Answer:
The rate of change for height is 1/6 cubic feet/min at 2 min.
Step-by-step explanation:
determine the probability of drawing either a king or a heart? write your answer as a reduced fraction.
Determine the probability of drawing either a king or a heart? write your answer as a reduced fraction.
There are four kings and thirteen hearts (including the king of hearts) in a regular 52-card deck of playing cards. To avoid counting it twice, we must deduct the king of hearts from the total number of hearts.
There are 4 + 12 = 16 cards, all of which are kings or hearts.
By dividing the number of cards in the deck that are either kings or hearts by the total number of cards in the deck, one may determine the likelihood of drawing one of these cards:
P=16/52 (king or heart)
By reducing the numerator and denominator by their largest common factor, which is 4, this fraction can be made smaller:
P = 4/13 (king or heart)
Therefore, there is a 4/13 chance of drawing either a king or a heart.
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Which of these describes the equation 3. 0 + 7y=8?
Select each correct answer
A
function
B. Linear
C nonlinear
U
D. Proportional
When x is 0, y is
F. When y is 2, 3 is 2 or -2.
B. Linear function describes the equation 3. 0 + 7y = 8. When x is 0, y is 8/7 and when y is 2, x is -2.
A linear function is defined in mathematics as a function with one or two variables but no exponents. It is a function that has a straight line graph. If the function has more variables, the variables should be constants or known variables for the function to continue in the same linear function condition. It is typically a polynomial function with a degree of 1 or 0.
Now, we have equation as 3x + 7y = 8
So, if we put 0 in place of x, we can calculate y as:
3 × 0 + 7y = 8
0 + 7y = 8
7y = 8
y = 8/7
Now, is we put y = 2 in the equation, we can find x as:
3x + 7y = 8
3x + 7×2 = 8
3x + 14 = 8
3x = 8 - 14
3x = -6
x = -6 / 3
x = -2
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Correct question:
Which of these describes the equation 3x + 7y = 8?
Select each correct answer.
A function
B. linear
C. nonlinear
D. proportional
E.
When x is 0, y is
F. When y is 2, x is 2 or -2.
Evaluate the line Integral ter F. dr, where C is given by the vector function r(t). F(x, y, z) = xi + y + xy k, r(t) = sin(t) i + cos(t) j + tk, Osts TT X The force exerted by an electric charge at
The line integral of F along C is π - (1/2).
We can evaluate the line integral using the formula:
∫CF.dr = ∫ab F(r(t)).r'(t) dt
where a and b are the limits of the parameter t that traces out the curve C.
First, we need to compute r'(t):
r'(t) = cos(t) i - sin(t) j + k
Next, we need to compute F(r(t)):
F(r(t)) = sin(t) i + cos(t) j + sin(t)cos(t) k
Now, we can set up the integral:
∫CF.dr = ∫0π F(r(t)).r'(t) dt
= ∫0π (sin(t) i + cos(t) j + sin(t)cos(t) k) · (cos(t) i - sin(t) j + k) dt
= ∫0π (sin(t)cos(t) + 1) dt
= [-(1/2)cos2(t) + t] from 0 to π
= π - (1/2)
Therefore, the line integral of F along C is π - (1/2).
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sandra is making sandwiches for her family's camping trip. she has 72 slices of turkey, 48 slices of cheese, and 96 pieces of lettuce. what is the greatest number of sandwiches she can make if each sandwich has the same filling of turkey, cheese, and lettuce?
Sandra can make 48 sandwiches with the given ingredients of 72 slices of turkey, 48 slices of cheese, and 96 pieces of lettuce.
To determine the maximum number of sandwiches that Sandra can make, we need to find the bottleneck ingredient. This means we need to figure out how many sandwiches she can make with the least common multiple amount of any of the three fillings.
Each sandwich requires one slice of turkey, one slice of cheese, and two pieces of lettuce. Therefore, the bottleneck ingredient is the cheese, which she only has 48 slices of cheese . Since she has enough turkey and lettuce for more sandwiches, she can make a maximum of 48 sandwiches with the available cheese. Each of these sandwiches will have one slice of turkey, one slice of cheese, and two pieces of lettuce. Hence, Sandra can make 48 sandwiches with the given ingredients.
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what is the difference between a sample mean and the population mean called? multiple choice point estimate standard error of the mean
A point estimate is the difference between a sample mean and a population mean, while the standard error of the mean is a measure of the variability between the two.
