What is the volume of the prism below

The expression that is equivalent to √17 is √(68)/2

From the question, we have the following parameters that can be used in our computation:

Expression = √17

Multiply the expression by 1

so, we have the following representation

Expression = √17 * 1

Express 1 as 2/2

so, we have the following representation

Expression = √17 * 2/2

The square root of 4 is 2

So, we have

Expression = √(17 * 4)/2

Evaluate the products

Expression = √(68)/2

Hence, the expression that is equivalent to √17 is √(68)/2

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The diffusion time of the red blood cell to take oxygen through the membrane is 25uS.

The small capillaries in the lungs are in close contact and it takes a red blood cell 0.5 seconds to squeeze through the capillary.

The diffusion time for the oxygen across the 1 um thick membrane separating the air is given by,

t = x²/2D

Where,

t is the diffusion time,

x is the thickness of the membrane,

D is the diffusion coefficient.

Putting values,

t = (1 x 10⁻⁹)²/2 x 2 x 10⁻¹¹

t = 10⁻⁷/4

t = 25 x 10⁻⁹ seconds.

t = 25 uS.

so, the diffusion time is 25uS.

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Answer:

C. ΔGTA ≅ ΔQME

good luck, i hope this helps :)

Answer:

square root of 25

Step-by-step explanation:

Answer:

Square foot of 25

Step-by-step explanation:

I took the test and got it right!

Answer:

4 x X = y

Step-by-step explanation:

x = the amount of weeks

y = the amount you save

4 times the amount of weeks you put $4 in equals the amount of money you saved.

Answer:

It's just a simultaneous equation

Step-by-step explanation:

Let a big bag of sugar = x

Let a small bag of flour = y

x+x+y = 12kg

2x+y = 12kg ... 1

x-y = 2kg ... 2

Add 1 and 2

2x+y = 12

+

x -y = 2

3x = 14

x = 14/3 = 4.66

Substitute value of x into 1

2(4.66)+y = 12

9.333 + y = 12

12 - 9.333= 12

y = 2.66

Hope you understand it

And I hope my answer was of help to you.

Step-by-step explanation:

ax2+2x3−24x+1=y

Step 2: Add -2x^3 to both sides.

ax2+2x3−24x+1+−2x3=y+−2x3

ax2−24x+1=−2x3+y

Step 3: Add 24x to both sides.

ax2−24x+1+24x=−2x3+y+24x

ax2+1=−2x3+24x+y

Step 4: Add -1 to both sides.

ax2+1+−1=−2x3+24x+y+−1

ax2=−2x3+24x+y−1

Step 5: Divide both sides by x^2.

ax2

x2

=

−2x3+24x+y−1

x2

a=

−2x3+24x+y−1

x2

Answer:

a=

−2x3+24x+y−1

x2

The expected number of times that they will end up flipping the coin \(\boxed{N}$.\)

Let P be the probability that Alpha goes bankrupt before either player reaches 2N dollars. We can calculate this probability using a recursive approach. Let p_i be the probability that Alpha goes bankrupt given that Alpha has i dollars and Beta has 2N-i dollars. Then we have:

\($p_i = \frac{1}{2}p_{i-1} + \frac{1}{2}p_{i+1}$\)

The first term represents the probability that Alpha loses the next flip and ends up with i-1 dollars, while the second term represents the probability that Alpha wins the next flip and ends up with i+1 dollars. The boundary conditions are\(p_0 = 1\) (Alpha is already bankrupt) and \($p_{2N} = 0$\) (Alpha has reached 2N dollars). We can solve this system of equations to find:

\($p_i = \frac{i}{2N}$\)

This result can be verified by induction.

