Perry's paycheck was $100. To find Perry's paycheck, we can work backward from the final amount he had after finding $10 and ending up with $24.
Let's denote Perry's paycheck as "x". After buying the shirt and jeans, he spent a total of $26 + $52 = $78. So he had "x" - $78 left. He then spent half of what he had left on a snack, leaving him with 1/2 * ("x" - $78) = 1/2*x - $39.
When he found $10, he ended up with $24, so we can set up the equation:
1/2*x - $39 + $10 = $24
Simplifying this equation gives us:
1/2*x = $53
Multiplying both sides by 2, we get:
x = $106
Therefore, Perry's paycheck was $100.
In summary, we used a series of calculations to work backward from the final amount Perry had to determine his original paycheck. We accounted for the amount he spent on a shirt, jeans, and a snack, as well as the amount he found on his way home.
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13. The diagonals of a trapezium ABCD intersect at O. AB is parallel to DC, AB = 3 cm and DC = 6 cm. If CO = 4 cm and OB = 3 cm, find AO and DO.
Answer:
AO = 2 cmDO = 6 cmStep-by-step explanation:
You want the measures of AO and DO in a trapezium in which AB║CD, the diagonals intersect at O, and AB = 3 cm, CD = 6 cm, CO = 4 cm, OB = 3 cm.
Similar trianglesDiagonal AC is a transversal to parallel lines AB and CD, so alternate interior angles BAO and DCO are congruent. Vertical angles AOB and COD are also congruent, so ∆ABO ~ ∆CDO by the AA similarity postulate.
This means the side lengths are proportional, so ...
AB/CD = AO/CO = BO/DO
3/6 = AO/4 = 3/DO ⇒ AO = 2, DO = 6
The measures of AO and DO are 2 cm and 6 cm, respectively.
__
Additional comment
It can help to draw a diagram.
x cos y = 1, (2, pi/3), Find the derivative.
The derivative of the implicit function x · cos y = 1 at point (2, π / 3) is equal to y' = √3 / 6.
How to find the derivative of a function by implicit differentiation
In this problem we find the case of a implicit function of the form f(x, y), whose derivative must be found. This can be done by implicite differentiation, whose procedure is shown:
Derive the function by derivative rules.Clear y' within the resulting expression. Substitute x and y.Step 1 - Derive the expression by derivative rules:
cos y - x · sin y · y' = 0
Step 2 - Clear y' within the expression:
y' = cos y / (x · sin y)
Step 3 - Clear x and y in the resulting expression:
y' = cos (π / 3) / [2 · sin (π / 3)]
y' = 1 / [2 · tan (π / 3)]
y' = √3 / 6
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use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.
To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.
Let's consider a cross section of the solid taken at a distance x from the center of the circle.
Since the cross section is an equilateral triangle, all its sides have the same length.
Let this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:
[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]
Therefore, the area of the cross section at a distance x from the center of the circle is:
[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]
Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):
[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]
To find the limits of integration for y, we need to consider the equation of the circle:
[tex]x^2 + y^2= 3^2[/tex]
Solving for y, we get:
[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]
Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:
[tex]y = 3*\sqrt{3}[/tex]
Substituting this into the integral, we get:
[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]
[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]
Integrating, we get:
[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]
[tex]= 81/2*\sqrt{3}[/tex]
Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units
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The general form of the equation of a circle is x2 y2 8x 22y 37 = 0. the equation of this circle in standard form is (x )2 (y )2 = . the center of the circle is at the point ( , ).
The centre οf the circle is (-4, -11).
What is a circle's general equatiοn?We knοw that the general equatiοn fοr a circle is (x - h)² + (y - k)² = r² with (h, k) representing the centre and r representing the radius. Sο multiply bοth sides by 21 tο get the cοnstant term οn the right side οf the equatiοn. Then, fοr the y terms, cοmplete the square.
Tο write a circle equatiοn in standard fοrm, we must cοmplete the square fοr bοth x and y.