The difference between a sample mean and a population mean is known as a point estimate. A sample mean is the average of a group of observations taken from a larger population, while a population mean is the average of all observations in the entire population. A sample is a subset of the population that is selected for analysis, while the population is the entire group that is being studied. To make inferences about a population from a sample, researchers use point estimates, which are calculated from the sample data and used to estimate the population parameter. The point estimate is a single value that represents the best guess of the population mean based on the available sample data. The standard error of the mean is a measure of how much variability exists in the sample mean compared to the population mean. It reflects the amount of sampling error that can be expected when estimating the population mean from the sample mean.
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formulate but do not solve the problem. lawnco produces three grades of commercial fertilizers. a 100-lb bag of grade a fertilizer contains 16 lb of nitrogen, 6 lb of phosphate, and 7 lb of potassium. a 100-lb bag of grade b fertilizer contains 20 lb of nitrogen and 4 lb each of phosphate and potassium. a 100-lb bag of grade c fertilizer contains 24 lb of nitrogen, 3 lb of phosphate, and 6 lb of potassium. how many 100-lb bags of each of the three grades of fertilizers should lawnco produce if 26,200 lb of nitrogen, 4,700 lb of phosphate, and 6,600 lb of potassium are available and all the nutrients are used? (let a, b, and c denote the number of bags of grade a, b, and c fertilizer, respectively.)
The goal is to find the values of a, b, and c that satisfy these equations, representing the number of 100-lb bags of each grade of fertilizer that Lawnco should produce.
Lawnco needs to produce a certain number of bags of grade A, grade B, and grade C fertilizers to meet the nutrient requirements with the given amounts of nitrogen, phosphate, and potassium. The number of bags produced for each grade of fertilizer is denoted by a, b, and c respectively. The nutrient composition of each grade of fertilizer in terms of nitrogen, phosphate, and potassium is also given. By using this information and the nutrient requirements, we can set up the following system of equations:
16a + 20b + 24c = 26200 (for nitrogen)
6a + 4b + 3c = 4700 (for phosphate)
7a + 4b + 6c = 6600 (for potassium)
We can solve this system of equations to find the values of a, b, and c that satisfy all three equations simultaneously.
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To make violet paint, Iris mixes 0. 25
liter of red paint, 0. 25 liter of blue paint,
and 4. 5 centiliters of white paint. How
many centiliters of paint are in the
mixture?
There are 54.5 centiliters of paint in the mixture.
To find the total amount of paint in the mixture, we need to convert the volumes of red and blue paint from liters to centiliters, since white paint is already given in centiliters.
0.25 liter of red paint is equal to 25 centiliters (since 1 liter = 100 centiliters)
0.25 liter of blue paint is equal to 25 centiliters
So the total amount of paint in the mixture is:
25 centiliters (red paint) + 25 centiliters (blue paint) + 4.5 centiliters (white paint)
= 54.5 centiliters
Therefore, there are 54.5 centiliters of paint in the mixture Iris made to make violet paint.
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______ can be thought of as the chi-square type equivalent to the paired t-test.
The McNemar's Test can be thought of as the chi-square type equivalent to the paired t-test.
The McNemar's Test is a non-parametric statistical method used to analyze the differences between paired or matched categorical data, such as repeated measurements on a single group. Like the paired t-test, which is used to compare continuous data, the McNemar's Test evaluates the changes in the proportions of success or failure between the paired observations.
This test is particularly useful when dealing with small sample sizes or when the assumptions of normality and homogeneity of variances required for the paired t-test are not met. By using the chi-square distribution, McNemar's Test provides a way to determine the significance of the differences between paired categorical data, while accounting for the dependency between the observations.
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An electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. Let C represent the total cost of the visit when the electrician spends t hours at the house working. The table below has select values showing the linear relationship between t and C. Determine the set fee for the house call. t 3 CT 5 9 C 330 460 720
The linear function for this problem is given as follows:
C(t) = 65t + 135.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.Two points on the graph of the linear function are given as follows:
(3, 330) and (5, 460).
Hence the slope is given as follows:
m = (460 - 330)/(5 - 3)
m = 65.
Hence the equation is:
C(t) = 65t + b.
When t = 3, C(t) = 330, hence the intercept b is obtained as follows:
330 = 65(3) + b
b = 330 - 65 x 3
b = 135.
