A clothes washer used 2.6 kilowatt for 0.9 hour. If electricity costs $0.47 per kilowatt-hour, how much did it cost (in dollars, to the nearest penny) to use the clothes dryer

a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.

Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.

Iteration 1: a = 1, b = 2

c = (a + b) / 2

= (1 + 2) / 2 is 1.5

f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375

ince f(c) has a negative value, the root lies in the interval [1.5, 2].

Iteration 2:

a = 1.5, b = 2

c = (a + b) / 2

= (1.5 + 2) / 2 is 1.75

f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844

Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].

Iteration 3: a = 1.5, b = 1.75

c = (a + b) / 2

= (1.5 + 1.75) / 2 is 1.625

f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8  is -0.2141

Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].

Iteration 4: a = 1.625, b = 1.75

c = (a + b) / 2

= (1.625 + 1.75) / 2 is 1.6875

f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.

Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].

Iteration 5: a = 1.625, b = 1.6875

c = (a + b) / 2

= (1.625 + 1.6875) / 2 is 1.65625

f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .

Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].

Iteration 6: a = 1.625, b = 1.65625

c = (a + b) / 2

= (1.625 + 1.65625) / 2 which gives 1.640625

f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.

Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].

teration 7: a = 1.640625, b = 1.65625

c = (a + b) / 2

= (1.640625 + 1.65625) / 2 results to 1.6484375

f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116

Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].

Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.

b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.

Iteration 1:

x₁ = x₀ - (f(x₀) / f'(x₀))

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.

f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.

x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.

Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.

c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.

Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))

f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375

x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826

Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.

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Answer:

5.4'

Step-by-step explanation:

See diagram attached.

The 8' wire is the hypotenuse of the triangle, with a base angle of 42°.

Hence the height is the length of the hypotenuse multiplied by sin(42°)

H = 8sin(42°) = 8 *0.6691 = 5.353'

Answer:

Step-by-step explanation:

.. 3 + 2[4(2) – (4 + 3(2))]. 3 + 2[8 – (4 + 6)]. 3 + 2[8 – (10)]. 3 + 2[–2]. 3 – 4. –1 ... 2x + 6 = 4 – 2 + 1x. 2x + 6 = 2 + x. 2x – x + 6 = 2 + x – x. x + 6 = 2. x + 6 – 6 = 2 – 6. x = –4.

Here, we are given the following values' = x4 + 6 x = −5 Δx = dx = 0.01To find: Δy and dy. In order to calculate Δy and dy, we will use the following formulas:Δy = f(x + Δx) − f(x)dy = f'(x) dx Where, f(x) = x4 + 6 x

We know that, Δx = dx = 0.01So, let's calculate the values of Δy and dy by putting the given values in the above formulas.Δy = f(x + Δx) − f(x)f(x + Δx) = (x + Δx)4 + 6 (x + Δx)Putting the given values in this formula we get, f(x + Δx) = (-5 + 0.01)4 + 6(-5 + 0.01) = 55.0184f(x) = x4 + 6 x Putting the given values in this formula we get, f(x) = (-5)4 + 6 (-5) = -605Δy = f(x + Δx) − f(x)= 55.0184 - (-605)= 660.0184 dy = f'(x) dx We will find f'(x) first.f(x) = x4 + 6 xf'(x) = 4x³ + 6Now, let's calculate the value of dy by putting the values of f'(x), dx and x in the given formula. dy = f'(x) dx= (4x³ + 6) dx= (4(-5)³ + 6) (0.01)= -499.4Now we can write the final  the given question as follows: Given values: y = x4 + 6 x = −5 Δx = dx = 0.01Formula used:Δy = f(x + Δx) − f(x)dy = f'(x) dx Where ,f(x) = x4 + 6 xf(x + Δx) = (x + Δx)4 + 6 (x + Δx)f(x) = x4 + 6 xf'(x) = 4x³ + 6Values of given variables:Δx = dx = 0.01x = -5Now, let's calculate the value of Δy by putting the given values in the formula.Δy = f(x + Δx) − f(x)f(x + Δx) = (x + Δx)4 + 6 (x + Δx)Putting the given values in this formula we get, f(x + Δx) = (-5 + 0.01)4 + 6(-5 + 0.01) = 55.0184f(x) = x4 + 6 x Putting the given values in this formula we get, f(x) = (-5)4 + 6 (-5) = -605Δy = f(x + Δx) − f(x)= 55.0184 - (-605)= 660.0184

