A gas station started the weekend selling gas for $3.79 per gallon. Towards the end of the weekend, gas was $3.49 per gallon. What is the percent decrease in gas price per gallon? Round percentage to the tenths place.

The value of a + b is 57, when the sets A = {3; a} and B = {b; 54} are unitary sets.

Given that A = {3; a} and B = {b; 54} are unitary sets To calculate a + b, we need to determine the values of a and b. Let's consider set A, since it has an unknown element 'a' Unitary sets have only one element and since set A is unitary, we can say that it contains only one element which is {3,a}.This means that there is only one possible value of 'a' that can be included in set A. So, we can say that a = 3

Similarly, the set B is also unitary and it contains only one element which is {b, 54}. This means that there is only one possible value of 'b' that can be included in set B. So, we can say that b = 54. Therefore,

\(a + b = 3 + 54 = 57\) Hence,

\(a + b = 57\)

Here, the given sets A and B are unitary sets. A unitary set is defined as a set containing only one element. Let

A = {3; a}

be a unitary set, then it contains only one element. So, the value of a is equal to the value of 3. Therefore,

a = 3.

Let B = {b; 54} be another unitary set, then it also contains only one element. So, the value of b is equal to the value of 54. Therefore,

b = 54. Now, we need to calculate the sum of a and b. Therefore,

\(a + b = 3 + 54 = 57\)

Thus, we can say that the value of a + b is equal to 57, when the sets

A = {3; a} and B = {b; 54} are unitary sets.

Hence, the value of a + b is 57, when the sets A = {3; a} and B = {b; 54} are unitary sets.

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Answer:

Step-by-step explanation:

Side of the smaller figure:

The chances of availability from lest to most likely is Blueberry cheesecake, Chocolate chip and Caramel Critters.

Probability determines the chances that an event would happen. The probability the event occurs with certainty is 1 and the probability that the event would not occur with certainty is 0.

The chances of availability:

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Answer:

(C-D)/A = B

Step-by-step explanation:

C = AB + D

Subtract D from both side

C-D = AB + D-D

C-D = AB

Divide each side by A

(C-D)/A = AB/A

(C-D)/A = B

Answer:

A spurious correlation wrongly implies a cause and effect between two variables. For example, the number of astronauts dying in spacecraft is directly correlated to seatbelt use in cars: Use your seatbelt and save an astronaut life!

Interesting correlations are easy to find, but many will turn out to be spurious. Three examples are the skirt length theory, the Super Bowl indicator, and a suggested correlation between race and college completion rates.

Step-by-step explanation:

The particular solution for the given second-order linear differential equation using transfer functions, impulse response, and convolutions cannot be obtained due to the inability to evaluate the required integral.

To find a particular solution for the given second-order linear differential equation using transfer functions, impulse response, and convolutions, we first need to determine the transfer function and impulse response associated with the given differential equation.

The transfer function H(s) of a linear time-invariant system is obtained by taking the Laplace transform of the differential equation with zero initial conditions. In this case, we have the differential equation:

y" + 4y' + 3y = 1/(1+e^t)

Taking the Laplace transform of both sides, and assuming zero initial conditions, we obtain:

s^2Y(s) + 4sY(s) + 3Y(s) = 1/(s+1)

Now, we can solve for Y(s):

Y(s) = 1/(s+1)/(s^2 + 4s + 3)

Factoring the denominator, we have:

Y(s) = 1/(s+1)/((s+1)(s+3))

Canceling out the common factor (s+1), we get:

Y(s) = 1/(s+3)

Therefore, the transfer function H(s) associated with the given differential equation is H(s) = 1/(s+3).

To find the impulse response h(t) of the system, we need to take the inverse Laplace transform of the transfer function H(s). In this case, the inverse Laplace transform of 1/(s+3) is simply e^(-3t).

Now, using the impulse response h(t) = e^(-3t), we can find a particular solution for the given differential equation using the convolution integral.

The convolution integral states that the output y(t) of a linear time-invariant system is given by the convolution of the input x(t) and the impulse response h(t):

y(t) = x(t) * h(t)

In this case, the input x(t) is 1/(1+e^t). Therefore, we can write:

y(t) = 1/(1+e^t) * e^(-3t)

To evaluate the convolution integral, we can rewrite it as:

y(t) = ∫[0 to t] (1/(1+e^τ)) * e^(-3(t-τ)) dτ

Simplifying this expression, we have:

y(t) = ∫[0 to t] e^(-3(t-τ)) / (1+e^τ) dτ

Unfortunately, the calculation of this integral does not have a closed-form solution. Therefore, we cannot find an explicit particular solution using the convolution integral method.

