Evaluate the integral by reversing the order of integration.

∫∫y cos(x^2) dxdy

Solution of the given fractional equation x over 2 plus x over 5 equals 1 is 10/7

What is a Fractional equation ?

A fractional equation is one that contains one or more terms that are fractions. The first step in solving a fractional equation is to remove the fractions by multiplying both sides of the equation by the LCD of each term. We are able to accomplish this because an equation does not get out of balance when both sides are multiplied by the same amount, in this example, the LCD. The fractions are now gone, and the equation may now be solved like any other nonfractional problem.

A fractional equation is one in which one or more of its terms have the unknown as their denominator.

X/2 + X/5 = 1

X(1/2 +1/5)= 1

X(7/10)= 1

X =  10/7

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Answer:

right 5 units

Step-by-step explanation:

given f(x) then f(x ± a) is a horizontal translation of f(x)

• if + a then a shift of a units left

• if - a then a shift of 5 units right

f(x) → g(x) = (x - 5)² with a = - 5

then f(x) is shifted 5 units right to obtain g(x)

The correct answer is option  A: The random variable is discrete. A decibel is a unit of measure used to quantify the loudness or intensity of sound.

From 0 dB (the quietest level of sound) to 140 dB (the loudest level of sound), it is measured on a logarithmic scale (the highest level of sound).

The decibel level of a siren is normally between 110 and 120 dB, which is regarded to be within or close to the threshold of human hearing.

The decibel level of a siren is measured on a logarithmic scale, making it a discrete variable. This indicates that it is measured in whole numbers rather than fractions of a decibel.

For instance, a siren's decibel level can be 110 dB, 111 dB, 112 dB, etc., but it cannot be 110.5 dB or 111.5 dB. Therefore, the decibel level of a siren is a discrete variable.

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If the angles are ∠1 = 2x + 4 and ∠2 = 3x - 3, then m∠TRS =  36°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of ∠1 = 2x + 4

The measure of ∠2 = 3x - 3

The measure of ∠TRS is -

∠TRS = ∠1 + ∠2

Since, PR is a bisector then ∠1 = ∠2.

The equation is -

2x + 4 = 3x - 3

2x - 3x = - 3 - 4

-x = -7

x = 7

Substitute the value of x in the angles -

∠1 = 2(7) + 4

∠1 = 14 + 4

∠1 = 18°

∠2 = 3(7) - 3

∠2 = 21 - 3

∠2 = 18°

So, the value of ∠TRS is -

∠1 + ∠2

18° + 18°

36°

Therefore, the measure of ∠TRS is 36°.

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Answer:

k = 0

Step-by-step explanation:

Step 1:

7k - 7 ( 2 - 6k ) = - 8k - 14   Equation

Step 2:

7k - 14 + 42k = - 8k - 14   Multiply

Step 3:

- 14 + 49k = - 8k - 14   Add

Step 4:

- 14 + 57k = - 14     Add 8k on both sides

Step 5:

57k = 0   Add 14 on both sides

Answer:

k = 0

Hope This Helps :)

Answer:

1.49 hrs or 1 hr and 30 minutes approximately

Step-by-step explanation:

if fran go 2.8m up then the river flow at a rate of 0.8m; the since we are taking the speed of fran and river to be constant. the ratio between their speed will always remain constant. that is if 0.8/2.8 = 0.286≈ this will be always constant.

so if he go up 4m then the horizontal length has to be 1.143 because 1.143/4 = 0.286.

now we find the distance between frans initial positon and final position. to find it we use pythagoras theorem.

\(\sqrt{(4^2 + 1.143^2)} =4.160 miles\)

to find the time divide distance traveled by speed;

4.160/2.8 = 1.49 hrs

Answer:

9 pencils were sharp

Step-by-step explanation:

3*4=12 so if three fourths were sharp then 9 were

To determine a formula for the n-th term of an arithmetic sequence, we need to find the common difference (d) first.

The common difference is the constant value that is added or subtracted to each term to get to the next term.

In this case, we can find the common difference by subtracting the fourth term from the seventh term:

d = a₇ - a₄

d = 31 - 19

d = 12

Now that we have the common difference, we can use it to find the formula for the n-th term of the arithmetic sequence. The formula is given by:

aₙ = a₁ + (n - 1)d

In this formula, aₙ represents the n-th term, a₁ represents the first term, n represents the position of the term, and d represents the common difference.

Since we don't have the first term (a₁) given in the problem, we can find it by substituting the known values for a₄ and d:

a₄ = a₁ + (4 - 1)d

19 = a₁ + 3(12)

19 = a₁ + 36

a₁ = 19 - 36

a₁ = -17

Now we can substitute the values of a₁ and d into the formula to get the final formula for the n-th term:

aₙ = -17 + (n - 1)(12)

Therefore, the formula for the n-th term (aₙ) of the given arithmetic sequence is aₙ = -17 + 12(n - 1).