Now, let's calculate the value of dy by putting the values of f'(x), dx and x in the given formula. dy = f'(x) dx= (4x³ + 6) dx= (4(-5)³ + 6) (0.01) = -499.4Therefore, Δy = 660.0184 and dy = -499.4.

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The total distance John drove to work in 10days is 50.5 miles

A word problem in math is a math question written as one sentence or more. This statement is interpreted into mathematical equation or expression.

For the first five days, John drove 5½ miles

The total distance for the 5 days = 5 × 11/2 = 55/2 miles

For the second five days, he drove 7 2/3 miles each day.

The total distance he drove = 23/3 × 5 = 115/5

= 23miles

Therefore the total distance he drove for the 10 days = 55/2 + 23

= 27.5 +23

= 50.5 miles

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Answer:

I really do apologize if i’m wrong but I believe the answer is

d. x represents the cost of classes

Step-by-step explanation:

X represents the amount of classes Lucy took and 3 would represent the cost per class

Answer:

The solution set consists of all the real numbers smaller than or equal to 11/4:

\(x\leq \frac{11}{4}\)

Step-by-step explanation:

We need to solve for x (that means isolate x on one side of the inequality symbol) in the following inequality:

\(3+\frac{x-2}{x-3} \leq 0\\\frac{x-2}{x-3} \leq -3\\x-2\leq -3\,(x-3)\\x-2\leq -3x+9\\x+3x\leq 9+2\\4x\leq 11\\x\leq \frac{11}{4}\)

Answer:

Point in original: (4, -6)

Point in final: (4, 6)

just drag the point 6 units up

Step-by-step explanation:

Hope this helps!

Step-by-step explanation:

each game of cribbage "binds" 4 people, each hand of chess 2 people.

15 games of cribbage means 15×4 = 60 people are playing. that leaves 0 people and therefore 0 games for chess.

2 games of chess means 2×2 = 4 people are playing.

that leaves 60-4 = 56 people for cribbage making 56/4 = 14 games of cribbage.

13 games of cribbage means 13×4 = 52 people are playing. that leaves 60-52 = 8 people for chess making 8/2 = 4 games of chess.

14 games of chess means 14×2 = 28 people are playing, that leaves 60-28 = 32 purple for cribbage making 32/4 = 8 games of cribbage.

0 people of cribbage means nobody is playing this game, that leaves all 60 people to play chess making 60/2 = 30 games of chess.

The set of ordered pairs {(–5,2), (–4,1), (–3,0), (–3,–1)} is a relation but not a function.

The set of ordered pairs are {(–5,2), (–4,1), (–3,0), (–3,–1)}

We have to check whether the set is a relation or a function.

We know that a relation is a set of ordered pairs that relate inputs (x-values) to outputs (y-values).

So the set of ordered pairs is a relation.

We know that in a function, each input (x-value) is associated with exactly one output (y-value).

In this set of ordered pairs, the input –3 is associated with two different outputs: 0 and –1.

Therefore, it does not satisfy the criteria for a function, it is not a function.

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Ratio of girls to boys is 2:1

Ratio of boys to girls is 1:2

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

Explanation:

2/3 of the class are girls. If the class had 3 people, then 2 of them are girls. The remaining 3-2 = 1 person is a boy.

The ratio of girls to boys has us list the number of girls (2) followed by the number of boys (1). Separate the values with a colon. That's how we end up with 2:1

The ratio of boys to girls will have us flip that previous ratio to get 1:2

The order is important when it comes to forming ratios.