Tο begin, cοnsider the fοllοwing equatiοn: x²+ y² + 8x + 22y + 37 = 0.
Let's separate the terms with x frοm the terms with y:
[tex](x^2 + 8x) + (y^2 + 22y) + 37 = 0[/tex]
We add (8/2)² = 16 tο bοth sides tο cοmplete the square fοr x: (x²+ 8x + 16) + (y² + 22y) + 37 = 16
Simplifying the left side οf the equatiοn and cοmbining cοnstants οn the right:
[tex](x + 4)^2 + (y^2 + 22y + 121) = 16 - 37 - 121\s(x + 4)^2 + (y + 11)^2 = 50[/tex]
The equatiοn can nοw be written in standard fοrm:
[tex](x + 4)^2/50 + (y + 11)^2/50 = 1[/tex]
The circle's centre is (-4, -11).
As a result, the standard fοrm οf the circle's equatiοn is (x + 4)²/50 + (y + 11)²/50 = 1, and the circle's centre is (-4, -11).
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Eddie est discutiendo con Tana sobre las probabilidades de los distintos resultados al lanzar tres monedas. Decide lanzar una moneda de un centavo, una de cinco centavos y una de die centavos. ¿ Cuál es la probabilidad de que las tres monedas salgan cruz?
The probability of getting tails in the three coins would be 0.125 or 12.5%.
How to calculate the probability?To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.
Probability of getting tails in any of the three coins:
1 / 2 = 0.5
Total probabilityy:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
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What is an equation of the line that passes through the point (5,1) and is parallel to
the line x +y = 9?
The line x + y = 9 is y = -x + 6 is keeps through the point (5,1).
To find the equation of the line that passes through the point (5,1) and is parallel to the line x + y = 9, we need to first find the slope of the line x + y = 9.
Rearranging the equation in slope-intercept form, we get y = -x + 9
The slope of this line is -1, since the coefficient of x is -1.
Since the line we want to find is parallel to this line, it will have the same slope of -1.
Using the point-slope form of a line, the equation of the line passing through the point (5,1) and with a slope of -1 is: y - 1 = -1(x - 5)
Simplifying and rearranging the equation, we get:
y - 1 = -x + 5
y = -x + 6
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Suppose we create a box model for the outcome of a game of darts. The player has a 1/3 chance of throwing a dart in the inner ring, and a 2/3 chance of the dart landing in the outer ring. In our model, we have two unique tickets marked "inner" and "outer." We put in 1 ticket marked "inner." How many tickets do we put in that are marked "outer?"
a. 0
b. 1
c. 2
d. 3
As per the combination method, the number of tickets that we put in that are marked "outer" is 3 (option d).
In this case, we want to choose the number of tickets marked "outer." Let's call this number k. We know that we already put one ticket marked "inner" in the box, so the total number of tickets in the box is 2. Therefore, n = 2.
Now we need to determine k. We want to know how many tickets we need to put in that are marked "outer." We can represent this as a. So we have:
ᵃC₁ = a! / ((1!)(a-1)!) = a
We want to find the value of a that satisfies the condition that the probability of choosing an "inner" ticket is 1/3 and the probability of choosing an "outer" ticket is 3/2.
Since we already put in 1 ticket marked "inner," the probability of choosing an "inner" ticket is 1/2, which means the probability of choosing an "outer" ticket is also 1/2.
We know that the probability of choosing an "outer" ticket is 3/2, so we can set up the following equation:
ᵃC₁ / 2 = 3/2
Solving for a, we get:
a = 3
In conclusion, the answer is (d) 3.