Thus the function is:
C(t) = 65t + 135.
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The area of a parallelogram is base times height (A = bh). Since the height of this parallelogram is r and the base is πr, the area is (πr)r or πr2. Since the area of the parallelogram is equal to the area of a circle, the area of the circle is equal to (πr)r, or πr2.
The area of the circle is also equal to the area of the parallelogram which is πr².
A = bh is the formula for calculating the area of a parallelogram, where A stands for the area, b for the base, and h for the height. In this case, the base of the parallelogram is πr and the height is r. So, the area of the parallelogram is:
A = (πr) × r
A = πr²
The formula for the area of a circle is A = πr².
The two formulas can be set equal to one another because the area of the parallelogram and the area of the circle are equal.
πr² = πr²
This confirms that the area of the circle is also equal to πr².
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true or false: the graphical method can be used to solve linear programming problems with four decision variables.
False. The graphical method is only suitable for linear programming problems with two decision variables. For problems with more than two variables, programming techniques such as the simplex method are used.
Variables play a crucial role in both graphical and programming methods as they represent the unknown quantities in the problem.
True, the graphical method can be used to solve linear programming problems with four decision variables. However, it may be more challenging and less efficient compared to other methods, such as the simplex method, when dealing with a higher number of variables.
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On a snow day, Caroline created two snowmen in her backyard. Snowman A was built
to a height of 36 inches and Snowman B was built to a height of 57 inches. The next
day, the temperature increased and both snowmen began to melt. At sunrise,
Snowman A's height decrease by 3 inches per hour and Snowman B's height
decreased by 6 inches per hour. Let A represent the height of Snowman At hours
after sunrise and let B represent the height of Snowman B t hours after sunrise.
Graph each function and determine how tall each snowman is when they are the
same height.
The graph of each function is given below.
When they are the same height, the height of the snowman is 15 inches.
Initial height of snowman A = 36 inches
At sunrise, Snowman A's height decrease by 3 inches per hour.
Slope = 3
Function can be represented as.
A(t) = 36 - 3t
Initial height of snowman B = 57 inches
At sunrise, Snowman B's height decrease by 6 inches per hour.
Slope = 6
Function can be represented as.
B(t) = 57 - 6t
Graph of each function will be a line.
The height of the two snowmen will be equal after,
36 - 3t = 57 - 6t
3t = 21
t = 7 hours
Height = 36 - (3 × 7) = 15 inches
Hence the height of each snowmen is 15 inches after 7 hours.
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select the correct answer. a window maker creates a round window to be placed into a square frame. the circumference of the window is feet. the picture shows a circle inside a square. the circle touches the sides of the square. how long will each side of the square frame be? a. 4 ft b. 8 ft c. 2 ft d. 16 ft
The problem presents a scenario where a round window is to be placed into a square frame, and the circumference of the window is given.
The question asks for the length of each side of the square frame. The answer choices are 4 ft, 8 ft, 2 ft, and 16 ft.
To solve the problem, we need to know the relationship between the circumference of a circle and its diameter. The circumference is the distance around the circle, and it is equal to pi times the diameter, where pi is a constant approximately equal to 3.14. So, if we know the circumference, we can find the diameter, and from that, we can determine the length of each side of the square frame.
To find the diameter of the circle, we need to divide the circumference by pi. The circumference given in the problem is not in a numerical form, so we cannot directly compute the diameter. However, we can still determine the length of each side of the square frame by using a geometric property of a circle inscribed in a square.
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Answer:
4ft
Step-by-step explanation:
the prisoner's dilemma has all of these characteristics except group of answer choices it is a noncooperative game. there is no communication between players. there will be inferior results for both players. it is a sequential game.
The prisoner's dilemma is a classic example of a noncooperative game. This means that the players involved are not working together to achieve a common goal,
But rather competing against each other to achieve their own individual goals. The lack of cooperation means that there is no communication between the players. This lack of communication can lead to inferior results for both players. In the prisoner's dilemma, both players are incentivized to defect and betray the other player,
which ultimately leads to a worse outcome for both parties involved. The game is also a simultaneous game, meaning that both players make their decisions at the same time, rather than sequentially.
Overall, the prisoner's dilemma is a powerful demonstration of the challenges that can arise in noncooperative situations and the importance of communication and cooperation in achieving optimal outputs.