Now, let\($E_i$\)be the expected number of flips required to reach the endpoint of the game (either bankruptcy or 2N dollars) starting from the state where Alpha has i dollars and Beta has \($2N-i$\)dollars. Then we have:

\($E_i = 1 + \frac{1}{2}E_{i-1} + \frac{1}{2}E_{i+1}$\)

The first term represents the flip that is about to be made, while the second and third terms represent the expected number of flips required to reach the endpoint starting from the new state after the next flip. The boundary conditions are \($E_0 = E_{2N} = 0$\)(we have already reached an endpoint). We can solve this system of equations to find:

\($E_i = 2N\left(1 - \frac{i}{2N}\right)^2$\)

Therefore, the expected number of flips required to reach the endpoint of the game starting from the initial state where both players have N dollars is:

\($E = E_N = 2N\left(1 - \frac{1}{2}\right)^2 = \boxed{N}$\)

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Answer:

oh lord may we put our head down and pray this manz aces his test or whatever it is amen.

The equation of a line through the origin and (-5,6) is y =  -1.2x

It is important to note that the equation of a line is expressed as;

y = mx + c

Where;

From the information given, we have the points;

(0, 0) and ( -5, 6)

The formula for slope is given as;

slope, m = y₂ - y₁/ x₂ -x₁

slope, m = 6 - 0/ -5 - 0

slope, m = 6/ -5

slope, m = - 1. 2

To determine the intercept, we have;

6 = -1. 2(-5) + c

expand the bracket

c = 6 - 6

c = 0

The equation is given as;

y = -1.2x

Hence, the equation is y = -1.2x

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Answer:

5/6

Step-by-step explanation:

2/3 times 2 = 4/6

4/6 plus 1/6 =

5/6

The difference in height between Sarah and Tayjen kite is 1060 cm (10.6 m)

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 m = 100 cm

Sara's kite flew 48 meters in the air. Hence:

Height of Sarah kite = 48 m = 48 m * 100 cm per m = 4800 cm

Tayjen's kite flew 5,860 centimeters in the air. Therefore:

Difference in height = 5860 - 4800 = 1060 cm = 1060 cm * 1 m per 100 cm = 10.6 m

The difference in height is 1060 cm (10.6 m)

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The slope-point form of the linear equation with a slope of -3 and the given point is:

y = -3*(x - 3) - 1

Remember that a general linear equation with a slope a and a point (h, k) can be written in the slope-point form as:

y = a*(x - h) + k

In this case, we know that the slope of the linear equation must be -3, so the linear equation can be written as:

y = -3*(x - h) + k

Now we also want this line to pass through the point on the graph, which is (3, -1), then we need to replace the values:

h = 3

k = -1

Replacing that in the linear equation above we will get:

y = -3*(x - 3) - 1

That is the linear equation in the slope-point form.

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Answer:

\(2.28*10^7\)

Step-by-step explanation:

\((2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7\)

Answer:

228,000

Step-by-step explanation:

(2.4x10^3) x (9.5x10^3)

(2.4x100) x (9.5x100)

240x950

228,000

Answer:

\(y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Step-by-step explanation:

Given the second-order differential equation, \(y'' + y = cos2(x)\), solve it using variation of parameters.

(1) - Solve the DE as if it were homogenous and find the homogeneous solution\(y'' + y = cos2(x) \Longrightarrow y'' + y =0\\\\\text{The characteristic equation} \Rightarrow m^2+1=0\\\\m^2+1=0\\\\ \Longrightarrow m^2=-1\\\\\ \Longrightarrow m=\sqrt{-1} \\\\\Longrightarrow \boxed{m=\pm i} \\ \\\text{Solution is complex will be in the form} \ \boxed{y=c_1e^{\alpha t}\cos(\beta t)+c_2e^{\alpha t}\sin(\beta t)} \ \text{where} \ m=\alpha \pm \beta i\)

\(\therefore \text{homogeneous solution} \rightarrow \boxed{y_h=c_1\cos(x)+c_2\sin(x)}\)

(2) - Find the Wronskian determinant

\(|W|=\left|\begin{array}{ccc}y_1&y_2\\y'_1&y'_2\end{array}\right| \\\\\Longrightarrow |W|=\left|\begin{array}{ccc}\cos(x)&\sin(x)\\-sin(t)&cos(x)\end{array}\right|\\\\\Longrightarrow \cos^2(x)+\sin^2(x)\\\\\Longrightarrow \boxed{|W|=1}\)

