Please help I forgot how to do this completely

a) a/5 + 3 = 8

Step 1 : Minus both sides by 3

a/5 + 3 - 3 = 8 - 3 -> a/5 = 5

Step 2 : Multiply both sides by 5

a/5 x 5 = 5 x 5 -> a = 25.

b) (3b)/7 - 1 = 5

Step 1 : Add both sides by 1

(3b)/y - 1 +1 = 5 + 1 -> (3b)/7 = 6

Step 2 : Multiply both sides by 7

(3b)/7 x 7 = 6 x 7 -> 3b = 42

Step 3 : Divide both sides by 3

3b : 3 = 42 : 3 -> b = 14.

Answer:

x = -4/3, 2/3

Step-by-step explanation:

Step 1: Factor

(3x + 4)(3x - 2) = 0

Step 2: Find roots

3x + 4 = 0

3x = -4

x = -4/3

3x - 2 = 0

3x = 2

x = 2/3

Answer:

x₁ = -4/3

x₂ = 2/3

Step-by-step explanation:

9x² + 6x - 8 = 0

9x² + 12x - 6x - 8 = 0

3xx(3x + 4) - 6x - 8 = 0

3xx(3x + 4) - 2(3x + 4) = 0

(3x + 4) × (3x - 2) = 0

3x + 4 = 0 → x = -4/3

3x - 2 = 0 → x = 2/3

Hope this helps! :)

First, determine the number of miles covered per day:

Her car already has 45,300 miles on it.

(a)The total number of miles, f(x), Stefanie's car will have been driven after x more days will be:

(b) Stephanie works 4 days a week.

After 3 weeks, the number of days worked = 4 x 3 = 12 days

Therefore, when x=12:

Answer:

5.5369

Step-by-step explanation:

tan(64) = 13/x

2.3478 = 13/x

Multiply both sides by x

2.3478x = 13

Divide both sides by 2.3478

5.5369 = x

Step-by-step explanation:

5.5369=x is the answer to the question

The diameter of a hemisphere with a volume of 863 in^3 is 40.596 in.

In the given question we have to find the diameter of a hemisphere with a volume of 863 in^3.

As we know that the volume of hemisphere is (2/3)πr^3 cubic unit.

The given volume of hemisphere is 863 in^3.

Now we firstly finding the radius of hemisphere then we find the diameter of hemisphere

The volume of hemisphere = 863 in^3

(2/3)πr^3 = 863

We know that; π = 22/7

(2/3) * (22/7) *r^3 = 863

44/21 * r^3 = 863

Multiply by 21/44 on both side, we get

r^3 = 863*21/44

r^3 = 411.89

r^3 = 412 (approx)

Taking cube root on both side, we get

r = 20.298

Now finding the diameter,

Diameter = 2*radius

Diameter = 2*20.298

Diameter = 40.596 in

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Answer:

x=6

Step-by-step explanation:

Let us expand the left side:

3x+12 = 2x+ 4x -6

Let us then simplify the right side:

3x+12=6x-6

We can now put the same variables on one side to isolate x:

12+6=6x-3x

18=3x

x=6

I hope this helped! :)

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

You need to adjust the tube of the microscope to 6.83cm in order to view the sample in focus with a completely relaxed eye

Given, Focal length of the eyepiece,  = 2.50 cm

The focal length of the converging lens, f = 1.00 cm

The distance of the object, p = 1.30 cm

Lens equation, \(\frac{1}{f} = \frac{1}{p} + \frac{1}{q}\)

Substitute the values in the above equation

\(\frac{1}{1.00} = \frac{1}{1.30} + \frac{1}{q}\)

q = 4.33 cm

now, the image is formed at the focal point of the eyepiece,

therefore, the distance between the objective and the eyepiece, d =  + q = 2.50 cm + 4.33 cm

d = 6.83 cm

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The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.