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You have seventeen identical unit regular pentagonal tiles on a tabletop. If you arrange them all into a single polyform (so each pentagon placed after the first shares a side with an already-placed pentagon, but no two pentagons overlap other than along their boundaries), what is the smallest nonzero distance you can create between two of the pentagons? give your answer rounded to seven decimal places
To minimize the distance between two adjacent pentagons. Rounded to seven decimal places, the smallest nonzero distance between two of the pentagons is approximately 1.618034.
We should arrange them in a regular dodecagon pattern with each vertex of the dodecagon touching the center of one of the pentagons. To see why this is the optimal arrangement, we can consider the fact that the regular dodecagon is the polygon with the most vertices (12) that can be inscribed in a circle. Since the pentagon has five sides, we can't fit a regular pentagon pattern into a circle without leaving some gaps between the pentagons. However, we can fit a regular dodecagon pattern without any gaps.
Since there are 12 vertices in the regular dodecagon pattern, and we have 17 pentagons, there will be 5 pentagons in the center of the pattern that are adjacent to two other pentagons. These 5 pentagons will have a distance of 0 between them.
The remaining 12 pentagons will be arranged around the perimeter of the dodecagon, with each pentagon adjacent to two others. The distance between adjacent pentagons in this arrangement can be found by dividing the circumference of the dodecagon by 12. The circumference of a regular dodecagon with side length s is: C = 12s
Since the side length of the dodecagon is equal to the distance between adjacent pentagons, we can divide the circumference by 12 to get:
[tex]s = C/12[/tex]
[tex]s = (12s)/12[/tex]
[tex]s = s[/tex]
So the distance between adjacent pentagons is equal to the side length of the regular dodecagon, which is:[tex]s = (1/2) * (1 + √5) * a[/tex]
where a is the side length of the pentagon.
Plugging in a = 1, we get:
[tex]s = (1/2) * (1 + \sqrt{5} )[/tex]
[tex]s= 1.618034[/tex]
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The value P(t), in dollars, of bank account is growing according to the equation. dP/dt - 0.05P = 15. If an initial amount of P(0) = $1,300 is deposited to the account, then the future value of this account at time t = 6 is approximately
The given differential equation is dP/dt - 0.05P = 15. Solving this first-order linear differential equation, we get P(t) = Ce^(0.05t) + 300, where C is a constant of integration. Since P(0) = 1300, we have C = 1300 - 300 = 1000. Therefore, the solution to the differential equation is P(t) = 1000e^(0.05t) + 300.
Substituting t = 6 into this expression for P(t), we find that the future value of the account at time t = 6 is approximately P(6) = 1000e^(0.05 * 6) + 300 ≈ $1,349.86.
So the future value of this account at time t = 6 is approximately $1,349.86.
a basket contains 9 blue ribbons, 7 red ribbons, and 6 white ribbons. what is the probability that three ribbons selected at random will be red?
The probability of selecting three red ribbons at random from the basket is approximately 2.27%.
In order to calculate the probability of selecting three red ribbons from a basket containing 9 blue, 7 red, and 6 white ribbons, we need to use the concept of combinations.
A combination represents the number of ways to choose items from a larger set without considering the order.
First, let's determine the total number of ways to choose 3 ribbons from the 22 ribbons in the basket (9 blue + 7 red + 6 white). This can be calculated using the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose. In this case, n = 22 and k = 3. So, C(22, 3) = 22! / (3!(22-3)!) = 22! / (3!19!) = 1540 possible combinations.
Now, let's find the number of ways to choose 3 red ribbons from the 7 red ribbons available. Using the combination formula again, C(7, 3) = 7! / (3!(7-3)!) = 7! / (3!4!) = 35 combinations.
Finally, to calculate the probability of choosing three red ribbons, we'll divide the number of ways to choose 3 red ribbons by the total number of ways to choose any 3 ribbons: Probability = 35/1540 ≈ 0.0227, or approximately 2.27%.
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A quadratic expression is shown. x^2-6x+7 Rewrite the expression by completing the square. Will give BRAINIEST
Answer:
(x-3)^2-2
Step-by-step explanation:
Answer:
To rewrite the quadratic expression x^2 - 6x + 7 by completing the square, we need to follow these steps:
Take the coefficient of the x-term, which is -6, and divide it by 2. This gives us -3.
Square the result from step 1, which gives us 9.