(3) - Find W_1 and W_2

\(\boxed{W_1=\left|\begin{array}{ccc}0&y_2\\g(x)&y'_2\end{array}\right| and \ W_2=\left|\begin{array}{ccc}y_2&0\\y'_2&g(x)\end{array}\right|}\)

\(W_1=\left|\begin{array}{ccc}0&\sin(x)\\\cos^2(x)&\cos(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_1= -\sin(x)\cos^2(x)}\\\\W_2=\left|\begin{array}{ccc}\cos(x)&0\\ -\sin(x)&\cos^2(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_2= \cos^3(x)}\)

(4) - Find u_1 and u_2

\(\boxed{u_1=\int\frac{W_1}{|W|} \ and \ u_2=\int\frac{W_2}{|W|} }\)\

u_1:

\(\int(\frac{-\sin(x)\cos^2(x)}{1}) dx\\\\\Longrightarrow-\int(\sin(x)\cos^2(x)) dx\\\\\text{Let} \ u=\cos(x) \rightarrow du=-sin(x)dx\\\\\Longrightarrow\int u^2 du\\\\\Longrightarrow \frac{1}{3}u^3\\ \\\Longrightarrow \boxed{u_1=\frac{1}{3}\cos^3(x)}\)

u_2:

\(\int\frac{\cos^3(x)}{1}dx\\ \\\Longrightarrow \int \cos^3(x)dx\\\\ \Longrightarrow \int (\cos^2(x)\cos(x))dx \ \ \boxed{\text{Trig identity:} \cos^2(x)=1-\sin^2(x)}\\\\\Longrightarrow \int[(1-\sin^2(x)})\cos(x)]dx\\\\\Longrightarrow \int \cos(x)dx-\int (\sin^2(x)\cos(x))dx\\\\\Longrightarrow \sin(x)-\int (\sin^2(x)\cos(x))dx\\\\\text{Let} \ u=\sin(x) \rightarrow du=cos(x)dx\\\\\Longrightarrow \sin(x)-\int u^2du\\\\\Longrightarrow \sin(x)-\frac{1}{3} u^3\)\

\(\Longrightarrow \boxed{u_2=\sin(x)-\frac{1}{3} \sin^3(x)}\)

(5) - Generate the particular solution

\(\text{Particular solution} \rightarrow y_p=u_1y_1+u_2y_2\)

\(\Longrightarrow y_p=(\frac{1}{3}\cos(x))(\cos(x))+(\sin(x)-\frac{1}{3} \sin^3(x))(\sin(x))\\\\ \Longrightarrow y_p=\frac{1}{3}\cos^4(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)\\\\\Longrightarrow \boxed{y_p=\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}\)

(6) - Form the general solution

\(\text{General solution} \rightarrow y_{gen.}=y_h+y_p\)

\(\boxed{\boxed{y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Thus, the solution to the given DE is found where c_1 and c_2 are arbitrary constants that can be solved for given an initial condition. You can simplify the solution more if need be.

The measure of the angles of the cyclic quadrilateral are:

Arc PQ = 130

QR = 50°

Arc RS = 70°

∠PSQ = 65°

∠PSB = 65°

∠SBP = 80°

AQS = 30°

PS = 110°

From the figure, the arc PQ is subtended by the angle PAQ.

This means that:

PQ = ∠PAQ

Given that ∠PAQ = 130, it means that:

Arc PQ = 130

The measure of PSQ is then calculated using:

∠PSQ = 0.5 * Arc PQ ----- inscribed angle is half a subtended angle.

This gives: ∠PSQ = 0.5 * 130

∠PSQ = 65°

Hence, the measure of ∠PSQ is 65°

The measure of arc QR

A semicircle measures 180°

Thus:

QR + PQ = 180°

Thus, we get:

QR = 180° - PQ

Substitute 130° for PQ

QR = 180° - 130°

QR = 50°

Hence, the measure of QR is 50°

The measure of arc RS

The measure of arc RS is then calculated using:

∠RPS = 0.5 * Arc RS ----- inscribed angle is half a subtended angle.

