The exact value of the integral [tex]\int\limits^0_{\pi/6}[/tex] 2/cos²θ dθ is √3/3 using the Fundamental Theorem of Calculus.
To calculate the integral ∫[0 to π/6] 2/cos²θ dθ using the Fundamental Theorem of Calculus, we need to find the antiderivative of the integrand and evaluate it at the upper and lower limits of integration.
The antiderivative of 2/cos²θ is tan(θ), so applying the Fundamental Theorem of Calculus:
[tex]\int\limits^0_{\pi/6}[/tex] 2/cos²θ dθ = [tan(θ)] evaluated from θ = 0 to θ = π/6
Substituting the upper and lower limits of integration:
= tan(π/6) - tan(0)
Since tan(0) = 0, we have:
= tan(π/6)
Using the value of tan(π/6) = √3/3, the exact value of the integral is √3/3.
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The question is -
Use the Fundamental Theorem to calculate the following integral exactly:
[tex]\int\limits^0_{\pi/6}[/tex] 2/cos²∅ d∅ = _______
In physics, we can find the amount of force needed to push or pull an object by multiplying the object’s mass by the object’s acceleration. The units of force are called Newtons.
force = mass × acceleration
F = ma
Find the amount of force it takes to push Jeff’s race car if the mass of the race car is 750 kg and the acceleration is 2.5 StartFraction m Over s squared EndFraction
The amount of force needed to push Jeff’s race car is
Newtons.
ALSO I DONT KNOW IF THIS IS MATH OR SCIENCE SO IMA PUT IT AS MATH
Answer:
1875
Step-by-step explanation:
750 x 2.5 = 1,875
Which of the following is false? (No (i) |ez| = |e³|, Vz #0
The false statement among the following statements is: |ez| = |e³|. Here, e is the Euler number, and z is a complex number. Therefore, the correct answer is option (i) |ez| = |e³|.
We know that e^(ix) = cos(x) + i sin(x)
It is also known as Euler's formula, where e is the Euler number, i is the imaginary unit, x is the angle in radians. This formula connects the trigonometric functions with the exponential function. In this question, e is the Euler number, and z is a complex number. So, ez = |ez| × e^(iθ), where θ is the angle of the complex number z from the positive real axis. In the same way, e³ = |e³| × e^(i3θ)Here, the modulus of ez is |ez|, and the modulus of e³ is |e³|. It is not necessary that both will be equal because the value of θ may differ. Hence, the false statement is |ez| = |e³|.
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Pleaseee help!!!!!!!!!
the scatterplot shows the number of hours that 12 people spent learning to type on a keyboard and each persons average typing speed. Based on the scatterplot, what is the best prediction of a persons average typing speed in words per min. if the person has spent 70 hours learning to type?
Answer:
85 wpm
Step-by-step explanation:
From the scatter plot, we can see the following;
At 20 hours, average typing speed = 34 wpm
At 30 hours, the average typing speed = 40 wpm
At 40 hours, the average typing speed = 51 wpm
At 50 hours, the average typing speed = 65 wpm
Average differences = ((40 - 34) + (51 - 40) + (65 - 51))/3 = 10.3
Approximating to a whole number = 10
Now, we can approximate that at 60 hours, average typing speed = 65 + 10 = 75 wpm
At 70 hours, the average typing speed = 75 + 10 = 85 wpm
Answer:
85 wpm
Step-by-step explanation:
I took this test!
what is the 43th term of 11,16,21
for points sorry Answer:
Step-by-step explanation:
Ok So could you please tell me where I went wrong?
Answer:
lateral surface area =perimeter of base×height=
={4+7+7+11)×6=174 km²
Step-by-step explanation:
Computer world has all computer has all computers on sale for 20% off. If the regular price of a laptop is $750, what is the sale price?
Answer:
Selling price of the laptop is $600.
Step-by-step explanation:
Let the sale price of the laptop = $x
Regular price of the laptop = $750
Discount on each computer = 20%
Selling price of the laptop 'x' = 750 - (20% of 750)
= 750 - [tex](\frac{20}{100}\times 750)[/tex]
= 750 - 150
= $600
Therefore, selling price of the laptop is $600.
This tutorial will show you how to do an independent samples t test in SPSS and how to
interpret the result.
