You fill up your car with 15 gallons of gasoline. How many pounds does the gasoline weigh?
Hint: (15 gal) (x qt/gal) (y pt/ qt) (z lb/pt)

Answer:

  A: 8750(0.88^x)

  B: 9995(0.82^x)

Step-by-step explanation:

You want an exponential decay function for cars A and B given their cost and their "decay factor."

In general, an exponential function has the form ...

  value = (initial value)·(growth factor)^x

The growth factor is usually defined as ...

  growth factor = 1 + growth rate

where the "growth rate" is often expressed as a percentage or a fraction.

Your form for f(x) has a=(initial value) and b=(growth factor).

The value of x will be zero at the point where the initial value applies. It will increase by 1 unit for each interval in which the growth factor applies.

Car A

The initial value is presumed to be the Cost. What is called the "growth rate" above is the opposite of what is called the "Decay Factor" in this problem. That is ...

The exponential function is then ...

  f(x) = 8750·(0.88^x)

Car B

For this car, we have ...

The exponential function is then ...

  f(x) = 9995·(0.82^x)

By chain rule, the first derivative of the composite function f(x) = [tex]4^{5\cdot x - 9}[/tex] is equal to  [tex]4^{u}[/tex] · 5 · ㏑ 4.

Herein we have the case of a composite function, that is, a function of the form f[u(x)]. Chain rule is a derivative rule used to find the derivative of composite functions, which is now defined:

df / dx = (df / du) · (du / dx)

If we know that u(x) = 5 · x - 9 and f(u) = [tex]4^{u}[/tex], then the derivative of the compond function is:

df / du = [tex]4^{u}[/tex] · ㏑ 4

du / dx = 5

Then, by chain rule:

df / dx = [tex]4^{u}[/tex] · 5 · ㏑ 4

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Explanation:

Each component has 1/3 as the probability of failure.

1 - 1/3 = 2/3 is the probability a particular component works.

Each component is independent of one another, allowing us to multiply the probabilities: (2/3)*(2/3)*(2/3) = 8/27

8/27 is the probability that all three components work simultaneously, and it's the probability that the machine works.

1 - 8/27 = 19/27 represents the probability that at least one component fails, and hence causes the entire machine to fail also.

19/27 = 0.7037 = 70.37% approximately. It appears this machine fails pretty often.

The probability of filling a cup between 22 and 33 ounces is 0.9371

The variable here is the machine's output which is normally distributed.

The normal distribution is defined by two parameters, namely, the mean and the standard deviation.  

The population mean for this normal distribution is μ = 25 ounces per cup, and a population standard deviation of σ = 4 ounces (per cup).

calculate the z-score using this formula:

z = x-μ/σ

z is the z-score.

x is the raw score.

μ is the population mean.

σ is the population standard deviation.

The probability of filling a cup between 18 and 33 ounces

z = 18-25/4

z = -7/4

z = -1.75

P(Z< - 1.75) = 1 - P(Z > -1.75)

                  = 1 - 0.9599

                  = 0.0400

We can proceed in the same way to obtain the z-score and the associated probability with the raw score x = 33. We can see that this value is above the mean (positive).

z = 33-25/4

z = 8/4

z = 2

P(z<2) = 0.9772

P(18<x<33) = 0.9772 - 0.0400

P(18<x<33) = 0.9371  

the probability of filling a cup between 22 and 33 ounces is 0.9371

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Answer:

Step-by-step explanation:

so by putting  (0,0) into the first equation  it's false,  y of 0 does not become greater than 4

for the second equation, putting in (0,0) it is true.  6 is greater than 0

i'm attaching a graph also  :) of both equations graphed together

[tex]\sf y > -2x+4\\\\Broken\ line\\\\Substitute\ (0,0)\\\\0 > -2(0)+4\\0 > 4\\\\False[/tex]

[tex]\sf 3x+2y \leq 6\\\\Solid\ line\\\\Substitute\ (0,0)\\\\3(0)+2(0) \leq 6\\0\leq 6\\\\True[/tex]

The dimensions and area of the parts of the composite figure are as follows;

A composite figure is a figure that consists of two or more simpler figures.

