Given the expression below, write an equivalent expression that does not contain parentheses.​

Answer:

19.9

Step-by-step explanation:

As 21 is opposite the right angle this side must be the hypotenuse :

Pythagoras Theorem says :

a² + b² = c²

Where c is the hypotenuse.

Substituting values in gives us (a and b do not matter) :

x² + (√43)² = 21²

Now we simplify :

Using the surd law:

√a ×√a = a

(√43)² = √43×√43 = 43

21² = 441

x² + 43 = 441

Subtract 43 from both sides :

x² + 43 - 43 = 441 - 43

x² = 398

Square root both sides :

x = √398

√398 = 19.9 to 1 d.p.

Hope this helped and have a good day

The variance of the sample mean is 12/35 = 0.3429.. This is a result of uniform distribution.

The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.

According to the question, we have

Sample size (n) = 36; uniform continuous distribution has a maximum of 14 and a minimum of 2.

The notation for the uniform distribution is

X U(a,b), where  a=  the lowest value of x  and  b=  the highest value of x. The probability density function is f(x) = 1/(ba ) fo axb .

b = 14 and a = 2.

Variance in uniform distribution = (b-a)² / 12.

Put the value of a and b, 

Variance = ( 14-2)²/12 = 12

Sample variance is used to calculate the variability of sample sets.

The variance of the sample means = variance / (sample size- 1) 9= (b-a)²/ (n-1)

= 12/35= 0.342

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Answer:

Yes.

Step-by-step explanation:

It is given that, A sponge can filter 8 liters of water in 10 hours or 12 liters in 15 hours.

8 L = 10 h

1 h = \(\dfrac{10}{8}\) = 1.25 h

or

12 L = 15 h

1 h = \(\dfrac{15}{12}\) = 1.25 h

Hence, this relationship is proportional.

Use BODMAS

first solving 12×8

which is = 12×8=96

than add +5

so, 96+5= 101

Answer: 12x8=26+5= 31

Step-by-step explanation:

Answer:

Point-slope form: y - 3 = -6/5 (x + 5)

Slope-intercept form: y = -6/5x - 3

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

When the parabola has a y^2 term it opens horizontally. (Positive and negative values of y give the same value of x.)

When the parabola has an x^2 term it opens vertically. (Positive and negative values of x give the same value of y.)

The sign is negative when the opening is down or to the left.

__

The opening directions are shown in the attachment.

Answer:

look below

Step-by-step explanation:

i did it

x=74°

look at the given picture for stepwise

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

The equation y = x^2 + 5x - 6 can be factored as y = (x - 1)(x + 6). The x-intercepts of the equation are (1, 0) and (-6, 0).

To convert the equation y = x^2 + 5x - 6 to factored form, we factor the quadratic expression. The factored form is y = (x - 1)(x + 6).

To identify the x-intercepts, we set y = 0 and solve for x. Setting each factor equal to zero gives us x - 1 = 0, which leads to x = 1, and x + 6 = 0, which gives x = -6.

Therefore, the x-intercepts of the equation y = x^2 + 5x - 6 are (1, 0) and (-6, 0).

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Answer: x = 10

Explanation:

Line A is parallel to line B only when the corresponding angles 4x and 3x+10 are congruent

4x = 3x+10

4x-3x = 10

x = 10

Answer:

3:10

Step-by-step explanation:

In order to find the ratio of red to green sweets, we first need to find the ratio of yellow to green sweets. We know that the ratio of yellow to green is 1:5 and we also know that the ratio of red to yellow is 3:2.

We can use this information to find the ratio of red to green by cross-multiplying the ratio of red to yellow and the ratio of yellow to green.

So (3:2) x (1:5) = (3:10)

This means the ratio of red to green is 3:10.

Alternatively, we can find the ratio of red to green by using the following formula:

(red:yellow) x (yellow:green) = (red:green)

So (3:2) x (1:5) = (3:10)

The ratio of red to green is 3:10.

Answer:

Step-by-step explanation:

The ratio of red : yellow = 3:2 and yellow:green = 1:5

So, the ratio of red : yellow : green = 3:2:5

To find the ratio of red: green, we can find the ratio of red : yellow : green and then divide the red and green portions.

So, the ratio of red: green = (3/(3+2+5)) : (5/(3+2+5)) = 3/10 : 5/10 = 3:5

Answer: Hmm

Step-by-step explanation:

The solution to the given differential equation is xsin(x) + ycos(x) - ysin(y) = C.

The differential equation is given;

(siny - ysinx)dx + (cosx + xcosy - y)dy = 0

We need to verify the following condition:

d/dy(M) = d/dx(N)

Here M and N are the coefficients of dx and dy.

Taking the partial derivatives;

d/dy(siny - ysinx) = cosy - sinx

d/dx(cosx + xcosy - y) = -siny

Since d/dy(M) is not equal to d/dx(N), the differential equation is not exact.

cos(y) - xsin(x) - ysin(x))/[\(e^{ysin(x)} * e^{-xcos(x)}\)] = -∂/∂y(sin(y) - ysin(x))

(sin(y) - ysin(x) + xcos(y))/[\(e^{ysin(x)} * e^{-xcos(x)}\)] = ∂/∂x(cos(x) + xcos(y) - y)

Now, the left-hand sides of both equations depend only on y and x respectively.