Steps
1. Independent-Samples T Test Compare Means 1. Click on Analyze
2. Drag and drop the dependent variable into the Test Variable(s) box, and the grouping
variable into the Grouping Variable box
3. Click on Define Groups, and input the values that define each of the groups that make
up the grouping variable (i.e., the coded value for Group 1 and the coded value for
Group 2)
4. Click Continue, and then click on OK to run the test
5. The result will appear in the SPSS data viewer
This tutorial provides step-by-step instructions on how to perform an independent samples t-test in SPSS and interpret the results.
The tutorial outlines the following steps to conduct an independent samples t-test in SPSS:
Access the Analyze menu.
Select "Compare Means" and then "Independent-Samples T Test."
Drag and drop the dependent variable into the "Test Variable(s)" box and the grouping variable into the "Grouping Variable" box.
Define the groups by clicking on "Define Groups" and inputting the coded values that represent each group.
Click "Continue" and then "OK" to run the test.
The results will be displayed in the SPSS data viewer.
By following these steps, users can conduct an independent samples t-test to compare means between two groups and assess whether there is a statistically significant difference. The result provides information such as the t-value, degrees of freedom, and p-value, which is used to interpret the significance of the difference between the means of the two groups. Researchers can then make conclusions based on the statistical findings from the independent samples t-test.
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Which of the following sets of vectors in R3 are linearly de- pendent? (a) (4, -1,2). (-4, 10, 2) (b) (-3.0.4). (5. -1,2), (1,1.3) (c) (8,-1,3), (4,0,1) (d) (-2, 0, 1), (3, 2, 5), (6.-1.1), (7,0, -2) 11 ofrector in p4 are linear de
The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R3 are linearly independent.
Let's review the given sets of vectors in R₃ to determine which ones are linearly dependent.
(a) (4.-1,2), (-4, 10, 2).
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(4,-1,2) + b(-4,10,2) = (0,0,0).
The system of equations can be written as;
4a - 4b = 0-1a + 10b = 00a + 2b = 0.
Clearly, a = b = 0 is the only solution.
So, the set is linearly independent.
(b) (-3,0,4), (5,-1,2), (1, 1,3)
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(-3,0,4) + b(5,-1,2) + c(1,1,3) = (0,0,0).
The system of equations can be written as;
-3a + 5b + c = 00a - b + c = 00a + 2b + 3c = 0
Clearly, a = 2, b = 1, and c = -2 is a solution.
So, the set is linearly dependent.
(c) (8.-1.3). (4,0,1).
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(8,-1,3) + b(4,0,1) = (0,0,0).
The system of equations can be written as;
8a + 4b = 01a + 0b = 0-3a + b = 0.
Clearly, a = b = 0 is the only solution.
So, the set is linearly independent.
(d) (-2.0, 1), (3, 2, 5), (6,-1, 1), (7,0.-2).
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(-2,0,1) + b(3,2,5) + c(6,-1,1) + d(7,0,-2) = (0,0,0)
The system of equations can be written as;
-2a + 3b + 6c + 7d = 00a + 2b - c = 00a + 5b + c - 2d = 0
Clearly, a = b = c = d = 0 is the only solution.
So, the set is linearly independent.
Therefore, The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R₃ are linearly independent.
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the ratio of the angle measures in a triangle is 2:3:10 . what is the measure of each angle?
The measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.
Let's denote the three angles of the triangle as A, B, and C. According to the given ratio of 2:3:10, we can assign the values 2x, 3x, and 10x to angles A, B, and C, respectively, where x is a common factor.
The sum of the angle measures in a triangle is always 180 degrees. Therefore, we can set up the following equation:
2x + 3x + 10x = 180
Simplifying the equation, we get:
15x = 180
Dividing both sides by 15, we find:
x = 12
Now we can substitute x back into the expressions for each angle:
Angle A = 2x = 2(12) = 24 degrees
Angle B = 3x = 3(12) = 36 degrees
Angle C = 10x = 10(12) = 120 degrees
Therefore, the measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.
