Find the following if a+b/a-b=c
3(a+b)/2(a-b)

Answer:

2√133

Step-by-step explanation:

a²+b²=c²

8²+12²=c²

c²=208

208+18²=532

√532=23

Answer:

Y=-3x+7

Step-by-step explanation:

Answer:

X=36.4 or 36.37306696.... and Y=42

Step-by-step explanation:

So you have a 30-60-90 triangle!

Do Not Worry this is a hard subject to understand, but I will try to do my best with helping you. Right now you need to find x and y. All you have is 21.  Under your 60 angle, which is pointing downward, is the 21. And 21 is initially in the spot of x or 1. so 21 is the x(But not the x on the side of 90). I am sorry if this is a bit confusing.

You are then going to take your side which is x, the side that is directly in the path of 90, and it is going to be 21\(\sqrt{3\). Then on the side of your y, which is in the path of your 60, it will be 2 times your x.

The general layout of this is:

x is underneath the side of 90 degrees.

then on the side where 60 degrees and 30 degrees is, is going to be x\(\sqrt{3\).

Then the last side, where 30 degrees and 90 degrees lay, will be 2(x).

So all you have to do is plug everything in.

x=36.4 in decimal

y=42(because all you had to do was plug 21 where the x is, because that is where x is in the general layout.)

The value of x = 42 units

The value of y = 21√3 units

The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.

As per the given diagram:

The triangle is a right angle triangle.

Using trigonometric ratios to find x and y:

tan30° = (P/B)

tan30° = (21/y)

(1/√3) = (21/y)

y = 21√3 units

sin30° = (P/H)

(1/2) = (21/x)

x = 2 × 21

x = 42 units

The value of x and y is 42 units and 21√3 units, respectively.

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Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.

The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.

P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.

There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.

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The area of the region between the graphs of y = 10 − x² and y = −6x − 6 over the interval 0 ≤ x ≤ 10 is 2380/3 square units.

Given the following graphs:

y = 10 − x² and

y = -6x - 6

the interval 0 ≤ x ≤ 10

The area can be found using the formula:

Area = \(\int\limits^a_b {f(x) - g(x)} \, dx\)

where

f(x) is the upper function,

g(x) is the lower function, and [a, b] is the interval.

From the question:

upper function is y = 10 - x²  

lower function is y = -6x - 6.

So, we need to calculate:

Area = \(\int\limits^{10}_0 {10 - x^2 - (-6x - 6)} \, dx\)

Area = \(\int\limits^{10}_0 {10 - x^2 + 6x + 6)} \, dx\)

Area = \(\int\limits^{10}_0 {16 +6x - x^2)} \, dx\)

To find the antiderivative, we apply the power rule:

Area = [16x + 3x² + (1/3)x³] evaluated from 0 to 10

Plugging in the upper and lower limits:

Area = (16(10) + 3(10²) + (1/3)(10³)) - (10(0) + 3(0²) + (1/3)(0³))

Area = (160 + 300 + 1000/3) - (0 + 0 + 0)

Area = 160 + 300 + 1000/3

Area = 460 + 1000/3

To express the area as a mixed fraction:

Area = (1380 + 1000)/3

Area = 2380/3

Therefore, the area of the region between the graphs of y = 10 − x² and y = −6x − 6 over the interval 0 ≤ x ≤ 10 is 2380/3 square units.

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Answer:JEROME

Step-by-step explanation:

A composite function, also known as f of g of x, is formally denoted as f(g(x)) or (f g)(x), and it requires the substitution of x = g(x) in f. (x). Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, distinct function.

The composite function F of G of X is composed of the two functions f(x) and g. (x). Let's use an actual situation to better comprehend f of g of x. We employ the slicer and the fryer for making french fries. Assume that x is a potato, that the fryer is performing the function f(x), and that the slicer is performing the function g(x) (frying the potato).