Hence, the given differential equation is now a total differential.

Thus, integrating both sides with respect to x and y respectively, we get:

∫(cos(y) - xsin(x) - ysin(x))dy - ∫(sin(y) - ysin(x) + xcos(y))dx = C

On simplifying, we get:

xsin(x) + ycos(x) - ysin(y) = C, where C is a constant of integration.

Hence, the solution to the given differential equation is xsin(x) + ycos(x) - ysin(y) = C.

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We will get the areas of each one of the given triangles:

7) A = 12.69 mm²

8) A = 19.21 in²

9) A = 16.81 yd²

7) First, we have an equilateral triangle, where all the sides measure 5.4mm

For an equilateral triangle of side length S, the area is:

\(A = \frac{\sqrt{3} }{4}S^2\)

In this case, S = 5.4 mm, replacing we get:

\(A = \frac{\sqrt{3} }{4}(5.4mm)^2 = 12.62 mm^2\)

8) Now we have two equal sides and one different. The general area of a triangle of base B and height H is:

A = B*H/2.

In this case, the base measures 3.4 in.

To get the height, let's divide the triangle into two right triangles, such that one cathetus is 3.4in/2 = 1.7 in.

The hypotenuse measures 5.9 in

And the other cathetus is the height of the triangle.

Then, by using the Pythagorean theorem, we see that the height is:

\(H = \sqrt{(5.9 in)^2 - (1.7in)^2} = 5.65 in\)

Then the area of this triangle is:

\(A = (3.4 in)*(5.65 in)/2 = 19.21 in^2\)

9) Here the base measures 8.2 yds, and the height 4.1 yds, so the area is just:

\(A = (4.1 yd)*(8.2 yd)/2 = 16.81 yd^2\)

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Given data ; Initial distance between cars, d = 960m Speed of Car A, vA = 50 m/sSpeed of Car B, vB = 30 m/sSpeed of sound, vS = 340 m/s

Let's solve the parts given in the question;

a) Find vAB; Relative speed, \(vAB = vA + vBvAB = 50 m/s + 30 m/svAB = 80 m/s\)

b)Let t be the time until the two cars collide.In time t, the distance traveled by Car A = vA0t

The distance traveled by Car B = vBt

The total distance covered by both cars is d:

Therefore, \(vAt + vBt = dd/t = (vA + vB)t = 960 mt = d / (vA + vB)t = 960 / 80t = 12 s\)

Let ΔsSound be the displacement of the sound during that time.

Distance traveled by Car \(A = vA x t = 50 m/s x 12 s = 600 mDistance traveled by Car B = vB x t = 30 m/s x 12 s = 360 m\)

Therefore, the distance between the cars will be \(960 - (600 + 360) = 0 m.\) So, the sound wave will have traveled the displacement of 4080 m from Car B to Car A.

Hence, ΔsSound = 4080 m.

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Answer:

I am pretty sure the answer is is C. WVR and VRQ

Step-by-step explanation:

Answer:

top answer is 'c' and the bottom is 'a'

Answer:

2144.7

Step-by-step explanation:

Volume of a sphere is V= \(\frac{4}{3} \pi r^{3}\)

V= \(\frac{4}{3} \pi 8^{3}\)

V=(4 /3)·π·8^3≈2144.66058 --> 2144.7

The equation x = 7 - 4√3 is a radical expression, and the value of the radical expression is \((x + \frac 1x)^2 = 3650401 -2107560\sqrt 3\)

The equation is given as:

x = 7 - 4√3

So, we have:

\((x + \frac 1x)^2 = (7 - 4\sqrt 3 + \frac{1}{7 - 4\sqrt 3})^2\)

Take the LCM

\((x + \frac 1x)^2 = (\frac{49 -56\sqrt3 + 48}{7 - 4\sqrt 3})^2\)

Evaluate the like terms

\((x + \frac 1x)^2 = (\frac{97 -56\sqrt3 }{7 - 4\sqrt 3})^2\)

Rationalize

\((x + \frac 1x)^2 = (\frac{(97 -56\sqrt3)(7 - 4\sqrt 3) }{49 -48})^2\)

Evaluate the difference

\((x + \frac 1x)^2 = ((97 -56\sqrt3)(7 - 4\sqrt 3))^2\)

Expand

\((x + \frac 1x)^2 = (679 -388\sqrt 3 -392\sqrt 3 + 672)^2\)

Evaluate the like terms

\((x + \frac 1x)^2 = (1351 -780\sqrt 3 )^2\)

Expand

\((x + \frac 1x)^2 = 1825201 +1825200 -2107560\sqrt 3\)

\((x + \frac 1x)^2 = 3650401 -2107560\sqrt 3\)

Hence, the value of the radical expression is \((x + \frac 1x)^2 = 3650401 -2107560\sqrt 3\)

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Answer:

∠2 and ∠5 are corresponding angles

Step-by-step explanation:

Answer:

corresponding angles

Step-by-step explanation:

Answer:To divide 15a^6b^4 by 5a^2b, we can divide the coefficients and then divide the variables using the quotient rule of exponents, which states that when dividing two exponential terms with the same base, you can subtract the exponents.

