How many solutions does the following equation have?

4(y - 30) = 4y + 12

a. No solutions
b. Exactly one solution
c. Infinitely many solutions

Answer:

Jon eats 2 apples; Jon eats more than 2 apples.

Step-by-step explanation:

Mutually exclusive events are events which have no common element between them.  They are completely disjoint and the intersection would be a null set

Hence probability for the intersection of mutually exclusive events =0

Here we are given 4 options to select.

Jon eats more than 1 apple; Jon eats 3 apples.

These two are not mutually exclusive as eating 3 apples includes eating 1 apple.

Jon eats 4 apples; Jon eats 1 apple.

These two are not mutually exclusive as eating 4 apples includes eating 1 apple.

Jon eats 2 apples; Jon eats more than 2 apples.

These two are mutually exclusive since he cannot eat 2 applies exactly and also more than 2 apples

Jon eats 2 apples; Jon eats 4 apples.

These  two are not mutually exclusive as eating 4 apples includes eating 2 apple.

Hence correct answer is

Jon eats 2 apples; Jon eats more than 2 apples.

Answer:

Step-by-step explanation:

The square root of 252 in simplest radical form is 6√7.

To find the square root of 252 in simplest radical form, we can break it down into its prime factors. The prime factorization of 252 is 2 * 2 * 3 * 3 * 7. To simplify the square root, we group the factors into pairs and put one factor from each pair outside the square root and leave the other inside. In this case, we have (2 * 3) * (2 * 3) * 7. Simplifying this further, we get 6 * 6 * 7, which equals 252.

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Answer:

The elevator will take you up at 300 feet in 36 seconds.

Step-by-step explanation:

Let the time taken to go up 300 feet be = t seconds

Given is that the elevator takes you up at 500 feet in 60 seconds.

So, we can derive a relation as:

[tex]\frac{500}{60}= \frac{300}{t}[/tex]

=> [tex]500t=300\times60[/tex]

=> [tex]500t=18000[/tex]

t = 36 seconds

So, the elevator will take you up at 300 feet in 36 seconds.

The required form can be given as,
5 thousand into standard form can be given as = 5000,
456 in word form would be written as four hundred fifty-six,
68 in point form 0.68

Given that,
To write 5 thousand, 456 and 68 hundredths in standard form, word form, and point form.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
5 thousand = 5000
456 in word form = four hundred fifty-six
Point form of 68 hundredths, = 0.68

Thus, the solution is given above in the solution part,

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Answer:

[tex](2;3)[/tex]

Step-by-step explanation:

We can find the solution directly on the graph. The solution of a system of equations is the intersections between the two lines. Remember that each equation in this case represent a line, where the common points are always shown as an intersection.

To prove this result, we can apply other methods. Using the substitution method, we have to isolate one variable from one equation and then replace it in the other equation, like this:

[tex]\left \{ {{y=-x+52'} \atop {y=2x-1}} \right.[/tex]

The variable y is already isolated, now we just replace the first equation in the second:

[tex]-x+5=2x-1\\5+1-2x+x\\6=3x\\x=\frac{6}{3}=2[/tex]

Then, we replace the x-value in one equation, no matter which one:

[tex]y=2x-1\\y=2(2)-1\\y=4-1=3[/tex]

[tex](2;3)[/tex]

1. The Temple in Jerusalem was destroyed in the year of 70 AD.

The first Temple was built by King Solomon for seven years in the 10th century BC. The first Temple was destroyed by the Babylonians in 586 BC. The construction of the new Temple began 535 BC and it is completed in 516 BC. The rebuilding of the Temple was approved by Darius I. It was, however, destroyed by the Romans in 70 AD. Despite the fact that the Temple was destroyed, all the outer walls still stand, and for a long time, it was believed that only the west wall stood.

The provincial governors in Rome were given orders to openly persecute the Christians by Emperor Trajan.

This can be concluded from the letter sent to him by Pliny, governor of Bithynia (province of Asia Minor). He had doubts about the investigation and the way of punishing those who were accused as Christians because he never been present at any trials of Christians. This implies that there have already been trials for Christians and that he did not know the details about Trajan’s decree of prosecuting Christians.

The Roman emperor who passed a decree to require everyone to participate in the cult of emperor worship was Decius.

Emperor Decius (249-251) announced the edict that orders everyone to do sacrifice to the Roman gods and to him personally. According to the edict, the sacrifice had to be carried out in the presence of a Roman magistrate who issued a certificate that this had been done. There is no evidence that it was directed against the Christians, but it was fatal for them because was contrary to their beliefs.

1 Peter 3:17: "For it is better, if  God should will it so, that you suffer for doing what is right rather than for doing what is wrong."

The quote is from the First Epistle of Peter, which is part of the New Testament. It is written by Peter the Apostle in Rome (where he was a bishop) as the letter which is sent to believers in Asia Minor who were persecuted and tortured.

The most damaging charge brought against the Christians in Rome was that they were constant law-breakers who did not discharge their duties to the state.

