Evaluate nonlinar expressions

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ORIGINAL EQUATION

|5x - 4| = 11

~~~~~~~~~~~~~~~~~~~~
Possible EQUATION #1

5x - 4 = 11

ADD 4 to BOTH SIDES

5x - 4 + 4 = 11 + 4

CANCEL out: -4 + 4 because it gives you 0

KEEP: 11 + 4 because it help solve for the x-value

NEW EQUATION: 5x = 11 + 4

SIMPLIFY IT!

5x = 15

DIVIDE 5 to BOTH SIDES

5x/5 = 15/5

CANCEL out: 5/5 because it gives you 1

KEEP: 15/5 because it help solve for the x-value

NEW EQUATION: x = 15/5

SIMPLIFY IT!

x = 3

~~~~~~~~~~~~~~~~~~~~
Possible EQUATION #2

5x - 4 = -11

ADD 4 to BOTH SIDES

5x - 4 + 4 = -11 + 4

CANCEL out: -4 + 4 because it gives you 0

KEEP. -11 + 4 because it help solve for the x-value

NEW EQUATION: 5x = -11 + 4

SIMPLIFY IT!

5x = -7

DIVIDE 5 to BOTH SIDES

5x/5 = -7/5

CANCEL out: 5/5 because it gives you 1

KEEP: -7/5 because it help solve for the x-value

NEW EQUATION: x = -7/5

SIMPLIFY IT!