As given in the question,

Let success be defined by health department inspection is passed by restaurant

Probability of success rate 'p' = 0.94

Value of ' 1 - p ' = 1 - 0.94

                        = 0.06

Number of owners of restaurant which are surveyed 'n' = 58

For the given binomial experiments calculation of the following distributions are:

Mean 'μ' = np

             = 58 × 0.94

             = 54.52

Standard deviation 'σ' = √ np (1 - p)

                                   = √ 58 × 0.94 × 0.06

                                   = √3.2712

                                   = 1.808

Variance 'σ²' =  np( 1 - p )

                    = 58 × 0.94 × 0.06

                   = 3.2712

Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.

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Answer:

\(X=25.98cm\)

Step-by-step explanation:

From the question we are told that:  

Length of each side \(l=30cm\)

Let the triangle be divide by two form a right angle triangle with base angles as \(90 \textdegree\)(angle of perpendicularity) and \(60 \textdegree\) (angle on each vertices of an equilateral triangle)

Generally the equation for the Altitude X is mathematically given by

Trigonometric Rule

\(X=30sin60\)

\(X=15\sqrt{3}\)

\(X=25.98cm\)

Answer:

KE = 68.4J

The formula for Kinetic Energy is

KE = 1/2mv^2

m = mass (kg)

v = velocity (m/s)

152 grams to kilograms is 19/125kg

m=19/125

v=30

KE = 19/125 x 30^2

= 342/5

= 68.4

KE = 68.4J

Answer:

79 degrees

Step-by-step explanation:

180 - 101 = 79

Answer:4,2

Step-by-step explanation: is u divide both side with 2 that will be your answer

Answer:

Your answer is: Midpoint =  (0.5, -0.5)

Step-by-step explanation:

(xa+xb/2 , ya+yb/2)

Plug the points ---> (5,2)(-4,-3)

= (1/2 , -1/2)

In decimal form it would be: (0.5,-0.5)

Hope this helped : )

Assuming the function has the form r(t) = (t^2 + 3, 2t - 1, t + 1), the curvature can be found as follows:

To find the curvature, κ(t), of a vector-valued function r(t), you can use the formula:

κ(t) = || r'(t) × r''(t) || / || r'(t) ||^3

First, compute the first and second derivatives of r(t):

r'(t) = (2t, 2, 1) and r''(t) = (2, 0, 0)

Next, compute the cross product r'(t) × r''(t):

r'(t) × r''(t) = (0, -2, 4)

Now, find the magnitudes:

|| r'(t) × r''(t) || = sqrt(0^2 + (-2)^2 + 4^2) = sqrt(20)
|| r'(t) || = sqrt((2t)^2 + 2^2 + 1^2) = sqrt(4t^2 + 5)

Then, compute the curvature κ(t):

κ(t) = sqrt(20) / (sqrt(4t^2 + 5))^3

This is the curvature of the given vector-valued function for any value of t.

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The solution to  the Cubic equation 5/(3b³ -2b² - 5) = 2/(b³ - 2) are b = 0 and b =4

Given Cubic equation is 5/(3b³ -2b² - 5) = 2/(b³ - 2)

5×(b³ - 2)=2×(3b³ -2b² - 5)

5b³  - 10 = 6b³ - 4b²  - 10

5b³  - 6b³ = - 4b²

-b³ = - 4b²

b³- 4b²= 0

b²(b - 4) = 0

b²= 0 and b - 4 = 0

So we  get b = 0 and b = 4

The solution to the Cubic equation 5/(3b3 -2b2 - 5) = 2/(b3 - 2) are b = 0 and b = 4.

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To verify the inequality without evaluating the integrals, we can use the properties of integrals.

