7.4 x 10^-8 - 6.7 x 10^-9 =

The value of opposite side of angle θ would be,

⇒ EF

Since, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that,

A right triangle EFD is shown in figure.

And, At angle E, right angle is shown.

We know that;

The Opposite side of a angle is called perpendicular side.

Hence, The value of opposite side of angle θ would be,

⇒ EF

Thus, Option A is true.

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Answer:

x<2

Step-by-step explanation:

Answer:

The answer you selected is correct.

Step-by-step explanation:

Converse of corresponding angles theorem:

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

The correct label is ∠CBA.

The correct label for the angle formed by rays BC and BA is ∠CBA. When  Angles labeling , it is important to consider the vertex of the angle, which is the point where the two rays meet. The vertex is usually labeled with a capital letter, and the angle itself is labeled with three letters, with the vertex letter in the middle. In this case, the vertex is at point B, and the two rays are BC and BA. Therefore, the angle is labeled as ∠CBA. It is important to use the correct labeling when communicating about angles in mathematics, as it ensures clarity and accuracy in solving problems and expressing ideas.

The correct label for the angle formed by rays BC and BA is ∠CBA.

Therefore, in this case, the correct label for the angle formed by rays BC and BA is ∠CBA.

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Answer:

The answer is <CBA

Step-by-step explanation:

Bc if the vertex is on "b" its going to be {bc} and {ba}. and sinces the vertex is in the middle in the image so should the letter. So its <CBA.

hope this helps

The lower quartile is 13 (in minutes ) and the upper quartile is 27(in minutes) for the data collected by Ashley on number of minutes students ride the bus before getting to school.

Ashley has collected data on the number of minutes students ride the bus before getting to school as,

10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32

There are three types of quartile in data set as, first (or lower) quartile, second quartile (or median), and third (or upper) quartile.

The formula to calculate quartiles for ungrouped data are as follow,

Lower (or first) quartile = {(n +1)4} th term

where, n is the total number of observations in the data set, that is n = 11

Therefore, Lower (or first) quartile = {(11 +1)4} th term

= (3)rd term = 13

Therefore, Upper (or third ) quartile = {3(n +1)/4} th term

= { 3(11+ 1)/4} th term

= 9th term = 27

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The given question is incomplete, the complete question is

"Already Ashley collects data on the number of minutes students ride the bus before getting to school.

10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32

What is the lower and upper quartile."

The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

What is Standard Deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; Hence, the higher the standard deviation, the more dispersed the data.

We know that:

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

where \(x_{i}\)  is the mean and n is the number of observations.

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

98% Confidence interval:  

\(\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}\)

Putting the values, we get,  

\(t_{\text {critical }} \alpha_{0.02}\\=\pm 2.14535.07 \pm 2.145\left(\frac{6.02}{\sqrt{15}}\right)\\=35.07 \pm 3.33\\=(31.74,38.4)\)

Hence, The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

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Answer:

I am 100% sure its 4.03 x 10^7

Step-by-step explanation:

Answer: 1st 173 2nd 396

Step-by-step explanation: I hope this helps!

Answer:

180

Step-by-step explanation:

2:5

? : 450

5u-> 450

1u->90

2u-> 180

Answer:

72 cm²

Step-by-step explanation:

Given the ratio of diameters = a : b , then

ratio of areas = a² : b²

Here the ratio of diameters = 2 : 5 , then

ratio of areas = 2² : 5² = 4 : 25

let x be the area of smaller circle then using proportion

\(\frac{25}{450}\) = \(\frac{4}{x}\) ( cross- multiply )

25x = 1800 ( divide by 25 )

x = 72

That is the area of the smaller circle is 72 cm²

Explanation

The question wants us to determine the domain of the function graphed

The domain of a function is the set of all possible inputs for the function

From the graph, we can observe that the x-values span from negative infinity to positive infinity

Thus

Thus

The domain is All Real Numbers

Answer:

The square root of 12 is 3.46

Answer:3.4641

How? Google

The integration is (1/4)x sin 4x + (1/16)cos 4x + C.

To evaluate the integral ∫ x cos 4x dx using integration by parts, we need to use the formula ∫u dv = uv - ∫v du. We are given that u = x and dv = cos 4x dx. Now, we need to find v and du.

To find v, we need to integrate dv. So, v = ∫cos 4x dx = (1/4)sin 4x + C.

To find du, we need to differentiate u. So, du = dx.

Now, we can plug in the values of u, v, du, and dv into the formula and simplify:

∫ x cos 4x dx = x(1/4)sin 4x - ∫(1/4)sin 4x dx

= (1/4)x sin 4x - (1/4)∫sin 4x dx

= (1/4)x sin 4x - (1/4)(-1/4)cos 4x + C

= (1/4)x sin 4x + (1/16)cos 4x + C

So, the final answer is (1/4)x sin 4x + (1/16)cos 4x + C.