So we have:

(15a^6b^4) / (5a^2b) = (15/5) * (a^6/a^2) * (b^4/b)

= 3a^(6-2)b^(4-1)

= 3a^4b^3

Therefore, the simplified result of dividing 15a^6b^4 by 5a^2b is 3a^4b^3

Step-by-step explanation:

The solution to the division is 3a⁴b³.

Given that we need to divide the expression (15a⁶b⁴) by (5a²b),

To divide the expression (15a⁶b⁴) by (5a²b), you need to apply the rules of division with variables and exponents.

Here's how you can simplify the expression:

When dividing with the same base, you subtract the exponents. In this case, the base is "a" and the exponents are 6 and 2.

Subtracting the exponents gives us a⁶ - a² = a⁶⁻² = a⁴.

Similarly, for the variable "b," the exponents are 4 and 1.

Subtracting the exponents gives us b⁴ - b¹ = b⁴⁻¹ = b³.

Now, let's simplify the coefficients. The coefficient 15 divided by 5 is 3.

Putting it all together, the expression (15a⁶b⁴) / (5a²b) simplifies to:

3a⁴b³

Hence the solution to the division is 3a⁴b³.

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False. Data mining can automatically find beneficial patterns for a business by utilizing various techniques and algorithms to extract valuable insights and uncover hidden patterns from large datasets.

Data mining refers to the process of discovering patterns, relationships, and insights from large datasets. It involves using various techniques and algorithms to extract valuable information and knowledge from data. One of the primary goals of data mining is to uncover patterns that can be beneficial for businesses, such as identifying customer preferences, market trends, or predicting future outcomes.

Through automated analysis and pattern recognition, data mining can uncover hidden patterns and relationships that may not be apparent through traditional manual analysis. Therefore, data mining has the potential to automatically find beneficial patterns for businesses, making the statement "Data Mining cannot automatically find beneficial patterns for a business" false.

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Answer:

120 ft²

Step-by-step explanation:

The length of each of the congruent sides is (50-16)/2 = 17 ft.

So, using the Pythagorean theorem, the altitude drawn from the vertex angle to the base has a length of 15 ft.

Thus, the area is (1/2)(15)(16) = 120 ft².

Answer:

The answer is above. Numbers 2 and 3

Answer:

\(-12-10i\)   is the required answer.

Step-by-step explanation:

\(\left(-9-8i\right)-\left(3+2i\right)\\\\\mathrm{Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number}\\\\=\left(-9-3\right)+\left(-8-2\right)i\\\\=-12-10i\)

Best Regards!

The current when the resistance is 90 ohms is 2.7 amperes (rounded to one decimal place), with units of amperes.

The relationship between current and resistance is given by the equation I = V/R, where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms. If we assume that the voltage is constant, then we can use the fact that the current is inversely proportional to the resistance to find the current when the resistance is 90 ohms.

To do this, we can use the formula I1R1 = I2R2, where I1 and R1 are the initial current and resistance, and I2 and R2 are the final current and resistance. Plugging in the values given, we get:

1.2 A x 200 ohms = I2 x 90 ohms

Simplifying, we get:

I2 = (1.2 A x 200 ohms) / 90 ohms

I2 = 2.67 A

Therefore, the current when the resistance is 90 ohms is 2.7 amperes (rounded to one decimal place), with units of amperes.

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Answer:

D I guess is the answer for the question

Step 1:

Write the equation of the line in the form of y = mx + c

m = slope

Step 2

Step 3

From the equation

Step 4:

Final answer

The measure of acute angle = 26.6

Answer:

A. To find a linear equation that models the temperature T when crickets are chirping at x chirps per minute, we need to use two points that are known. In this case, we are given that a cricket produces 120 chirps per minute at 70 degrees F and 168 chirps per minute at 80 degrees F. We can use these two points to find the slope and y-intercept of the line.

The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1)

In this case, we can substitute the given values to get:

m = (168 - 120) / (80 - 70) = 48/10 = 4.8

The y-intercept of a line can be found using the formula: b = y - mx

We can use the point (70, 120) and the slope that we found to get:

b = 120 - (4.8 * 70) = -264

So the linear equation that models the temperature T when crickets are chirping at x chirps per minute is:

T = 4.8x - 264

B. If the crickets are chirping at 150 chirps per minute, we can substitute this value for x in the equation we found above to estimate the temperature:

T = 4.8x - 264

T = 4.8(150) - 264 = 720 - 264 = 456

So the estimated temperature is 456 degrees F.

C. The y-intercept of the line is -264, it represents the temperature when x (chirps per minutes) is zero. In this case it represents the temperature when the cricket is not chirping which is impossible, so it doesn't have any physical meaning.