(a) The standard error of the mean is 129. (b) The probability that the sample mean will be more than $27,175 is 0.50 (c) The probability that the sample mean will be within $1,000 of the population mean is 0.955. (d) The probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100 is 0.999.
(a) The standard error of the mean is the square root of the population standard deviation divided by the sample size, which in this case is 7,400/57 = 129.12. The value of the standard error of the mean is therefore 129 (rounded to the nearest whole number).
(b) To find the probability that the sample mean will be more than $27,175, you can use the Z-score formula. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175)/129 = 0. The probability that the sample mean will be more than $27,175 is 50%, since the probability of any Z-score of 0 is 0.50.
(c) To find the probability that the sample mean will be within $1,000 of the population mean, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/129 = ±7.8. The probability that the sample mean will be within $1,000 of the population mean is 95.5%, since the probability of any Z-score of ±7.8 is 0.955.
(d) To find the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/74 = ±13.5. The probability that the sample mean will be within $1,000 of the population mean is 99.9%, since the probability of any Z-score of ±13.5 is 0.999.
Know more about probability here:
https://brainly.com/question/13604758
#SPJ11
Need HELP ASAP!!! RIGHT NOW!!!!
In a laboratory experiment, the population of bacteria in a petri dish started off at 7400 and is growing exponentially at 13% per hour. Write a function to represent the population of bacteria after t hours, where the rate of change per minute can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per minute, to the nearest hundredth of a percent.
Please put it in equation form.
In a lab experiment, the number of bacteria on a petri dish began at 7400 and is now increasing exponentially at a rate of 13% per hour. P(t) = [tex]7400(1 + 0.13)^t[/tex] is a function that may be used to represent the population of bacteria after t hours and in which a constant can be used to calculate the rate of change each minute. The rate of change in percentage is 0.21667% per minute.
The function to represent the population of bacteria after t hours can be expressed as:
P(t) = [tex]7400(1 + 0.13)^t[/tex]
where P(t) is the population of bacteria after t hours, 7400 is the initial population, and 0.13 is the growth rate per hour expressed as a decimal.
To find the rate of change per minute, we need to convert the growth rate per hour to a growth rate per minute. There are 60 minutes in an hour, so the growth rate per minute can be found by dividing the growth rate per hour by 60:
0.13/60 = 0.0021667 (rounded to seven decimal places)
So the growth rate per minute is approximately 0.0021667 or 0.21667% (rounded to two decimal places).
Therefore, the function to represent the population of bacteria after t hours is:
P(t) = [tex]7400(1 + 0.13)^t[/tex]
and the rate of change per minute is approximately 0.21667%.
To learn more about function, refer:-
https://brainly.com/question/30721594
#SPJ1
A package of 5 pairs of insulated socks costs $33.45. What is the unit price of the pairs of socks ?
Answer: 6.69 dollars
Step-by-step explanation: 33.45/5 = 6.69
Answer:6.69
Step-by-step explanation:you basically divide 33.45 by 5 and the will get you 6.69 which is the unit price of pairs of socks
Solve the system of equations.
7x+10y = 36
y = 2x +9
X =
y =
After solving the given equations the value of x and y are -2 and 5 respectively.
What are equations?An equation is a mathematical statement consisting of two expressions joined by an equal sign.
For example, 3x – 5 = 16 is an equation.
Solving this equation gives the value of the variable x as x = 7.
So, the equations are:
7x+10y = 36 ...(1)
y = 2x +9 ...(2)
Now, insert 2x+9 in equation (1):
7x+10y = 36
7x+10(2x +9) = 36
7x+20x+90 = 36
27x = -54
x = -54/27
x = -2
Then, the value of y:
y = 2x +9
y = 2(-2) +9
y = -4+9
y = 5
Therefore, after solving the given equations the value of x and y are -2 and 5 respectively.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ1
Determine the slope and the y-intercept of the description.
Ernesto spent $56 on T-shirt printing supplies and $5.75 for each T-shirt.
Practice Problems
Directions: Using the Interest Formula, solve for the unknown.
1. Find P
P = ?
R = 10%
T = 16 mo
Interest $1047.20
Therefore, the principal is $654.50 when rate of interest is 10% and time period is 16 months.
What is percent?Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express ratios, proportions, and rates. They are used in many areas of everyday life, such as in finance, business, and statistics.