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The mathematical relationship that best describes the dependence of capacitance on plate separation is an inverse relationship.

This means that as the plate separation increases, the capacitance decreases and vice versa. The equation that describes this relationship is:

C = εA / d

where C is the capacitance, ε is the permittivity of the dielectric material between the plates, A is the area of the plates, and d is the plate separation. As we can see from the equation, the capacitance is inversely proportional to the plate separation, meaning that as the plate separation increases, the capacitance decreases.

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The area of the triangle formed by the vertices (-4,1), (5,2), and (2,-3) is 21 square units.

To find the area of a triangle given its vertices, we can use the formula for the area of a triangle using coordinates:

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Using the given vertices (-4,1), (5,2), and (2,-3), we can substitute the values into the formula: Area = 0.5 * |(-4)(2 - (-3)) + (5)(-3 - 1) + (2)(1 - 2)|

Simplifying the expression inside the absolute value:

Area = 0.5 * |(-4)(5) + (5)(-4) + (2)(-1)|

Area = 0.5 * |-20 - 20 - 2|

Area = 0.5 * |-42|

Area = 0.5 * 42

Area = 21

Therefore, the area of the triangle formed by the given vertices is 21 square units.

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We need to use the fact that the percentages of all three categories must add up to 100%. Therefore, the percentage of independent voters can be found by subtracting the percentages of democrat and republican voters from 100%.
Percentage of independent voters = 100% - 35% - 40% = 25%
So, 25% of the registered voters are independent.
In conclusion, the percentage of independent voters is 25%. This is because the percentages of democrat, republican, and independent voters must add up to 100%. The percentages of democrat and republican voters are given, so we can find the percentage of independent voters by subtracting those from 100%.
Based on the given information, 35% of registered voters are classified as Democrats, and 40% are classified as Republicans. To find the percentage of registered voters who are independent, we need to subtract the total percentage of Democrats and Republicans from 100%.
100% - (35% + 40%) = 100% - 75% = 25%
Therefore, 25% of the registered voters are classified as independent.

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Therefore, the probability of selecting a white or blue marble is approximately 0.3910 or 39.10% when rounded to four decimal places.

To find the probability of selecting a white or blue marble, we need to determine the total number of white and blue marbles and divide it by the total number of marbles in the box.

Total white and blue marbles = Number of white marbles + Number of blue marbles

= 58 + 3

= 61

Total number of marbles = Number of red marbles + Number of white marbles + Number of blue marbles

= 95 + 58 + 3

= 156

Probability = (Total white and blue marbles) / (Total number of marbles)

= 61 / 156

≈ 0.3910 (rounded to four decimal places)

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A sine function has an amplitude of 3, a period of pi, and a phase shift of pi/4, then y-intercept of the sine function is 3√2 / 2.

To locate the y-intercept of a sine function with the information given here, we can use the general form of a sine function:

y = A * sin(Bx - C) + D

Here, it is given that:

Amplitude (A) = 3

Period (P) = π

Phase Shift (C) = π/4

The frequency (B) can be calculated as B = 2π / P.

y = 3 * sin(Bx - π/4) + D

0 = 3 * sin(B * 0 - π/4) + D

0 = 3 * sin(-π/4) + D

0 = 3 * (-1/√2) + D

0 = -3/√2 + D

0 = -3 + √2D

√2D = 3

D = 3/√2

D = (3/√2) * (√2/√2)

D = 3√2 / 2

Therefore, the y-intercept of the sine function is 3√2 / 2.

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Claim: The measures of \(\angle B\) and \(\angle B'\) are equal

Answer: True

Explanation: Dilations preserve the shape of an image, so this means the angles are kept the same whether you shrink or enlarge the preimage.

====================================================

Claim: The coordinates of A and A' are the same

Answer: True

Explanation: The phrasing "dilating about point A" means that point A is the center of the universe, so to speak, in terms of this dilation operation. Point A is the fixed point that does not move while every other point does move. Because the scale factor is 2/3, which is less than 1, this means every other point comes closer to point A. So something like segment AB will get shorter.

Answer:

\(\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}\)

\(\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10\)

\(\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10\)

\(\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}\)

\(\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}\)

\(\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}\)

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The mean scores are the same.

Nilo's standard deviation is higher than Lisa's.  Therefore, Nilo's test scores are more spread out that Lisa's, which means Lisa's test scores are more consistent.