Where ∠RPS = 35

So, we have:

35 = 0.5 * Arc RS

Multiply both sides by 2

Arc RS = 70°

The measure of angle AQS

In (a), we have:

∠PSQ = 65°

This means that:

∠PSQ = ∠PSB = 65°

So, we have:

∠PSB = 65°

Next, calculate SBP using:

∠SBP + ∠BPS + ∠PSB = 180° ---- sum of angles in a triangle.

So, we have:

∠SBP + 35 + 65 = 180°

∠SBP + 100 = 180

∠SBP = 80°

The measure of AQS is then calculated using:

AQS = AQB = 180 - (180 - SBP) - (180 - PAQ)

AQS = 180 - (180 - 80) - (180 - 130)

AQS = 30°

The measure of arc PS

A semicircle measures 180°

This means that:

PS + RS = 180°

This gives

PS = 180 - RS

RS = 70

Thus:

PS = 180 - 70

PS = 110°

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Answer:

-3 degrees per hour

Step-by-step explanation:

Answer:

h = — 10.071

Step-by-step explanation:

Look at the picture for my work.

A permutation is an arrangement of outcomes in which the order does matter.

A combination is an arrangement of outcomes in which the order does not matter.

In this case, for example, the password HI is different from the password IH. In both cases, the outcomes (letters H and I) are the same, but the order of them changes the arrangement (the password). Therefore, the problem involves a permutation because the order of letters selected does matter

Answer:

P = 2x + 24

Step-by-step explanation:

P = 2(l + w)

P = 2(7 + x + 5)

P = 2(x + 12)

P = 2x + 24

Answer:

B

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

Ella purchased 8 passes to the skating rink for $58.00. Each pass cost the same amount. What was the cost of each pass in dollars and cents?

To find the probability that exactly 15 lights out of 20 have a useful life of at least 1000 hours, we can plug in the values: P(X = 15) = (20 choose 15) * 0.8^15 * 0.2^5

Given that the probability that a fluorescent light has a useful life of at least 1000 hours is 0.8, we can use the binomial distribution formula to find the probabilities that among 20 such lights, a certain number will have a useful life of at least 1000 hours. The formula is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the number of lights that have a useful life of at least 1000 hours, n is the total number of lights (20 in this case), k is the number of lights with a useful life of at least 1000 hours, p is the probability that a single light has a useful life of at least 1000 hours (0.8), and (n choose k) is the binomial coefficient.

For example, to find the probability that exactly 15 lights out of 20 have a useful life of at least 1000 hours, we can plug in the values:

P(X = 15) = (20 choose 15) * 0.8^15 * 0.2^5

Using a calculator or a statistical software, we can find that this probability is approximately 0.202. Similarly, we can find the probabilities for other values of k, such as P(X = 10), P(X = 5), or P(X = 0). The probabilities will follow a binomial distribution, which is a discrete probability distribution that models the number of successes in a fixed number of trials.
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Answer:

3.1

Step-by-step explanation:

Pls check if this is correct

The two linear equations are:

1)  y = -x + 5

2) y = (-1/2)*x - 1

Remember that two linear equations are parallel if and only if have the same slope and different y-intercept.

So to find a linear equation:

y = m*x + b

Parallel to:

x + y = 4

y = -x + 4

The slope needs to be m = -1 and the y-intercept b ≠ 4

So our line will be:

y = -x + b

To find the value of b, we use the fact that this line passes through (2, 3), replacing the values of the point in the line we get:

3 = -2 + b

3 + 2 = b

5 = b

The linear equation is y = -x + 5

For the second case, we want to find a line perpendicular to:

2x - y = 5

y = 2x - 5

Two lines are perpendicular if the product of the slopes is -1, then:

m*2 = -1

m = -1/2

So the perpendicular line is something like:

y = (-1/2)*x + b

To find the value of b we use the fact that this line needs to pass through (6, -4)

Replacing these values we get

-4 = (-1/2)*6 + b

-4 = -3 + b

-4 + 3  =b

-1 = b

The line is:

y = (-1/2)*x - 1

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A) The measure of central tendency that best describes the data for time spent on the internet (min/day) is the median.

The median is the middle value in a set of data when the data is arranged in numerical order. In this case, the data arranged in numerical order is 38, 43, 48, 52, 65, 75, 120. The median value is 52, which is the middle value in the data set.