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A rectangle has a width of 3 cam and a length of 9cm. the rectangle is to be enlarged by a scale factor of 8 what is the length of the enlargement. (include units)
Answer:
72 cm
Step-by-step explanation:
It would be multiplied by 8 so the length would become 72 cm
The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.8 grams with a standard deviation of 0.17 grams. For parts (a) through (c), enter your responses as a decimal with 4 decimal places. a) What is the probability that a randomly chosen mouse has a mass of less than 20.7 grams? b) What is the probability that a randomly chosen mouse has a mass of more than 21.02 grams? c What proportion of mice have a mass between 20.65 and 20.95 grams? d) 10% of all mice have a mass of less than grams.
a. Using the z-score, the probability of a randomly chosen mouse having a mass of less than 20.7 grams is approximately 0.2794.
b. The probability that a randomly chosen mouse has a mass more than 21.02g is 0.0985
c. The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.
d. About 10% of all mice have a mass of less than 20.5649 grams.
What is the probability that a randomly chosen mouse has a mass of less than 20.7g?a) To find the probability that a randomly chosen mouse has a mass of less than 20.7 grams, we can use the normal distribution.
First, we need to standardize the value of 20.7 grams using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
The z-score for the data is;
z = (20.7 - 20.8) / 0.17 = -0.5882
P = 0.2794
b) To find the probability that a randomly chosen mouse has a mass of more than 21.02 grams, we also need to standardize the value:
z = (21.02 - 20.8) / 0.17 = 1.2941
P = 0.0985
Using the standard normal distribution table or a calculator, we find that the probability corresponding to this z-value is approximately 0.0985.
c) To find the proportion of mice that have a mass between 20.65 and 20.95 grams, we can standardize both values:
For 20.65 grams:
z₁ = (20.65 - 20.8) / 0.17 = -0.8824
For 20.95 grams:
z₂ = (20.95 - 20.8) / 0.17 = 0.8824
Using the standard normal distribution table or a calculator, we can find the probabilities corresponding to these z-values. The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.
d) To find the mass of mice that corresponds to the 10th percentile, we need to find the z-score associated with the 10th percentile. We can use the standard normal distribution table or a calculator to find this value.
The z-score associated with the 10th percentile is approximately -1.2816.
Next, we can use the z-score formula to find the corresponding mass value:
z = (x - μ) / σ
-1.2816 = (x - 20.8) / 0.17
Solving for x, we get:
x = -1.2816 * 0.17 + 20.8 ≈ 20.5649 grams
Therefore, 10% of all mice have a mass of less than 20.5649 grams.
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Can someone help me with this. Will Mark brainliest. Need answer and explanation/work. Thank you.
Answer:
[tex]14/50\\[/tex]
Step-by-step explanation:
The equation for sine is sine = opposite/ hypotenuse
The opposite of W is 14 and the hypotenuse the the side across the 90° angle, which is 50.
So, when you set up the equation it should be [tex]14/50[/tex].
(x2-1)dy/dx+2y=(x+1)4 (integrating factor)
The integrating factor for the given differential equation is |x^2 - 1|.
To find the integrating factor for the given differential equation, we start by rearranging the equation in the form:
dy/dx + (2y)/(x^2 - 1) = (4(x + 1))/(x^2 - 1)
The integrating factor (IF) is given by the exponential of the integral of the coefficient of y, which in this case is (2/(x^2 - 1)). Therefore, the integrating factor IF is:
IF = exp ∫ (2/(x^2 - 1)) dx
To evaluate this integral, we can use a substitution. Let u = x^2 - 1, then du = 2x dx. Substituting this back into the integral, we get:
IF = exp ∫ (1/u) du = exp(ln|u|) = |u|
Since u = x^2 - 1, we have:
IF = |x^2 - 1|
Therefore, the integrating factor for the given differential equation is |x^2 - 1|.
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A reporter surveyed 300 randomly selected people of all ages about their opinion of a new song. The results are shown in the table. Which of the following is a valid conclusion about data? select all that apply.
Answer:
the answers is A and E <3
Step-by-step explanation:
i took this test
please help quickly!
Answer:
answer I have no clue sorry dude
a simple random sample of 800 elements generates a sample proportion p= 0.77 ( round awsners to 4 decimal places)
a) provide a 90% confidence interval for the population proportion
b) provide a 95% confidence interval for the population proportion
The 95% confidence interval for the population proportion is approximately (0.7465, 0.7935).
(a) To calculate a 90% confidence interval for the population proportion, we can use the formula:
Confidence Interval = sample proportion ± z * sqrt((sample proportion * (1 - sample proportion)) / sample size)
Given that the sample proportion is p = 0.77 and the sample size is n = 800, we need to find the critical value, z, corresponding to a 90% confidence level.