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The graph of f(t) = 7•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answer:
When it was purchased (year 0) the coin was worth $7
Step-by-step explanation:
we have
[tex]f(t) = 7(2)^t[/tex]
This is a exponential function of the form
[tex]y=a(b)^x[/tex]
where
a is the initial value
b is the base
In this problem we have
[tex]a=\$7[/tex]
[tex]b=2[/tex]
[tex]b=1+r[/tex]
so
[tex]2=1+r[/tex]
[tex]r=1[/tex]
[tex]r=100\%[/tex]
The y-intercept is the value of the function when the value of x is equal to zero
In this problem
The y-intercept is the value of a rare coin when the year t is equal to zero
[tex]f(0)=7(2)^0[/tex]
[tex]f(0)=\$7[/tex]
therefore
The meaning of y-intercept is
When it was purchased (year 0) the coin was worth $7
Answer:
Value of the coin when it was first released
-------------------------------
The y-intercept is the value of f(0).
Substitute t = 0 and find the y-intercept:
f(0) = 7 · 2⁰ = 7 · 1 = 7This is representing the value of the coin when it was released.
16^(3x-1) = 32. pls help
Answer:x=33/4096=0.008
Step-by-step explanation: 1.1 16 = 24
(16)3 = (24)3 = 212
Equation at the end of step
1
:
((212 • x) - 1) - 32 = 0
STEP
2
:
Equation at the end of step 2
4096x - 33 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : 4096x-33 = 0
Add 33 to both sides of the equation :
4096x = 33
Divide both sides of the equation by 4096:
x = 33/4096 = 0.008
6=a/4+2 two step equations
Answer:
12
Step-by-step explanation:
6=a/4+2
L.C.M=4
4(6)=a+6(2)
24=a+12
24-12=a
a=12
Gill opened an account at a different bank. The banks rate of interest was 6%. After one year the bank paid Gill interest. The amount in her account was now $2306
Answer:
Step-by-step explanation:
To solve this problem, we can use the formula for calculating simple interest:
I = P * r * t
where:
I = interest earned
P = principal (initial amount of money)
r = rate of interest
t = time (in years)
We can rearrange the formula to solve for the principal:
P = I / (r * t)
In this case, we know that Gill earned $2306 in interest after one year at a rate of 6%. So:
I = $2306
r = 0.06
t = 1 year
Substituting these values into the formula, we get:
P = $2306 / (0.06 * 1)
P = $38,433.33
Therefore, the initial amount of money that Gill deposited into her account was $38,433.33.
10. Write the equation that is represented by the data in the table below.
Time (years)
0
1
2
3
4
5
No. of cars
5
10
20
40
80
160
How many years would it take to over 10,000 cars?
A manufacturer of paper used for packaging requires a minimum strength of 1400 g/cm2. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. The standard deviation of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 140 g/cm2, and the strength measurements are normally
distributed.
a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?
b) If the mean of the population of strength measurements is 1450 g/cm2, what is the
approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400?
The sample mean is 1450g/cm², the standard deviation is 44.3 g/cm² and the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2 is 0.8708
What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?a) The sampling distribution of the sample mean of n = 10 test pieces of paper is approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:
mean of sample mean = mean of population = 1450 g/cm²
standard deviation of sample mean = standard deviation of population / square root of sample size
= 140 g/cm2 / √(10)
= 44.3 g/cm²
Therefore, the sampling distribution of the sample mean is approximately normal with mean 1450 g/cm2 and standard deviation 44.3 g/cm2.
b) To find the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2, we need to standardize the sample mean using the sampling distribution calculated in part (a):
z = (x - mean of sample mean) / standard deviation of sample mean
= (1400 - 1450) / 44.3
= -1.13
Using a standard normal distribution table or calculator, we can find the probability that z is less than -1.13 and subtract that probability from 1 to find the probability that z is greater than -1.13:
P(z > -1.13) = 1 - P(z < -1.13)
= 1 - 0.1292
= 0.8708
Therefore, the approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm² is 0.8708.
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Solve equation for x
216=6^4x+5
Answer: x=211/1296
Step-by-step explanation:
what is the vertex of h=-16t^2+29t+6 and its domain and range, and x and y axis?
