Grace is finishing her scrapbook by printing out several photos from her latest trips. She printed not less than 60 photos on 2R and 3R. Each 2R print costs P3 and a 3R print costs P5 and she spent a maximum of P200 for her printing needs. Let x represent the number of 2R prints and y represent the number of 3R orints she had for her scrapbook.

Occupants are 10 times more likely to be killed in a crash when not buckled in. option c.

Wearing a seatbelt is one of the simplest ways to protect oneself while in a vehicle. When properly worn, it decreases the likelihood of being seriously injured or killed in a collision by as much as 50%. When an individual is not wearing a seatbelt, they are putting their lives at risk. Wearing a seatbelt should be a routine habit whenever an individual sits in a vehicle.

Buckling up is the easiest and most effective way to prevent injuries and fatalities on the road. If drivers, passengers, and children buckle up every time they travel in a vehicle, the likelihood of being killed or injured in a collision is greatly reduced. When occupants of a vehicle do not buckle up, they are 10 times more likely to be killed in a crash. This means that the likelihood of being killed is significantly higher when not wearing a seatbelt.

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It will take approximately 69.9 years for only 10 grams of the substance to remain, assuming that the decay is exponential.

If the decay of the radioactive substance is exponential, then the amount of the substance remaining after a certain amount of time can be modeled by the equation:

N(t) = N0 * e^(-kt)

where N(t) is the amount of the substance remaining at time t, N0 is the initial amount of the substance, k is the decay constant, and e is the mathematical constant approximately equal to 2.71828.

To solve for the decay constant k, we can use the information given in the problem:

N(5) = N0 * e^(-5k) = 200

N0 = 300

Solving for e^(-5k), we get:

e^(-5k) = 200/300 = 2/3

Taking the natural logarithm of both sides, we get:

-5k = ln(2/3)

Solving for k, we get:

k = -ln(2/3)/5 ≈ 0.088

Now we can use this value of k to answer the question of how much time must elapse before only 10 grams of the substance remain. We can set N(t) to 10 and solve for t:

10 = 300 * e^(-0.088t)

Dividing both sides by 300, we get:

e^(-0.088t) = 1/30

Taking the natural logarithm of both sides, we get:

-0.088t = ln(1/30)

Solving for t, we get:

t ≈ 69.9 years

Therefore, it will take approximately 69.9 years for only 10 grams of the substance to remain, assuming that the decay is exponential.

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Answer:

6

Step-by-step explanation: first convert 4 1/2 into an improper fraction: 9/2

9/2 ÷ 3/4 = 9/2 · 4/3 (multiply fractions)

36/6

6

Answer:

to find the perimeter, you would need to add, so I the answers would be 36 units.

Step-by-step explanation:

The distance of the point 3 4 5 from the origin is 5√2

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

Consider the two points A (x 1, y 1, z 1) and B (x 2, y 2, z 2) in a three-dimensional plane to get the distance formula for two points in the plane.

Let d be the separation between points A and B. The distance between two points in 3D may be calculated using the same reasoning (as outlined in the preceding section) as the distance between two points in 2D.

d = √{(x1 - x2)² + (y1 - y2)² + (z1 - z2)²}

The points are (3,4,5) and (0,0,0)

The distance between the points is

d = √{(3-0)² + (4-0)² + (5-0)²}

⇒ d = √{3² + 4² + 5²} = √(9 + 16 + 25) = 5√2

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Considering the expression of a line, the slope intercept form is y= -x+2.

A linear equation o line can be expressed in the form y = mx + b

where

This is known as the slope-intercept form. This form is one of the most common forms used to represent the equation of a line and can be used to find the equation of a line when given the slope of the straight line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis).

In this case, the line is x+y=2. Expressed in the form y = mx + b, you get:

y= 2 -x     or     y= -x +2

Finally,  x+y=2 in slope intercept form is y= -x+2.

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Mark and Don have 18  and 92 marbles respectively.

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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let the number of marbles Mark has be x.

According to the question,

Don has (5x+2) marbles.

