The probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI is approximately 0.304.
This problem can be solved using the binomial distribution, which models the probability of a certain number of successes in a fixed number of independent trials, each with the same probability of success.
Let X be the number of Indianapolis residents in a sample of 30 who wanted the Giants to beat the Patriots. Then X follows a binomial distribution with n = 30 and p = 0.97, since the probability of success (rooting for the Giants) is 0.97 for each resident.
We want to find the probability that fewer than 95% of the sample wanted the Giants to win. That is, we want to find P(X < 0.95*30) = P(X < 28.5), where X has the binomial distribution with parameters n = 30 and p = 0.97.
We can use a continuity correction and approximate this probability by the cumulative distribution function of a normal distribution with mean np and variance np(1-p). That is,
P(X < 28.5) ≈ P(Z < (28.5 - np) / sqrt(np(1-p)))
where Z is a standard normal random variable. Substituting the values of n and p, we get
P(X < 28.5) ≈ P(Z < (28.5 - 300.97) / sqrt(300.97*0.03))
≈ P(Z < -0.51)
Using a standard normal table or calculator, we find that P(Z < -0.51) ≈ 0.304. Therefore, the probability that fewer than 95% of the sample wanted the Giants to win is approximately 0.304.
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The given question is incomplete, the complete question is:
Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city’s own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 97% of Indianapolis residents wanted the Giants to beat the Patriots.
What is the probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLIV?
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.
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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
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.
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Complete question is in the image attached below
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]
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.
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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
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 +∞.
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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.
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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.
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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
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.
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Can you help me with these questions
Answer:
Step-by-step explanation:
xy=34
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.
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.
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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.
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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.
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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%
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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.
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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%.
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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
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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.
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sylvia was playing a shooting game and she attempts. Find the number of attempts where she missed her target?
find the area and circumference of each circle, rounding to the nearest tenth. use 3.14 for π look at the formula for finding the area and circumference if you need help.
Step-by-step explanation:
1) area= 2.4^2×3.14=18.0864
rounded=18ft^2
circumference= 4.8×3.14=15.072
rounded= 15ft
2) area= 6^2×3.14=113.04
rounded= 110ft^2
circumference= 12×3.14=37.68
rounded= 38ft
3) area= 32^2×3.14=3215.36
rounded=3220ft^2
circumference= 64×3.14=200.96
rounded=200ft
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).
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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°.
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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
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
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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
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Use the table to describe the intervals over which f(x) = 15x² is increasing and decreasing.
f(x)=15x²
(x,y)
(-2,60)
60
15
(-1,15)
0
15
60
X
-2
-1
0
1
2
(0,0)
(1,15)
(2,60)
The function f(x) is increasing over the interval x>0¹.
(Simplify your answer. Type an inequality.)
The function f(x) is decreasing over the interval
(Simplify your answer. Type an inequality.)
Answer:
Step-by-step explanation:
The function f(x) = 15x² is increasing over the interval x > 0.
To see why, we can look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. When x is zero, f(x) reaches its minimum value of zero. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is increasing over the interval x > 0.
The function f(x) is decreasing over the interval x < 0.
To see why, we can again look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. But as x approaches zero from the left, f(x) begins to decrease, reaching its minimum value of zero at x = 0. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is decreasing over the interval x < 0.
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! :)
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%.
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