Ted is five times as old as Rosie was when Ted was Rosie's age. When Rosie
reaches Ted's current age, the sum of their ages will be 72. Find Ted's current age.
Answer:
45 yo
Step-by-step explanation:
Let's start by defining some variables to represent the ages of Ted and Rosie:
- Let's call Ted's current age "T"
- Let's call Rosie's current age "R"
From the problem statement, we know that:
- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:
T = 5(R - (T - R))
Simplifying this equation, we get:
T = 5(R - T + R)
T = 10R - 5T
- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:
R + T = 72 - T
We now have two equations with two variables. We can use substitution to solve for T.
Substitute the second equation into the first equation to eliminate R:
T = 10R - 5T
T = 10(72 - T) - 5T
T = 720 - 15T
16T = 720
T = 45
Therefore, Ted's current age is 45.
what proportion of values for a standard normal distribution are less than 2.98?
Regardless of the appearance of the normal distribution or the size of the standard deviation, approximately less than 2.98% of observations consistently fall within two deviations types (one high and one low).
The normal distribution, also known as the Gaussian distribution, is a probability distribution symmetrical about the mean, indicating that data near the mean occurs more frequently than data far from the mean. In graphical form, the normal distribution is represented by a "bell curve".
The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the mean of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases. Therefore, physical quantities assumed to be the sum of many independent processes, such as measurement errors, tend to have a near-normal distribution.
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when solving arithmetic expressions, oracle 12c always resolves addition and subtraction operations first from left to right in the expression. true or false?
When solving arithmetic expressions, Oracle 12c resolves addition and subtraction operations first from left to right in the expression. This statement is true.
By following these rules, Oracle 12c is able to resolve arithmetic expressions accurately and efficiently. This is particularly important when dealing with large amounts of data, where the correct order of operations is critical to ensure that the correct result is obtained.
Oracle 12c is a database management system that is used to handle large amounts of data. It has a variety of features that enable it to manage and maintain data effectively.
Oracle 12c has a SQL engine that allows it to execute SQL statements and expressions to retrieve and manipulate data.
When performing arithmetic operations in Oracle 12c, the order of operations is critical. The order of operations is the set of rules that dictate the sequence in which arithmetic operations should be performed in a mathematical expression.
These rules are also known as the rules of precedence.In Oracle 12c, the rules of precedence dictate that arithmetic operations should be resolved from left to right in an expression. This means that addition and subtraction operations should be resolved before multiplication and division operations.
This is because addition and subtraction operations have a lower precedence than multiplication and division operations. As a result, Oracle 12c always resolves addition and subtraction operations first from left to right in an expression .This order of operations ensures that the correct result is obtained when performing arithmetic operations in Oracle 12c.
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You have five student groups to present in class one group cannot go first because they need additional set up time and how many orders can they present
They can present in 96 different orders. Given, there are five student groups to present in class and one group cannot go first because they need additional set-up time.
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
We have 5 positions to fill here.
First position: 4 ways (one of the rest 4 groups will present first)
Second position: 4 ways (one of the rest 3 groups and the group which could not present first, will present second)
Third position: 3 ways (one of the rest 3 groups will present third)
Fourth position: 2 ways (one of the rest 2 groups will present fourth)
Fifth position: 1 way (rest group will present last)
Total ways in which they can present = 4*4*3*2*1 = 96
Hence, the answer is 96.