x = -7/5

~~~~~~~~~~~~~~~~~~~~~~~

ANSWER

x = 3 or x = -7/5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: The answer to this math question about translating this given expression to an English phrase is C). 3 more than the product of 7 and 4.

Step-by-step explanation: The keywords are times and the sum, which tells us that the 2 operations are multiplication and addition, let's translate this math expression into an English phrase by looking at the 2 operation signs "×" and "+" in order to find the words to translate the given math expression into an English phrase that looks in the equation form and an English phrase like this:

I hope that my full given answer with my full given step-by-step explanation is very helpful to your own math question about translating this given expression to an English phrase, please mark me as Brainliest after her answer was been reported by someone and got deleted by The Brainly Moderator, take care, always be safe, and have a great rest of the day! :D  

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The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.

Answer:

An adult cheetah can run 103 feet per second!

Step-by-step explanation:

First we need to convert our miles to feet, there are 5,280 feet in one mile.

So 70 miles multiplied by 5,280 feet is 369,600 feet.

Now we need to convert an hour to seconds.

There are 60 seconds in one minute, so we multiply 60 seconds by 60 minutes, there are 3,600 seconds in one hour.

Now we need to divide the number of feet by the number of seconds.

369,600 ÷ 3,600 = 102.666667

102.666667 rounded to the nearest whole number is 103.

Given information, we are required to find the Joint Probability Mass Function of (X, Y), where X and Y are the smaller and larger number of points, respectively, when two dice are rolled.

The sample space of rolling two dice is {1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {3, 1}, {3, 2}, {3, 3}, {3, 4}, {3, 5}, {3, 6}, {4, 1}, {4, 2}, {4, 3}, {4, 4}, {4, 5}, {4, 6}, {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5}, {5, 6}, {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6}. Let A = {1, 2, 3, 4, 5, 6} be the sample space of a dice, which means the probability of each outcome is 1/6.

Now, we need to calculate the probability of rolling i and j, where X is the smaller number, and Y is the larger one. Therefore, P (X = i, Y = j) = P (i, j) - P (i, i) - P (j, j) if i≠j, where P (i, j) represents the probability of rolling i and j.

However, if i = j, then P (X = i, Y = i) = P (i, i). For i=1,2,3,4,5,6, P (X = i, Y = i) = 1/6.

We can also write P (X = i, Y = i) = P (X = i)P (Y = i). Therefore, P (X=i, Y=j)=P(i,j)−P(i,i)−P(j,j)={1/36 if i≠j}{1/18 if i=j}.

(b) X and Y are not independent since knowing X affects Y. If X is known to be 2, then Y can only be in the range of 3 to 6. Therefore, P(Y=5|X=2) ≠ P(Y=5). This shows that X and Y are not independent.

(c) Let p(i) represent the probability mass function of X, which is the probability of the smaller number being i. For i = 1, 2, 3, 4, 5, 6, P(X=i)=P(X=i,Y>i)+P(X=i,Y=i)={5/36 if i=1}{4/36 if i=2}{3/36 if i=3}{2/36 if i=4}{1/36 if i=5}{0 if i=6}

(d) The required probability of P(Y=5|X=2) = P(X=2,Y=5)/P(X=2). The probability of X=2 is P(X=2) = 4/36 = 1/9. Since X=2, the favorable outcome is {(2, 5)}, therefore, P(X=2,Y=5) = 1/36. The required probability is P(Y=5|X=2) = P(X=2,Y=5)/P(X=2) = (1/36)/(1/9) = 1/4 = 0.25. Hence, the probability that Y=5 when X=2 is 0.25.

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Answer:

12 x 12 = 144

Step-by-step explanation:

12 times by 12 is 144

Answer:

43.96 cm

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = 2πr

where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

Given that the radius of the circle is 7 cm, we can substitute this value into the formula and simplify:

C = 2πr

C = 2 × 3.14 × 7

C = 43.96

Therefore, the circumference of the circle is approximately 43.96 cm.

The correct answer among the choices provided is A. 11.48.

Given that side XY of triangle XYZ corresponds to side JK of triangle JKL, we can set up the following proportion:

XY/JK = YZ/LJ

Substituting the given values:

8.7 / 12.18 = 7.8 / LJ

We solve this for LJ:

LJ = (7.8 * 12.18) / 8.7

Calculating that gives us:

LJ ≈ 11.48

So, the correct answer among the choices provided is A. 11.48.