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Using Dot product

Two vectors x and y are said to be orthogonal if their dot product is zero

⇒ x.y = 0

This is because orthogonal vectors are make an angle of 90° with each other and therefore θ becomes 90°

Dot product is given by :

x.y = x*y*cosθ = xycos90°

∵cos90° is zero , x.y=0 for orthogonal vectors.

Let u,v,y be vectors in R

y is orthogonal to u and v

⇒ y.u = 0   and  y.v=0

Now, we have to prove that y is orthogonal to (u+v)

The dot product of these vectors is given by:

y.(u+v) = y.u + y.v  (Dot product is distributive) = 0 + 0 = 0

∵The dot product is zero , vector y and (u+v) are orthogonal

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Answer:

p = - 2 , q = - 1

Step-by-step explanation:

Rearrange the left side into standard form

- x² + 4x - 5

Factor out - 1 from - x² + 4x

= - (x² - 4x) - 5

Using the method of completing the square

add/subtract ( half the coefficient of the x- term)² tp x² - 4x

= - (x² + 2(- 2)x + 4 - 4) - 5

= - (x - 2)² - (- 4) - 5

= - (x - 2)² + 4 - 5

= - 1 - (x - 2)²

Comparing to q - (x + p)²

with p = - 2 and q = - 1

Answer:

144

Step-by-step explanation:

Multiply each option together 9X4X4=144

Answer:

Step-by-step explanation:

The sum of the squares of the shorter sides is equal to the square of hypotenuse!

Answer:

Step-by-step explanation:

it is hard to know exactly by eye balling the graph  I can't dissern the y intercept it might be 4.5 but it could be 4.33, but it looks for sure like the x intercept equals 6 but does it

the dots on the line are at (-2, -6) and (2, 3)  so we can find the slope m

in the y = mx + b line equation   b is the y intercept

m = Δy/Δx     =  (y1 - y2) / (x1 - x2)

                     =  (-6 - -3) /  (-2 - 2)

                     =     -3 / -4

                 m = 3/4

       y = 3x/4  +  y intercept     which i can't dissern (read directly from the

                                                  graph, but we believe y = 0   when x is six

       0 = 3(6)/4  + y intercept

       -18/4 = 18/4 -18/4  + y intercept

        -9/2 = y intercept

        -4.5 = y intercept

   y = 3x/4 - 9/2          i think exact number means NO FRACTIONS but that is whole number so let me gaggle it  What are exact numbers?  Gaggle indicates exact numbers are integers   example  3 ft in a yard 12 eggs in a dozen

    y = 3x/4 - 9/2               multiple both sides by 4

   4y = 3x  - 36/2

   4y = 3x - 18    <------------------  FINAL ANSWER

Answer

two-thirds

Step-by-step explanation:

8 over 1 2simplified is 2 over 3

The value of h ( 12 ) is 26

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the value of equation A is

h ( x ) = 4x - 22   be equation (1)

Now , to find the value of h ( 12 ) , substitute the value of x = 12 in the equation , we get

h ( x ) = 4x - 22  

h ( 12 ) = 4 x 12 - 22

On simplifying the equation , we get

h ( 12 ) = 48 - 26

           = 22

Therefore , the value of h ( x ) when x = 12 is 22

Hence , The value of h ( 12 ) is 26

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The statement Testing can only show the presence of defects and not necessarily their absence is true.

Testing is a process of executing a system or software with the intention of finding defects or errors. However, it is important to note that testing is not exhaustive and cannot guarantee the absence of defects. Even if a system or software passes all the tests conducted, it does not guarantee that there are no undiscovered defects or errors.

Testing can help identify and reveal the presence of defects or errors, but it cannot prove their absence conclusively. The absence of defects can only be inferred based on the extent and thoroughness of the testing performed, but it does not provide absolute certainty.

Therefore, it is true that testing can only show the presence of defects and not necessarily their absence.

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Answer:

95%

Step-by-step explanation:

Divide how many deliveries Jane has made by the total number of deliveries she has to make this week.

38/40 = 0.95

Then multiply this decimal by 100 to convert it into a percent.

0.95 x 100 = 95%

Jane has completed 95% of her deliveries for the week.