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We can use the initial condition y(0) = -3 to solve for the constant C. Plugging in t = 0 and y = -3 into the above equation.

To solve the given differential equation, we can use the method of integrating factor.

The given differential equation is: dy/dt - 2ty = \(12t^2\times e^(t^2)\)

First, we identify the integrating factor (IF), which is given by the exponential of the integral of the coefficient of y. In this case, the coefficient of y is -2t, so we integrate -2t with respect to t:

IF = e^∫(-2t)dt

IF = e^(-t^2)

Next, we multiply the entire differential equation by the integrating factor:

\(e^(-t^2)\times (dy/dt - 2ty) = e^(-t^2) \times 12t^2\times e^(t^2)\)

This simplifies to:

\(e^(-t^2) \times dy/dt - 2ty \times e^(-t^2) = 12t^2\)

Now, we can integrate both sides of the equation with respect to t. Integrating the left-hand side (LHS) requires integration by parts, while the right-hand side (RHS) can be integrated directly:

∫(e^(-\(t^2\)) \(\times\) dy/dt) dt - ∫(2ty \(\times\) e^(-\(t^2\))) dt = ∫(12\(t^2\)) dt

Using integration by parts on the LHS with u = e^(-\(t^2\)) and dv = dy/dt dt, we get:

e^(-\(t^2\)) \(\times\)y - ∫(e^(-\(t^2\)) \(\times\) y') dt - ∫(2ty \(\times\) e^(-\(t^2\))) dt = 12\(t^3\) / 3 + C

where C is the constant of integration.

Rearranging the equation and simplifying, we get:

e^(-\(t^2\)) \(\times\) y - ∫(e^(-\(t^2\)) \(\times\) y') dt - 2∫(ty \(\times\) e^(-\(t^2\))) dt = 4\(t^3\) + C

Now, we can integrate the remaining integrals. For the second term on the left-hand side, we use u = t and dv = y \(\times\) e^(-\(t^2\)) dt, and for the third term on the left-hand side, we use u = y and dv = t \(\times\) e^(-\(t^2\)) dt. This gives us:

e^(-\(t^2\)) \(\times\) y - (y \(\times\) e^(-\(t^2\))) - (e^(-\(t^2\))\(\times\) t \(\times\) y) = 4\(t^3\) + C

Combining like terms and multiplying both sides by e^(t^2) to eliminate the exponential factor, we get:

y - y \(\times\) e^(-\(t^2\)) - t \(\times\) y = 4\(t^3\) \(\times\) e^(\(t^2\)) + C \(\times\) e^(\(t^2\))

Factoring out y on the left-hand side and simplifying, we get:

y \(\times\) (1 - e^(-\(t^2\)) - t) = 4t^3 \(\times\)e^(\(t^2\)) + C \(\times\)e^(\(t^2\))

Finally, dividing both sides by (1 - e^(-\(t^2\)) - t) to isolate y, we get:

y(t) = (4\(t^3\) \(\times\) e^(\(t^2\)) + C \(\times\) e^(\(t^2\))) / (1 - e^(-\(t^2\)) - t)

Now, we can use the initial condition y(0) = -3 to solve for the constant C. Plugging in t = 0 and y = -3 into the above equation.

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3 -> 1

6 -> 3 -> 1

4 -> 2 -> 1

i don't know

Answer:

y= 10/11x + 67/11

Step-by-step explanation:

Just follow the slope-intercept form formula-

Formula: y=mx+b

Key:

y = y-coordinate

m = slope

x = x-coordinate

b = y-intercept

Let me know if you have any questions, hope this helps! (:

Answer:

Around 12.25

Step-by-step explanation:

There are around 2205 (2204.62) lbs  per metric tonnes.

So 27000/2204.62  or 27000/2205 gives you between 12.24-12.25

100 ml of the first solution and 200 ml of the second are required.

a. The total distance traveled by the object between times \(\( t = 0 \) and \( t = 5 \)\) is 32 feet. b. The object is accelerating from \(\( t = 0 \) to \( t = 3 \)\)  and decelerating from \(\( t = 3 \) to \( t = 5 \).\)

a. To find the total distance traveled by the object, we need to consider both the positive and negative displacements. We calculate the displacement by subtracting the initial position from the final position. In this case\(, \( s(0) = 15 \) feet and \( s(5) = 65 \)\)feet. Therefore, the displacement is\(\( 65 - 15 = 50 \)\) feet. Since the object changes direction at \(\( t = 3 \),\) we need to consider the absolute value of the displacement. Hence, the total distance traveled is\(\( |50| = 50 \)\) feet.

b. The acceleration of the object is given by the second derivative of the position function, \(\( a(t) = s''(t) \).\) We find the second derivative by differentiating the position function twice.\(\( a(t) = 6t - 18 \).\)To determine when the object is accelerating or decelerating, we examine the sign of the acceleration function. The object is accelerating when \(\( a(t) > 0 \)\)and decelerating when\(\( a(t) < 0 \).\) For the given time interval, from \(\( t = 0 \) to \( t = 5 \),\) the object is accelerating from \(\( t = 0 \) to \( t = 3 \)\) and decelerating from \(\( t = 3 \) to \( t = 5 \).\)

Therefore, the total distance traveled is 32 feet and the object is accelerating from \(\( t = 0 \) to \( t = 3 \)\)and decelerating from \(\( t = 3 \) to \( t = 5 \).\)

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Answer:

the third one

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

The experimental probability that of 5 students, at least 3 will make a C is approximately 0.68256 or 68.256%.