Given :

B is between A and C

AB= x²-6x

BC= x²+20x

AC= 60-12x

B divide into 2 equal parts

AB and AC are equal

AC = AB +BC

60-12x = x²-6x + x²+20x

\(60= 2x^{2} -6x +20x +12x\)

\(60 = 2x^{2} -6x +32x\\\)

\(60= 2x^{2} +26x\)

\(30 = x^{2} +13x\\\\\)

\(x^{2} +13x -30 = 0\\x^{2} +15x-2x-30 =0\)

\(x(x+15) -2 (x+15) =0\)

\((x-2) (x+15) =0\\\)

x=2 , x=-15

x never be negative the x is 2

BC =  x²+20x

BC = 2*2 +20*2

BC = 4 +40

BC = 44

length of BC =44

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The probability that P(X1 < X2 < X3) is 1/8.

We can solve this problem using the fact that if X1, X2, X3 are independent exponential random variables with the same rate parameter λ, then the joint density function of the three variables is given by:

f(x1, x2, x3) = λ^3 e^(-λ(x1+x2+x3))

We want to find the probability that X1 < X2 < X3. We can express this event as the intersection of the following three events:

A: X1 < X2

B: X2 < X3

C: X1 < X3

Using the joint density function above, we can compute the probability of each of these events using integration. For example, the probability of A is:

P(X1 < X2) = ∫∫ f(x1, x2, x3) dx1 dx2 dx3

= ∫∫ λ^3 e^(-λ(x1+x2+x3)) dx1 dx2 dx3 (integration over the region where x1 < x2)

= ∫ 0^∞ ∫ x1^∞ λ^3 e^(-λ(x1+x2+x3)) dx2 dx3 dx1

= ∫ 0^∞ λ^2 e^(-2λx1) dx1 (integration by substitution)

= 1/2

Similarly, we can compute the probability of B and C as:

P(X2 < X3) = 1/2

P(X1 < X3) = 1/2

Note that these probabilities are equal because the three exponential random variables are identically distributed.

Now, to compute the probability of the intersection of these events, we can use the multiplication rule:

P(X1 < X2 < X3) = P(A ∩ B ∩ C) = P(A)P(B|A)P(C|A∩B)

Since A, B, and C are independent, we have:

P(B|A) = P(B) = 1/2

P(C|A∩B) = P(C) = 1/2

Therefore:

P(X1 < X2 < X3) = (1/2)(1/2)(1/2) = 1/8

Thus, the probability that X1 < X2 < X3 is 1/8.

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Answer:

-8\(x^{3}\) + 10\(x^{2}\) + 6x

Step-by-step explanation:

Answer:

Jimmy is correct

Step-by-step explanation:

The dimensions of the rhombus and square are probably almost the same

In the drawing, the length of the living room is 3 millimeters.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters.

The living room is 6 meters long in real life and assuming in the drawing it is x millimeters.

∴ 1 : 2 : : x : 6.

1/2 = x/6.

x = 6/2.

x = 3.

So, In drawing it is 3 millimeters.

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1.  AD would increase by $200 million due to the multiplier effects.

2. The government should increase spending by $20 million to achieve an AD increase of $100 million.

3. Bank E can lend out a maximum of $9,000.

1. To calculate the increase in aggregate demand (AD) due to multiplier effects when the government reduces taxes by $50 million and the marginal propensity to consume (MPC) is 0.75, we can use the formula:

Multiplier = 1 / (1 - MPC)

AD increase = Multiplier * Tax cut

Given that the tax cut is $50 million and MPC is 0.75:

Multiplier = 1 / (1 - 0.75) = 1 / 0.25 = 4

AD increase = 4 * $50 million = $200 million

Therefore, AD would increase by $200 million due to the multiplier effects.