\(\huge\text{Hey there!}\)

\(\mathsf{3 - 5g = 33}\)

\(\mathsf{-5g + 3 = 33}\)

\(\large\text{Subtract by 3 to both sides:}\)

\(\mathsf{-5g + 3 - 3 = 33 - 3}\)

\(\large\text{Simplify it:}\)

\(\mathsf{-5g = 33 - 3}\)

\(\mathsf{-5g = 30}\)

\(\large\text{Divide -5 to both sides:}\)

\(\mathsf{\dfrac{-5g}{-5} = \dfrac{30}{-5}}\)

\(\large\text{Simplify it:}\)

\(\mathsf{g = \dfrac{30}{-5}}}\)

\(\mathsf{g = -6}\)

\(\huge\text{Therefore, your answer should be: \boxed{\mathsf{g = -6}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Step-by-step explanation: Start by Isolating the Variable.

-5g=33-3

-5g=30

g=-6 is what makes this true. let's check:

3-5(-6)=33

3+30=33

33=33

hence -6 is the solution.

Pseudocode refers to a language that uses a combination of informal English language and a programming language. It's utilized to specify the steps that a computer program will follow to achieve a particular aim. In the context of programming, pseudocode is commonly used to explain a program's algorithm before it is turned into actual code.

In a nutshell, pseudocode is a way of expressing computer code in a human-readable format that can be easily interpreted. Here is the pseudocode for the manager's scenario:

1. Declare variable: sales = 0, vat = 0.

2. Request input of sales amount in Rands from user.

3. Multiply sales by 15% to calculate the VAT payable.

4. Add VAT payable to the sales amount to determine the total sales amount.

5. Display total sales amount and VAT payable.

the pseudocode for a scenario where a food store manager wants to keep track of the amount of sales of food and the amount of VAT that is payable on it will entail the use of variables, multiplication, and display functions. In addition, requesting input from the user is a critical step that cannot be ignored.

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The expression will be given as h(8) = -0.3(8-5)²+7.5 the value of the function h(8) will be 6.3 feet.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

Now from the question when the boy jumped from a certain height he lands 8 feet farther away this condition will be expressed in the expression as follows:-

h(x) = -0.3( x - 8)² +7.5

Put x = 8 feet as

h(8) = -0.3(8-5)²+7.5

h(8) = -0.3 ( 3 )² + 7.5

h(8) = -2.7 + 9

h( 8 ) =  6.3 feet

Therefore expression will be given as h(8) = -0.3(8-5)²+7.5 the value of the function h(8) will be 6.3 feet.

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C'(56) represents the rate of change of carbon dioxide concentration in the atmosphere at 56 years since 1960, in parts per million per year.

What C'(56) represents?

The atmospheric carbon dioxide levels in Barrow, Alaska can be modeled using the function

C(t) = 0.04t^2 + 0.6t + 330 + 7.5 sin(2 pi t),

where C(t) represents the concentration of carbon dioxide in parts per million, and t is measured in years since 1960. The function C is the sum of a quadratic function and a sine function.

The physical significance of each function is as follows:

The quadratic function (0.04t^2 + 0.6t + 330) represents the btrend of increasing carbon dioxide levels over time. This increase is due to factors such as human activities and natural processes.

The sine function (7.5 sin(2 pi t)) represents the seasonal fluctuations in carbon dioxide levels due to the natural carbon cycle, which includes processes like photosynthesis and respiration.

To estimate C'(56) using points close to t = 56, we can use the difference quotient method:

C'(56) ≈ (C(56.01) - C(55.99)) / (56.01 - 55.99)

Calculate C(56.01) and C(55.99) using the given function:

C(56.01) = 0.04(56.01)^2 + 0.6(56.01) + 330 + 7.5 sin(2 pi (56.01))
C(55.99) = 0.04(55.99)^2 + 0.6(55.99) + 330 + 7.5 sin(2 pi (55.99))

Now, plug these values into the difference quotient:

C'(56) ≈ (C(56.01) - C(55.99)) / (56.01 - 55.99)

Finally, interpret the value C'(56) in terms of rate of change:

C'(56) represents the rate of change of carbon dioxide concentration in the atmosphere at 56 years since 1960, in parts per million per year. If the value is positive, it means the concentration is increasing at that point in time, while if the value is negative, the concentration is decreasing.

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Answer:

P(2,3) thats the answer ;)

The total driving distance can be calculated by adding the number of blocks in each direction: 1 + 1 + 5 + 2 = 9 blocks. If you could fly like a bird, your trip would be 1/4 mile shorter.

In your neighborhood, you need to drive from your house to the grocery store following a path of 1 block south, 1 block east, 5 blocks north, and 2 blocks east. Each block is 1/16 of a mile.

Convert this to miles: 9 blocks * (1/16 mile/block) = 9/16 miles.

If you could fly like a bird, you would take a direct path. To find this distance, use the Pythagorean theorem for a right triangle formed by the east-west and north-south distances.

