -3
Hence, the solution is x > -3
Learn more on Solving compound inequality here: https://brainly.com/question/28600203
#SPJ1
Solve the inequality
[tex]16 - < 6k + 2 < 0[/tex]
The answer of the inequality is [tex]-3 < k < -\frac{1}{3}[/tex]
What does algebraic inequality mean?
An inequality in maths shows the relationship between the two values in an uneven algebraic expression. A sign of inequality can be employed to indicate that one of the two variables is less than, greater than or equal to, less than, or equal to another value.
Given That:
-16<6k+2<0
Now to solve this equation we will subtract 2 from all the side
-16-2<6k<-2
now we will divide by 6 on all the side
-18/6<k<-2/6
[tex]-3 < k < -\frac{1}{3}[/tex]
Hence this the answer to the question
Learn more about inequality
https://brainly.com/question/25275758
#SPJ9
What is mean by amplitude in maths?.
The distance that a function's graph moves above and below its midline is referred to as its amplitude. When graphing a sine function, the amplitude's value corresponds to the sine function's coefficient.
What is amplitude?The distance that a function's graph moves above and below its midline is referred to as its amplitude. When graphing a sine function, the amplitude's value corresponds to the sine function's coefficient. The height between the center line and the peak is known as the amplitude (or to the trough). Alternatively, we might multiply the height from highest to lowest places by 2. The Phase Shift is the horizontal displacement of the function from its initial point.
To know more about amplitude,
https://brainly.com/question/8662436
#SPJ4