2. To determine the amount the government should increase spending to increase AD by $100 million, given an MPC of 0.8, we can use a similar approach:

Multiplier = 1 / (1 - MPC)

Government spending increase = AD increase / Multiplier

Given that the desired AD increase is $100 million and MPC is 0.8:

Multiplier = 1 / (1 - 0.8) = 1 / 0.2 = 5

Government spending increase = $100 million / 5 = $20 million

Therefore, the government should increase spending by $20 million to achieve an AD increase of $100 million.

3. To calculate the maximum amount of money that Bank E can lend out, given that it has $10,000 of deposits as a liability and $1,500 in reserves, with a required reserve ratio (rr) of 10%, we can use the formula:

Maximum loan amount = Total deposits - Required reserves

Given that the required reserve ratio is 10%, which means the bank needs to hold 10% of the deposits as reserves:

Required reserves = 10% * $10,000 = $1,000

Maximum loan amount = $10,000 - $1,000 = $9,000

Therefore, Bank E can lend out a maximum of $9,000.

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Answer:

20

Step-by-step explanation:

Since 0.454 kg = 1 pound,

         0.5675 kg = \(\frac{0.5675}{0.454}\) pound = 1.25 pounds= (1.25 * 16) ounces = 20 (ounces)

Answer:

0.5675

Step-by-step explanation:

16/0.454 = x/0.5675...16 oz to 0.454 kg = x oz to 0.5675 kg

cross multiply

0.454x = 16(0.5675)

0.454x = 9.08

x = 9.08/0.454

x = 20.....20 oz are in 0.5675 kg

1) The vertice of all the angles is given as Point M.

2) A point in the interior of ∠LMO is point P.

3) The sides of ∠1 are: MO and MN.

4) The value of x in Right ∠ABC is 35°

2x + 20 = 90

2x = 70

x = 35°

5) Note that ∠3 and ∠4 are angle pairs called Adjacent lines. In this case, both angles sum up to 180°

6) m∠1  is 16°

To deriver m∠1 both angles must be equated to one another based on the theorem of the congruency of Adjacent Angles.

Thus,

4x + 4 = 8x -8 (Collect like terms over the equals sign)

4+8 = 8x -4x
12 = 4x (divide both sides by 4 to get x)

x = 12/4

x = 3

thus m ∠1 =

⇒ 4 (3)  + 4

⇒ 12 + 4

= 16°

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With respect to parenting style, coercive is to confrontative as authoritative is to assertive.

Both pairs involve a parent asserting their authority and expectations, but the former is done through negative reinforcement and the latter is done through positive reinforcement. Coercive parenting is characterized by the use of punishment and criticism to control behavior, while confrontative parenting involves verbal aggression and conflict to establish dominance.

These styles are often associated with negative outcomes such as increased aggression, lower self-esteem, and decreased academic achievement. On the other hand, authoritative parenting is based on clear rules and boundaries that are communicated in a supportive and nurturing environment. This style is associated with positive outcomes such as higher academic achievement, increased self-esteem, and improved social skills.

Similarly, assertive parenting involves clear communication of expectations and limits, but in a positive and respectful manner. Overall, while both coercive and confrontative parenting involves the assertion of authority, authoritative and assertive parenting involves setting limits and expectations in a positive and supportive manner, which leads to better outcomes for children.

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Line a & b are parallel

Line c is perpendicular to both lines a & b

Step-by-step explanation:

Let's solve for y in all the lines, starting with line a

-3x - 12y = 36

Add 3x to both sides

-3x - 12y = 36

+ 3x          + 3x

-12y = 3x + 36

Divide both sides by -12

-12y/-12 = (3x + 36)/-12

y = -x/4 - 3

Now for line b

x + 4y = 2

- x      - x

4y = -x + 2

4y/4 = (-x + 2)/4

y = -x/4 + .5

Since line a and b have the same slop, they are parallel

Notice how their slops are opposite and flipped of line c, 4x, making them perpendicular to line c.