First, we know that the integral of a positive function gives the area under the curve. Therefore, the integral of √(1-x^2) from -1 to 1 gives the area of a semicircle with radius 1. This area is equal to π/2, which is approximately 1.57.
Next, we can use the fact that the integral of a function over an interval is less than or equal to the product of the length of the interval and the maximum value of the function on that interval. Since the function √(1-x^2) is decreasing on the interval [-1,1], its maximum value is at x=-1, which is √2/2.
Using this property, we have:
∫1 -1 √(1-x^2) dx ≤ (1-(-1)) * √2/2 = √2
Finally, we can use a similar argument to show that the integral is greater than or equal to 2. Therefore, we have:
2 ≤ ∫1 -1 √(1-x^2) dx ≤ √2
To verify the inequality 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2 using properties of integrals, let's first establish that the integrand is non-negative on the interval [-1, 1]. Since 0 ≤ x^2 ≤ 1, we have 0 ≤ 1 - x^2 ≤ 1, so √(1 - x^2) is non-negative.
Now, consider the areas of two squares: one with side length 2 and the other with side length √2. The area of the first square is 2² = 4, and the area of the second square is (√2)² = 2. Since the integrand lies between 0 and 1, the area under the curve is less than the area of the first square but more than half of it (as it resembles half of the first square).
Therefore, 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2, as the area under the curve is between half of the first square's area and the second square's area.

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Answer:

C. x=18

Step-by-step explanation:

note that PQ is the diameter of circle O. this means that angle QRP is a 90 degree angle. now we have 5x=90 so x=18

The distance between P and Q is sqrt(40), which can also be simplified to 2*sqrt(10) or approximately 6.3246 units.

To find the distance between two points P (-4, 1) and Q (2, 3), we use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) are the coordinates of point P and (x2, y2) are the coordinates of point Q.

Substituting the values for P and Q, we get:

d = sqrt((2 - (-4))^2 + (3 - 1)^2)

d = sqrt((2 + 4)^2 + 2^2)

d = sqrt(36 + 4)

d = sqrt(40)

Therefore, the distance between P and Q is sqrt(40), which can also be simplified to 2*sqrt(10) or approximately 6.3246 units.

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The mathematical definitions of H(X∣Y) and H(X) in the discrete case are as follows: H(X∣Y) = ∑ P(x,y) log(P(x|y)) and H(X) = ∑ P(x) log(P(x)). To prove that I(X;Y) = 0 when X and Y are independent, we start from the equation I(X;Y) = H(X) - H(X∣Y) and substitute the values of H(X) and H(X∣Y) from their respective definitions.

The mutual information between two random variables X and Y, denoted as I(X;Y), is defined as the difference between the entropy of X and the conditional entropy of X given Y: I(X;Y) = H(X) - H(X∣Y). In the case where X and Y are independent, their joint probability distribution P(x,y) can be factorized as P(x,y) = P(x)P(y).

Starting from the equation I(X;Y) = H(X) - H(X∣Y), we substitute the definitions of H(X) and H(X∣Y) in terms of probabilities and logarithms: I(X;Y) = ∑ P(x) log(P(x)) - ∑ P(x,y) log(P(x|y)).

For independent variables, P(x|y) = P(x), which means that the conditional probability of X given Y is equal to the marginal probability of X. Substituting this into the equation above, we have: I(X;Y) = ∑ P(x) log(P(x)) - ∑ P(x,y) log(P(x)).

Using the fact that P(x,y) = P(x)P(y) for independent variables, the equation simplifies to: I(X;Y) = ∑ P(x) log(P(x)) - ∑ P(x)P(y) log(P(x)).

Simplifying further, we get: I(X;Y) = ∑ P(x) log(P(x)) - ∑ P(x) log(P(x)) = 0.

Therefore, the mutual information between X and Y is zero when X and Y are independent, as proven mathematically.

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The question mentions obtaining the iterative Cochrane-Orcutt estimates using data related to barium. It also asks whether the Prais-Winsten and Cochrane-Orcutt estimates are similar and whether such similarity was expected.