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WHAT IS THE CENTRAL ATOM OF NITRIC OXIDE (NO)
Answer:
The answer is Nitrogen
Hope this helps :)
You have a circular loop of wire in the plane of the page with an initial radius of 0.40 m which expands to a radius of 1.00 m. It sits in a constant magnetic field B = 24 mT pointing into the page. Assume the transformation occurs over 1.0 second and no part of the wire exits the field. Also assume an internal resistance of 30 Ω. What average current is produced within the loop and in which direction? Express your answer with the appropriate units. Enter positive value if the current is clockwise and negative value if the current is counterclockwise. My INCORRECT work: emf = -BAcos(theta)/dt emf = -B*1*(dA/dt) emf = -B*pi*(2*(expansion rate/1)^2*t+2*r0*(expansion rate/1) Then V=IR so emf=IR so I=emf/R I = -[B*pi*(2*(expansion rate/1)^2*t+2*r0*(expansion rate/1)]/R I = -[24x10^-3*pi*(2*.6^2*1+2*.4*.6)]/30 I ~ -3.015928947x10^-3 I ~ -3.0x10^-3 Which is wrong.
In the given scenario, the average current produced within the loop is approximately 2.13 A.
We can begin by computing the change in magnetic flux across the loop as it expands to determine the average current generated within the loop.
The following equation provides the magnetic flux across a loop:
Φ = B * A * cos(θ)
ΔΦ = B * ΔA
ΔA = A₂ - A₁ = π * (1.00 m)² - π * (0.40 m)² = π * (1.00² - 0.40²) = π * (1.00 + 0.40)(1.00 - 0.40) = π * (1.40)(0.60) = 0.84π m²
So,
ΔΦ = B * ΔA = (24 mT) * (0.84π m²) = 20.25π m²·T
emf = ΔΦ / Δt = (20.25π m²·T) / (1.0 s) = 20.25π V
As:
emf = I * R
So, again
I = emf / R = (20.25π V) / (30 Ω) ≈ 2.13 A
Thus, the average current produced within the loop is approximately 2.13 A.
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The island of Martinique has received $32,000
for hurricane relief efforts. The island’s goal is to
fundraise at least y dollars for aid by the end of
the month. They receive donations of $4500
each day. Write an inequality that represents this
situation, where x is the number of days.
An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.
What is inequality?Inequality is an algebraic statement that two or more mathematical expressions are unequal.
Inequalities can be represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total amount received by the island = $32,000
The daily receipt of donations = $4,500
Let the number of days = x
Let the funds raised for aid = y
Inequality:y ≤ 32,000 + 4,500x
Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.
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The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds Construct a 95% confidence interval for the population mean weight of newborn elephants. State the confidence interval (Round your answers to two decimal places.) Sketch the graph. (Round your answers to two decimal places.) CL - 0.95 X Calculate the error bound (Round your answer to two decimal places)
The error bound for the 95% confidence interval is (1.96 x Standard Deviation/√n), which in this case is (1.96 x 11/√50) = 2.56. This means that the true mean weight of newborn elephant calves lies within +/-2.56 pounds of the interval range.
The 95% confidence interval for the population mean weight of newborn elephants can be calculated using the sample mean of 244 pounds and the sample standard deviation of 11 pounds. The confidence interval is calculated using the following formula:
Confidence Interval = (Mean - (1.96 x Standard Deviation/√n)), (Mean + (1.96 x Standard Deviation/√n))
Where n is the sample size.
Therefore, the 95% confidence interval for the population mean weight of newborn elephants is (231.14, 256.86).
This can also be represented in a graph. The graph would have the x-axis representing the confidence interval, with a range from 231.14 to 256.86, and the y-axis representing the probability, which would be 0.95.
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I don’t know helppp
Me
[tex]f(x) = -2(x - 0.5)^2 + 6[/tex] is the equation of the quadratic function that passes through the points (-1, 14), (0, 8), (1, 6), and (2, 8).
What is quadratic function?
f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero, is a quadratic function.