Here,
The Interest Formula is:
I = P * R * T
where I is the interest earned, P is the principal (initial amount of money), R is the interest rate, and T is the time period.
We can rearrange the formula to solve for P:
P = I / (R * T)
Substituting the given values, we have:
P = 1047.20 / (0.10 * 16)
= $654.50
To know more about percent,
https://brainly.com/question/29172752
#SPJ1
What is the solution set for the following system of linear inequalities? Graph the solution set of the system of linear inequalities in the coordinate plane. First, select the Graph 1 button to graph the line and choose the line style. To graph a line, select two points in the coordinate plane. A line will connect the points. Then select the Graph 2 button to graph the line and choose the line style. Then select the Solution Set button to select the desired region.
The solution set for the stated system of linear inequalities;
y ≥ -2x + 4 and y ≥ x - 2 is the dark area below represents the intersection of a two solutions ranging upto +∞.
Explain about the solution set of linear inequalities?The collection of all solutions makes up the solution set for an inequality. Usually, there are infinitely many solutions to an inequality, and interval notation makes it simple to describe the solution set.
The group of values that fulfil a certain inequality is known as a solution set. This indicates that every single value with in solution set will fulfil the inequality, and not one other value will do so.
By utilising the equations to locate certain locations and drawing a line to reflect the point in two dimensions, you can draw the lines produced by the two equations.
y ≥ -2x + 4 and y ≥ x - 2
The coloured area thus provides the answer to this problem.
Putting together the two solutions, the intersection of both solutions, as seen in the dark zone below, reveals the answer to the system of inequality, ranging upto +∞.
Know more about the linear inequalities.
https://brainly.com/question/11897796
#SPJ1
you deposit $3000 in an account earning 2% interest compounded monthly. how much will you have in the account in 15 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.02}{12}\right)^{12\cdot 15} \implies A \approx 4048.57[/tex]
sofia has a rectangular poster that is 42 inches long and 30 inches high
Sofia has a rectangle poster that is 42 inches long and 30 inches wide. The area of the poster is 1260 square inches.
The area of a rectangle depends on its sides. Basically, the area formula is equal to the product of the length and width of a rectangle. When we talk about the perimeter of a rectangle, it is equal to the sum of its four sides. Therefore, we can say that the area bounded by the perimeter of a rectangle is its area. But in the case of a square, since all sides are equal, the area of the square will be equal to the square of its length.
area of rectangle = length x width
We know that :
Area of rectangle = Length × Breadth
= 42 × 30 inches
= 1260 square inches.
Therefore, the area of a rectangle is 1260 square inches.
Complete Question:
Sofia has a rectangular poster that is 42 inches long and 30 inches wide. What is the area of the poster in square inches? Do not round your answer. Be sure to include the correct unit in your answer.
Learn more about Rectangle:
https://brainly.com/question/29123947
#SPJ4
find the ratio of 8m to 30cm
Answer:
80:3
Step-by-step explanation:
8m = 800cm, so the ratio is 800cm:30cm
This can be divided by 10cm on both sides to get 80:3
determine the value of such that the matrix is the augmented matrix of a linear system with infinitely many solutions.
The value of such that the matrix is the augmented matrix of a linear system with The system has an infinite number of solutions if $k=-1$.
To find out the value of $k$ that results in the matrix being the augmented matrix of a linear system with infinitely many solutions, you need to reduce the matrix to row echelon form and check the conditions. If you get a row of all zeroes but the last entry in that row is not zero, then there is no solution. If you get a row of all zeroes including the last entry in that row, then there are infinitely many solutions. Therefore, the value of $k$ that leads to the augmented matrix of a linear system with infinitely many solutions is $k=-1$.
A system of linear equations has an infinite number of solutions if and only if its augmented matrix, after being transformed to row-echelon form, has at least one free variable column.
The matrix in question is given as:
[tex]$$\begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix}$$[/tex]
To find the value of $k$, we need to convert it to a row-echelon form.
[tex]$$ \begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix} \overset{R2\rightarrow R2+\frac{3}{2}R1}{\longrightarrow} \begin{bmatrix}2 & -2 & 4 \\ 0 & 0 & 0 \\ 1 & -1 & k\end{bmatrix} $$[/tex]
Notice that the second row of the matrix is all zeros, so the system either has no solution or has an infinite number of solutions. Therefore, we need to determine the value of $k$ to figure out which of the two cases apply. Since the third row is independent, we can choose to work with it only.