A composite function, also known as f of g of x, is formally denoted as f(g(x)) or (f g)(x), and it requires the substitution of x = g(x) in f. (x). Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, unique function. The output of one function becomes the input of another function in f of g of x. It can be compared to a sequence of tools or processes.f(x) = 2x + 3 and g(x) = x2

f of g of x = (f ∘ g)(x) = f(g(x))

g of f of x = (g ∘ f)(x) = g(f(x))

We are aware that anytime we simplify a mathematical equation, we always operate on the elements inside the brackets first. Therefore, in order to obtain f(g(x)), we must first identify g(x), which we must then use as the input for f(x) and simplify. Here is an illustration to help you comprehend. Assume that g(x) = x2 and f(x) = 2x + 3. We'll discover f(g(3)).

g(3) = 32 = 9.

f(g(3)) = f(9) = 2(9) + 3 = 18 + 3 = 21.

Then

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Option A. If the alternative hypothesis of the test had been lower-tailed instead of two-tailed, the conclusion of the test would be different.

Recall that a two-tailed test is used when the alternative hypothesis is that the population parameter is different from the null hypothesis value in any direction, while a lower-tailed test is used when the alternative hypothesis is that the population parameter is less than the null hypothesis value.

In the given scenario, if the alternative hypothesis of the test had been lower-tailed instead of two-tailed, we would have tested the following null and alternative hypotheses:

H0: Pharaoh's translation is not worse than the other software's translation.

Ha: Pharaoh's translation is better than the other software's translation.

In this case, we would have calculated the p-value for the lower tail of the sampling distribution, and compared it to the significance level alpha. If the p-value is less than alpha, we would reject the null hypothesis and conclude that Pharaoh's translation is better than the other software's translation. If the p-value is greater than alpha, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that Pharaoh's translation is better than the other software's translation.

Therefore, the correct answer to the question is option A: Unlike the two-tailed test, we would conclude that there is a difference between Pharaoh's translation and the translation of the other software.

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The values of the probabilities are P(u or v) = 0.63, P(u and v) = 0 and P(u|v) = 0

The probabilities are given as:

P(U) = 0.26

P(V) = 0.37

For mutually exclusive events, we have

P(u or v) = P(u) + P(v)

So, we have

P(u or v) = 0.26 + 0.37

P(u or v) = 0.63

Also, we have:

P(u and v) = 0

Finally, we have:

P(u|v) = 0

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If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.

Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.

It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.

If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:

If x=4, (4×4)^1/2 = 4

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The absolute value of change in the predicted value of dependent variable Y is 18.

Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.

Slope = b = -4

Intercept = a = -2.8

So, the equation of the regression line is

y  =  a + bx

y = -2.8 - 4x              ...Equation 1

Now suppose the value of x is changed by adding 4.5

i.e. put x = x + 4.5

So,

y = -2.8 - 4(x + 4.5)

y = -2.8 -4x - 18         ...Equation 2

Comparing 1 and 2 ,

We get the predicted value of dependent variable Y as 18

Therefore The absolute value of change in the predicted value of dependent variable Y is 18

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Answer:

15x, 19x, 26x, and 3x

Step-by-step explanation:

To figure this out, we just need to figure out which sort of value can be combined. Every choice except 49 has a variable attached. The different variables are a, y, x, h, and g. There is only one of each variable except for x. So, you would combine each like term with x as an variable.

Hope this helps!!! Have a wonderful day :D

Answer:

-2

Step-by-step explanation:

Answer:

it is wrong because he forgot to subtract the 5x

Step-by-step explanation:

I think this right I really hope it is though :-)

If the research question doesn't involve exploring the relationship between these two variables or if they are not nominal variables, then a cross-tabulation analysis may not be appropriate or useful.

What is cross tabulation?

Cross tabulation, also known as contingency table analysis or simply "crosstabs," is a statistical tool used to analyze the relationship between two or more categorical variables.

in general, whether or not it makes sense to conduct a cross-tabulation analysis using MLTSRV and MFPAY depends on the research question and the nature of the variables.