Total number of marbles=110

Thus, the required equation is:

x+5x+2=110

6x=108

x=108/6

x=18

Mark has 18 marbles.

Don has (5*18+2)=92 marbles.

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Answer: The value of x is 6.

Step-by-step explanation:

TO find the volume of a cube you cube any side length. so if the side  length is 6.

6^3 = 216

To find the surface area of a cube you will square one of the side lengths and multiply it by 6.

so the side length is 6 and 6 squared is 36

36*6 = 216

Answer:

(x^2-3)(x+1)

Step-by-step explanation:

we can split this into 2 equations

x^3+x^2

-3x-3

first one we can take x^2 out of the equations

x^2(x+1)

second one we can take out -3 of the equation

-3(x+1)

now we can combine them

(x^2-3)(x+1)

hopes this helps

Answer:

\( (x+1)(x+\sqrt3)(x-\sqrt3) \)

Step-by-step explanation:

We need to factor out ,

\(\longrightarrow x^3 + x^2 -3x -3 = p(x) \ \ \rm[say]\\\)

Look out for factors of 3 , which could be , ±1 or ±3 . That is : 1 , -1 , 3 , -3

Substitute these factors one by one in the given cubic polynomial and look out for that value for which the expression becomes 0 .

Substitute \( x = 1 \) ,

\(\longrightarrow 1^3 + 1^2 -3(1) -3 \\\)

\(\longrightarrow 2 -3-3 = -4 \neq 0\\\)

Again substitute \( x = -1\) , we have ;

\(\longrightarrow (-1)^3+(-1)^2-3(-1)-3\\\)

\(\longrightarrow -1 + 1 +3 - 3 = \boxed{0 } \\\)

This implies \( x +1 \) is a factor of the given cubic polynomial. Now on dividing the polynomial by \( x +1\) , we have; ( see attachment)

\(\longrightarrow p(x) = (x+1)(x^2-3)\\\)

Now we can further factorise \( x^2-3\) as ,

\(\longrightarrow x^2 - 3 \\\)

can be written as ,

\(\longrightarrow x^2-(\sqrt3)^2 \\\)

on using identity \( a^2-b^2=(a-b)(a+b)\) , we have;

\(\longrightarrow (x+\sqrt3)(x-\sqrt3) \\\)

So the final factorised form of the given cubic polynomial is ,

\(\longrightarrow \underline{\underline{ p(x)= (x+1)(x+\sqrt3)(x-\sqrt3)}} \\\)

and we are done!

The rate of heat transfer through the wall is 1.54 kW/m² of wall surface area. The rate of exergy transfer accompanying heat transfer at the inner wall surface is 1.44 kW/m² and at the outer wall surface is 0.097 kW/m².

Given data:

Thickness of insulation, x = 0.066 m
Thermal conductivity, k = 0.05 × 10³ W/m-K
Temperature of inner metal sheet, T1 = 575 K
Temperature of outer metal sheet, T2 = 310 K
Surrounding temperature, To = 293 K

(a) Rate of heat transfer through the wall

The rate of heat transfer through the wall is calculated using the formula:

Q = k A (T1 – T2) / x

Where Q is the rate of heat transfer, A is the surface area, and x is the thickness of the insulation.

Surface area, A = 1 m² (given)

Substituting the values, we get:

Q = (0.05 × 10³) × 1 × (575 – 310) / 0.066

Q = 1540 W

Therefore, the rate of heat transfer through the wall is 1.54 kW/m² of wall surface area.

(b) Rates of exergy transfer accompanying heat transfer at the inner and outer wall surfaces

The rate of exergy transfer accompanying heat transfer at the inner wall surface is calculated using the formula:

I1 = Q (1 – To / T1)

Where I1 is the rate of exergy transfer at the inner wall surface.

Substituting the values, we get:

I1 = 1540 (1 – 293 / 575)

I1 = 1440 W

Therefore, the rate of exergy transfer accompanying heat transfer at the inner wall surface is 1.44 kW/m².