Using a standard normal distribution table or a statistical software, the critical value for a 90% confidence level is approximately 1.645.
Substituting these values into the formula, we have:
Confidence Interval = 0.77 ± 1.645 * sqrt((0.77 * (1 - 0.77)) / 800)
Calculating the confidence interval, we get:
Confidence Interval = 0.77 ± 0.0191
Therefore, the 90% confidence interval for the population proportion is approximately (0.7509, 0.7891).
(b) Similarly, to calculate a 95% confidence interval, we need to find the critical value corresponding to a 95% confidence level. The critical value is approximately 1.96 for a 95% confidence level.
Using the same formula and substituting the values, we have:
Confidence Interval = 0.77 ± 1.96 * sqrt((0.77 * (1 - 0.77)) / 800)
Calculating the confidence interval, we get:
Confidence Interval = 0.77 ± 0.0235
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Can someone help me solve these equations?
1. 2y^2+5Y+2 |
2. 5x^2-18x+9 |
3. 16b^2+60b-100 | 4.-6a^2-25a-25 |
5. 49x^2-14x+1 |
6. 81x^2-49
This is the equation: f(x)=x^2
e) Is f(x) symmetric? If so, what is the equation of the line of symmetry?
f) Does f(x) have a maximum or minimum? If so, at what point?
g) What are the x-intercept(s) of f(x)?
Answer:
e) yes, symmetric around the y-axis
f) minimum at (0,0)
g) x-intercept at 0
Step-by-step explanation:
what is the value of A and B (5x + b)(5x - b) = ax^2 - 49
Answer:
a=25
b=7
Step-by-step explanation:
complete the square to rewrite the following equation in standard form
By completing the square, the equation in standard form is (x - 2)² + (y + 4)² = 4².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.From the information provided below, we have the following equation of a circle:
x² - 4x + y² + 8y = -4
x² - 4x + (-4/2)² + y² + 8y + (8/2)² = -4 + (-4/2)² + (8/2)²
x² - 4x + 4 + y² + 8y + 16 = -4 + 4 + 16
(x - 2)² + (y + 4)² = 16
(x - 2)² + (y + 4)² = 4²
Therefore, the center (h, k) is (2, -4) and the radius is equal to 4 units.
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Complete Question:
Complete the square to rewrite the following equation in standard form. x² - 4x + y² + 8y = -4.
Joseph orders some pizza for himself and his friends. The cost of each pizza is £12.50, and the delivery charge is £1.50. If Joseph orders 11 pizzas, how much does Joseph pay in total?
Answer:
£139
Step-by-step explanation:
£12.50 * 11 = 137.50
137.50 + 1.50 = £139
Answer:
137.5 + 1.50 = £139
Step-by-step explanation:
Please Give brainliest
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
2/11
Step-by-step explanation:
Let's say x = 0.18181818..
Then, 100x = 18.1818181....
so, if you put x in the repeating decimal in 18.1818,
you get the equation,
100x = 18+x
so, 99x = 18
x = 18/99 = 2/11
Answer:
18/100 = 9/50
Answer is 9/50
Do you really think you’re going to give me brainliest lol
2) The equation y = 18x represents the relationship between 2, the number of hours biked, and
y, the distance traveled,
Which ordered pairs represent a number of hours and the corresponding
distance in the given equation? Choose ALL that apply.
(2,36)
(3,54)
(5,23)
(23,5)
(36,2)
(54,3)
Answer:(2,36)and (3,54)
Step-by-step explanation:
Answer:
(2, 36) and (3, 54)
Step-by-step explanation:
I just answer the question from iready and I got it correct.
HELPL ME QUICK I STUCK
Answer:
red = 28 apples
green = 13 apples
equations:
r + g = 41
r = g + 15
Step-by-step explanation:
r = number of red
g = number of green
r = g + 15 (the number of red apples is 15 more than the number of green apples)
r + g = 41
Substitute the first equation into the second and solve for a numerical value of g
(g + 15) + g = 41
2g + 15 = 41
2g = 26
g = 13
Now solve for a numerical value of r
r = g + 15
r = 13 + 15
r = 28
checking the math:
r + g = 41
28 + 13 = 41
Please lmk if you have any questions.