The Roman authorities consider Christians as opponents of the state that promoted treasonous activities and they were apprehended for disobedience. Suspected Christians have often refused to deviate from Christianity in order to comply themselves with acts of a state cult, which was understood as a public cancellation of loyalty to the state.

c(2) = 50 +5(2) = 60

p(2) = 80-2(2) = 76

60 * 76 = 4560 when the price is 60

the answer would have to be 7.8

Answer: 7.8

Step-by-step explanation:

We find that Grayson charges more than Ian when the number of hours of service h is less than 2.

To determine for how many hours Grayson charges more than Ian, we can set up an equation where the cost of Grayson's tax preparation service is greater than Ian's service. Grayson charges $35 per hour plus a $35 administration fee, while Ian charges $45 per hour plus a $15 administration fee. The number of hours for which the service is required is represented by h.

Grayson's total charge for h hours would be:

Grayson's Cost = $35h + $35

Ian's total charge for h hours would be:

Ian's Cost = $45h + $15

To find the number of hours where Grayson's cost is more than Ian's cost, we set Grayson's Cost > Ian's Cost:

$35h + $35 > $45h + $15

Simplifying, we get:

$35h - $45h > $15 - $35

-$10h > -$20

Dividing both sides by -10 (and remembering to reverse the inequality when dividing by a negative):

h < 2

Thus, Grayson charges more than Ian for fewer than 2 hours of tax preparation.

Final answer:

Quick Fix Inc. breaks even after 7 hours of labor. This is determined by setting the revenue function equal to the overhead cost function and solving for the variable h (hours), which results in a quadratic equation that factors to reveal the break-even point.

Explanation:

To find out after how many hours Quick Fix Inc. breaks even, we need to set the company's revenue function equal to its overhead cost function. The revenue function is given by R(h) = 220h - 160 and the overhead cost function is given by C(h) = 20h2 - 400. The break-even point occurs when R(h) = C(h).

To solve for h (hours), we rearrange the equation: [tex]20h^2 - 220h + 160 + 400 = 0, or \\20h^2 - 220h + 560 = 0.[/tex]

Divide through by 20 to simplify: [tex]h^2 - 11h + 28 = 0.[/tex]

Factoring the quadratic equation gives us: (h - 7)(h - 4) = 0.

Set each factor equal to zero and solve for h: h - 7 = 0 or h - 4 = 0, thus h = 7 hours or h = 4 hours.

Since we are looking for a positive number of hours, we need to test which solution makes sense in the context of the problem. After examining both possibilities, we conclude that the company breaks even at 7 hours, because at 4 hours, the cost would still exceed the revenue.

Final answer:

The ratio of surface area to volume for the square prism is 4/9 when b = 12 ft and h = 18 ft.

Explanation:

The expression for the ratio of surface area to volume of the square prism is 2b + 4h/bh. To find the ratio when b = 12 ft and h = 18 ft, substitute these values into the expression.

Ratio = 2(12) + 4(18)/(12)(18)

= 24 + 72/216

= 96/216

= 4/9

Therefore, the ratio of surface area to volume for the given square prism is 4/9 when b = 12 ft and h = 18 ft.

The ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is calculated using the formula 2b + 4h / bh, which results in a ratio of 4 / 9 ft⁻¹.

The student has asked to find the ratio of surface area to volume for a square prism when given specific dimensions. The formula provided is 2b + 4h / bh, where b is the base length and h is the height of the prism. To find the ratio for b = 12 ft and h = 18 ft, we substitute these values into the formula:

Ratio = (2 × 12 ft) + (4 × 18 ft) / (12 ft × 18 ft) =
24 ft + 72 ft / 216 ft² =
96 ft / 216 ft².

After performing the calculations, we simplify the expression to get the ratio:

Ratio = 96 ft / 216 ft² = 4 / 9 ft⁻¹.

Thus, the ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is 4 / 9 ft⁻¹.

We are given transformation rule

(x, y) --> (x + 4, y + 7).

The coordinate of the pre-image is (4,5).

The coordinate of the transformed image is (0,-2).

Please see, if we apply

(x, y) --> (x + 4, y + 7) rule.

(4,5) coordinate would become (4 +4 , 5+7 ) = (8,12).

But we need (0,-2) instead of (8,12).

Let us reverse operation in the given rule and check.

Let us change (x + 4, y + 7)  to (x-4, y-7) and now check.

(4,5) coordinate would become (4-4 , 5-7) = (0,-2).

So, we got exact coordinate of the transformed image.

Therefore, error was

(x, y) --> (x + 4, y + 7) rule should be (x, y) --> (x - 4, y - 7) rule.

Transformation involves changing the position of a point.

John's error is that, he subtracted the points instead of adding them.

The pre-image is given as:

[tex]\mathbf{(x,y) = (4,5)}[/tex]

The image is given as:

[tex]\mathbf{(x,y) = (0,-2)}[/tex]

The transformation rule is given as:

[tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex]

When the rule [tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex] is applied on [tex]\mathbf{(x,y) = (4,5)}[/tex], we have:

[tex]\mathbf{(x,y) = (4+4,5+7)}[/tex]

[tex]\mathbf{(x,y) = (8,12)}[/tex]

Hence, John's claim is incorrect.