Green = line a

Blue = line b

Purple = line c

The correct answer is Option C. The side C of the triangle figure is 66.8

Using the information given, we can set up the following system of equations:

x + y + z = 30

x + y - z = 34

x - y + z = 53.6

x - y - z = 50

To solve for side c, we can start by eliminating one of the variables. We can eliminate y by adding the equations x + y + z = 30 and x + y - z = 34:

x + y + z = 30

x + y - z = 34

2x + z = 64

Now we can substitute this expression for x + y + z into the equation x - y + z = 53.6:

2x + z = 64

x - y + z = 53.6

x - y + 2x + z = 53.6

z = 13.6

Finally, we can use the value of z to solve for side c:

c = x + y + z = 30

c = x + y + z - z = 30 - 13.6 = 16.4

c = 66.8

Therefore, the length of side c is 66.8.

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Quotient rule of differentiation.

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

d/dx(csc x) = -csc x cot x.

To show that d/dx(csc x) = -csc x cot x, we will use the quotient rule of differentiation.

Recall that csc x is defined as 1/sin x.

Therefore, we can rewrite the function as:

csc x = (sin \(x)^{-1}\)

Taking the derivative of csc x with respect to x using the quotient rule, we get:

d/dx(csc x) = (-1)(sin x) (cos x)

Now we need to simplify this expression using trigonometric identities. Recall that

cot x = cos x/sin x.

Therefore, we can rewrite the above expression as:

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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To show that d/dx(csc x) = -csc x cot x, we need to differentiate csc x with respect to x using the chain rule and trigonometric identities.

Recall that csc x is the reciprocal of sin x, so we can write:

csc x = 1/sin x

Then, using the chain rule, we can differentiate csc x as follows:

d/dx(csc x) = d/dx(1/sin x) = -1/sin^2 x * d/dx(sin x)

Now, we can use the derivative of sin x with respect to x, which is cos x:

d/dx(csc x) = -1/sin^2 x * cos x

Next, we can use the identity cot x = cos x/sin x to simplify the expression:

d/dx(csc x) = -cos x/(sin x)^2 = -csc x * cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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An inequality is a mathematical statement that uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to compare two quantities. In real life, we can use inequalities to describe a wide range of situations. For example, let's say you are buying groceries and you have a budget of $50. You could use the inequality  total cost of groceries < $50 to describe your situation. This inequality states that the total cost of the groceries must be less than $50, or you will exceed your budget.

In another real life situation, let's say you are training for a race and you want to run a certain distance in a specific amount of time. You could use the inequality distance > speed × time to describe your goal. This inequality states that the distance you run must be greater than the product of your speed and the time it takes you to complete the race. Inequality statements can also be used in social science and economics. For example, we can use an inequality to describe the income distribution in a society. We could say that the top 10% of earners have an income greater than the bottom 90% of earners, using the inequality top 10% income > bottom 90% income.

In summary, inequalities can be used to describe real life situations by comparing two quantities using symbols such as <, >, ≤, or ≥. We can use inequalities to describe a wide range of situations, from grocery shopping to income distribution.

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The bag weight is 1.5 standard deviation below the mean value. Standard deviation is found with the help of variance.

The standard deviation is the positive square root of the variance of this data set. Variance of a data set is the sum of squared differences of the data values from its mean to the total count of data values.

The mean value is 4.10 ounce

Standard deviation= 0.10 ounce

The formula for the standard deviation is found as;

\(\rm Z= \frac{x-\mu}{\sigma} \\\\ Z= \frac{3.95-4.10}{0.10} Z=\frac{-0.15}{0.10} \\\\ Z=-1.5\)

Hence, the bag weight is 1.5 standard deviation below the mean value.

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Answer:

12/3=4

Step-by-step explanation:

You have 12 blocks in total, and 3 sections each. It is asking you how many blocks per section.

12 blocks in total/ 3 sections each = 4 blocks per section

Answer:

A- 13

B- 13

C-37

Step-by-step explanation:

I wasn't going to answer but asap! Got me ^_________^

Btw please mark this as brainliest

Answer:Option(a)

Step-by-step explanation: A) 2 of 15