A van can ferry a maximum of 12 people. By setting up an inequality, find the maximum number of vans that are needed to ferry 80 people

Answer:

99th term is -488.

Step-by-step explanation:

This is arithmetic sequence with a1 = 2 and d = -5.

a99 = a1 + (99-1)d

       = 2 + 98*-5

       = -488.

Answer: 420 kg

Step-by-step explanation: 80(the weight of each person) x5 (the ppl) = 400

400+20(the weight of tools) =420

About two minutes long after shaking begins during the tangshan earthquake does it take the last building collapses.

At 3:42 am, an earthquake of magnitude 7.8 to 8.2 struck Tangshan, a Chinese industrial city of about one million people. The quake was particularly costly in terms of human life because most people slept in beds rather than outside the relatively safe streets. occurred along an unknown fault in the Cangdong fault system near the confluence of the The Tangshan fault is a north-northeast-trending strike-slip fault. An estimated 242,000 people died in Tangshan and surrounding areas, making the earthquake one of the deadliest in recorded history, with 300,000 killed in the Calcutta earthquake of 1737, believed dead in 1556. Shaanxi Province, where 830,000 people died of Chinese nationality. It lasted 23 seconds and destroyed 90% of Tangshan's buildings. At least 250,000 killed and 160,000 injured

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Dοmain is x is all real numbers where x dοes nοt equal -2.

Range is y is all real numbers where y dοes nοt equal -8.

In mathematics, the dοmain οf a functiοn is the set οf all pοssible input values (οften represented by the variable x) fοr which the functiοn is defined. It is the set οf all numbers οr values that can be plugged intο the functiοn tο prοduce a valid οutput.

The given functiοn is:

\($ f(x) = (x^2 - 4x - 12)/(x + 2)\)

Tο find the dοmain, we need tο cοnsider the values οf x that make the denοminatοr zerο, as divisiοn by zerο is undefined. Here, x + 2 = 0 gives x = -2, sο x cannοt be -2. Therefοre, the dοmain οf the functiοn is all real numbers except -2. That is,

Dοmain: x ≠ -2

Tο find the range, we can analyse the behaviοr οf the functiοn as x apprοaches pοsitive οr negative infinity. When x is very large (either pοsitive οr negative), the highest pοwer term dοminates, sο the functiοn behaves like  \(f(x) \approx x^2/x = x.\)

Therefοre, as x apprοaches pοsitive infinity οr negative infinity, f(x) apprοaches pοsitive infinity οr negative infinity respectively. Thus, the range οf the functiοn is all real numbers except fοr the value f(-2) = -8 (which is nοt in the dοmain). Therefοre,

Range: y ≠ -8

Sο the cοrrect answer is: dοmain is x is all real numbers where x dοes nοt equal negative 2, and range is y is all real numbers where y dοes nοt equal negative 8.

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Answer:

47x+42/2

Step-by-step explanation:

simplify 9/2

((19x+20)+(9/2×x))+1

(47x+40)/2+1

(47+42)/2

Answer:

28

Step-by-step explanation:

Determine which integer in the solution set will make the equation true. t − 42 = −14 {−56, −28, 3, 28}

replace 28 for t:

t − 42 = −14

28 − 42 = −14

−14 = −14

Answer:

  28

Step-by-step explanation:

You want the value of t that satisfies t − 42 = −14.

The solution to this 1-step linear equation is to add the opposite of the unwanted constant (-42).

Adding 42 to both sides of the equation gives ...

  t -42 +42 = -14 +42

  t = 28

The integer that makes the equation true is 28.

Answer:

The probability that five of the eight students exhibit an higher IQ than the median of the general population is 0.21875

Step-by-step explanation:

The given parameters are;

The number of students in the sample, n = 8

The number of the students, x, that exhibit higher IQ's than the median = 5

The probability of obtaining the given result by chance is given as follows;

P(x) = n!/((n - x)!x!) × pˣ × qⁿ⁻ˣ

The probability that a student exhibit higher IQ's than the median = 0.5 = p

Similarly, we have, the probability that a student exhibit lower IQ's than the median = 0.5 = q

Substituting the known values, gives;

P(5) = (8!/((8 - 5)!×5!)) × 0.5^(5) × 0.5^(8 - 5) = 0.21875

Therefor, the probability that 5 of the 8 students exhibit an higher IQ than the median of the general population, P(5) = 0.21875.

Let's take the subspace (X,T) of (Y,T*), where (Y,T*) is a subspace of (Z,T**). Here, we are required to show that (X,T) is also a subspace of (Z,T**). Let's start our proof.

To show that (X,T) is a subspace of (Z,T**), we must show that (X,T) satisfies the subspace axioms. The subspace axioms that must be satisfied are:

1. The zero vector, 0, is in (X,T).

2. If u and v are in (X,T), then u + v is also in (X,T).

3. If u is in (X,T) and a is a scalar, then au is also in (X,T).

So, let's prove each axiom for (X,T) to be a subspace of (Z,T**):

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Answer: y=mx+b find any two points on the line

Step-by-step explanation:

Surface area of a rectangular prism is 160ft².

