David drove 420 miles using 18 gallons of gas. At this rate, how many gallons of gas would he need to drive 357 miles?

The equation is \(182 - 117 + 72 - 15 = 122\)

The expression is given as:

\(182 - 117 + 72 - 15\)

Rewrite the above expression as an equation:

\(182 - 117 + 72 - 15 = 182 - 117 + 72 - 15\)

Evaluate the expression on the right-hand side

\(182 - 117 + 72 - 15 = 122\)

Hence, the equation is \(182 - 117 + 72 - 15 = 122\)

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Answer:

28

Step-by-step explanation:

area is equal on leng × with, or 36 × w =1008

1008:36 = 28

The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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The value of angle BCD is determined as 108⁰.

option B is the correct answer.

The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc AB =  m∠ACB

m∠ACB =  72⁰

The value of angle BCD is calculated as follows;

angle BCD = 180 - 72⁰ (sum of angles in a circle)

angle BCD = 108⁰

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Answer:

Increase the learning rate after each mini-batch by multiplying it by a small constant.

The velocity of the object is 108.8 m/s and the object will take 0.45 seconds to fall 50 feet.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

The time = 3.4 seconds

There is no air resistance.

v = 32t

v = 32(3.4)

v = 108.8 m/s

T = D/S = 50/108.8 = 0.45 seconds

Thus, the velocity of the object is 108.8 m/s and the object will take 0.45 seconds to fall 50 feet.

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The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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The  expression represents the total surface area of the prism is

2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

The term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the  sum of the areas of all the faces (including the bases) of the prism.

for the rectangular prism, the Total Surface Area can be calculated using the formula:

TSA = 2lw + 2lh + 2wh

where

l = 5

w = 4

h = 7

plugging in the values gives

TSA = 2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

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The directional derivative of f at P = (2,0) in the direction of the unit vector u = cos θ i + sin θ j is given by D_u f(P) = ∇f(P) - u = sin θ/12

Theorem 13.9 relates the directional derivative of a function to its gradient and the direction in which we are taking the derivative. Specifically, if f(x,y) is a differentiable function and u is a unit vector, then the directional derivative of f at a point P in the direction of u is given by:

D_u f(P) = ∇f(P) · u

where ∇f(P) is the gradient of f at P, and · denotes the dot product.

To use this theorem to find the directional derivative of the function f(x,y) = y/(6x+y) at P = (2,0) in the direction of the unit vector u = cos θ i + sin θ j, we first need to compute the gradient of f at P:

∇f(x,y) = (∂f/∂x, ∂f/∂y)

= (-y/(6x+y)^2, 1/(6x+y))

So at P = (2,0), we have:

∇f(2,0) = (0, 1/12)

Next, we need to compute the dot product of ∇f(2,0) with u:

∇f(2,0) · u = (0, 1/12) · (cos θ, sin θ)

= 0 + (1/12) sin θ

= sin θ/12

Note that the value of the directional derivative depends on the angle θ, and varies between -1/12 and 1/12 as θ varies between 0 and 2π.

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Answer:

4/D a reflection fallowed by a rotation.

sorry if I am wrong

We are asked to find the principal for an amount compounded quarterly. Let's remember the formula for a future compounded quarterly:

We solve for P:

We are given the following values:

Replacing we get:

Solving the operations:

Therefore, the initial value must be $4709.88

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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The 9 adult tickets and 93 children tickets were purchased.Let's assume the number of adult tickets purchased is "a" and the number of children tickets purchased is "c."

According to the given information, children tickets cost $9 and adult tickets cost $11. So, the total cost of children tickets is 9c, and the total cost of adult tickets is 11a.

The problem also states that the total cost of all the tickets is $936. Therefore, we can write the following equation:

9c + 11a = 936

Additionally, it is mentioned that the number of children tickets purchased was three more than ten times the number of adult tickets purchased:

c = 10a + 3

We can now solve this system of equations to find the values of "a" and "c." By substituting the value of "c" from the second equation into the first equation, we have:

9(10a + 3) + 11a = 936

90a + 27 + 11a = 936

101a = 936 - 27

101a = 909

a = 909 / 101

a = 9

Substituting this value back into the second equation, we find:

c = 10(9) + 3

c = 90 + 3

c = 93.

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If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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Answer:

Using 22/7 as pi, the area of a circle with a diameter of 14 metres is:

154 m²

Step-by-step explanation:

To solve, use the formula for the area of a circle.

Remember the formula for area of a circle. Be careful not to mix up the formula for area with the formula for circumference!