Answer:

197.1

Step-by-step explanation:

The solution set to the given inequality is

(-∞, -4) U (2,∞)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5(x – 2)(x + 4) > 0

First we solve for x, we replace the inequality sign by = sign

5(x – 2)(x + 4) = 0

Divide both sides by 5

(x – 2)(x + 4) = 0

Now we set each factor =0  and solve for x

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we use number line and make three intervals

First interval -infinity to -4

second interval -4 to 2

third interval 2 to infinity

Now we check each interval with our inequality

First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

solution set are the intervals that make the inequalities true

(-∞, -4) U (2,∞)

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Question:

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

Answer:

\(Rate = 8640 fl\ oz/hour\)

Step-by-step explanation:

Given

Rate: 9 gallon in every 8 minutes

Required

Express in fluid ounces per hour

Express rate as follows;

\(Rate = \frac{9\ gallon}{8\ minutes}\)

1 gallon = 128 fluid ounces;

So:

\(Rate = \frac{9 * 128 fl\ oz}{8\ minutes}\)

1 minutes = 1/60 hour;

So:

\(Rate = \frac{9 * 128 fl\ oz}{8 * \frac{1}{60} hour}\)

\(Rate = \frac{1152 fl\ oz}{ \frac{8}{60} hour}\)

\(Rate = 1152\ fl\ oz/ \frac{8}{60}\ hour\)

\(Rate = 1152* \frac{60}{8}\ fl\ oz/hour\)

\(Rate = \frac{1152*60}{8}\ fl\ oz/hour\)

\(Rate = \frac{69120}{8}\ fl\ oz/hour\)

\(Rate = 8640 fl\ oz/hour\)

Answer: 3x + 6

Step-by-step explanation: PLEASE MARK ME AS BRAINLISTI AND HAVE A GREAT DAY!!!

Answer:

3x+6

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Answer:

1) d 2) b

Step-by-step explanation:

1) 36÷24 = 1.5 15×1.5= answer

2) 4÷3.2= 1.25 7.5÷1.25= answer

Answer:

Since they're both equated to y...

7x² + 6x – 13 = 3x – 3

Bringing all the left

7x² + 3x – 10 = 0

Solving for x

you have

x = 1 or x = –10/3

Now substitute to get y

y = 0 or –13

The expected value of the bet is -15.693

According to the question we have been given that

If we draw a card with value 5 or less, we will be payed = 57

If failed to draws cards, we have to pay = 48

Now first we will find the probability of drawing cards with value less than or equal to 5.

Cards with value less than five are : 2,3,4,5

Total number of cards will be 16.

Probability = 16/52

Also number of cards with values greater than five is 36

Probability = 36/52

Thus the expected value of the bet will be

   = 57*(16/52) + (-48)*(36/52)    [ negative sign as we have to pay if we loose to draw the required card]

   = 17.538 - 33.231

   = -15.693

Hence the expected value is -15.693

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Answer:

Hope it helps you............

Answer:

-170 2/3

Step-by-step explanation:

Divide both sides by 3 to get p by itself

p = -512/3

Simplify

- 170 2/3

Answer:

p=−8

Step-by-step explanation:

Let's solve your equation step-by-step.

\( \rightarrow \sf \: p {}^{3} =−512\)

Step 1: Take cube root.

\( \sf p={(−512) }^{ ( \frac{1}{3} )}\)

\( \sf \: p=−8\)

The angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\),\) which is approximately 1.107 radians or 63.43 degrees.

To determine the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\),\) we can follow these steps:

1. Express \(\(z_0\)\) in polar form: To find the polar form of \(\(z_0\)\), we need to calculate its magnitude \((\(r_0\))\) and argument \((\(\theta_0\))\). The magnitude can be obtained using the formula \(\(r_0 = |z_0| = \sqrt{\text{Re}(z_0)^2 + \text{Im}(z_0)^2}\)\):

\(\[r_0 = |2i + 1| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}\]\)

  The argument \(\(\theta_0\)\) can be found using the formula \(\(\theta_0 = \text{arg}(z_0) = \arctan\left(\frac{\text{Im}(z_0)}{\text{Re}(z_0)}\right)\)\):

\(\[\theta_0 = \text{arg}(2i + 1) = \arctan\left(\frac{2}{1}\right) = \arctan(2)\]\)

2. Find the polar form of \(\(w\)\): The polar form of \(w\) can be expressed as \(\(w = |w|e^{i\theta}\)\), where \(\(|w|\)\) is the magnitude of \(\(|w|\)\) and \(\(\theta\)\) is its argument. Since \((w = z^2\)\), we can substitute z with \(\(z_0\)\) and calculate the polar form of \(\(w_0\)\)using the values we obtained earlier for \(\(z_0\)\):

 \(\[w_0 = |z_0|^2e^{2i\theta_0} = \sqrt{5}^2e^{2i\arctan(2)} = 5e^{2i\arctan(2)}\]\)

3. Determine the argument of \(\(w_0\):\) To find the argument \(\(\theta_w\)\) of \(\(w_0\)\), we can simply multiply the exponent of \(e\) by 2:

  \(\[\theta_w = 2\theta_0 = 2\arctan(2)\]\)= 1.107 radians

Therefore, the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\).\)

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The complete question is:

"Determine the angle of rotation, in radians and degrees, at the point z0 = 2i + 1 when w = z^2."