If the price of gas is $9.475, what will the price be when we round it to the hundredths place?

The absolute deviation of each of the data values are 4, 1 and 3 respectively.

The absolute deviatuon gives the distance of any given value in a dataset to the mean value. The absolute deviation is always positive as it does not consider the side to which the value belongs.

Absolute deviation = |value - mean|

Mean = 4

Absolute deviation of 0 = |0 - 4| = 4

Absolute deviation of 3 = |3 - 4| = 1

Absolute deviation of 7 = |7 - 4| = 3

Hence, The absolute deviation of each of the data values are 4, 1 and 3 respectively.

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Answer:

Explained below

Step-by-step explanation:

We are told that; Line CA = Line CD

Thus, it means that;

∠ACD = ∠BCD

Line CE is equal in both triangles. Thus,

Line CE = Line CE

This then implies that;

ΔACD = ΔBCD

Finally, it means that;

Line AD = Line BD

Since Line AD = Line BD, it means the perpendicular line from point C touching D is a bisector of Line AB

Step-by-step explanation:

so this is the process to find out the percentage

The number 37 out of the number 50 is 74 percent.

We need to find what percent is 37 out of 50.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, 37/50

= 0.74

In percentage 0.74×100

= 74%

Therefore, the number 37 out of the number 50 is 74 percent.

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Answer:

B, C, G

Step-by-step explanation:

If we look at the graph, it shows that if an employee works for 5 hours, then they will earn $36.25.

We can take 36.25 and divide that by 5 to get the hourly wage.

36.25 ÷ 5 = 7.25

We now know that employees get $7.25 every hour.

Using this we can look back to the graph.

'A' says that if an employee does not work, they will earn $7.25.

We know that this is wrong because if you do not work, then you do not earn money.

Let's look at 'B'.

If employees work for one hour, they will earn $7.25

We know this is correct because we now know the hourly wage.

Let's look at 'C'

If employees work for 4 hours, then they will get a revenue of $29.

We can figure this out by using this equation.

number of hours × hourly wage = total payment

4 × 7.25 = 29

Then this means that this is correct.

Let's look at 'D'

It says that if employees work for 10 hours, they will earn $73

Let's use that same equation again.

10 × 7.25 = 72.5

Employees earn $72.5 for working 10 hours, not $73.

So, this is obviously incorrect.

Let's look at 'E'

It says that if employees work for 3.5 hours, they will get a revenue of $21.75.

3.5 × 7.25 = 25.375

Therefore, this is incorrect.

Now let's take a look at 'F'.

It says that if employees work for 7.25 hours, then they earn $1.

This is incorrect.

And lastly, 'G'.

We know that if you do not work, then you do not earn money.

Therefore, A, B and G are the correct answers.

1) x = 3

2) x = 3

3) x = 15

4) x =13

5) x = -0.8

~nightmare 5474 ~

The values of x in the equations are: -3, 3, 15, 13 and -0.8

Question 6:

\(3(x - 7) - 3(2x - 4) = 4(x + 3)\)

Open brackets

\(3x - 21 - 6x + 12 = 4x + 12\)

Collect like terms

\(3x - 6x - 4x= 12 - 12+21\)

\(-7x= 21\)

Divide both sides by -7

\(x=-3\)

Question 8:

\(8(x - 1) + 17(x - 3) = 4(4x - 9) + 4\)

Open brackets

\(8x - 8 + 17x - 51 = 16x - 36 + 4\)

Collect like terms

\(8x - 16x + 17x = 51+8- 36 + 4\)

\(9x = 27\)

Divide both sides by 9

\(x=3\)

Question 10:

\(7(25 - x) -2x = 2(3x - 25)\)

Open brackets

\(175 - 7x -2x = 6x - 50\)

Collect like terms

\(- 7x -2x -6x= - 50-175\)

\(-15x= -225\)

Divide both sides by -15

\(x=15\)

Question 12:

\(5x -17 + 3x - 5 = 6x -7-8x + 115\)

Collect like terms

\(5x + 3x -6x +8x = -7 + 115+17+5\)

\(10x = 130\)

Divide both sides by 10

\(x = 13\)

Question 14:

\(118 - 65x - 123 = 5x + 35 - 20x\)

Collect like terms

\(20x - 65x - 5x =123 + 35 - 118\)