\(A = \pi r^{2}\)

From the question, we know:

To use the formula, we need the radius ("r").

The radius is a line that goes from the centre point of the circle to the circle outline. It is half the length of the diameter.

The diagram shows the diameter ("d"), which goes through the centre point of the circle. It is twice the length of the radius.

Solve for "r".

r = d/2

r = (14 m)/2

r = 7 m

Substitute r = 7 m and π = 22/7  into the formula for the area of a circle.

\(A = \pi r^{2}\)                         Start with the formula and substitute.

\(\displaystyle{A = \frac{22}{7} (7\ m)^{2}}\)                Square "7" and the "m".

Remember that the answer for area is always squared units.

\(\displaystyle{A = \frac{22}{7} (49\ m^{2})}\)      

Multiplying a fraction and whole number is the same as multiplying the whole number in the numerator (top of the fraction).

\(\displaystyle{A = \frac{22*49}{7}m^{2}}\)              Simplify the numerator.

\(\displaystyle{A = \frac{1078}{7}m^{2}}\)                  Divide.

\(A = 154\ m^{2}\)                   Final answer

∴ The area of the circle is 154 m².

This question is incomplete, the complete question is;

he Eco Pulse survey from the marketing communications firm Shelton Group asked individuals to indicate things they do that make them feel guilty (Los Angeles Times, August 15, 2012).

Based on the survey results, there is a 0.39 probability that a randomly selected person will feel guilty about wasting food and a 0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room.

Moreover, there is a 0.12 probability that a randomly selected person will feel guilty for both of these reasons.

Required:

a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?

b. What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

Answer:

a)

the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both is 0.54

b)

the probability that a randomly selected person will not feel guilty for either of these reasons is 0.46

Step-by-step explanation:

Given the data in the question;

lets A represent person feels guilty about wasting food and B represent leaving the light on when not in room;

probability; feel  guilty about wasting food P(A) = 0.39

probability; feel guilty about leaving light on P(B) = 0.27

probability; feel guilty for both P(A ∩ B ) = 0.12

a)

probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both

p( A ∪ B ) = P(A) + P(B) - P(A ∩ B )

we substitute

p( A ∪ B ) = 0.39 + 0.27 - 0.12

p( A ∪ B ) = 0.54

Therefore, the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both is 0.54

b)

probability that a randomly selected person will not feel guilty for either of these reasons;

p( A ∪ B )' = 1 - p( A ∪ B )

p( A ∪ B )' = 1 - 0.54

p( A ∪ B )' = 0.46

Therefore, the probability that a randomly selected person will not feel guilty for either of these reasons is 0.46

Answer:

12 more games

Step-by-step explanation:

15 + 12 = 27

27 is 90% of 30 , so they need to win 12 more games but 27 overall out of the 30

30 = 100%

27 = x

x = 27×100%/30

x = 2700%/30

x = 90%

Answer:

Step-by-step explanation:

a) Recall the quantifiers \(\forall, \exists\).

Then, we can translate the proposition as follows

\(\forall m \in M \exists x \in D \exists y \in D S(x,m)\land S(y,m)\)

b) Recall that an expression of the form \(\exists x P(x)\) its negation is of the form \(\forall x \neg P(x)\) which means that it is not true that for all elements the proposition P holds. Equivalently, we have that the negation of an expression of the form \(\forall x P(x)\) is \(\exists x \neg P(x)\) which means that there is at least one x such that P doesn't hold. Using this, we get the following

\(\neg(\forall m \in M \exists x \in D \exists y \in D S(x,m)\land S(y,m))= \exists m \in M \neg (\exists x \in D \exists y \in D S(x,m)\land S(y,m))= \exists m \in M \forall x \in D \neg (\exists y \in D S(x,m)\land S(y,m))= \exists m \in M \forall x \in D \forall y \in D \neg(S(x,m)\land S(y,m))\)

By De Morgan's law, we have that \(\neg (A \land B) = \neg A \lor \neg B\)

So, the final statement is

\(\exists m \in M \forall x \in D \forall y \in D \neg S(x,m) \lor \neg S(y,m)\)

c)

This statement means: There is a movie that for every pair of students, at least one of the students hasn't seen the movie yet.

Answer:

The minimum exam score to be awarded an A is about 8.52.

Step-by-step explanation:

Let X represent the scores on a common final exam.

It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.

It is provided that according to the department policy is that the top 10% of students receive an A.

That is, P (X > x) = 0.10.