[tex]$$1a - 1b = c \rightarrow c = a - b$$[/tex]
We can also write it as a linear combination of $a$ and $b$:
[tex]$$\begin{aligned} c &= a - b \\ &= a(1) + b(-1) \end{aligned}$$[/tex]
Therefore, it follows that if $k$ equals -1, we can rewrite the last row as a linear combination of the first two rows.
for such more question on infinite number
https://brainly.com/question/30304852
#SPJ11
Thomas needs to prove the following theorem.
If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram.
He draws the figure below and begins his proof.
The reason for step 2 is as follows:
If parallel lines are cut by a transversal, then the corresponding angles are said to be congruent to each other.
What is a parallelogram?A unique sort of quadrilateral made up of parallel lines is called a parallelogram. Any angle between adjacent sides of a parallelogram is possible, but only if the sides are parallel.
If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Hence, if both sets of opposite sides are parallel and equal, a quadrilateral is referred to as a parallelogram.
Here in the question,
Its already given that AB and DC re parallel and equivalent to each other.
So, the AB and DC are cut by a transversal AC and the corresponding angles that are ∠BAC and ∠DCA are congruent to each other.
Hence, the quadrilateral is a parallelogram.
To know more about parallelograms, visit:
https://brainly.com/question/29147156
#SPJ1
In the coordinate plane , quadrilateral ABCD has verticies A(- 2, 3) , B(4, 5); C(10,- 1) and D(8, - 9) Let E , F , G , and H be the midpoints of overline AB; overline BC , overline CD and dot DA , respectively
This would give us the coordinates for E as (1, 4). Similarly, we can use the same method to find the coordinates for F, G, and H. F would be (7,2), G would be (9,-5), and H would be (3,-6).
The coordinates of E can be found by taking the average of the x and y coordinates of points A and B. This would give us the coordinates for E as (1, 4). Similarly, we can use the same method to find the coordinates for F, G, and H. F would be (7,2), G would be (9,-5), and H would be (3,-6). To find the coordinates for these points, we use the formula [tex](x1 + x2)/2, (y1 + y2)/2[/tex]. For example, to find the x coordinate for E, we would use (-2 + 4)/2 = 1, and for the y coordinate of E, we would use (3 + 5)/2 = 4. We can then use this formula to find the coordinates for all of the midpoints.Step 1: Find coordinates of E, F, G, and H E: (1, 4) F: (7, 2) G: (9, - 5) H: (3, - 6) Step 2: Calculate the perimeter of the quadrilateral ABCD,Perimeter = |AB| + |BC| + |CD| + |DA = |(-2, 3) - (4, 5)| + |(4, 5) - (10, -1)| + |(10, -1) - (8, -9)| + |(8, -9) - (-2, 3)| = (6 + 14 + 18 + 10) = 48
Learn more about coordinates here:
https://brainly.com/question/16634867
#SPJ4
pregnancy length (in days) is a normally distributed random variable with a mean of 266 days and a standard deviation of 16 days. births that occur before 245 days are considered premature. what is the probability that a randomly selected newborn baby is premature? use the appropriate applet. enter a number in decimal form, e.g. 0.68 not 68 or 68%.
The probability of a birth occurring before 245 days, which is the probability of a newborn baby being premature.
To do this, we need to calculate the area under the normal distribution curve that represents the probability of a birth occurring before 245 days.
We can use a standard normal distribution table or an appropriate applet to find this probability. Using the applet, we can enter the mean, standard deviation, and the value of 245 days to find the probability.
In mathematical terms, we can write this as:
P(birth before 245 days) = probability of a randomly selected newborn baby being premature
= P(X < 245), where X is the random variable representing pregnancy length
Using the normal distribution table or applet, we can find P(X < 245) by calculating the area under the normal distribution curve to the left of 245 days.
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
The radius of the circular base of a cone measures 1.6 inches, and its slant height measures 2.5 inches.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest tenth in the box.
Answer:
ans=8.80inch
Step-by-step explanation:
given,
radius(r)=1.6 inch
height(h=2.5 inch
laternal area of cone = AL=√πrh2+r2
√3.14*2.5^2+1.6^2
8.80 inch
The approximate lateral area of the cone is,
⇒ LSA = 10.5 inches
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
To find the approximate lateral area of the cone, we need to know the height of the cone.