Add and subtract the value obtained in step 2 to the quadratic expression, like this:
x^2 - 6x + 7 + 9 - 9
Group the first three terms and the last two terms separately and factor out the common factor from the first group:
(x^2 - 6x + 9) + (7 - 9)
Simplify the terms inside the brackets:
(x - 3)^2 - 2
Therefore, the expression x^2 - 6x + 7 can be rewritten as (x - 3)^2 - 2, which is in vertex form. The vertex of the parabola represented by this quadratic expression is (3, -2).
what is the volume of this building?
Answer:
8(9)(12) + (1/2)(8)(3)(12) = 864 + 144
= 1,008 cubic feet
Find all second order partial derivatives of f(x.y) = e^-x^2y^3
The second order partial derivatives of f(x.y) = e^-x^2y^3 are
f(xx) = (-2y^3 + 4x^2y^6) e^(-x^2y^3)f(xy) = (-6xy^5 + 12x^3y^4) e^(-x^2y^3)f(yx) = (-6xy^5 + 12x^3y^4) e^(-x^2y^3)f(yy) = (-6x^2y^4 + 9x^4y^2) e^(-x^2y^3)To find the second-order partial derivatives of f(x,y) = e^(-x^2y^3), we need to differentiate the function twice with respect to each variable.
First, we find the first-order partial derivatives:
f(x) = -2xy^3 e^(-x^2y^3)
f(y) = -3x^2y^2 e^(-x^2y^3)
Now, we can differentiate these partial derivatives again to find the second-order partial derivatives:
f(xx) = (-2y^3 + 4x^2y^6) e^(-x^2y^3)
f(xy) = (-6xy^5 + 12x^3y^4) e^(-x^2y^3)
f(yx) = (-6xy^5 + 12x^3y^4) e^(-x^2y^3)
f(yy) = (-6x^2y^4 + 9x^4y^2) e^(-x^2y^3)
Therefore, the second-order partial derivatives of f(x,y) are:
f(xx) = (-2y^3 + 4x^2y^6) e^(-x^2y^3)
f(xy) = (-6xy^5 + 12x^3y^4) e^(-x^2y^3)
f(yx) = (-6xy^5 + 12x^3y^4) e^(-x^2y^3)
f(yy) = (-6x^2y^4 + 9x^4y^2) e^(-x^2y^3)
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z2 + 8z + 9 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
Answer:
Z= 0.00 or Z= -8.00
Step-by-step explanation:
Find the limit: limz+7 3: V2+2 21 O (E) O 7 O 3 09
To find the limit of the given function limz+7 3: V2+2 21 O (E) O 7 O 3 09, we need to substitute z+7 into the function and simplify it.
limz+7 3: V2+2 21 O (E) O 7 O 3 09 = limz→-7 V2+2 21 O (E) O 7 O 3 09
Now, we can simplify the function by rationalizing the numerator:
limz→-7 V2+2 21 O (E) O 7 O 3 09 = limz→-7 (V2+2 21 O (E) O 7 O 3 09) * (V2+2 21 O (E) O 7 O 3 09) / (V2+2 21 O (E) O 7 O 3 09) = limz→-7 (4z+28) / (V2+2z+49)
Now, we can substitute z=-7 into the function: limz→-7 (4z+28) / (V2+2z+49) = (4(-7)+28) / (V2+2(-7)+49) = 0 / 47
= 0
Therefore, the limit of the given function is 0.
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My teacher gave me the answer already but didn’t explain. Can someone explain why it’s 350?
Volume of the prism in cubic meters is given as 350 cm
How to solve for the volume of the cubeThe formula is given as 1 / 2 l * h * w
we have to define the variables
l = length = 5 m
h = heigt = 17. 5 m
w = width = 8 m
From the formula we have to put in the variables
1 / 2 x 5m * 17.5 m * 8m
= 1/ 2 x 700 m
= 700m / 2
= 350
Hence the volume of the prism in cubic meters is given as 350 cm
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find two values of theta in [0.2pi) such that costheta = 5/17
The two values of [tex]\theta[/tex] in [tex][0.2\pi)[/tex] such that cos([tex]\theta[/tex]) = 5/17 are approximately 0.915 radians and 0.533 radians.
To find two values of [tex]\theta[/tex] in [tex][0.2\pi)[/tex] such that [tex]cos(\theta)[/tex] = 5/17, we can use inverse trigonometric functions. Specifically, we will use the arccosine function ([tex]cos^{-1[/tex]) to solve for [tex]\theta[/tex].