The Cochrane-Orcutt method is a procedure used for estimating parameters in a time series regression model when there is serial correlation in the error terms. It involves using an iterative process to estimate an autoregressive model. The Prais-Winsten method is a similar approach that addresses serial correlation in a time series regression model.

Without specific data related to barium or the estimated coefficients, it is not possible to determine the similarity between the Prais-Winsten and Cochrane-Orcutt estimates in this context. However, both methods aim to address the issue of serial correlation, and thus, their estimates are expected to be similar in terms of addressing this specific problem.

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The length of A"B" is 20 units

From the figure, we have:

A = (1, 4)

B = (4, 8)

The distance AB is:

\(AB = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2\)

So, we have:

\(AB = \sqrt{(1 -4)^2 + (4-8)^2\)

Evaluate

\(AB = \sqrt{25\)

This gives

AB = 5

The scale factor of dilation is 4.

So, we have:

A'B' = 5 * 4

Evaluate

A'B' = 20

Hence, the length of A"B" is 20 units

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Answer:

A = 49\(\pi\)

Step-by-step explanation:

First, we need to find the length of the wire. We can calculate this because we are given the area of the square, so we can work backwards.

Use the area formula and plug in the numbers:

A = s²

121 = s²

11 = s

We can calculate the length of the wire by multiplying 11 by 4, which is 44.

Now, we know the circumference of the circle is 44 units because that is how long the wire is.

We can work backwards again to find the radius, using the circumference formula:

C = 2\(\pi\)r

44 = 2\(\pi\)r

22 = \(\pi\)r

7 = r

Now, we can find the area of the circle:

A = \(\pi\)r²

A = \(\pi\)(7)²

A = 49\(\pi\)

Answer:

70.74

Step-by-step explanation:

2 -----  15.72

9  ------  ?

x = 9 * 15.72 / 2

= 70.74

Answer:

x = 30

Step-by-step explanation:

110 and 3x - 20 are supplementary angles, sum to 180° , then

110 + 3x - 20 = 180

90 + 3x = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer:

x = 30

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

For this question, you must be clear of the angle properties.

z + 110 = 180 (Sum of Angles on a straight line)

z = 180 - 110 = 70

z = 3x - 20 (Corresponding Angles)

3x - 20 = z

3x - 20 = 70

3x = 70 + 20

3x = 90

x = 90 / 3 = 30

a) The dipole moment of this arrangement is zero.

b) The value 'd' required for the dipole moment to be the same as the hemisphere arrangement is zero.

c) V(r,θ) very far away from the hemisphere arrangement is zero.

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Answer:

graph 1  

Step-by-step explanation:

Graph using table of values

x           y

2       -2/3

1         -4/3

0          -2

they are all on that graph

The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

Using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

According to the question

Represents a line with a slope of -2/3  

i.e ,

m = -2/3  

y-intercept equal to that of the line

y = \(\frac{2}{3}x-2\)

i.e ,

at y-intercept , x = 0

y = -2

Now, Putting value in standard form of line

y = mx + c

-2 = 0 + c  

c = -2

now , substituting the values of m and c in standard form of line

y = mx + c  

y =  \(\frac{-2}{3}x-2\) --------- (equation of graph )

Now ,

x             y

0            -2

3/2         1

3             0

Only option 4 have these points

Hence, The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

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Calculate distance of G from x and y axis(1 box=1unit)

So

the coordinate is

Answer:

(5,8)

Step-by-step explanation:

x=5

y=8

(x,y)= (5,8)

The output obtained after executing the java code snippet,

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

will be 4.

As per the question statement, we are provided with a java code snippet, which goes as:

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We are required to determine the output, that we will obtain on executing the above mentioned code.

That is, on executing the code

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We will obtain an output of 4, as "++" is the post increment function.

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Answer:

Yeah good job! u got it right :)

Step-by-step explanation:

How to find perimeter?

Frist you will add up all the sides

then thats your answer :)

In this case the same logic applies

Hope this helps :3