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Answer:

the cone is not a prism, as it is not a cylinder. the star prism(lookimg like thing) is. alsp it is circular so it cannot be a prism(like the cylinder)

The probability of winning $3,899 is 0.0001, which is a very small probability, but still possible.

To write the probability distribution for a player's winnings in the Pick 4 game, we need to consider all the possible outcomes and their probabilities.

There are a total of 10,000 possible four-digit numbers that can be drawn in the game. Since the player has to match the numbers in the exact order, there is only one winning combination for each four-digit number. Therefore, the probability of winning is 1/10,000.

To calculate the player's winnings, we need to subtract the $1 cost of playing from the $3,900 prize. Thus, the player's net winnings can be calculated as follows:

Net Winnings = $3,900 - $1 = $3,899

The probability distribution for the player's winnings can be summarized in the following table:

| Winnings (x) | Probability (P) |
|--------------|-----------------|
| $0           | 0.9999          |
| $3,899       | 0.0001          |

Note that the table shows the possible winnings (x) in ascending order, as requested. The probability of winning $0 is 0.9999, which means that the player is most likely to lose their $1 bet.

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a) The derivative of g(x) at x=2 is g'(2) = 2.

b) The second derivative of k(x) at x=1 is k"(1) = -30.

c) The derivative of n(x) at x=0 is n'(0) = -18.

a) To find g'(x), we need to take the derivative of g(x) with respect to x. Let's differentiate each term separately:

g(x) = 3x³ - 8x² - 2x + 35

The derivative of 3x³ is obtained by applying the power rule, which states that if we have a term of the form \(ax^n\), the derivative is given by \(nax^{(n-1)\). In this case, the derivative of 3x³ is 3 * 3x², which simplifies to 9x².

The derivative of -8x² is obtained in a similar manner, resulting in -16x.

The derivative of -2x is -2.

Since 35 is a constant term, its derivative is zero.

Now, let's combine these derivatives to find g'(x):

g'(x) = 9x² - 16x - 2

To find g'(2), we substitute x = 2 into the derivative:

g'(2) = 9(2)² - 16(2) - 2

= 9(4) - 32 - 2

= 36 - 32 - 2

= 2

Therefore, g'(2) = 2.

b) To find k"(x), we need to take the second derivative of k(x) with respect to x. Let's differentiate each term:

k(x) = 1 / \(x^5\)

The derivative of 1/\(x^5\) can be found using the power rule and the chain rule. The power rule states that the derivative of \(x^n\) is n\(x^{(n-1)\), and the chain rule applies when we have a function within another function. In this case, the derivative of 1/\(x^5\) is -5/\(x^6\).

Taking the derivative of -5/\(x^6\), we apply the power rule again, resulting in 30/\(x^7\).

Now, let's find k"(x) by differentiating -5/\(x^6\) again:

k"(x) = -30/\(x^7\)

To find k"(1), we substitute x = 1 into the second derivative:

k"(1) = -30/(\(1^7\))

= -30/1

= -30

Therefore, k"(1) = -30.

c) To find n'(x), we need to take the derivative of n(x) with respect to x. We can apply the product rule to differentiate the two factors of n(x):

n(x) = (-4x + 2)(3x² - 5x + 2)

Using the product rule, the derivative of n(x) is given by:

n'(x) = (-4x + 2)(d/dx)(3x² - 5x + 2) + (3x² - 5x + 2)(d/dx)(-4x + 2)

To differentiate each term, we use the power rule:

(d/dx)(3x² - 5x + 2) = 6x - 5

(d/dx)(-4x + 2) = -4

Substituting these derivatives back into n'(x), we get:

n'(x) = (-4x + 2)(6x - 5) + (3x² - 5x + 2)(-4)

Now, let's find n'(0) by substituting x = 0 into the derivative:

n'(0) = (-4(0) + 2)(6(0) - 5) + (3(0)² - 5(0) + 2)(-4)

= (2)(0 - 5) + (0 - 0 + 2)(-4)

= (2)(-5) + (2)(-4)

= -10 - 8

= -18

Therefore, n'(0) = -18.

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Answer:

The correct option are;

On a coordinate plane, a cubic function has an x-intercept of (0, 0)

On a coordinate plane, an oval is in quadrant 1

Step-by-step explanation:

Rotational symmetry of a shape is a shape that when it is rotated on its axis to a given angle less than one complete revolution, the shape looks exactly like the pre-image or original appearance of the shape

For a cubic function that has x-intercept = (0, 0) we have;

y = f(x) = a·x³ + b·x² + c·x

Has the shape f a fan blade and therefore, looks the sane when rotated when rotated through 180°