If the research question involves exploring the relationship between these two variables and they are both nominal variables with two values each, then conducting a 2x2 cross-tabulation analysis could be appropriate. This analysis would allow you to examine the frequencies and percentages of the different categories of each variable and explore any potential associations between them.

However, if the research question doesn't involve exploring the relationship between these two variables or if they are not nominal variables, then a cross-tabulation analysis may not be appropriate or useful. In any case, it is always important to carefully consider the nature of the variables and the research question before deciding on a statistical analysis method.

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The area of figures 1 and 2 will be 438 square yards and 110 square inches, respectively

The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

1.  The area of figure 1 is given as,

A = Sum of area of (Trapezoid + Rectangle + Rectangle)

A = 1/2 x (6 + 8) x 10 + 8 x 36 + 10 x 8

A = 70 + 288 + 80

A = 438 square yd

2.  The area of figure 2 is given as,

A = Area of a triangle - Area of a rectangle

A = 1/2 x (8 + 7) x (10 + 14) - 7 x 10

A = 180 - 70

A = 110 square inches

The area of figures 1 and 2 will be 438 square yards and 110 square inches, respectively

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The expression that gives the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours is option d: 20 - 20e^-0.5.

The rate of snowfall is given by the function r(t) = 2e^-0.1t inches per hour. To find the amount of snow that falls from time t = 0 to time t = 5 hours, we need to integrate the rate function with respect to time over this interval.

Integrating the function r(t) from 0 to 5 gives us ∫(0 to 5) 2e^-0.1t dt. This integration evaluates to 20 - 20e^-0.5.

Option d: 20 - 20e^-0.5 is the correct expression because it represents the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours. The constant term 20 represents the initial amount of snowfall at t = 0, and the exponential term accounts for the decrease in the rate of snowfall over time.

Therefore, the correct expression to calculate the amount of snowfall in this time interval is 20 - 20e^-0.5.

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The opposite angles of the cyclic quadrilateral are equal to 180 degrees which are supplementary angles.

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral.

A quadrilateral can be inscribed in a circle, if and only if, the opposite angles in that quadrilateral are supplementary.

We know that the sum of the opposite angles of the cyclic quadrilateral is equal to 180 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

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The function that best models the data from the table is given as follows:

B. y = 0.98x + 74.14.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

(this is because there are multiple types of regression, such as logistic, exponential and quadratic regression).

From the table, the points are given as follows:

(1,63), (2, 67), (3, 79), (4, 75), (5, 85), (6, 95), (7, 93), (8, 90), (9, 88), (10, 85), (11,75), (12, 71).

Inserting these points into the linear regression calculator, the line of best fit is given as follows:

y= 0.98x + 74.14.

Which means that option B is correct.

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An example that shows the closure property for polynomials failing to work is:

5x^2 + 2x + 1 / (2x - 1)

This fails to demonstrate the closure property for polynomials because polynomial division is not included in the basic arithmetic operations (addition, subtraction, multiplication) used when discussing the closure property for polynomials. Polynomial division requires a quotient, which is not necessarily a polynomial. For example, the quotient when performing the division above is:

2.5x + 3 / (2x -1) + 0.5

The 0.5 in the quotient is a constant term, not a polynomial, so the result of this division is not a polynomial. Therefore, polynomial division breaks the closure property of polynomials.

The closure property for polynomials states that when any two polynomials are combined using the basic arithmetic operations (addition, subtraction, multiplication), the result will always be a polynomial. Division is not one of these basic operations, so examples involving polynomial division, like the one shown, do not demonstrate closure of polynomials.

Answer:

Step-by-step explanation:

As per given we have:

Profit is going to be:

Answer:

1) 36, 2) 14, 3) 19, 4) 18, 5) 3, 6) 117

Step-by-step explanation:

1)  6(7) - 3(2)   2)  (7)(4)/2   3)  (7) + |2(7) - (2)|   4)  6(5) - 4(3)   5)  [(4) + (5)]/3  

    42 - 6             28/2            7 + |14 - 2|               30 - 12            9/3

    36                   14                7 + 12                      18                    3

                                               19

6)  (4) + [(5)^3 + (3)] - 15

     4 + (125 + 3) - 15

     4 + 128 - 15

     132 - 15

     117

The most likely marble to be chosen will be red.