First, we need to recognize that cos([tex]\theta[/tex]) = adjacent/hypotenuse. Therefore, if [tex]cos(\theta)[/tex] = 5/17, we can draw a right triangle with the adjacent side equal to 5 and the hypotenuse equal to 17.
Using the Pythagorean theorem, we can solve for the opposite side of the triangle. It turns out that the opposite side is equal to [tex]\sqrt(17^2 - 5^2)[/tex] = 16.
Now we have all three sides of the triangle and we can use trigonometry to find the two possible values of [tex]\theta[/tex]. Using the arccosine function, we can solve for the angle [tex]\theta[/tex]:
[tex]\theta[/tex] = [tex]cos^{-1}(5/17)[/tex] = 1.184 radians (rounded to three decimal places)
However, since we are looking for two values of [tex]\theta[/tex] in [tex][0.2\pi)[/tex], we need to add [tex]2\pi[/tex] to this result until we get a value within the specified range:
[tex][0.2\pi)[/tex]
This value is not within the specified range of [tex][0.2\pi)[/tex], so we subtract [tex]2\pi[/tex] until we get a value within the range:
[tex]\theta[/tex] = 7.036 - [tex]2\pi[/tex] = 0.915 radians (rounded to three decimal places)
Therefore, the first value of [tex]\theta[/tex] such that cos([tex]\theta[/tex] ) = 5/17 in [tex][0.2\pi)[/tex] is approximately 0.915 radians.
To find the second value of [tex]\theta[/tex], we need to use the symmetry of the cosine function. Since cos( [tex]\theta[/tex]) = cos(- [tex]\theta[/tex]), we can solve for the negative angle that has the same cosine value:
[tex]\theta[/tex] = -[tex]cos^{-1}(5/17)[/tex] = -1.184 radians (rounded to three decimal places)
Again, we need to add and subtract [tex]2\pi[/tex] until we get a value within the specified range:
[tex]\theta[/tex] = -1.184 + [tex]2\pi[/tex] = 5.159 radians (rounded to three decimal places)
[tex]\theta[/tex] = 5.159 - [tex]2\pi[/tex] = 0.533 radians (rounded to three decimal places)
Therefore, the second value of [tex]\theta[/tex] such that cos( [tex]\theta[/tex]) = 5/17 in [tex][0.2\pi)[/tex] is approximately 0.533 radians.
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please help it doesn’t make any sense
The matching of expressions is 3/4(24s + 8) → 18s + 6, 3(rs - 3st) → 3rs - 9st, 0.7(30 + 10s) → 21 + 7s, 27r - 3st → 3(9r - st).
To match column a to column b, we need to evaluate the expressions in column a and simplify them, and then match them with the corresponding expressions in column b.
For the first expression, we distribute the 3/4 to get 18s + 6. For the second expression, we distribute the 3 to get 3rs - 9st. For the third expression, we distribute the 0.7 and simplify to get 21 + 7s. For the fourth expression, we factor out 3 to get 3(9r - st).
After simplifying each expression in column a, we can match them with the corresponding expressions in column b. The matching is 3/4(24s + 8) → 18s + 6, 3(rs - 3st) → 3rs - 9st, 0.7(30 + 10s) → 21 + 7s, and 27r - 3st → 3(9r - st).
Therefore, the expressions in column a are evaluated, simplified, and matched with the corresponding expressions in column b to complete the matching process.
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find the standard deviation of the following data. round your answer to one decimal place. x 66 77 88 99 1010 1111 p(x=x)p(x=x) 0.10.1 0.30.3 0.10.1 0.10.1 0.10.1 0.30.3 copy data
The standard deviation of the given data is approximately 288.9
To find the standard deviation of the given data, we will use the following terms: x-values (77, 88, 99, 1010, 1111), and the corresponding probabilities P(X=x) (0.1, 0.1, 0.2, 0.2, 0.4).