The shape of an oval looks the same when rotated through 180°

Answer:

This graph has rotational symmetry about the point

(0,0).

This graph has rotational symmetry about the point (2,4).

Step-by-step explanation:

second part on edge 2020 !

The margin of error is (31.15, 32.85).

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor. A higher error indicates a high chance that the result of the sample reported may not be the true reflection of the whole population. The formula for the margin of error is calculated by multiplying a critical factor (for a certain confidence level) with the population standard deviation. Then the result is divided by the square root of the number of observations in the sample.

Mathematically, it is represented as,

Margin of Error = Z * ơ / √n

Given:

Number of people = n = 16

Mean = μ = $32

Standard deviation = σ = $7

Confidence level = 95%

Thus, the z value would be 1.96.

The confidence interval can be calculated as follows:

Confidence interval = μ ± z(σ/√n)

= 32 ± 1.96 × (7/16)

= 32 ± 0.85

= (31.15, 32.85)

Thus, the margin of error is (31.15, 32.85).

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Answer:

Step-by-step explanation:

Find the volume of the cube

Find the value of the expression

Answer:

15)  2744 in³

16)  584

Step-by-step explanation:

Volume of a cube

\(\sf V=s^3\)

(where s is the side length)

Given:

Substitute the given value into the formula and solve for V:

\(\implies \sf V=14^3\)

\(\implies \sf V=14 \cdot 14 \cdot 14\)

\(\implies \sf V=196 \cdot 14\)

\(\implies \sf V=2744\:\:in^3\)

Given expression:

To solve:

\(=\sf 8 + (8 \cdot 8) + (8 \cdot 8 \cdot 8)\)

\(\sf = 8 + 64 + 512\)

\(\sf = 72+512\)

\(= \sf 584\)

Therefore, 584 people were sent your email.

Answer:

Step-by-step explanation:

a. (I) x = 65

(ii) vertically opposite angles are equal.

b. (i) 71 degrees

(ii) alternate interior angles are equal

c. (i) z = 180 - 71 = 109 degrees

(ii) angles on a line add up to 180 degrees

Answer:

x = 65°, y = 71°, z = 44°

Step-by-step explanation:

x and 65 are vertical angles and congruent, thus

x = 65°

y and 71 are alternate angles and congruent, thus

y = 71°

The sum of the 3 angles in a triangle = 180°, thus

z = 180° - (65 + 71)° = 180° - 136° = 44°

Hence

x = 65°, y = 71° and z = 44°

Answer:

a)286 ways

b)1,037,836,800 ways

Step-by-step explanation:

a. How many ways are there to choose 10 players to play the game?

We have to take note of a key word here which is CHOOSE. For question a, order does not matter.

Hence, we use the combination formula. This is given as:

C(n, r) = nCr = n!/r! (n - r)!

n = 13, r = 10

13C10 = 13!/10! (13 - 10)!

= 13!/ 10! × (3!)

= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (3 × 2 × 1)

= 1716/6

= 286 ways.

b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?

For question b as well, we take note of a key word which is ASSIGN. For question b, order is very important.

Therefore, the formula we use is the permutation formula.

P(n, r) = nPr = n!/(n - r)!

n = 13, r = 10

13P10 = 13!/ (13 - 10)!

= 13!/ 3!

= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (3 × 2 × 1)

= 1,037,836,800 ways

Answer: 1/6.

Step-by-step explanation:

3/18 is just 1/6 because you have to divide the numerator and denominator by 3.

Answer:

-4x²y + 17xy² - 15xy

Step-by-step explanation:

Step 1: Write out expression

6x²y + 8xy² - 10x²y - 15xy + 9xy²

Step 2: Combine like terms (x²y)

-4x²y + 8xy² - 15xy + 9xy²

Step 3: Combine like terms (xy²)

-4x²y + 17xy² - 15xy

Answer:

Mean = 5.08

Step-by-step explanation:

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

\( \frac{2.3 + 0.3 + 7 + 6.1 + 9.7}{5} \)

\( = \frac{25.4}{5} \)

= 5.08

The relationship between the variables in terms of direction form and strength.

Given :

the relationship of between the variables in terms of direction ( positive or negative slope ) , form (a straight line or a curve), and strength.

The straight line form with variables is :

y = mx + b is a straight line equation

here x and y are variables

m = slope

b = y - intercept

example :

y = 3x + 3

m = + 3 is a positive slope

y = -2x + 4

here

m = - 2 is a negative slope

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a) 500 -25x ≥ 200 b) 12 weeks

1) Gathering the data

$500

At least : ≥ 200

Withdrawal = -25

A) Since she wants at least 200 in the account, and the summer has 12 weeks, We can write this inequality:

500 - 25x ≥ 200

B) To find how many weeks we need to solve an equation

500-25x= 200

-25x = 200 -500

-25x = -300

25x = 300

x=12

Under these conditions, 12 weeks in the 13th week she won't be able to keep at least $200 in her account with these weekly withdrawals

Answer:

-5

Step-by-step explanation:

Answer:

0.343283582

HOPE IT HELPS

Answer:

36 minutes.

Step-by-step explanation:

Piggly takes 6 minutes and Wiggly takes 5 minutes. Therefore Wiggly is travelling one minute slower.

If we just think about the first lap to start, and break it up into minute sections (like in the diagram attached), we can think about each pigs placement on the diagram for each lap.

At the end of the first lap, Piggly will have reached the end of the 6th minute section and will be back at the start/finish. Wiggly will only be at the end of the 5th minute section.

For the second lap, Piggly will again end up back at the start/finish, but Wiggly, having started his lap one section behind (at the end of the 5th section) will now end up even further behind (at the end of the 4th section).

Go ahead and count it out. Every lap he only covers 5 section, so every lap he falls one section further behind.

After six laps he will finish back at the start, at the same time as Piggly (but Piggly will be a lap ahead of him. Our sections have 6 minutes in each, and 6 laps are completed.

6 x 6 = 36 minutes

Answer:

\(\large \boxed{\sf B. \ 34}\)

Step-by-step explanation:

\(5(14 - 2^3 ) +8 \div 2\)

\(\sf Solve \ brackets.\)

\(2^3 =8\)

\(5(14 - 8 ) +8 \div 2\)

\(14-8=6\)

\(5(6 ) +8 \div 2\)

\(\sf Multiply \ and \ divide.\)

\(5(6)=30\)

\(8 \div 2 = 4\)

\(30 +4\)

\(\sf Add.\)

\(34\)

Answer: 34

Step-by-step explanation: It's very easy to make mistakes in order of operations problems if you try to do too much of the problem in your head.

It really is worth the extra time it takes to write out every step.

P  E  M  D  A  S

Parenthses

Exponents

Multiplication/Division

Addition/Subtraction

In this problem, simplify (14 - 2³) first

because it's located inside the parenthses.

2³ is 8 so our second step reads 5(14 - 8) + 8 ÷ 2.

14 - 8 is 6 so we have 5(6) + 8 ÷ 2.

Now multiplication and division are based on order of appearance.

Since multiplication comes first, we do it first.

5(6) is 30 so we have 30 + 8 ÷ 2.

Now we can do the division.

8 ÷ 2 is 4 and we have 30 + 4 which is 34.

Then, we can divide both sides by 100 to get y = 12. Thus, we travel 12 feet vertically driving 200 feet on this road with a 6% uphill grade.

The road is inclined at a 6% gradient. This indicates that the slope of the road is (6)/ (100). To estimate the amount of vertical change in position when driving 200 feet on a road that has a 6% uphill grade, you will need to use the formula for slope.

It is commonly represented by the letter mi. the case of the road; the slope is 6%. In other words, for every 100 feet horizontally traveled, the vertical change in position is 6 feet. We can use this slope to calculate the vertical change in position when we drive 200 feet. To begin, we need to find out how much vertical distance we would travel if we traveled 100 feet horizontally.

Then, we can divide both sides by 100 to get y = 12. Thus, we travel 12 feet vertically driving 200 feet on this road with a 6% uphill grade.

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Answer:

70 mph

Step-by-step explanation:

Here we want to calculate average speed

Mathematically, average speed = Total distance/Total time

Kindly recall distance = speed * time

for the first part;

We have: 60 * 2 = 120 miles

For the second: 4 * 75 = 300 miles

Average speed = (300 + 120)/(4 + 2) = 420/6 = 70 mph

Answer:

Ok, sabemos que Carlos ha construido un 3/7 de una casa.

Queremos saber cuanto le falta para terminar de construirla.

Entonces podemos realizar el cálculo:

1 casa - lo que Carlos ya construyo = Lo que le falta.

Entonces:

1 casa - 3/7 de una casa = X

Podemos reescribir:

1 casa = 7/7 de una casas

así tenemos:

7/7 de una casa  - 3/7 de una casa = X

(7/7 - 3/7) de una casa = X

4/7 de una casa  = X

Así podemos concluir que a Carlos le falta construir 4/7 de una casa para acabar.

Answer:

Step-by-step explanation:

\(-9x+1=80\)

\(-9x=79\)            (-1 both sides)

  \(x=-\frac{79}{9} =-8\frac{7}{9}\)     (÷ -9 both sides)