A cuboid or rectangular prism is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid implies "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces.

Six faces make up the three-dimensional shape of a rectangular prism. The prism's faces are all rectangles. The shape of a rectangular prism is cuboidal. There are two sets of parallel and congruent bases in this polyhedron. It has eight vertices, 12 sides, and six faces.

A=2(wl+hl+hw)

=2·(4·8+4·8+4·4)

=160ft²

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An LED light bulb is 40% efficient, compared to an incandescent, which is 5% efficient which means that an LED light bulb will convert 40% of the energy used into visible light, while an incandescent light bulb will only convert 5% of the energy used into visible light.

The other 95% of the energy used by an incandescent bulb is lost as heat, making it less efficient. LEDs are much more energy efficient than incandescent bulbs. LEDs are able to produce the same amount of light as an incandescent bulb with only a fraction of the energy. This is because LEDs emit light in a narrow spectrum which reduces energy loss due to the amount of light that is not visible to the human eye. In addition, LEDs do not contain filaments that require power to heat up, meaning that much less energy is wasted as heat.

LEDs also have a longer lifespan than incandescent bulbs. This is due to the fact that LEDs have no filament to burn out, meaning they can last up to 50,000 hours or more. On the other hand, an incandescent bulb typically has a lifespan of around 1,000 hours. This means that an LED light bulb can potentially last up to 50 times longer than an incandescent bulb.

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Answer:

x≈ 11.9 cm

Step-by-step explanation:

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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In triangle ∆PKH, the measures of the angles P = 30.8299, K = 82.8452, and H = 66.3249 to the four decimal place using the cosine rule.

In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Considering the given triangle, angle H is calculated with cosine rule as follows;

h² = p² + k² - 2(p)(k)cosH

19.4² = 29.8² + 13.9² - 2(29.8)(13.9)cosH

cosH = (376.36 - 43.7)/2(29.8)(13.9)

H = cos⁻¹(332.66/828.44)

H = 66.3249

k² = p² + h² - 2(p)(h)cosK

13.9² = 29.8² + 19.4² - 2(29.8)(19.4)cosK

cosK = (193.21 - 49.2)/2(29.8)(19.4)

K = cos⁻¹(144.01/1156.24)

K = 82.8452

P = 180 - (82.8452 + 66.3249) {sum of interior angles of a triangle}

P = 30.8299

Therefore, in triangle ∆PKH, the measures of the angles P = 30.8299, K = 82.8452, and H = 66.3249 to the four decimal place using the cosine rule.

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To approximate the integral ∫2.4 to 2 f(x) dx using Simpson's rule, we divide the interval [2, 2.4] into subintervals and approximate the integral within each subinterval using quadratic polynomials.

Given the data points (x, f(x)) = (2, 0.6931), (2.2, 0.7885), and (2.4, 0.8755), we can use Simpson's rule to approximate the integral.

Step 1: Determine the step size, h.

Since we have three data points, we can divide the interval [2, 2.4] into two subintervals, giving us a step size of h = (2.4 - 2) / 2 = 0.2.

Step 2: Calculate the approximations within each subinterval.

Using Simpson's rule, the integral within each subinterval is given by:

∫f(x)dx ≈ (h/3) * [f(x₀) + 4f(x₁) + f(x₂)]

where x₀, x₁, and x₂ are the data points within each subinterval.

For the first subinterval [2, 2.2]:

∫f(x)dx ≈ (0.2/3) * [f(2) + 4f(2.1) + f(2.2)]

≈ (0.2/3) * [0.6931 + 4(0.7885) + 0.8755]

For the second subinterval [2.2, 2.4]:

∫f(x)dx ≈ (0.2/3) * [f(2.2) + 4f(2.3) + f(2.4)]

≈ (0.2/3) * [0.7885 + 4(0.4545) + 0.8755]

Step 3: Sum up the approximations.

To obtain the approximation of the total integral, we sum up the approximations within each subinterval.

Approximation ≈ (∫f(x)dx in subinterval 1) + (∫f(x)dx in subinterval 2)

Calculating the values, we get the final approximation of the integral ∫2.4 to 2 f(x) dx using Simpson's rule.

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Answer:

Step-by-step explanation:

Think about how many boxes he had bought, which totals to over £80 which means he had received an 8 percent discount hope this is right

Answer:

30?

Step-by-step explanation:

I think that's the answer

Answer:

A

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, thus

the triangle formed by the 2 tangents is isosceles with base angles of 74°

m = 180° - (74 + 74)° = 180° - 148° = 32° ( sum of angles in Δ )

The value of the measured angle of m is 32°.

A tangent of a circle is defined as a single point where a single straight line touches or intersects the circle. A line that never touches the inside of the circle is called a tangent.

The line connecting the outer point will cut the angle between the tangents in bisect and the center are equal to each other.