First, we need to calculate the mean (µ) of the data using the formula: µ = Σ[x * P(X=x)]
µ = (77 * 0.1) + (88 * 0.1) + (99 * 0.2) + (1010 * 0.2) + (1111 * 0.4) = 975.8
Next, we'll find the variance (σ²) using the formula: σ² = Σ[(x - µ)² * P(X=x)]
σ² = ((77 - 975.8)² * 0.1) + ((88 - 975.8)² * 0.1) + ((99 - 975.8)² * 0.2) + ((1010 - 975.8)² * 0.2) + ((1111 - 975.8)² * 0.4) ≈ 83464.36
Now, to find the standard deviation (σ), take the square root of the variance:
σ = √83464.36 ≈ 288.9
So, the standard deviation of the given data is approximately 288.9 (rounded to one decimal place).
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Complete question:
Find the standard deviation of the following data. Round your answer to one decimal place.
x 77 88 99 1010 1111
P(X=x)P(X=x) 0.10.1 0.10.1 0.20.2 0.20.2 0.40.4
a worker needs to produce 1,357 bolts in a week. its thursday and he has 1,029 completed. how many does he have to make on friday?
Answer: Assuming a work week is 5 days the worker has to make 328 bolts on Friday
Step-by-step explanation:
1357-1029=328
stat please! thanks!Evaluate the integral S(2x-5) in (2x-5) 2 dx 2 dx = (2x - 5) In (2x-5) 0
The evaluation of integral (2x-5) ln(2x-5) with respect to x gives the result (x^2 - 5x + C) ln(2x-5) - ∫(x^2 - 5x + C)(2/(2x-5)) dx.
To evaluate the integral of (2x-5) ln(2x-5) with respect to x, we will use integration by parts. Integration by parts formula is ∫u dv = uv - ∫v du, where u and dv are functions of x.
Choose u and dv.
Let u = ln(2x-5) and dv = (2x-5) dx.
Find du and v.
To find du, differentiate u with respect to x: du = (1/(2x-5)) * 2 dx = (2/(2x-5)) dx.
To find v, integrate dv with respect to x: v = ∫(2x-5) dx = x^2 - 5x + C.
Apply the integration by parts formula.
∫(2x-5) ln(2x-5) dx
= uv - ∫v du
= (x^2 - 5x + C) ln(2x-5) - ∫(x^2 - 5x + C)(2/(2x-5)) dx.
The integral of (2x-5) ln(2x-5) with respect to x gives (x^2 - 5x + C) ln(2x-5) - ∫(x^2 - 5x + C)(2/(2x-5)) dx.
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Look at the picture graphs. How many fewer students walk to school in Class A than in Class B?
A picture graph is titled
Enter your answer in the box.
fewer students
There are 1 student who is fewer students walk to school in Class A than in Class B
In mathematics, a graph is a visual representation of data that displays the relationship between two variables. The two variables are typically shown on the x-axis and y-axis, respectively. Graphs are used to represent various types of data such as numerical, categorical, and qualitative data.
Now, coming to the picture graph that you are analyzing, it represents the number of students in Class A and Class B who walk to school. The graph displays the information using pictures, which are used to represent the number of students.
Therefore, to find the answer, count the number of pictures in the bar representing Class A, and count the number of pictures in the bar representing Class B. Subtract the number of pictures in Class A from the number of pictures in Class B to find the number of fewer students in Class A.
Then we get,
=> 1 - 0 = 1.
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Find t'(-4) if f(x) = 3 7x 1'(-4)=(Simplify your answer. Type an integer or a fraction.) Get more help Clear all Cleanser
The answer is -17. To find the derivative of a function, we use calculus. The derivative tells us the rate at which the function is changing at any given point. In this particular problem, we were asked to find t'(-4) if f(x) = 3x^2 + 7x + 1. We first found the derivative of f(x) using the power rule, which is a basic rule in calculus.
The power rule states that the derivative of x^n is nx^(n-1). Using this rule, we found that f'(x) = 6x + 7. To find t'(-4), we simply plugged in -4 for x in the equation for f'(x). The final answer we obtained was -17, which tells us the rate at which f(x) is changing at the point x = -4. Calculus is an important branch of mathematics that has many practical applications in fields such as physics, engineering, and economics. It allows us to understand how things change over time and how we can optimize various systems.
To find t'(-4), we need to first find the derivative of f(x).
f(x) = 3x^2 + 7x + 1
To find the derivative of f(x), we use the power rule:
f'(x) = 6x + 7
Now we can plug in -4 for x to find t'(-4):
t'(-4) = f'(-4)
t'(-4) = 6(-4) + 7
t'(-4) = -17
Therefore, the answer is -17.
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