The value of sin(2x) is -120/169 when x terminates in quadrant iii.
Since sinc(x) is negative and terminates in quadrant III, we know that sin(x) is negative and cos(x) is positive.
Let's first solve for sin(x) using the given value of sinc(x):
sinc(x) = sin(x)/x = -5/13
sin(x) = -5x/13
Using the Pythagorean identity, we can solve for cos(x):
cos(x) = sqrt(1 - sin^2(x)) = sqrt(1 - 25x^2/169)
Now we can use the double angle formula for sine:
sin(2x) = 2sin(x)cos(x) = 2(-5x/13)(sqrt(1 - 25x^2/169))
To simplify this expression, we can substitute sin(x) = -5x/13:
sin(2x) = -10x(sqrt(1 - 25x^2/169))/13
Note that x terminates in quadrant III, so it is negative. Thus, we can simplify further:
sin(2x) = 10x(sqrt(1 - 25x^2/169))/13
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What is the classification of the angle shown??
A. acute
B. right
C. straight
D. obtuse
Answer:
Acute
Step-by-step explanation:
Josiah plants vegetable seeds in rows. Each row has the same number of seeds in it. He plants more than one row of seeds. What could be the total number of seeds he plants?
The total number of seeds that Josiah would plant would be = nR×S
How to determine the total number of seeds that Josiah will plant?To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.
Let each row be represented as = nR
Where n represents the number of rows planted by him.
Let the seed be represented as = S
The total number of seeds he planted = nR×S
Therefore, the total number of seeds that was planted Josiah would be = nR×S.
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what is the weighted mean, mean, and median overall rate of return on this investment portfolio?
The weighted mean takes into account the weight of each investment and can provide a more accurate measure of the overall rate of return on the portfolio than the mean or median.
The weighted mean, mean, and median overall rate of return on this investment portfolio can be calculated using the following formulas:
Weighted Mean: Weighted mean = (R1 x W1) + (R2 x W2) + (R3 x W3) + ...
Mean: Mean = (R1 + R2 + R3 + ...) / N
Median: Median = (N + 1) / 2
where R1, R2, etc. are the returns on individual investments, W1, W2, etc. are the weights assigned to each investment, and N is the total number of investments in the portfolio.
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Type the integer that makes the following subtraction sentence true:
-57 - ? = -151
Answer:
94
Step-by-step explanation:
Its pretty simple,
The easiest way to find the missing number is to do 151-57, which = 94
Please help me
-5 x (-5)
Answer:
25x
Step-by-step explanation:
\(-5x\left(-5\right)\)
Frist Multiply the numbers: 5(-5) = -25
\(=-\left(-25\right)x\)
remove the parentheses.
=25x
Answer: 25x
Step-by-step explanation:
Brayen purchased a house that was worth $190,000. The value of the house increased by 7% each year for the next 5 years. a. The value of the house at any given moment during the first five years) is what percent of the value of the house exactly one year earlier? 1% Preview b. What number do we multiply the house's value by to determine the house's value one year later? Preview c. Write a function that determines the value of the house in thousands of dollars) in terms of the number of yearst since Taylor purchased the house, f(t) =
To determine the house's value one year later, we multiply the house's value by 1.07.
a. The value of the house at any given moment during the first five years is 107% of the value of the house exactly one year earlier. This is because the value increased by 7% each year.
b. To determine the house's value one year later, we multiply the house's value by 1.07. This is because the value increased by 7%.
c. The function that determines the value of the house in thousands of dollars in terms of the number of years since Brayen purchased the house is:
f(t) = 190(1.07)^t
where t is the number of years since Brayen purchased the house and f(t) is the value of the house in thousands of dollars.
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Factor the expression completely.
2x-5x^2
If done correctly ill give brainliest and this is a test so please help fast!
Answer:
2
−
5
2
Step-by-step explanation:
=0.3
Is x+2 a factor of the polynomial f(x)=2x^4-3x^2-4x+1?
a. f(2)=0, so (x+2) is a factor.
b. f(-2)=29, so (x+2) is not a factor.
c. f(-2)=0, so (x+2) is a factor.
d. f(2)=13, so (x+2) is not a factor.