To find the experimental probability that of 5 students, at least 3 will make a C using the given random-number table, we can use:

Count the number of digits that represent students who make a C, which is 6 out of 10 digits.

Determine the probability of a single student making a C, which is 60% or 0.6.

Use the binomial probability formula to calculate the probability of getting at least 3 students who make a C out of 5 students:

P(X ≥ 3) = 1 - P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = C(5,0) * 0.6^0 * 0.4^5 + C(5,1) * 0.6^1 * 0.4^4 + C(5,2) * 0.6^2 * 0.4^3

P(X < 3) = 0.01024 + 0.07680 + 0.23040

P(X < 3) = 0.31744

P(X ≥ 3) = 1 - P(X < 3)

P(X ≥ 3) = 1 - 0.31744

P(X ≥ 3) = 0.68256

Therefore, the experimental probability that of 5 students, at least 3 will make a C is approximately 0.68256 or 68.256%.

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Answer:

C

Step-by-step explanation:

Answer:

b= a

60

Step-by-step explanation:

In constructing 95% confidence intervals for the difference in means, we expect that, over the long run, the correct answer will be option A, i.e., % of the time, the difference in population means will fall inside the confidence interval.

Confidence intervals are a statistical tool used to estimate population parameters based on sample data. In constructing a 95% confidence interval, we expect that in 95% of all possible samples, the true population parameter will fall within the calculated interval. In other words, if we were to repeat the sampling process many times and construct a confidence interval for each sample, we would expect that about 95% of these intervals would contain the true population parameter. Therefore, we can say that there is a 95% probability that the true population parameter lies within the calculated interval. For the difference in means, this means that there is a 95% chance that the true difference in population means falls within the confidence interval, and only a 5% chance that it falls outside the interval.

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Answer: R0, 90°, (x, y) → (–y, x)

Step-by-step explanation:

If we consider Y(0,-2) mapping onto Y(2,0), we know that this was a rotation 90 degrees about the origin.

Answer:

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example

You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).

Step-by-step explanation:

Answer: The answer is A.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Partial derivative with respect to\(X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ\)

Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)

The first partial derivatives of the function F(X,Y) = X2Y - 3Y2 + X/(X + Y)2 + XY2e-XZ can be found by taking the partial derivative with respect to each of the variables X and Y separately.
For the partial derivative with respect to X, we have:
Partial derivative with respect to X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ
For the partial derivative with respect to Y, we have:
Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)
This completes the calculation of the first partial derivatives of the function F(X,Y).
The first partial derivatives of the functions are given below:

\(F(x, y) = x^2y - 3y^2\)

The first partial derivative with respect to x,

Fx (x, y) = 2xy

The first partial derivative with respect to y,\(Fy (x, y) = x^2 - 6yW = xy^2 e^-xz\)

The first partial derivative with respect to x,

\(Wx (x, y, z) = y^2e^-xz - x^2y^2e^-xz\)

The first partial derivative with respect to y, Wy (x, y, z) = 2xye^-xz

The first partial derivative with respect to z, \(Wz (x, y, z) = -xy^2e^-xz\)

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The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.

What is a function ?

Function can be defined as which relates an input to output.

Given,

Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms.

Height = b

Volume V = 6³-6b²+9b.

Length of each side (s) :

V = 6³-6b²+9b.

s^2 b  = b (b^2 - 6b + 9 )

s^2 = b^2 - 6b + 9

(a - b ) ^2 = a^2 + b^2 -2ab

s^2 = (b-3) ^2

s = b-3

height is 18 inches and height is given as b

Hence, b = 18

s= b-3 (from i)

= 18 - 3

s = 15

Therefore volume:

volume of rectangle = l x b x h

V= 18 x15 x15= 4,050

(If height = 15

then, b = 15

b -15 = 0

Definition of remainder theorem:

we divide a polynomial P(x) by a factor ( x – a); to find a smaller polynomial along with a remainder. The factor doesn't have to be a part of the polynomial.

b^3 - 6b^2 + 9b  /  b-15  = 2160

Therefore Volume with b = 15 is 2160

Therefore, The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.

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Answer:6

Step-by-step explanation:

Answer: no they are not

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

KM=11-7=4

if parallel, KM/KJ=LN/LJ

substituting:

4/11 is not equal to 3/8

From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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