PROVING THEOREMS OF SQUAD can someone help me pleasee ASAP
Answer:
40 units
Step-by-step explanation:
For a square, all the sides are equal and the interior angles are equal and all equal to 90. Hence;
m<BOJ = 90 degrees
m<BOJ = 4x - 6
Equating both to get x;
4x - 6 = 90
4x = 90+6
4x = 96
x = 96/4
x = 24
Since all the sides are equal, hence BO = JO = 2x-8
JO = 2x - 8
Substitute x = 24 into JO
JO = 2(24) - 8
JO = 48 - 8
JO = 40
Hence the measure of JO is 40 units
ANSWER ISN'T DECIMALS ANSWER ASAP!
Answer:
972 cubic feet
Step-by-step explanation:
12 by 9 by 7.5
+
1.5 by 9 by 12
Answer:
891 ft³
Step-by-step explanation:
First I'll find the volume of the rectangular prism. (l * w * h)
12 * 9 * 7.5
Multiply 12 by 9 to get 108.
108 * 7.5
Now, multiply 108 by 7.5 to get 810. (756 + 54 = 810)
810
Now for the triangular prism. (1/2(l * w * h))
1/2(12 * 9 * 1.5) (I figured the height was 1.5 since the height of the rectangular prism was 7.5; the entire figure's height was 9)
Multiply 12 by 9 to get 108.
1/2(108 * 1.5)
Multiply 108 by 1.5 to get 162. (108 + 54 = 162)
1/2(162)
Multiply 162 by 1/2 to get 81. (162/2)
81
Now add that to 810 to get 891.
810 + 81
891 ft³
The volume of the garage is 891 ft³.
A right cylinder has a radius of 5 and a height of 9. What is its surface area? A. 457 units2 B. 1407 units2 C. 907 units? D. 700 units2
Answer: B
The surface area of the right cylinder is 140π cubic units or 439.60 cubic units.
Step-by-step explanation:
We have formula to find the surface area of a right cylinder.
Surface area = 2πr(h + r)
Given: r = 5 and h = 9,
Now plug in the value of r and h in the above formula, we get
Surface area = 2π.5 (9 + 5)
= 10π(14)
Surface area = 140π
The value of π = 3.14, when we plug in the value of π, we get
The surface area = 140 × 3.14
= 439.60 cubic units.
Therefore, the surface area of the right cylinder is 140π cubic units or 439.60 cubic units.
Hope this helped!!!
Define a relation Ron R by for a,beR (a,b) e Rif and only if a-bez Which of the following properties does have? Reflexive Symmetric Antisymmetric Transitive
In summary:
The relation R is reflexive. The relation R is not symmetric. The relation R is antisymmetric. The relation R is transitive.
Let's analyze the properties of the relation R:
Reflexive:
A relation R is reflexive if every element in the set is related to itself. In this case, we need to check if (a, a) belongs to R for every a in the set.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
Since a - a = 0, (a, a) satisfies the condition and is in R for every a in the set. Therefore, the relation R is reflexive.
Symmetric:
A relation R is symmetric if for every (a, b) belongs to R, (b, a) must also be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
However, if a - b = 0, it does not imply that b - a = 0. Therefore, the relation R is not symmetric.
Antisymmetric:
A relation R is antisymmetric if for every distinct (a, b) belongs to R, (b, a) cannot be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
Since a - b = 0 implies b - a = 0, it means that if (a, b) and (b, a) are in R, then a must be equal to b. Thus, for distinct elements a and b, it is not possible for both (a, b) and (b, a) to be in R. Therefore, the relation R is antisymmetric.
Transitive:
A relation R is transitive if for every (a, b) and (b, c) belongs to R, (a, c) must also be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
If a - b = 0 and b - c = 0, it implies that a - c = 0. Therefore, if (a, b) and (b, c) are in R, then (a, c) is also in R. Thus, the relation R is transitive.
In summary:
The relation R is reflexive.
The relation R is not symmetric.
The relation R is antisymmetric.
The relation R is transitive.
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Find the factor form for each problem. (Show work)
1. 12x²+8x
2. 2x²-16x
Step-by-step explanation:
12x^2 + 8x
4x ( 3x + 2)
2x^2 - 16x
2x ( x - 8)