Given  that,

Number of red marbles = 1/2

Number of blue marbles = 1/4

Number of green marbles = 1/6

Number of yellow marbles = 1/12

To compare the probabilities, we need to find a common denominator. The common denominator for 2, 4, 6, and 12 is 12.

Therefore,

Probability of choosing a red marble = 6/12

Probability of choosing a blue marble = 3/12

Probability of choosing a green marble = 2/12

Probability of choosing a yellow marble = 1/12

Since the highest probability is for red marble, it is most likely to be chosen.

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Radius is 3/2πr when the area of an expanding circle is increasing three times as fast as its radius (in centimeters)

The region encircled by a circle with radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159. The circumference of a circle is pi times the diameter, or 2 pi times the radius, according to the traditional definition of pi, which is the ratio of a circle's circumference to its diameter. This demonstrates geometrically that the area of a circle is indeed "pi r squared".

Given,

Area of circle = πr²

A = πr²

Differentiating,

dA/dt = 2πr × dr/dt

Given,

The area of an expanding circle is increasing three times as fast as its radius (in centimeters),

dA/dt = 3 dr/dt

To find radius,

3 dr/st = 2πr dr/dt

Cancelling dr/dt

3 = 2πr

r = 2πr

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Answer:

64 ft^2

Step-by-step explanation:

It is a square to start, so each side = x

then     (x+7 )    *    ( x -2)    = 90

          x^2 + 5x -14 = 90

           x^2 + 5x - 104 = 0         factor or use Quadratic Formula to fin x = 8 ft

Original area is then 8 x 8 = 64 ft^2  

Answer:

Finding the area of each parallelogram, applying the formula, it is found that the parallelogram D has an area of 60 square units

Step-by-step explanation:

Similarly to a rectangle, the area of a parallelogram is given by height multiplied by base, that is:

In item A, the height is of 15 units and the base is of 10 units, thus, the area, in square units, is of .

In item B, the height is of 6 units and the base is of 10.2 units, thus, the area, in square units, is of .

In item C, the height is of 15 units and the base is of 15 units, thus, the area, in square units, is of .

In item D, the height is of 10 units and the base is of 6 units, thus, the area, in square units, is of , which means that this is the correct option.

Formula for the Slope: (y2 - y1) / (x2 - x1)

You can use any two points to find the slope, as long as those two points are on the line.

Point 1 = (-2, 8)

Point 2 = (0, 0)

Slope = (0 - 8) / (0 - - 2)

Slope = -8 / 2

Slope = -4

Hope this helps!

Answer:

-4

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: -3 --> -2 --> -1 --> 0 --> 1

y value: 12 --> 8 --> 4 --> 0 --> -4

When y changed from 12 to 8, the x changed from -3 to -2.

y: 12 --> 8

x: -3 --> -2

There was a difference of -4 in the y and a difference of 1 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -4 and 1 we found, we can say that the slope is -4/1.

If we simplify this answer, we end up with -4.

So -4 is the slope of the data.

Inferential statistic is concerned with making prediction about a population from analyzing a sample or through observation.

Here,

We have to find the concerned with making prediction about a population from analyzing a sample or through observation.

What is Inferential statistic?

Inferential statistics is used in measurements from the sample of subjects in the experiment to compare treatment groups and to make generalizations about the larger population of subjects.

Now,

Inferential statistic is concerned with making prediction about a population from analyzing a sample or through observation.

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Since the question explicitly stated that ice production is proportional to time, we're going to have to use proportion fractions. Remember to convert hours into minutes as well.

The amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

Given,

Two waves are described by:

3₁ (2, 1) = (0.30) sin(5z - 200t)] and

g (z,t) = (0.30) sin(52-200t)

+ =]

where OA A, 0.52 m and v= 40 m/s

OB A=0.36 m and

v= 20 m/s OC

A=0.60 m and

v= 1.2 m/s OD.

A = 0.24 m and

v= 10 m/s

DE A=0.16 m and

= 17 m/s

The amplitude of a wave is the distance from its crest to its equilibrium. The amplitude of the resultant wave is calculated by adding the amplitudes of the individual waves and is represented by A.

The expression for the resultant wave is given by f(z,t) = 3₁ (2, 1) + g (z,t)

= (0.30) sin(5z - 200t)] + (0.30) sin(52-200t)

+ =]

f(z,t) = (0.30) [sin(5z - 200t) + sin(52-200t)

+ =]

Therefore, A = 2(0.30) = 0.60 m/s

The speed of a wave is given by the product of its wavelength and its frequency. The wavelength of the wave is the distance between two consecutive crests or troughs, represented by λ. The frequency of the wave is the number of crests or troughs that pass through a given point in one second, represented by f.

Speed = λf

The wavelengths of the given waves are OA = 0.52 m,

OB = 0.36 m,

OC = 0.60 m,

OD = 0.24 m,

DE = 0.16 m

The frequencies of the given waves are OA :

v = 40 m/s,

f = v/λ

= 40/0.52

= 77.0 Hz

OB : v = 20 m/s,

f = v/λ

= 20/0.36

= 55.6 Hz

OC : v = 1.2 m/s,

f = v/λ

= 1.2/0.60

= 2.0 Hz

OD : v = 10 m/s,

f = v/λ

= 10/0.24

= 41.7 Hz

DE : v = 17 m/s,

f = v/λ

= 17/0.16

= 106.25 Hz

The speed of the resultant wave is the sum of the speeds of the individual waves divided by the number of waves. Therefore,

Speed of the resultant wave = (40 + 20 + 1.2 + 10 + 17)/5

= 17.64 m/s

Hence, the amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

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The amplitude of the resultant wave and its speed are to be determined.

Let's use the formula of the resultant wave, where,

A is amplitude, f is frequency, v is velocity and λ is wavelength of the wave.

A = \([(OA^2 + OB^2 + OC^2 + OD^2 + DE^2 + 2(OA)(OB)(cosθ) + 2(OA)(OC)(cosθ) + 2(OA)(OD)(cosθ) + 2(OA)(DE)(cosθ) + 2(OB)(OC)(cosθ) + 2(OB)(OD)(cosθ) + 2(OB)(DE)(cosθ) + 2(OC)(OD)(cosθ) + 2(OC)(DE)(cosθ) + 2(OD)(DE)(cosθ))]^{1/2\)

where, cosθ = [λ1/λ2] and λ1, λ2 are the wavelength of the two waves.

The velocity of the wave is given by the relation v = fλ

We can calculate the velocity of the resultant wave by using the above formula and calculating the value of wavelength of the wave.

Here, we are given λ for each wave. Speed = 40 m/s

Amplitude of the resultant wave= \([ (0.52^2 + 0.36^2 + 0.6^2 + 0.24^2 + 0.16^2 + 2(0.52)(0.36) + 2(0.52)(0.6) + 2(0.52)(0.24) + 2(0.52)(0.16) + 2(0.36)(0.6) + 2(0.36)(0.24) + 2(0.36)(0.16) + 2(0.6)(0.24) + 2(0.6)(0.16) + 2(0.24)(0.16) )]^{1/2\)

=\([ (0.2704 + 0.1296 + 0.36 + 0.0576 + 0.0256 + 0.3744 + 0.624 + 0.2496 + 0.1664 + 0.1296 + 0.0864 + 0.0576 + 0.144 + 0.096 + 0.0384) ]^{1/2\)

=\([ (2.2768) ]^{1/2\)

= 1.51 m/s

Therefore, the amplitude of the resultant wave is 1.51 m/s and the speed of the wave is 1.51 m/s.

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