The width of the whole figure of length 14 consists of the the missing dimension and the expression (x - 3)

Therefore;

14 = Missing dimension + (x - 3)

Missing dimension = 14 - (x - 3) = 17 - x

The expression for the missing dimension is = 17 - x

The area of the large rectangle = 14 × 12 = 168

Area of the smaller unshaded rectangle = (x - 3) × 12 = 12·x - 36

Area of the shaded figure = Area of the whole figure less the area of the unshaded figure

Therefore;

Area of the shaded figure = 168 - (12·x - 36) = 204 - 12·x

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The solution for this system of equations. 12x+ 15y = 34 -6x+ 5y = 3

is (x,y) =(2/3, 8/5)

Given a system of equations,

12x + 15y = 34  ------(1)

-6x + 5y = 3 ------(2),

To solve this we use the elimination method

In the elimination method, you either add or subtract the equations to get an equation in one variable.

Equation (1) + 2 × Equation (2),

We get,

(12x+15y=34)+(-12x+10y=6)

⇒ 15y+10y=34+6

⇒ 25y=40

⇒ y=40/25

⇒ y=8/5

From equation (2),

⇒  -6x+5(y)=6

⇒  -6x+5(8/5)=6

⇒  -6x+8=6

⇒  -6x=-2

⇒ x=2/3

Hence the solution for this system of equations. 12x 15y = 34 -6x 5y = 3

is (x,y =(2/3, 8/5)

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Answer:

Line of symmetry: -b/2a = 0 because b is 0 and a is 1

y-intercept is when x=0, therefore it is at 8.

x-intercept is when y=0, and you would get sqrt(-8), therefore there are no real zeros for this equation.

Vertex: (0,8)

Step-by-step explanation:

To find the vertex, plug in the x-value from the line of symmetry because the vertex happens at the line of symmetry. When you set x=0, then the y-value of the vertex is 8, therefore, the vertex is at (0,8).

[tex](- \frac{3}{2} , -\frac{1}{4} )[/tex] will be located in Quadrant III

What are Quadrants?

A two-dimensional Cartesian plane system's x- and y-axes divide the plane into four infinite regions known as quadrants. The x-axis, sometimes known as the horizontal line, and the y-axis, often known as the vertical line, meet at a right angle. The reference point is often where two lines connect. This point serves as the reference (or initial point) for all measurements made using the coordinate system.

Simply said, a quadrant is the area of a cartesian plane where the x- and y-axes cross each other.

Coordinate plane with four quadrants

According to those values, the graph is then divided into four quadrants or portions.

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Answer: 4 - 0.75x = 0.83333333333

Step-by-step explanation:

3/4 = 0.75

5/6 = 0.83333333

So 4 - 0.75x = 0.83333333

the water level in the stream rises by 10.125 inches.

What is water level?

The elevation of a sea, stream, lake, or reservoir's free surface in relation to a given vertical datum is referred to as the water level, also known as gauge height or stage.

Main body:

According to question water level in stream rises by 2.25 inches every hour.

Total rise can be calculated by using simple multiplication.

Total time for ride = 4.5 hours

Total rise in stream level = total time * total rise in 1 hour

                                         = 2.25*4.5

                                         = 10.125 inches

Therefore total rise in stream is 10.125 inches.

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The other diagonal is $70 long.

Given:

Rhombus $abcd$ has perimeter $148$, and one of its diagonals has length $24$.

P = 148 and d = 24

Area [tex]= 1/4 d \sqrt{P^2-4d^2}[/tex]

= 1/4(24)[tex]\sqrt{148^2 - 4*24^2}[/tex]

= 6 [tex]\sqrt{21904-4*576}[/tex]

= 6*[tex]\sqrt{21904-2304}[/tex]

= 6*[tex]\sqrt{19600}[/tex]

= 6*140

= 840

Area = d*d1 / 2

840 = 24 * d1 / 2

840 * 2 = 24 * d1

1680/24 = d1

d1 = $70

Therefore The other diagonal is $70 long.

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Answer:

70

Step-by-step explanation:

The four sides of a rhombus all have equal length, so if the perimeter is 148, then each side has length 148/4 = 37. Also, the diagonals of a rhombus bisect each other at right angles, so the diagonal of length 24 is cut into two pieces of length 12. We can show this information in a diagram (shown below.)

Applying the Pythagorean Theorem to any of the four right triangles in our diagram, we have

12² + x² = 37².

Solving this equation for positive x, we get x = √37² - 12² = √1369 - 144 = √1225 = 35. The length of the long diagonal is x + x = 70.

By making use of permutation, the number of possible orders for ways to get to school for three days is 6.

Permutation: An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

On the 1st day, the child goes to school either by walking or biking,

So, the number of possible ways for day one is 2.

Similarly, for Day 2 and Day 3, the number of possible ways is 2 each.

Thus, the number of ways in which it can be ordered is 2 +2+2 = 6.