To find the equation of the quadratic function that passes through the points (-1, 14), (0, 8), (1, 6), and (2, 8), we can use the vertex form of the quadratic function, which is:
[tex]f(x) = a(x - h)^2 + k[/tex]
[tex]f(1) = a(1 - h)^2 + k\\\\6 = a(1 - h)^2 + k[/tex]
We can use a second point to find a relationship between h and k. Let's use the point (0, 8):
[tex]f(0) = a(0 - h)^2 + k\\\\8 = a(-h)^2 + k\\\\6 - 8 = a(1 - h)^2 + k - (a(-h)^2 + k)\\\\-2 = a(1 - h)^2 - a(h)^2\\\\-2 = a(1 - 2h + h^2) - a(h^2)\\\\-2 = a - 2ah + ah^2 - ah^2\\\\-2 = a - 2ah\\\\a = -2/(2h - 1)[/tex]
Let's use the second equation:
[tex]8 = a(-h)^2 + k\\\\8 = (-2/(2h - 1))(h^2) + k\\\\8(2h - 1) = -2h^2 + k(2h - 1)\\\\16h - 8 = -2h^2 + k(2h - 1)\\\\-2h^2 + 16h - 8 = k(2h - 1)\\\\k = (-2h^2 + 16h - 8)/(2h - 1)[/tex]
Now we can substitute this value of h into our expressions for a and k to get:
[tex]a = -2/(2(0.5) - 1) = -2\\\\k = (-2(0.5)^2 + 16(0.5) - 8)/(2(0.5) - 1) = 6[/tex]
So the equation of the quadratic function is:
[tex]f(x) = -2(x - 0.5)^2 + 6[/tex]
Therefore, [tex]f(x) = -2(x - 0.5)^2 + 6[/tex] is the equation of the quadratic function that passes through the points (-1, 14), (0, 8), (1, 6), and (2, 8).
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prove that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other
We need to use mathematical logic to prove that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.
Let's take an example of two sets A and B.
Let's say, A={a, b} and B={1, 2, 3}
To find the cardinality of the cross-product of A and B, we need to make all possible ordered pairs with A and B.
{(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}
Counting the number of ordered pairs, we get six.
So, the cardinality of the cross-product of two sets A and B equals the cardinality of each set multiplied by the other. Here,
|A| = 2 and |B| = 3,
so |A x B| = 2 x 3
= 6.
Therefore, it is proved that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.
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What are the exact lengths of BC and CF?
The length, in feet, of BC is the square root of.
The length, in feet, of CF is the square root of
The length, in feet, of BC is the square root of √242 and, The length, in feet, of CF is the square root of √363
Cube:
In geometry, a cube is a three-dimensional solid object bounded by six faces, facets, or square sides, with three points of intersection at each vertex. Seen from a certain angle, it is a hexagon and its canvas is often represented by a cross.
Cube is the only regular hexahedron and one of the five Platonic solids. It has 6 faces, 12 edges and 8 vertices. Cube is also a cube, an equilateral cuboid, a rhombus and a 3-sonohedron.
Three orientations are square prisms and four orientations are triangular trapezoids. A cube is twice as large as an octahedron. It has cubic or octahedral symmetry. Cube is the only convex polyhedron whose faces are square.
Then the length CB is given by the Pythagorean theorem as:
CB = √(AC² +AB²)
= √{(2 cm)² + (√2 cm)²}
= √(4 +2) cm
CB = √6 cm
Now,
The length, in feet, of BC is the square root of
√242
And,
The length, in feet, of CF is the square root of
√363
Complete Question:
A cube. The top face has points C, A, B, D and the bottom face has points G, E, F, H. Diagonals are drawn from B to C and from C to F. Side B F is 11 feet.
What are the exact lengths of BC and CF?
The length, in feet, of BC is the square root of
The length, in feet, of CF is the square root of
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Answer:
The length, in feet, of BC is the square root of
✔ 242
The length, in feet, of CF is the square root of
✔ 363
Step-by-step explanation:
19. Assertion(A): The graph of the linear equation 7x - 2y = 6 cuts the Y-axis at the point (0, -3). Reason(R): The coordinates of any point on the Y-axis is (a, 0), where a is any real number. pls help
get the answer
Answer:
Pretty sure its C
Step-by-step explanation:
To cut through y axis, x axis is always 0, So it would be (0, a) where a is any real number, not (a,0) as is given in reason.