B) The measure of central tendency that best describes the data for the weight of books (oz) is the mode. The mode is the value that occurs most frequently in a data set. In this case, the data is 12, 10, 9, 15, 16, 10. The mode is 10, as it occurs twice in the data set and is the most frequent value.

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Given:

The height of the cylinder = 12 in

The diameter of the base of the cylinder = 8 in.

To find:

The volume of the cylinder.

Solution:

The diameter of the base of the cylinder is 8 in. The radius is half of its diameter. So,

\(r=\dfrac{8}{2}\)

\(r=4\)

So, the radius of the base of the cylinder is 4 in.

The height of the cylinder, h = 12 in.

Base area of the cylinder is:

\(B=\pi r^2\)

Where, B is the base area and r is the radius.

\(B=\pi (4)^2\)

\(B=16\pi \)

So, the base area is \(16\pi \) square inches.

The volume of the cylinder is:

\(V=\pi r^2h\)

\(V=Bh\)

Where, r is radius, h is height, B is base area.

Putting \(B=16\pi \) and \(h=12\), we get

\(V=(16\pi )12\)

\(V=192\pi \)

So, the volume is \(192\pi \) cubic inches.

Therefore, \(r=4\text{ in}, h=12\text{ in},B=16\pi \text{ in}^2,V=192\pi \text{ in}^3\).

The value of side a and b for the given triangle is 46.68 units and 17.92 units.

A triangle's angles and side lengths are related by the law of sines, a trigonometric identity. It asserts that the ratio of the sine of one angle to the length of the side opposite that angle is constant for all three angles for any triangle with sides a, b, and c and opposing angles a, b, and c:

If a/sin(A) = b/sin(B) = c/sin(C), then

As long as at least one angle and its matching side length are known, this can be used to solve for unknown angles or side lengths in a triangle.

For the given triangle we have:

cos B = a / c

Thus, substituting the values we have:

cos 21 = a / 50

a = 46.68 units.

Now, sin B = b/50

Sin 21 = b / 50

b = 17.92 units.

Hence, the value of side a and b for the given triangles is 46.68 units and 17.92 units.

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The complete question is:

(d)  x-intercept of 2 and a y-intercept of -4 is y = 2x - 4.

(e)  the equation of the vertical line through (-9, -8) is x = -9.

(f) The equation of the line through the point (-7, -1) and parallel to the line -4x - y = -4 is y = -4x - 29, in slope-intercept form.

(d) To find the equation of a line with an x-intercept of 2 and a y-intercept of -4, we can use the slope-intercept form of a line, which is given by y = mx + b, where m is the slope and b is the y-intercept.

The x-intercept is the point where the line crosses the x-axis, and in this case, it is (2, 0). The y-intercept is the point where the line crosses the y-axis, and in this case, it is (0, -4).

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the x-intercept (2, 0) and the y-intercept (0, -4), we get:

m = (-4 - 0) / (0 - 2)

m = -4 / -2

m = 2

Now we can substitute the slope and y-intercept into the slope-intercept form to get the equation of the line:

y = 2x - 4

Therefore, the equation of the line with an x-intercept of 2 and a y-intercept of -4 is y = 2x - 4.

(e) A vertical line has an undefined slope because its equation does not involve x. If a line passes through the point (-9, -8), then its equation will be x = -9. This is because regardless of the y-value, x will always be -9 on this vertical line.

Therefore, the equation of the vertical line through (-9, -8) is x = -9.

(f) The given line has the equation -4x - y = -4, which can be rewritten in slope-intercept form:

y = -4x + 4

Since we are looking for a line parallel to this line, the slope will be the same. Therefore, the slope of the desired line is -4.

Now we can use the point-slope form of a line, which is given by:

y - y1 = m(x - x1)

Plugging in the coordinates of the point (-7, -1) and the slope -4, we get:

y - (-1) = -4(x - (-7))

y + 1 = -4(x + 7)

y + 1 = -4x - 28

y = -4x - 29

Therefore, the equation of the line through the point (-7, -1) and parallel to the line -4x - y = -4 is y = -4x - 29, in slope-intercept form.

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