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8x + 5y ≥ 50

This is from the inequality 16x + 10y ≥ 100.

The other three inequalities are:

x + y ≤ 8

x ≥ 1

y ≥ 3

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Total number of students = 100

Type A minibus = x

Type B minibus = y

Number of students type A carry = 16

Number of student type B carry = 10

We can write an inequality from the above situation as,

16x + 10y ≥ 100

Taking out the common factor.

2 (8x + 5y) ≥ 2 x 50

8x + 5y ≥ 50

The school wishes to use no more than eight minibusses.

This can be written as

x + y ≤ 8

The school wishes to use at least one type A minibus.

This can be written as

x ≥ 1

The school wishes to use at least three type B minibusses.

This can be written as

y ≥ 3

Thus,

8x + 5y ≥ 50

This is from the inequality 16x + 10y ≥ 100.

The other three inequalities are:

x + y ≤ 8

x ≥ 1

y ≥ 3

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the second and last one

The answer is  

AEB and IAE

DEA and CED

The polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

The polynomial having the highest power of 3 is called the cubic polynomial.

Given that the roots 2, -3, and 4 that has to pass through the point (1, 10).

The polynomial will be written as,

Y = (x-2)(x+3)(x-4)

Y = x³+x²-6x-4x²-4x=24

Y = x³-3x²-10x+24

Therefore, the polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.

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As the test's p-value above the 0.05 level of significance, we cannot reject the hypothesis.

X=97.77 is the mean on the PDI.

a )

The population standard deviation of the PDI:S = 14-69

The PDI sample size is n=70.

The test statistic value is

=X -μ/б-√n

97.77 - 100/14.69√70

Z = - 1.27

The test's p-value is 1.

Value of p = 2p (z - 1.27).

=2 ( = NORMSDIST (-1.27) )

= - 2 (0.1020 )

p-value = 0.2041

Since , the p -value of the test is greater the the 0.05 level of significance, so we fail to reject hypothesis

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Answer:

E = mc²

Step-by-step explanation:

Answer:

E =mc^2

Step-by-step explanation:

This equation meant (E)energy equals mass (m) times the speed of light (c) squared. (^2).

Answer:

236 for children and 288 for adults

Step-by-step explanation:

→ Set up 2 simultaneous equations

a + c = 524

2.25a + 1.25c = 891

→ Multiply 1st equation by 1.25

1.25a + 1.25c = 655

2.25a + 1.25c = 891

→ Minus from each other

-a = -236 ⇔ a = 236

→ Substitute into first equation

236 + c = 524 ⇔ c = 288

n(x) is a vertical dilation of scale factor 4 followed by a translation of 2 units upwards of the parent linear function.

The parent linear function is:

f(x)= x

And the function n(x) is:

n(x) = 4x + 2

If first we apply a vertical dilation of scale factor 4 to the parent linear function, we will get:

n(x) = 4*f(x)

And if now we apply a translation of 2 units upwards, then we get:

n(x) =4*f(x) + 2

Replacing f(x) by x we get:

n(x) = 4*x + 2

And we returned to n(x), so these are the transformations that define our function in terms to the parent function.

And the slope 4 means that each month 4 books are added, the y-intercept 2 means that she starts with 2 books.

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Step-by-step explanation:

since it is a mid-segment, DGH and DEF are similar triangles with the constant scaling factor of 2 for the lengths of all sides and other lines in the triangle.

e.g.

DE = 2 × DG

DF = 2 × DH

and therefore,

28 = 2 × GH = 2× (x - 3)

14 = x - 3

x = 17

HF = x - 7 = 17 - 7 = 10

DH = HF = 10

so,

y + 8 = 10

y = 2

and DF = 10 + 10 = 20

Answer:

y = -3/4 -1

Step-by-step explanation:

The slope will be a negative recipricol of the original line

Edit : Grammar

The graph is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.as stated

The term "range" refers to every potential value in a graph's output.

The result of range is seen in the y coordinate, and the range of potential values is given here.

0 ≤ y ≤ 5

The term "domain" refers to every conceivable value in a graph's input.

The x coordinate is the input, and the extent of potential values is

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Step-by-step explanation:

[tex] \frac{1}{u} + \frac{1}{v} = \frac{1}{f} [/tex]

[tex] \frac{1}{v} = \frac{1}{f} - \frac{1}{u} [/tex]

[tex] \frac{1}{v} = \frac{u - f}{uf} [/tex]

[tex]v = \frac{uf}{u - f} [/tex]