The question may have one or more than one option correct
[tex]\displaystyle\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx[/tex]
The correct option is/are
A) 22/7 - π
B) 2/105
C) 0
D) 71/15 - 3π/2
Answer:
To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:
[tex]\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}[/tex]
Using partial fractions, we can write:
[tex]\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}[/tex]
Multiplying both sides by (x+i)(x-i), we get:
[tex]x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)[/tex]
Substituting x=i, we get:
[tex]i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ci + 2B[/tex]
Substituting x=-i, we get:
tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ai + 2D[/tex]
Substituting x=0, we get:
[tex]0 = Bi + Di[/tex]
Substituting x=1, we get:
[tex]0 = A+B+C+D[/tex]
Solving these equations simultaneously, we get:
A = -22/7 + π
B = 0
C = 22/7 - π
D = -2/5
Therefore, the integral can be written as:
[tex]\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx[/tex]
Integrating each term separately, we get:
[tex]\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)[/tex]
[tex]\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)[/tex]
[tex]\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)[/tex]
Therefore, the correct options are:
A) [tex]\pi-\frac{22}{7}[/tex]
B) [tex]\frac{2}{105}[/tex]
C) 0
D) [tex]\frac{71}{15}-\frac{3\pi}{2}[/tex]
refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
Confidence interval = (y ± t∗s/√n)g1 = y - t*s/√ng2 = y + t*s/√n Substituting the values, g1 = 26.22 - 1.860*(0.11)/√9 = 25.84g2 = 26.22 + 1.860*(0.11)/√9 = 26.59Therefore, the statistics g1 and g2 that will satisfy the required inequality are 25.84 and 26.59 respectively.
The formula for finding the confidence interval is as follows: n − 1, where t is the value of the t-distribution corresponding to the specified confidence level and the sample size minus one.
As per the given exercise 7.11, suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample.
If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p(g1 ≤ (y - u) ≤ g2) = 90
To find the statistics g1 and g2 that will satisfy the required inequality
the following formula can be used: Confidence interval = [tex](y ± t∗s/√n)[/tex]
From the formula, we can see that the confidence interval depends on the values of y, s, t and n.
The value of y is the sample mean
the value of s is the sample standard deviation
And the value of n is the sample size.
The value of t depends on the confidence level desired and the degrees of freedom for the t-distribution. In this case, the confidence level is 90%, which means that we want to find the value of t that will give us a total area of 0.90 under the t-distribution curve with 8 degrees of freedom .Using the t-table, the value of t can be found to be 1.860, where the value for 90% and 8 degrees of freedom is 1.860.t = 1.860Now, we need to calculate the value of s, which is the sample standard deviation.
Since we do not have any information about the population standard deviation, we will use the sample standard deviation as an estimate of the population standard deviations = σ/√nσ = s*√nσ = 0.11*√9σ = 0.33Substituting the values in the confidence interval formula
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Give the coordinates for the translation of Rhombus ABCD with vertices A(-3,-2), B(0, 3),
C(5, 6), and D(2, 1).
Given the rule (x, y) = (x+2, y-6)
The new position of Rhombus ABCD after the translation can be described as follows: point A is now at (-1,-8), point B is at (2,-3), point C is at (7,0), and point D is at (4,-5).
To translate Rhombus ABCD using the rule (x, y) = (x+2, y-6), we add 2 to the x-coordinate and subtract 6 from the y-coordinate for each vertex.
Thus, the new vertices for the translated rhombus are:
A' = (-3+2, -2-6) = (-1, -8)
B' = (0+2, 3-6) = (2, -3)
C' = (5+2, 6-6) = (7, 0)
D' = (2+2, 1-6) = (4, -5)
Therefore, the coordinates for the translated Rhombus ABCD are A'(-1,-8), B'(2,-3), C'(7,0), and D'(4,-5).
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