His error is that, he subtracted the points instead of adding them.

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Through a time, distance and speed optimization problem, we find the least amount of time to reach the house is approximately 2.11 hours. The person should land the boat 2 miles from the house.

The problem given is a classic time, distance and speed optimization problem which can be solved with a bit of calculus and geometric reasoning. The first step is to define variables. Let's say the person decides to row to a point x miles down the shore, and then walk the remaining distance.

The time taken to row is the distance rowed divided by the rowing speed, and since the rowing distance is the hypotenuse of the right triangle formed, it is sqrt(4+[tex]x^2[/tex]) miles. Hence, time rowing is sqrt(4+[tex]x^2[/tex])/3 hours.

The distance walked is 6-x and hence, the time walking is (6-x)/5 hours.

The total time is then T(x)=sqrt(4+[tex]x^2[/tex])/3+(6-x)/5. The task is to find an x that minimizes T(x). To do so, take the derivative of T(x), set it equal to 0 and solve for x. After conducting these steps, you find that the minimum time is attained at x=2. Therefore, the least amount of time required would be T(2) which is approximately 2.11 hours. The person should land the rowboat 2 miles from the house.

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Answer:

it's A u were correct

Step-by-step explanation:

This is the angle measured in radians for an arc that is 1 kilometre long is [tex]\({\theta = \frac{360}{\pi^2}}\)[/tex] radians.

To find the angle measure of an arc in radians, we use the formula:

[tex]\[ \text{Angle in radians} = \frac{\text{Arc length}}{\text{Radius}} \][/tex]

Given that the diameter of the circle is 8 kilometres, we can find the radius by dividing the diameter by 2:

[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{8 \text{ km}}{2} = 4 \text{ km} \][/tex]

The arc length is given as [tex]\(\pi\)[/tex] kilometres. Now we can calculate the angle in radians subtended by the arc:

[tex]\[ \theta = \frac{\text{Arc length}}{\text{Radius}} = \frac{\pi \text{ km}}{4 \text{ km}} = \frac{\pi}{4} \][/tex]

However, this is not the final answer. We need to find the angle measured in degrees. To convert radians to degrees, we use the conversion factor:[tex]\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \][/tex]

Thus, the angle in degrees is:

[tex]\[ \theta_{\text{degrees}} = \theta_{\text{radians}} \times \frac{180}{\pi} = \frac{\pi}{4} \times \frac{180}{\pi} = \frac{180}{4} = 45 \text{ degrees} \][/tex]

Now, we need to find the angle measured in radians that correspond to an arc length of 1 kilometre. Using the same formula:

[tex]\[ \theta_{\text{1 km}} = \frac{1 \text{ km}}{4 \text{ km}} = \frac{1}{4} \text{ radians} \][/tex]

To find the number of radians in the entire circle, we multiply by [tex]\(2\pi\)[/tex](since the circumference is [tex]\(2\pi r\)[/tex] and the radius is 4 km):

[tex]\[ \text{Full circle in radians} = 2\pi \times 4 \text{ km} = 8\pi \text{ radians} \][/tex]

Now, we want to find how many times the arc length of 1 km fits into the full circle's circumference:

[tex]\[ \text{Number of arcs} = \frac{8\pi \text{ radians}}{1/4 \text{ radians}} = 32\pi \][/tex]

This represents the number of times the 1 km arc goes around the circle, which is also the measure of the angle in radians that corresponds to a 1 km arc. Since the full circle is [tex]\(360\)[/tex] degrees, the angle measured in degrees for the 1 km arc is:

[tex]\[ \theta_{\text{1 km degrees}} = 32\pi \times \frac{180}{\pi} = 32\pi \times \frac{360}{2\pi} = 32 \times 180 = 5760 \text{ degrees} \][/tex]

However, this is not the final answer. We made a mistake in the calculation. We should not multiply the number of arcs by the full circle's degrees. Instead, we should divide the full circle's degrees by the number of arcs to find the angle measure for one arc:

[tex]\[ \theta_{\text{1 km degrees}} = \frac{360}{32\pi} = \frac{360}{\pi} \times \frac{1}{32} = \frac{360}{\pi^2} \times \frac{\pi}{32} = \frac{360}{\pi^2} \text{ degrees} \][/tex]

To convert this back to radians, we multiply by [tex]\(\frac{\pi}{180}\)[/tex]:

[tex]\[ \theta_{\text{1 km radians}} = \frac{360}{\pi^2} \times \frac{\pi}{180} = \frac{360}{\pi^2} \text{ radians} \][/tex]

This is the angle measured in radians for an arc that is 1 kilometre long.

Final answer:

To transform x²+14x into a perfect square trinomial, add 49 to it, which is the square of half the coefficient of x.

Explanation:

The number that should be added to the expression x²+14x to change it into a perfect square trinomial is obtained by taking half of the coefficient of x, which is 14, and then squaring that value. Therefore, (14 / 2)² = 7² = 49. So, the number to be added to make x²+14x a perfect square trinomial is 49.