Answer:
B
Step-by-step explanation:
the value of the x should be the same if we want to verify whether x+2 is a factor of f(x)
so if x=-2 ,f(-2) = 29
x+2=0 f(0) = 1
f(0) \(\neq\) f(-2) ,so x+2 is not a factor
what it actually means it that if we move the graphic of f(x) to left along to x axis 2 units, the graphic of new one cannot coincide with the original one.
can anyone pls help?
Answer:
Yes!!
Step-by-step explanation:
It is because -4 is smaller than 3. All negative numbers are smaller than positive ones. :)
Have an amazing day!!
Please rate and mark brainliest!!
Someone please Help me with this please
Answer:
x= 70 degrees
y= 70 degrees
z= 35 degrees
Step-by-step explanation:
What is the unit rate of 92 dollars for 2 video games
Answer:
It is $46 per video game because 92 divided by 2 is 46.
Step-by-step explanation:
one angle of a right angled triangle is 63degree .find the other angle in grades
Answer:
27°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
let the third angle be x , then
x + 90° + 63° = 180°
x + 153° = 180° ( subtract 153° from both sides )
x = 27°
Answer:
27 degrees
Step-by-step explanation:
A right angled triangle has 1 angle as 90 degree. And as you know the other angle is 63 degree, and the angle sum property of a triangle is 180 degrees. So-
Let's take 'x' as the other angle.
90 + 63 + x = 180
153 + x = 180
x = 180 - 153 = 27
x = 27 degrees
So, the other angle is 27 degrees.
All the angles of the right-angled triangle are- 90, 63, 27.
PLEASE HELP ASAP
ITS ENGLISH
The option that best narrate the main idea of the summary is option C in the image attached.
What is the main idea of a passage?The main idea is known to be a term that connote the key, or most vital, notion or idea in any given summary, paragraph or passage.
Note that it is one that tends to tell the aim and gives the direction of the paragraph or passage.
From the passage, we see that a lot of activities were going on as a result of the presence of the narrator who was held bound but was still treated well.
Therefore,The option that best narrate the main idea of the summary is option C in the image attached.
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PLEASE HELP thank you!!
find the distance between the skew lines with parametric equations x = 3 t, y = 1 6t, z = 2t, and x = 3 2s, y = 6 14s, z = −3 5s.
The distance between the skew lines is √[30625t² - 244000ts + 12864000].
What are skew lines?Skew lines are two lines in space that do not intersect and are not parallel. They are not planes, as they do not lie in a single plane.
Given,
x = 3t, y = 16t, z = 2t and x = 32s, y = 614s, z = -35s
We need to find the distance between the skew lines.
To solve this problem, we will use the formula for the distance between two skew lines.
Distance between two skew lines = √[(x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)²]
Substituting the given values in the above formula,
Distance between two skew lines = √[(3t - 32s)² + (16t - 614s)² + (2t - (-35s))²]
= √[(3t - 32s)² + (16t - 614s)² + (2t + 35s)²]
= √[9t² - 64ts + 1024s² + 256t² - 9696st + 38416s² + 4t² + 140ts + 1225s²]
= √[1225t² - 9760ts + 51456s²]
= √[(1225 x 25)t² - 9760ts + 51456 x 25]
= √[30625t² - 244000ts + 12864000]
Therefore, the distance between the skew lines is √[30625t² - 244000ts + 12864000].
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What is the probability of landing on a number greater then 5 and then landing on a number greater then 4
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating probability
\(Probability=\frac{number\text{ of required outcomes}}{number\text{ of total possible outcomes}}\)STEP 2: Find the probability of landing on a number greater than 5
\(\begin{gathered} Pr(greater\text{ than 5\rparen}=Pr(6\text{ and above\rparen} \\ Pr(greater\text{ than 5\rparen}=Pr(6)=\frac{1}{4} \end{gathered}\)STEP 3: Find the probability of landing on a number
May someone tell me if I’m correct cause I think I’m right but I need to double check with someone thanks
Answer: Proportional
Step-by-step explanation: Any table that starts with (0,0), it means it’s proportional!
Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025? a. $2,190. 75 b. $2,044. 70 c. $1,703. 92 d. $1,217. 8.
The maximum mortgage payment allowed for someone with an annual salary of $73.025 would be $2,190.75 per month, so the correct option is A.
How to determine the amount using the standard 28/36 guides?To determine, using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025, the following calculation must be made:
((73025 x 36) / 100) / 12 = XTherefore, the maximum mortgage payment allowed for someone with an annual salary of $73.025 would be $2,190.75 per month.
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Answer:a
Step-by-step explanation:
The diagrams below show two cereal boxes of different sizes and prices. (a) big box 500 g $8.00 small box 300 g $5.40 Which of the boxes is better value for money? Show your workings.
Answer: Small box has the lowest amount when divided, that box has the best value.
Step-by-step explanation:
Given data,
Big box = 500 g
It cost is $8.00
Small box = 300 g
It cost is $ 5.40
First switch the box that's in kilograms into grams.
One kilogram=1000 grams.
Then, Big box = 500 g = $ 8.00
Small box = 300 g = $ 5.40
Next divide the amount in each box by the cost of each box.
Big box = 500/8
Big box = 62.5
Small box = 300/540
Small box = 0.5555
Therefore,
So, since small box has the lowest amount when divided, that box has the best value.
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What is the equation of the line that passes through (-5, 0) and (-3, 6)?
Answer:
y = 3x + 15
Step-by-step explanation:
y = mx + b
m = (y_2 - y_1)/(x_2 - x_1) = (6 - 0)/(-3 - (-5)) = 6/2 = 3
y = 3x + b
0 = 3(-5) + b
b = 15
y = 3x + 15
Solve the equation AB=BCAB=BC for AA, assuming that A,BA,B and CC are square matrices and BB is invertible.
The equation AB=BC for \(A=BCB^{-1}\).
The solution of AB = BC for A, assuming that A,B and C are square matrices and B is invertible is
We have to solve the equation
AB = BC given that these all are square matrices and B is invertible.
Write the required Equation:
AB = BCMultiply both sides by inverse of B
The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.
Since the outcome of multiplying a matrix by an identity matrix is always the same original non-identity (non-unit) matrix, as was previously stated, the identity matrix is also known as a "unit matrix."⇒\(ABB^{-1} =BCB^{-1}\)
⇒\(AI=BCB^{-1}\)
⇒\(A=BCB^{-1}\)
Therefore, the solution of AB = BC is \(A=BCB^{-1}\).
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Which linear function represents the line given by the point-slope equation y - 8 = 1/2(x-4)?
Of(x) = x +4
Of(x) = x + 6
Of(x)=1/2x-10
Of(x)=1/2x-12
The linear function represents the line is y = 1/2x + 6
Linear functionsThese are functions that has a leading degree of 1. Given the function in slope-intercept form;
y - 8 = 1/2(x-4)
Make y the subject of the formula
y = 1/2(x - 4) + 8
Expand
y = 1/2x -4/2 + 8
y = 1/2x - 2 +8
y = 1/2x + 6
Hence the linear function represents the line is y = 1/2x + 6
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2. The following set of count readings was made in a gradient-free γ-ray field, using a suitable detector for repetitive time periods of one minute: 18,500;18,410; 18,250;18,760;18,600;18,220;18,540;18,270;18,670;18,540. (a) What is the mean value of the number of counts? (b) What is its standard deviation (S.D.)? (c) What is the theoretical minimum S.D. of the mean? (d) What is the actual S.D. of a single reading? (e) What is the theoretical minimum S.D. of a single reading?
The inflection point of f(t) is approximately t = 3.73.
(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.
Taking the derivative of f(t), we have:
f'(t) = -1.275t^2 + 9.516t + 6.741
To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:
-1.275t^2 + 9.516t + 6.741 = 0
Using the quadratic formula, we find two possible values for t:
t ≈ 0.94 and t ≈ 6.02
Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).