According to the given figure as

A circle with center O,

Since there are two tangents to the circle drawn from an external point.

therefore the lengths of tangents drawn from an external point to a circle are equal.

So, the triangle formed by the 2 tangents is isosceles with base angles of 74°

We know that sum of angles in the triangle is 180 degrees

So ∠ m = 180° - (74 + 74)°

⇒ ∠ m = 180° - 148°

⇒ ∠ m = 32°

Hence, the value of the measured angle of m is 32°.

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Hii :)

4/12 = 2/6=1/3

All you need to do is take the amount of grapes (4) and put it over the total amount of candy (12). Simplify,then solve.

Hope this helps.

~NatLikesAnime~

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Answer:

41.67%

Step-by-step explanation:

I guessing you want a percentage, and there’s two ways to find it but I’m going to do this way:

divide 100 by the denominator, and then multiply both numerator and denominator by the answer.

The numerator: 5

Denominator: 12

So we has 5/12

1. Divide 100 by 12

=  8.3333333333333

2. Now we multiply both sides by  8.3333333333333

5 x 8.3333333333333 = 41.666666666667

12 x 8.3333333333333 = 100

= 41.666666666667/100

3. Round

41.666666666667 = 41.67

Hence that means that, I have a 41.67 % chance of getting the lemon candy.

Answer:

1 1/12 pounds

Step-by-step explanation:

8/12 + 3/12

Answer:11/12

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

8m = 3.2

divide both sides by 8

m = 0.4

Answer:

m=0.4

Step-by-step explanation: i got it right on my test

The correct ranking of the spheres according to the magnitude of the electric field they produce at point P (greatest first) is: 1 > 2 > 3. The answer is option C.

Since all three spheres have the same charge Q and radius, the magnitude of the electric field at point P due to each sphere is proportional to 1/d^2, where d is the distance between the center of the sphere and point P. Therefore, the sphere closest to point P will produce the greatest electric field at that point.

Assuming that the three spheres are arranged in a straight line with sphere 1 being the closest to point P and sphere 3 being the farthest, we can rank the spheres according to the magnitude of the electric field they produce at point P as follows:

Sphere 1 produces the greatest electric field at point P since it is the closest to it.

Sphere 2 produces the second greatest electric field at point P since it is farther away from point P than sphere 1 but closer than sphere 3.

Sphere 3 produces the smallest electric field at point P since it is the farthest from it.

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Answer:

\(A) \sf \ \sf \dfrac{x^8}{16y^4}\)

Explanation:

 \(\sf \left(\dfrac{2y}{x^2}\right)^{-4}\)

inverse of the expression

 \(\sf \left(\dfrac{x^2}{2y}\right)^{4}\)

distribute power inside parenthesis

 \(\sf \left(\dfrac{(x^2)^4}{(2y)^4}\right)\)

apply exponent rules: \(\s(a^b )^c = a^{bc}\)

   \(\sf \dfrac{x^8}{16y^4}\)

Answer: g(x) =  -(1/2)*x + 3.

Step-by-step explanation:

First, let's define a reflection over the x-axis.

If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).

Now, when we have a function

f(x) = y, the points can be written as:

(x, y = f(x) ) = (x, f(x))

Then, after the reflection over the x-axis, we have:

(x, y = g(x)) = (x, -f(x))

So now we have g(x) = -f(x)

and we know that f(x) = (1/2)*x - 3

then our new function is g(x) =  y = -f(x) = -( (1/2)*x - 3) = -(1/2)*x + 3.

g(x) =  -(1/2)*x + 3.

Answer:

Step-by-step explanation:

Yes , because you when you draw vertical lines through the points, and no vertical line passes through more than 1 point.

Answer:

- is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step-by-step explanation:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step 1: Understand the problem.

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

Step 4: Look back (check and interpret).

The example using the polya's 4-steps in problem solving is created along with the answer.

Let's apply Polya's 4-step problem-solving process to the following word problem:

Problem: Lily has twice as many apples as John. Together, they have 27 apples. How many apples does each person have?

Step 1 - Understand the Problem:

To solve this problem, we need to find the number of apples that Lily and John each have. We know that Lily has twice as many apples as John, and together, they have 27 apples. We need to determine the number of apples for each person.

Step 2 - Devise a Plan:

Let's use algebra to represent the number of apples. Let's say the number of apples John has is "x." Since Lily has twice as many apples as John, the number of apples she has is "2x." We know that together, they have 27 apples, so we can set up an equation:

x + 2x = 27

Step 3 - Execute the Plan:

Now, we'll solve the equation to find the value of "x."

3x = 27

x = 27 / 3

x = 9

So, John has 9 apples. Now, we can find the number of apples Lily has:

Lily's apples = 2 * 9 = 18

Step 4 - Review the Solution:

John has 9 apples, and Lily has 18 apples. Together, they have 9 + 18 = 27 apples, which matches the information given in the problem. Therefore, the solution is correct.

Answer:

John has 9 apples, and Lily has 18 apples.

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