East-west distance: 1 block east + 2 blocks east = 3 blocks = 3/16 miles.
North-south distance: 5 blocks north - 1 block south = 4 blocks = 4/16 miles.

The direct flying distance can be calculated as:

√[(3/16)^2 + (4/16)^2] = √[(9/256) + (16/256)] = √(25/256) = 5/16 miles.

To find the shorter distance when flying, subtract the direct flying distance from the driving distance:

(9/16) - (5/16) = 4/16 miles, which simplifies to 1/4 mile.

So, if you could fly like a bird, your trip would be 1/4 mile shorter.

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Bpetro, this is the solution:

Let's recall that the general form of the line equation is:

y = mx + b

Let's find b, this way:

3 = 1/4 * 5 + b

3 = 5/4 + b

b = 3 - 5/4

b = 12/4 - 5/4

b = 7/4

In consequence, the equation of the line that passes through the point (5,3) with a slope of 1/4 is:

y = 1/4x + 7/4

The area of Maya's rectangular driveway, plotted in the coordinate plane of the graph the question, indicates;

9. The other two coordinates of Maya's rectangular driveway are; (-1, -8.5), and (1.5, 1).

The coordinates of a point on the coordinate plane, specifies the location of the point on the plane relative to the x- and y-axis.

The coordinates of the corners of Maya's driveway obtained from the graph on a similar questions posted online are; (-1, 1), (1.5, 1), (1.5, -8.5), (-1, -8.5)

The pair of points that have similar x- and y-values are indicative of lines parallel to the y-axis (vertical lines) and the the x-axis (horizontal lines).

9. The specified points of the plot on Maya's driveway are; (-1, 1), (1\(\frac{1}{2}\), -8\(\frac{1}{2}\)).

The other two coordinates of Maya's rectangular drive way are; (1.5, 1), and (-1, -8.5)

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Answer: (d)- 1.76 kg

Step-by-step explanation:

Given

The first laptop mass was 11 kg

The rate of mass decreases by 4.7% per year

In 1982, it was

\(\Rightarrow 11-11\times 4.7\%=11-11\times 0.047\\\Rightarrow 11(1-0.047)\ kg\)

In 1983, it was

\(\Rightarrow 11(1-0.047)-11(1-0.047)\times 0.047=11(1-0.047)^2\)

In 2019 i.e. after 38 years, it is

\(\Rightarrow 11(1-0.047)^38=11\times 0.953^{38}=1.76\ kg\)

The probability that Lamont reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie is 1/15

The probability can be calculated as follows:

P(peanut butter cookie) = 5/25 = 1/5

P(oatmeal cookie) = 8/24 = 1/3

P(peanut butter cookie and oatmeal cookie) = P(peanut butter cookie) x P(oatmeal cookie)

P(peanut butter cookie and oatmeal cookie) = (1/5) x (1/3)

P(peanut butter cookie and oatmeal cookie) = 1/15

Therefore, the probability that Lamont reaches back in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie is 1/15.

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The probability that the student plays a sport and is involved in theatre is 82%*20%=16.4% which is approximately equal to 14%.

The probability that the student plays a sport and is involved in theatre can be calculated using the following formula:

P(A∩B)=P(A)*P(B|A)

Where P(A) is the probability of playing a sport (70%) and P(B|A) is the probability of being involved in theatre given that the student plays a sport (20%).

Therefore, P(A∩B)=0.7*0.2=0.14

This means that the probability that the student plays a sport and is involved in theatre is 14%. This can also be calculated by subtracting the probability of not playing a sport or being involved in theatre (18%) from 100%. That is, 100%-18%=82%. Since 20% of the 82% are involved in theatre, the probability that the student plays a sport and is involved in theatre is 82%*20%=16.4% which is approximately equal to 14%.

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Answer:

The bottom right (v shaped one) is a function

Step-by-step explanation:

Hope this helps:)

Answer:

The one in the bottom right that is an absolute value function.

Step-by-step explanation:

You can use the "vertical line test" to determine whether a given graph is a function or not. If you can draw a straight, vertical, line anywhere and it intersects the graph more than once, then it is not a function. The one in the bottom right is therefore the answer.

Here, the y-axis represents different sports in which players are in.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

X = - 7/2 or -6

Step-by-step explanation:

2x^2 + 19x + 40 = -2

2x^2 +19x + 40+2 = 0

2x^2 + 12x +7x+42= 0

2x(x+6) 7(x+6) =0

(2x+7) (x+6) = 0

2x+7 = 0

2x = -7

2x÷2=-7÷2

X= -7÷2 and

X+6=0

X=-6