⇒ P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding z-score is:

z = 1.28

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52\)

Thus, the minimum exam score to be awarded an A is about 8.52.

Taking into account the definition of a system of linear equations, the speed of the first train is 363 mph and the speed of the second train is 356.8 mph.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In other words, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

So, the system of equations to be solved is

\(\left \{ {{F+S=719.8} \atop {F=S+6.2}} \right.\)

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first one you get:

S + 6.2 + S= 719.8

Solving:

2S + 6.2= 719.8

2S= 719.8 - 6.2

2S= 713.6

S= 713.6÷ 2

S= 356.8

Remembering that F= S+ 6.2, then:

F= 356.8 + 6.2

F= 363

In summary, the speed of the first train is 363 mph and the speed of the second train is 356.8 mph.

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Answers:

This forms the equation 1x-5y = -15, which is the same as x-5y = -15

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

Explanation:

Let's find the slope. I'll pick the first two rows to form the two points needed

(x1,y1) = (0,3)

(x2,y2) = (10,5)

These are then plugged into the slope formula.

m = slope

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

m = (5-3)/(10-0)

m = 2/10

m = 1/5

m = 0.2

The y intercept is b = 3 since this is the y value when x = 0.

With m = 0.2 and b = 3, we go from y = mx+b to y = 0.2x+3

Let's multiply both sides by 5 to turn that decimal value into a whole number. I'm picking 5 since 0.2 = 1/5

So we get

y = 0.2x+3

5y = 5*(0.2x+3)

5y = 5*0.2x+5*3

5y = x+15

Now let's get x and y together, but move that 15 to its own side

5y = x+15

x+15 = 5y

x = 5y-15

x-5y = -15

This is one way to write the equation in standard form.

Standard form is Ax+By = C, where A,B,C are integers. Some math textbooks insist that A > 0. In this case, A = 1, B = -5, and C = -15.

----------------------

As a way to check, we can plug in (x,y) = (15,6) from the third row of the table to see that..

x-5y = -15

15-5(6) = -15

15 - 30 = -15

-15 = -15

This verifies the third row. I'll let you check the first two rows of the table to fully confirm this equation works.

Answer:

x = 75

Step-by-step explanation:

x/15 = 5

Multiply each side by 15

15*x/15 = 5*15

x = 75

Answer:

x = 75

Step-by-step explanation:

Reverse the problem meaning you have to do multiplication

5 times 15 is 75

To check your work divided 75 by 15 and if it equals 5 it is correct

Hope this helped :]

The inverse of matrix A, if it exists, is:

A^(-1) = [7/43, 2/43; 10/43, 9/43]

To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.

Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:

det(A) = (9 * 7) - (-2 * -10)

= 63 - 20

= 43

Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.

The formula to calculate the inverse of a 2x2 matrix is:

A^(-1) = (1/det(A)) * [d, -b; -c, a]

Plugging in the values from matrix A and the determinant, we have:

A^(-1) = (1/43) * [7, 2; 10, 9]

Simplifying further, we get:

A^(-1) = [7/43, 2/43; 10/43, 9/43].

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Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

Answer:

The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

Step-by-step explanation:

To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.

First, we will determine y''.

From y = sin(kt)

y' = \(\frac{d}{dt}(y)\)

y' = \(\frac{d}{dt}(sin(kt))\\\)

y' = kcos(kt)

Now for y''

y'' = \(\frac{d}{dt}(y')\)

y'' = \(\frac{d}{dt}(kcos(kt))\)

y'' = \(-k^{2}sin(kt)\)

Hence, the equation y'' + 144y = becomes

\(-k^{2}sin(kt)\) + \(144(sin(kt))\) \(= 0\)

\((144 - k^{2})(sin(kt)) = 0\)

\((144 - k^{2})= 0\)

∴ \(k^{2} = 144\\\)

\(k =\) ±\(\sqrt{144}\\\)

\(k =\) ± \(12\)

∴ \(k = +12\) or \(-12\)

Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

The positive value of k that satisfies the differential equation is k = 12.

To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.

So, y' = dy/dt

= dsin(kt)/dt

= kcos(kt)

y" = dy'/dt

y" = dkcos(kt)/dt

y" = -k²sin(kt)

So, substituting y and y" into the differential equation, we have

y" + 144y = 0

-k²sin(kt) + 144sin(kt) = 0

-k²sin(kt) = -144sin(kt)

k² = 144

k = ±√144

k = ±12

Since we require a positive value, k = 12

So, the positive value of k that satisfies the differential equation is k = 12.

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Answer:

3.3166 That’s your answer