\(-50x =40\)

Divide both sides by -50

\(x =-0.8\)

Hence, the values of x in the equations are: -3, 3, 15, 13 and -0.8

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The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

Answer:

u

Step-by-step explanation:

Answer:

1. 490.6 mm²

2. 14.1 ft²

Step-by-step explanation:

1. 3.14×(12.5)²= 3.14 × 156.25 =490.6mm²

2. ½×3.14×3²= 3.14×4.5= 14.1 ft²

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Answer:

Step-by-step explanation:

sp = 504

gain = 12%

in this case

sp =100%+12%=504

112%=504

1%=504/112 =4.5

100%=450

so cost =$450

Hope im correct, if i am im glad to be of service.

Answer:

Step-by-step explanation:

The BAC (Blood Alcohol Concentration) of a person depends on several factors, such as the amount of alcohol consumed, the time over which the alcohol was consumed, and the weight and gender of the person. For this problem, we will assume that the woman has a normal metabolism and that the alcohol is completely absorbed into her bloodstream.

To calculate the BAC at 8 pm, we need to know the amount of alcohol that the woman consumed and the time over which she consumed it. We are given that she had 2 mixed drinks between 7-8 pm, which contained a total of 2 ounces of liquor. We are also given that she had a glass of wine at 10 pm, but we don't need to consider this for the BAC at 8 pm.

Using the Widmark formula, we can calculate the BAC at 8 pm:

BAC = (Alcohol consumed / (Body weight x r)) - (0.015 x Hours since first drink)

where r is the gender constant (0.55 for females) and 0.015 is the rate at which the liver metabolizes alcohol.

Plugging in the values we know, we get:

BAC = (2 oz / (130 lbs x 0.55)) - (0.015 x 1 hour)

BAC = 0.0208 - 0.015

BAC = 0.0058

Therefore, the woman's BAC at 8 pm was approximately 0.0058, which is below the legal limit for driving in most states in the US.

Answer:

(x=27/2) (y=1)

Step-by-step explanation:

I used my math plus (I put the equation in the exact way you put it)

Answer:

5/6

Step-by-step explanation:

Because there are 6 sides, and it's saying we need a greater number than 1. And there are 5 other numbers.

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

12v + 2

Step-by-step explanation:

4(3v -2) + 10

12v - 8 + 10

12v + 2

If the acceleration of the object becomes 3 m/s^2, the force is equal to 27 Newton.

Mathematically, a direct proportion can be represented the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 81/9

Constant of proportionality (k) = 9.

For the force when the acceleration of the object becomes 3 m/s^2, we have:

y = kx

y = 9(3)

y = 27 Newton.

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Complete Question:

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 81 N acts on a certain object, the acceleration of the object is 9 m/s^2. If the acceleration of the object becomes 3 m/s^2, what is the force?

Answer:

\(\Large \boxed{\sf a)\ 128 \ liters \ \ \ b)\ \$ \ 115.20}\)

Step-by-step explanation:

a) distance/unit rate = 1600/12.5 = 128

b) liters of gas × unit price = 128 × 0.90 = 115.2

Answer:

a) 128 liters

b) $ 115.2

Step-by-step explanation:

Part a)

12.5 km = 1 liter

1 km = 1/12.5 liters

Multiplying both sides by 1,600

1600 km = 1600 / 12.5 liters

1600 km = 128 liters

Part b)

1 liter = $ 0.90

128 liters = 128 * 0.90

128 liters = $ 115.2

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

30.98

Step-by-step explanation:

To solve for the mean/average of a set of numbers, you add them and divide by the number of numbers/data values.

(22+37+49+15.92)/4 = 123.92/4 = 30.98

Hope this helps and sorry if I made a mistake. :)

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

Answer:

y = 15x + 20 or 15x - y + 20 = 0

x = 11

Step-by-step explanation:

Line is passing through the points (0, 20) & (2, 50)

Slope of line = (50 - 20)/(2 - 0) = 30/2 = 15

Equation of line

y - 20 = 15(x - 0)

y - 20 = 15x

y = 15x + 20 or 15x - y + 20 = 0

Plug y = 185 in above equation, we find:

185 = 15x + 20

185 - 20 = 15x

165 = 15x

x = 165/15

x = 11

Answer:

There is a significant relation between weight and price

Step-by-step explanation:

              Brand Weight(x)          Price ($) (y)

A                  17.8                        2100

B                   16.1                        6,250

C                   14.9                        8,370

D                   15.9                        6,200

E                   17.2                        4,000

F                   13.1                         8,500

G                   16.2                        6,000

H                   17.1                         2,580

I                   17.6                          3,500

J                   14.1                         8,000

Null Hypothesis : \(H_0: \mu =0\)

Alternate Hypothesis : \(H_a: \mu \neq 0\)

Given : SST=51956800 SSE= 7312286.84 n = 10

SSR = SST-SSE

SSR=51956800-7312286.84

SSR=44644513.16

Level of significance =\(\alpha = 0.05\)

\(F=\frac{\frac{SSR}{m}}{\frac{SSE}{n-k}}\)

Where m = no. of restrictions

k = No. of independent variables

\(F=\frac{\frac{44644513.16}{1}}{\frac{ 7312286.84}{10-2}}\)

F=48.843

Degree of freedom 1 = 1

Degree of freedom 2 = 10-2=8

Using calculator

p-value is .000114.

p value < α

So, we reject the null hypothesis .

Hence There is a significant relation between weight and price

The inverse of the function j(x) = 1 + ∛( 2 + x ) is f⁻¹(x)  = ( x - 1 )³ - 2.

An inverse function is simply a function that undoes the original function.

Given the function in the question:

j(x) = 1 + ∛( 2 + x )

To solve for the inverse, start by replacing j(x) with y:

j(x) = 1 + ∛( 2 + x )

y = 1 + ∛( 2 + x )

Next, we solve for x in terms of y:

y - 1 = ∛( 2 + x )

( y - 1 )³ = ( ∛( 2 + x ) )³

( y - 1 )³ = 2 + x

( y - 1 )³ - 2 = x

x = ( y - 1 )³ - 2

Inter-change the variables

y = ( x - 1 )³ - 2

Replace y with f⁻¹(x) in the equation above:

f⁻¹(x)  = ( x - 1 )³ - 2

Therefore, the inverse is f⁻¹(x)  = ( x - 1 )³ - 2

Option d(x) = ( x - 1 )³ - 2 is the correct answer.

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The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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Answer:

a) 910

b) 1183

c) False

take these answers with a grain of salt, i cant guarantee accuracy but the process should be right?

Step-by-step explanation:

a)

Starting with 1300 dollars, we are given that the stock loses 30% of its value.

This means that we take 70% of 1300 as it is now at 70% of its value. This gives us 910.

b)

At 910 dollars, we are told that the stock's value rises by 30%, so if we multiply 910 by 1.3 or 130%, we get 1183. At this time, the stock is now worth 1183 dollars.

c)

It is false, as can be seen above a 30% loss followed by a 30% gain results in 91% of the original price. That's a 9% net loss.

This can be seen using variables, x -> 0.7x -> 0.7*1.3 x -> 0.91 x

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

The answer is 0.064

In order to get to the next term, look to see by what number the sequence is increasing.

In this case, each number is doubling in size, which means multiplying each number by 2.

The line integral of the given curve is equal to 125/3.

To use Green's theorem to evaluate the line integral of the given curve, we need to find a function F(x,y) and its partial derivatives such that the integrand of the line integral can be expressed as the curl of F. In this case, we can take

F(x,y) = xy^2

Then, we have

F_x = y^2

F_y = 2xy

Thus, the integrand of the line integral can be expressed as the curl of F:

curl F = F_y - F_x = 2xy - y^2

Applying Green's theorem, we have

line integral of curl F = integral over C (2xy - y^2) dx + (x^2 - 2xy) dy

= integral over C (2xy - y^2) dx + x^2 dy - 2xy dy

= integral over C x^2 dy

The given curve C is the boundary of the rectangle with vertices (0,0), (5,0), (5,3), and (0,3). Thus, the line integral of curl F along C is equal to the integral of x^2 over the x-values of the rectangle, which is

= (5^3 - 0^3)/3

= 125/3

Therefore, the line integral of the given curve is equal to 125/3.

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Answer: 6.4 miles/hour

Step-by-step explanation:

Speed = distance/time

19.2/3 = 6.4

Hope this helps!