Similarly, the rate of exergy transfer accompanying heat transfer at the outer wall surface is calculated using the formula:

I2 = Q (1 – To / T2)

Where I2 is the rate of exergy transfer at the outer wall surface.

Substituting the values, we get:

I2 = 1540 (1 – 293 / 310)

I2 = 97 W

Therefore, the rate of exergy transfer accompanying heat transfer at the outer wall surface is 0.097 kW/m².

(c) Rate of exergy destruction within the wall

The rate of exergy destruction within the wall is calculated using the formula:

Id = k A [(T1 / To) – (T2 / To)]

Where Id is the rate of exergy destruction.

Substituting the values, we get:

Id = (0.05 × 10³) × 1 × [(575 / 293) – (310 / 293)]

Id = 1340 W

Therefore, the rate of exergy destruction within the wall is 1.34 kW/m².

Hence, the rate of heat transfer through the wall is 1.54 kW/m² of wall surface area. The rate of exergy transfer accompanying heat transfer at the inner wall surface is 1.44 kW/m² and at the outer wall surface is 0.097 kW/m². The rate of exergy destruction within the wall is 1.34 kW/m².

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The length of AE is given as follows:

AE = 7 units.

The midsegment of a triangle states that the segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.

The midsegment of the triangle in this problem is given by the following segment:

BD.

The length of BD is given as follows:

BD = 2 - (-1.5)

BD = 3.5 units.

Hence the length of AE is obtained as follows:

AE = 2BD

AE = 2 x 3.5

AE = 7 units.

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Answer:

2 to the power of 7

Step-by-step explanation:

Since base equal base then subtract the powers

12-5 =7

Answer:

10,164

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello :

put  a=-3    and  n=4   in :  3n2 – 2an

you have : 3(4)² – 2(-3)(4) =3(16)+6(4) =48+24 = 72

We get that the radius is 3 ft and the length is 29 ft so the volume is

the approximate value is:

The exponential function has the following form:

The function goes through the points ( 0, 19) and ( 2, 171 )

We will use the points to find the values of a and b

Substitute with the point ( 2, 171 ) and the value of a to find b

So, the answer will be:

Answer:

Both use bh but triangle is 1/2bh

Step-by-step explanation:

Formulas

Parallelogram bh

Triangle 1/2bh

Answer:

-13x + 200

Step-by-step explanation:

Answer:

1. 2.2

2. 3.8

3. 9

Step-by-step explanation:

1. Plug in -1.6 for y in the equation.

\(3.8+0+-1.6=2.2\)

2. Plug in 0 for y in the equation.

\(3.8+0+0=3.8\)

3. Plug in 5.2 for y in the equation

\(3.8+0+5.2=9\)

Hope this helped C:

Answer:

Step-by-step explanation:

Owen's goal is to drink 6060 ounces of water each day for three days. On the first day, he met \frac{2}{3} 3 2 ​ of his daily goal, on the second day he met \frac{4}{5} 5 4 ​ of his daily goal, and on the third day he only met \frac{1}{4} 4 1 ​ of his daily goal. During the three-day period, how many ounces of water did he drink altogether? Use paper to show your work.

The value of the triple integral of f(ρ, θ, ϕ) = sin(ϕ) over the given region is equal to 15π/4.

To evaluate the triple integral of \(f(\rho, \theta, \phi) = \sin(\phi)\) over the given region in spherical coordinates, we need to integrate with respect to \(\rho\), \(\theta\), and \(\phi\) within their respective limits.

The region of integration is defined by \(0 \leq \theta \leq 2\pi\), \(\frac{\pi}{6} \leq \phi \leq \frac{\pi}{2}\), and \(2 \leq \rho \leq 7\).

To compute the integral, we perform the following steps:

1. Integrate \(\rho\) from 2 to 7.

2. Integrate \(\phi\) from \(\frac{\pi}{6}\) to \(\frac{\pi}{2}\).

3. Integrate \(\theta\) from 0 to \(2\pi\).

The integral of \(\sin(\phi)\) with respect to \(\rho\) and \(\theta\) is straightforward and evaluates to \(\rho\theta\). The integral of \(\sin(\phi)\) with respect to \(\phi\) is \(-\cos(\phi)\).