Since we are not given the height, we can use the Pythagorean theorem to find it:
Slant height² = h² + r²
2.5² = h² + 1.6²
6.25 = h² + 2.56
h² = 6.25 - 2.56
h² = 3.69
h = √3.69
h = 1.92 in
We know that;
The lateral surface area of a cone is calculated using the formula,
LSA =πr√(r² + h²) square units.
Substitute all the values, we get;
LSA =πr√(r² + h²) square units.
LSA = 3.14 × 1.4√(1.6² + 1.9²) square units.
LSA = 5 √2.6 + 3.6
LSA = 5 √4.2
LSA = 5 × 2.1
LSA = 10.5 inches
Thus, The approximate lateral area of the cone is,
⇒ LSA = 10.5 inches
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ2
What are the solutions to the quadratic equation 4x2 = 64?a. x= -16 and x = 16b. x= -8 and x = 8c. x= -4 and x = 4d. x= -2 and x = 2
The solutions to the quadratic equation 4x2 = 64 are: x= -4 and x = 4 therefore, Option (C) is correct.
The Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph).
We can Factor the Quadratic (find what to multiply to make the Quadratic Equation) Just plug in the values of a, b and c, and do
the calculations.
Given,
4x2 = 64
We need to solve the quadratic equation.
To solve this quadratic equation,We can rewrite the equation as:
4x2 - 64 = 0
Dividing both sides by 4x2 - 16 = 0x2 = 16
Taking square root on both sides,x = ±4
Hence,The solutions to the quadratic equation 4x2 = 64 are:
x= -4 and x = 4Option (C) is correct.
for such more question on quadratic equation
https://brainly.com/question/17482667
#SPJ11
calculate the area of the shaded segment
in the circle shown in Fig. 12.45
The area of the shaded segment of the circle will be 10.45cm².
How to calculate the areaThe area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.
The area of the segment will be calculated thus:
63°/360° × πr² - (1/2 × 10 × 10 × sin 63°)
= 63/360 × 22/7 ×10² × (1/2 × 10 × 10 × sin 63°)
= 55 - 44.55
= 10.45cm²
Therefore, the area of the shaded segment of the circle will be 10.45cm².
Learn more about area on;
https://brainly.com/question/25292087
#SPJ1
please help !! set up the function using tan
The value of x in the given triangle is 36.87°.
What is Trigonometric function?One of the six functions in mathematics is the trigonometric function (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) In trigοnοmetry, sin cοs and tan values are the primary functiοns we cοnsider while sοlving trigοnοmetric prοblems. These trigοnοmetry values are used tο measure the angles and sides οf a right-angle triangle. Apart frοm sine, cοsine and tangent values, the οther three majοr values are cοtangent, secant and cοsecant.
According to Trigonometric function,
Tan θ = Opposite side/Adjacent side
Therefore,
Tan θ = 6/8
θ = arctan(6/8)
θ ≈ 36.87°
This is simplest way to calculate, there is no other way to calculate.
Thus, the value of x in the given triangle is 36.87°.
To know more about Trigonometric function visit,
https://brainly.com/question/25618616
#SPJ1
2. A group of workers are harvesting oranges at a constant rate. An equation that represents the number of oranges the workers picked over a period of time, in hours, is y = 9x + 15. Complete sentences. Handwritten. Show work.
(a) What is the slope and the y-intercept for the equation that represents the number of oranges the workers picked over a period of time?
(b) What is the rate of change (slope) and the initial amount (y-intercept)? Explain the meaning of the rate of change and the initial amount for the situation. Answer in complete sentences
Step-by-step explanation:
(a) The slope of the equation y = 9x + 15 is 9, and the y-intercept is 15.
(b) The rate of change or slope of the equation y = 9x + 15 is 9, which represents the constant rate at which the workers are picking oranges. For every hour of work, they pick 9 more oranges. The initial amount or y-intercept of 15 represents the number of oranges they would have picked if they had started working from the beginning of time. However, since this is not possible, it can be interpreted as the number of oranges they picked before starting to work for the period of time that is being measured.
The equation for the number of baskets is an illustration of a linear function.