For t < 0.94, choose t = 0:
f'(0) = 6.741 > 0
For 0.94 < t < 6.02, choose t = 1:
f'(1) ≈ 14.982 > 0
For t > 6.02, choose t = 7:
f'(7) ≈ -5.325 < 0
From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).
(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.
Taking the second derivative of f(t), we have:
f''(t) = -2.55t + 9.516
Setting f''(t) = 0 and solving for t, we find:
-2.55t + 9.516 = 0
t ≈ 3.73
Therefore, The inflection point of f(t) is approximately t = 3.73.
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Consider the simple linear regression model: yi = β0 + β1xi + εi Show that minimizing the sum of squared residuals lead to the following least squares coefficient estimates: βˆ 0 = ¯y − βˆ 1x, ¯ βˆ 1 = Pn i=1(xi − x¯)(yi − y¯) Pn i=1(xi − x¯) 2 , where y¯ = 1 n Pn i=1 yi and x¯ = 1 n Pn i=1 xi .
The simple linear regression model is given by yi = β0 + β1xi + εi, where β0 is the intercept, β1 is the slope, xi is the predictor variable, yi is the response variable, and εi is the error term. These are the least squares coefficient estimates for the simple linear regression model.
The goal of least squares regression is to find the values of β0 and β1 that minimize the sum of the squared residuals.
To find the least squares coefficient estimates, we need to minimize the sum of the squared residuals. The residual is the difference between the observed value of yi and the predicted value of yi. The predicted value of yi is given by β0 + β1xi. Therefore, the residual can be written as yi - (β0 + β1xi).
The sum of squared residuals is given by:
Σi=1n (yi - β0 - β1xi)²
To find the values of β0 and β1 that minimize this sum, we take the partial derivatives with respect to β0 and β1 and set them equal to zero:
∂/∂β0 Σi=1n (yi - β0 - β1xi)² = 0
∂/∂β1 Σi=1n (yi - β0 - β1xi)² = 0
Solving these equations yields:
βˆ 0 = ¯y − βˆ 1x
and
βˆ 1 = Pn i=1(xi − x¯)(yi − y¯) / Pn i=1(xi − x¯)²
where y¯ = 1 n Pn i=1 yi and x¯ = 1 n Pn i=1 xi. These are the least squares coefficient estimates for the simple linear regression model.
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1. Find the slant height of a square pyramid with a surface area of 57 square feet and a base perimeter of 12 feet
Answer:
Slant height = 8 feet.
Step-by-step explanation:
If the perimeter of the square base = 12 then each side of the base = 12/4
= 3 feet and its area = 3*3 = 9 ft^2
The area of one of the triangular sides = 1/2 * 3 * h where h is slant height.
So total surface area = 57 = 9 + 4 * 1.5h
9 + 6h = 57
6h = 48
h = 8 feet.
A polynomial f and a factor of f are given. Factor f completely.
f(x) = 3x³ + 13x²+2x-8; x + 4
Answer:
(x+4)(3x-2)(x+1)
Step-by-step explanation:
PLSSS HELPP FOR 150 POINTS NO JOKE CAN EVEN SEND U 50 MORE IF U HELP
Answer:
what the other dude said
Step-by-step explanation:
a quadrilateral has 1 pair of equal sides what 2 shapes can it be
Answer: Square and rectangle
Step-by-step explanation:
Quadrilateral ABCD is reflected across the x-axis and then reflect across the y-axis to form quadrilateral A′B′C′D′. If the coordinates of vertex A are (-7, 3), what are the coordinates of vertex A′?
Someone please help me
Answer:
Slope = \(-\frac{1}{6}\)
Step-by-step explanation:
Slope = \(\frac{Rise}{Run}\)
Slope = \(\frac{6-10}{24-0}\)
Slope = \(-\frac{1}{6}\)
Answer:
-1/6
Step-by-step explanation:
Just use the formula Y2-Y1/X2-X1.
In this case if you substitute the coordinates of those numbers, then it would be 6-10/24-0 which is 24/-4 and if you simplify it, then you get the slope -1/6.