Thus, the triple integral can be computed as follows:

\[\int_0^{2\pi}\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\int_2^7 \sin(\phi) \, \rho \, d\rho \, d\phi \, d\theta.\]

Evaluating the innermost integral with respect to \(\rho\), we get \(\frac{1}{2}(\rho^2)\bigg|_2^7 = \frac{1}{2}(7^2 - 2^2) = 23\).

The resulting integral becomes:

\[\int_0^{2\pi}\int_{\frac{\pi}{6}}^{\frac{\pi}{2}} 23\sin(\phi) \, d\phi \, d\theta.\]

Next, integrating \(\sin(\phi)\) with respect to \(\phi\), we have \(-23\cos(\phi)\bigg|_{\frac{\pi}{6}}^{\frac{\pi}{2}} = -23\left(\cos\left(\frac{\pi}{2}\right) - \cos\left(\frac{\pi}{6}\right)\right) = -23\left(0 - \frac{\sqrt{3}}{2}\right) = \frac{23\sqrt{3}}{2}\).

Finally, integrating \(\frac{23\sqrt{3}}{2}\) with respect to \(\theta\) over \(0\) to \(2\pi\), we get \(\frac{23\sqrt{3}}{2}\theta\bigg|_0^{2\pi} = 23\sqrt{3}\left(\frac{2\pi}{2}\right) = 23\pi\sqrt{3}\).

Therefore, the value of the triple integral is \(23\pi\sqrt{3}\).

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Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The ratio of wins to losses is 3:1, out of 32 total games. 3:1 has a total of 4 parts (3+1).

Total games divided by total parts is 32/4 = 8.

Now multiplying number of parts to divisor gives us 3x8 : 1×8 or 24:8.

Therefore, they won 24 games, lost 8.

Answer:

The trip will take 4.8 hours

Step-by-step explanation:

Firstly, we need to calculate the distance from Boston to Washington

Mathematically:

Distance = speed * time

Distance = 80 mph * 6 hours = 480 miles

Now we want to calculate the time it will take a train that travels at a speed of 100 mph

Mathematically;

time = distance/speed

time = 480/100 = 4.8 hours

6x+9-4x-6

2x+3

assuming you simplify, hope this helps!

Answer:

It is 51° as it the triangle has a right angle in it

Answer:

Q₂ = 78

Step-by-step explanation:

Q₂ is the median of the data set.

The median is the middle value of the data arranged in ascending order.

If there is no exact middle value then it is the average of the values either side of the middle.

48,  64,  66,  70,  72,  84,  86,  90,  92,  94 ← in ascending order

                                 ↑ middle

median Q₂ = \(\frac{72+84}{2}\) = \(\frac{156}{2}\) = 78

Answer:

the answer is F

Step-by-step explanation:

beacuse I hope I helped :)

Answer:

(0,8) (1,7)

Step-by-step explanation:

The vertex is (0,8)

We must find a second point to plot so we will put x as 1, after further simplifying we have 7, so (1,7) is the second point.

The opportunity cost of spending $90,000 on advertising but only producing 12,000 units can be calculated by comparing the benefits of the advertising investment to the potential alternative uses of that money.

First, let's calculate the total cost of producing 12,000 units. Fixed costs amount to $48,000, and variable costs are $8 per unit, resulting in a total cost of $48,000 + ($8 × 12,000) = $144,000.

Next, we need to calculate the potential sales revenue without advertising. With a price of $16 per unit, the potential sales revenue would be $16 × 12,000 = $192,000.

Now, let's calculate the potential sales revenue after advertising. The advertising multiplier is given as (30,000 + advertising) / 30,000. In this case, the multiplier would be (30,000 + 90,000) / 30,000 = 4.

Therefore, the potential sales revenue after advertising would be $192,000 × 4 = $768,000.

The opportunity cost is the difference between the potential sales revenue after advertising ($768,000) and the potential sales revenue without advertising ($192,000), which is $768,000 - $192,000 = $576,000.

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