The slope is 9, and the y-intercept is 15The rate of change is 9, and the initial amount is 15The function is given as:
[tex]\bold{y=9x+15}[/tex]
(a) The slope and the y-intercept
A linear function is represented as:
[tex]\bold{y=mx+b}[/tex]
Where:
m represents the slope, and b represents the y-intercept
By comparison, the slope is 9, and the y-intercept is 15
(b) The rate of change and the initial amount
The rate of change is the slope, and the initial amount is the y-intercept
By comparison, the rate of change is 9, and the is 15
sylvia was playing a shooting game and she attempts. Find the number of attempts where she missed her target?
You are studying the lengths of time people spend reading books
each day. You randomly select 50 people and observe that, in average, they spend 25 minutes
reading books each day. Find the probability that the mean time they spend reading each day is
between 24.7 and 25.5 minutes? Assume that = 1.5 minutes and also you can use the Central
Limit Theorem.
As a result, the probability that individuals spend between 24.7 as well as 25.5 minutes per day on average reading books is roughly 0.919, or 91.9%.
How is probability determined?The probability that an occurrence will occur is determined by probability: P(A) = f / N. Probability and odds are linked, but probability determines what the percentages are.
Given:
Sample size (n) = 50
Sample mean (x) = 25 minutes
Standard deviation (σ) = 1.5 minutes
Range of interest: 24.7 minutes ≤ x ≤ 25.5 minutes
To find the probability that the mean time spent reading each day is between 24.7 and 25.5 minutes, we need to standardize the sample mean using the Central Limit Theorem and the z-score formula:
z = (x - μ) / (σ / √(n))
where μ is the population mean (unknown), σ is the population standard deviation (known), and √(n) is the square root of the sample size.
We can approximate the population mean with the sample mean since the sample size is large (n ≥ 30) and assume a normal distribution for the sample mean.
First, we standardize the lower bound of the range:
z1 = (24.7 - 25) / (1.5 / √(50)) = -1.76
Then, we standardize the upper bound of the range:
z2 = (25.5 - 25) / (1.5 / √(50)) = 1.76
Using a standard normal distribution table or calculator, we can find the area under the curve between z1 and z2:
P(-1.76 ≤ z ≤ 1.76) ≈ 0.919
Therefore, the probability that the mean time people spend reading books each day is between 24.7 and 25.5 minutes is approximately 0.919 or 91.9%.
To know more about Probability visit:
brainly.com/question/13604758
#SPJ1
C. If Brown has an imputed interest charge of 22%, compute the residual income of investment no. 3. Is this investment attractive from Glengarry's perspective? From Brown's perspective? Why?
A. Investment 1: ROI = 20%, Investment 2: ROI = 18%, Investment 3: ROI = 24%. B. Select Investment 3 with the highest ROI of 24% as it generates the most return for the investment amount.
C. Investment 3 is attractive with positive residual income, but from Brown's perspective, the imputed interest charge may reduce overall profitability.
A. To calculate the ROI for each investment, we can use the following formula:
ROI = (Income / Investment) x 100%
For Investment 1: ROI = (50,000 / 250,000) x 100% = 20%
For Investment 2: ROI = (54,000 / 300,000) x 100% = 18%
For Investment 3: ROI = (96,000 / 400,000) x 100% = 24%
B. If the manager's focus is on Glengarry's divisional performance, he would select Investment 3 because it has the highest ROI of 24%. This investment generates the highest return for the amount invested, which is the primary concern for divisional performance.
C. To calculate the residual income for Investment 3, we need to subtract the imputed interest charge from its profit margin traceable to the division:
Residual Income = Profit margin traceable to the division - (Average asset investment x Imputed interest rate)
Residual Income = 96,000 - (400,000 x 22%) = 96,000 - 88,000 = 8,000
From Glengarry's perspective, Investment 3 is attractive because it generates a positive residual income of $8,000. However, from Brown's perspective, it may not be as attractive because the imputed interest charge reduces the overall profitability of the investment.
Learn more about accounting here: brainly.com/question/22917325
#SPJ4
Complete question is in the image attached below
A few years ago, Mr. Cromleigh had been dying to go to a Taylor Swift concert. The tickets cost $65 each and he wanted to get 2 (for him and his mom of course!) He had been saving his allowance from his mom every week. He started with $40 and his mom would give him $10 a week to do chores around the house. How many weeks did it take him to earn the money to go to the concert?
It took him ------------------------------------ weeks until he was at the concert singing "Shake it Off" with his mom!
Answer: 9 weeks
i hope this helps you
which graph shows the solution to x-2y>9
The correct graph that shows the solution to x - 2y > 9 is B.
What is graph?
In mathematics, graphs can represent functions or equations, such as a line on a coordinate plane or a curve in a three-dimensional space. Graphs can also be used to represent data, such as a bar graph or a scatterplot, which can help to identify trends or correlations between different variables.
To graph the solution to the inequality x - 2y > 9, we can start by graphing the boundary line x - 2y = 9, which is the equation that results from replacing the inequality symbol with an equal sign.
The boundary line can be graphed by plotting two points on the line and connecting them with a straight line. To do this, we can choose any two values for x and y that satisfy the equation x - 2y = 9, such as:
x = 0, y = -4.5, giving us the point (0, -4.5)x = 9, y = 0, giving us the point (9, 0)We need to determine which side of the boundary line represents the solution to the inequality x - 2y > 9. To do this, we can choose a test point on one side of the boundary line, such as (0, 0), and substitute its coordinates into the inequality.
Substituting (0, 0) into the inequality x - 2y > 9 gives:
0 - 2(0) > 9
which simplifies to:
0 > 9
The side of the line containing (0, 0) is not the solution. Therefore, the solution to the inequality x - 2y > 9 is the side of the line that does not contain the point (0, 0).
Therefore, the correct graph that shows the solution to x - 2y > 9 is B.
To learn more about graph visit:
https://brainly.com/question/1638242
#SPJ1
Need help on my math homework
The classification of the angles are:
20° and 70°: complementary angles.
20° and 160°: supplementary angles
20° and 20°: vertical angles
How to interpret congruent angles?Congruent angles are defined as two or more angles that are identical to each other. Thus, the measure of these angles are equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.
Complementary angles are defined as two angle that sum up to 90 degrees. Thus: 20° and 70° are complementary angles.
Supplementary angles are defined as two angles that sum up to 180°. Thus: 20° and 160° are supplementary angles
Vertical angles are defined as angles that are opposite of each other when two lines cross. Thus they are congruent. Thus:
20° and 20° are vertical angles
Read more about Congruent angles at: https://brainly.com/question/14791175
#SPJ1
the radius of a circular disk is given as 19 cm with a maximum error in measurement of 0.2 cm. (a) use differentials to estimate the maximum error (in cm2) in the calculated area of the disk. (round your answer to two decimal places.) cm2 (b) what is the relative error? (round your answer to four decimal places.) what is the percentage error? (round your answer to two decimal places.)
a) The maximum error in the calculated area of the disk = 23.87 cm²
b) The relative error is: 0.0211 and the percentage error is 2.11%
Let us assume that r represents the radius of the circular disk and A represents the area.
Here, the radius of a circular disk is given as 19 cm
So, r = 19 cm
and the radius has a maximum error in measurement of 0.2 cm.
So, dr = 0.2
The area of the circular disk would be,
A = πr² ..........(1)
A = π × 19²
A = 361π cm²
Differentiating equation (1) with respect to r,
dA = 2πr × dr
dA = 2 × π × 19 × 0.2
dA = 7.6π
dA = 23.87 cm²
So, the maximum error in the calculated area is: 23.87 cm²
Now we find the relative error.
R = dA/A
R = 7.6π / 361π
R = 0.0211
And the percentage error would be:
P = relative error × 100
P = 0.0211 × 100
P = 2.11%
Learn more about the percentage error here:
https://brainly.com/question/28746643
#SPJ4
Owen invests money in an account paying a simple interest of 5.6% per year. If he invests $110 and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?
Owen will have $116.60 in one year. The same principal amount is used for the calculation every period, and the interest earned each period will be the same.
What is principal amount?Principal amount is the total amount of money borrowed or invested, excluding any interest, fees or other charges.
This can be calculated using the formula for simple interest, where
I = P x R x T, where P is the principal (the initial investment), R is the interest rate expressed as a decimal, and T is the time.
In this case, the principal (P)= $110,
the interest rate (R) = 0.056,
and the time (T)= 1 year.
Therefore, I = 110 x 0.056 x 1
= 6.16.
When this is added to the original principal of $110, we get $116.16.
This is happening because simple interest is calculated on the principal amount only.
It is not compounded, so the interest is not added to the principal and then used to calculate the interest in the next period.
Therefore, the same principal amount is used for the calculation every period, and the interest earned each period will be the same.
For more questions related to simple interest
https://brainly.com/question/20690803
#SPJ1
Answer:
11.16
Step-by-step explanation:
there are two methods
100%+5.6%=
105.6
%
105.6%
Whole balance before interest = 100%, then add on interest
105.6% of the current balance means
105.6
100
of it.
105.6% of the current balance means
100
105.6
of it.
"Percent" literally means "out of 100."
105.6
100
=
100
105.6
=
1.056
1.056
To find 105.6% of the current balance, multiply by 1.056:
To find 105.6% of the current balance, multiply by 1.056:
$110
×
1.056 = $110 × 1.056 =
$116.16
$116.16
method 2
Find the interest, 5.6% of $110:
Find the interest, 5.6% of $110:
5.6
100
=
100
5.6
=
0.056
0.056
$
110
×
0.056
=
$110×0.056=
$
6.16
$6.16
Add the interest to the current balance:
Add the interest to the current balance:
$
110
+
$
6.16
=
$110+$6.16=
$
116.16
$116.16
Can you help me with these questions
Answer:
Step-by-step explanation:
xy=34
For the following exercises, find the derivative
of y = sec−1 ⎛
⎝
1
x
⎞
the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²). To find the derivative of y = sec⁻¹(1/x), we will use the chain rule of differentiation. Let's start by using the definition of the inverse secant function:
sec⁻¹(θ) = cos⁻¹(1/θ)
Then we can rewrite the given function as:
y = cos⁻¹(x)
Using the chain rule, the derivative of y with respect to x is:
dy/dx = d/dx [cos⁻¹(x)]
= -1/√(1 - x²) * d/dx [x]
= -1/√(1 - x²)
Therefore, the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).
We can check this result by taking the derivative of y using the definition of the inverse secant function:
y = sec⁻¹(1/x)
sec(y) = 1/x
cos(y) = x
-sin(y) dy/dx = 1
dy/dx = -1/sin(y)
Using the Pythagorean identity sin²(y) + cos²(y) = 1, we can solve for sin(y) as:
sin(y) = √(1 - cos²(y)) = √(1 - x²)
Substituting this expression into the derivative, we get:
dy/dx = -1/√(1 - x²)
which is the same result we obtained using the chain rule. Therefore, we have confirmed that the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).
To know more about inverse secant function: click here:
brainly.com/question/7181576
#SPJ4
Which fraction is equivalent to 25%? (in simplest fraction form)
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
To find a fraction equivalent to a percentage we have to simply put the number over 100!
For 25% this would look like [tex]\frac{25}{100}[/tex]
Now to simply this, we have to find the highest common factor in both which is 25! This means that both values (25 and 100) can divide by 25 to give a whole number!
To divide both the numerator and denominator we will get the result [tex]\frac{1}{4}[/tex]
Hope this helps, have a lovely day! :)
to avoid an unbalanced lineup, the coach wants to choose 2 of her guards and 3 of her forwards/ centers. to do this, she places the names of her 5 guards in one hat and the names of her 7 forwards/centers in a second hat. then, she will randomly select 2 guards from the first hat and 3 forwards/ centers from the second hat.how many different lineups are possible?
There are 350 different lineups that can be created.
The question here is regarding the possibility of different lineups given that there are two groups of players available - guards and forwards/centers. The coach wants to choose 2 of her guards and 3 of her forwards/ centers. To avoid an unbalanced lineup, she places the names of her 5 guards in one hat and the names of her 7 forwards/centers in a second hat. Then, she will randomly select 2 guards from the first hat and 3 forwards/ centers from the second hat.
How many different lineups are possible?In order to get the different possibilities of lineups, we need to calculate the total number of ways we can select the guards and the forwards/centers separately.
Total number of ways to select guards =[tex]5C_2 = (5 \times 4) / (2 \times 1) = 10[/tex]
Total number of ways to select forwards/centers = [tex]7C_3 = (7 \times 6 \times 5) / (3 \times 2 \times 1) = 35[/tex]
Thus, the total number of ways the lineup can be created is 10 × 35 = 350.
for such more question on lineups
https://brainly.com/question/28535543
#SPJ11