A group of Mupuvr CLC MLMMS4 students were questioned how they got to school half of the students saod they walk one third said they take a taxi amd the rest claimed they drive

Calculate the number of students delivered by car using proper fractions

Answer:

For example, a borrower takes a $100,000 loan with a 6% annual interest rate for three years.

Step-by-step explanation:

Have a GREAT DAY !

The length of the blue ribbon given the length of red ribbon is 8 inches

length of blue ribbon = 2/3 of red ribbon

= 2/3 × 12

= (2×12)/3

= 24/3

= 8 inches

Let

3x = 15

x = 15/3

x = 5 books

Therefore, the number of books Mai has is 5 books

Complete question:

The length of the blue ribbon is two-thirds the length of the red ribbon. How long is the blue ribbon if the red ribbon is 12 inches?

Tyler has 3 times as many books as Mai. How many books does Mai have if Tyler has 15 books?

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Answer:

\(\sqrt{37}\)

Step-by-step explanation:

you can use the pythagorean theorem. form a triangle, the distance on one side should be 6, the other 1. \(6^{2} +1^{2} =c^{2} , 37=c^{2} , c=\sqrt{37}\)

Step-by-step explanation:

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16c + 30t =2000 ,is the equation shows the possible number of cars and possible number of trucks.

Equation:

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Each car's gas tank holds 16 gallons of fuel, while each truck's gas tank holds 30 gallons. Consequently, the fleet's total gas requirement is  16c+30t

Additionally, to fill the fleet's empty gas tanks, 2,000 gallons of gasoline are needed. As a result, the following equation depicts the potential number of vehicles, c, and trucks, t, in the fleet

16c + 30t =2000.

Therefore,the equation shows the possible number of cars and possible number of trucks is 16c + 30t =2000.

Hence,16c + 30t =2000 ,is the equation shows the possible number of cars and possible number of trucks.

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As we know that perimeter of a shape is the sum of all it's boundaries. Also , let assume that the missing side be y . So ,here ;

\({:\implies \quad \sf (4x-4)+(3x+1)+y=13x-8}\)

\({:\implies \quad \sf 4x-4+3x+1+y=13x-8}\)

\({:\implies \quad \sf y+7x-3=13x-8}\)

\({:\implies \quad \sf y=13x-8-7x+3}\)

Collecting like terms :

\({:\implies \quad \sf y=(13x-7x)+(-8+3)}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{y=6x-5}}}\)

Hence , the length of Missing side is 6x-5

Answer and Step-by-step explanation:

0 to the power of 4 is 0.

#teamtrees #PAW (Plant And Water)

Answer:

A. x=-15 and x=3

Step-by-step explanation:

|x+6|+8=17

|x+6|=9

-1(x+6)=9   x+6=9

-x-6=9      x=3

-x=15

x=-15

Answer:

100 hours

Step-by-step explanation:

To find the amount of liters in one hour, you divide 10 by 1000, which gives 0.01 liters each hour. From here, the 1 is in the hundredths place, so if you multiply by 100 hours, if will be at 1 liter.

Answer:

294.1 pounds

Step-by-step explanation:

We find the z score for 90th percentile

= 1.282

Step 2

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score ??

μ is the population mean = 230 pounds

σ is the population standard deviation= 50 pounds

1.282 = x - 230/50

Cross Multiply

1.282 × 50 = x - 230

64.1 = x - 230

x = 230 + 64.1

x = 294.1 pounds

The second statement is the most commonly used way of writing 223 as a combination of a whole number and a fraction, but there are many other ways to express it.

What is a fraction ?

A fraction is a mathematical concept used to represent a part of a whole. It is represented by two numbers separated by a line, called a fraction bar or a solidus. The number above the line is called the numerator, and the number below the line is called the denominator

223 can be written as:

223 wholes and 0/1 as the fraction

222 wholes and 1/1 as the fraction

221 wholes and 2/1 as the fraction

...

0 wholes and 223/1 as the fraction

Note that

Therefore, the second statement is the most commonly used way of writing 223 as a combination of a whole number and a fraction, but there are many other ways to express it.

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The  store manager reports estimated margin of error is  ±18.45 dollars and the sample mean is 62.52.

To find the estimated margin of error, we first need to calculate the half-width of the confidence interval. The half-width is calculated by subtracting the lower limit of the interval from the upper limit and then dividing by 2:

Half-width = (Upper limit - Lower limit) / 2

In this case, the upper limit is 80.97 and the lower limit is 44.07. So, the half-width is:

Half-width = (80.97 - 44.07) / 2 = 18.45

This means that the estimated margin of error is ±18.45 dollars.

To find the sample mean, we take the average of the upper and lower limits of the confidence interval:

Sample mean = (Upper limit + Lower limit) / 2

In this case, the sample mean is:

Sample mean = (80.97 + 44.07) / 2 = 62.52

Therefore, the store manager estimates that the mean price for the population of textbooks is $62.52, with a margin of error of ±18.45 dollars at a confidence level of 95%.

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The standard deviation of this binomial distribution is 4

The given parameters are:

The standard deviation is calculated using:

\(\sigma = \sqrt{np(1 - p)\)

So, we have:

\(\sigma = \sqrt{100 * 20\% * (1 - 20\%)\)

Evaluate

\(\sigma = 4\)

Hence, the standard deviation of this binomial distribution is 4

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Therefore, the number of ways to choose a committee of size 10 with at least 2 men is: 961379655

We are to find the number of ways to choose a committee of size 10 with at least 2 men if there are 30 women in the club and 20 men in the club using set difference. We can use the following formulas: (1) A set difference B = {elements of A that are not in B} (2) The number of ways to choose k elements from n elements is represented by nCk.

(3) The complement of an event E is the set of all outcomes in the sample space that are not included in the outcome of E.(4) If E is an event, then P(E) represents the probability of E happening.(5) P(E') + P(E) = 1 (where E' is the complement of E).

To choose a committee of size 10 with at least 2 men, we can first find the total number of committees possible (which includes committees with 0, 1 or 2 men) and then subtract the committees that do not have at least 2 men. So, the total number of ways to choose a committee of size 10 is 50C10. Using the formula nCk = n!/k!(n-k)!, we can write it as follows: 50C10 = 50! / 10!40! = 10272278170.

The number of ways to choose a committee of size 10 with no men is 30C10.Using the formula nCk = n!/k!(n-k)!, we can write it as follows:30C10 = 30! / 10!20! = 30045015. The number of ways to choose a committee of size 10 with exactly 1 man is (20C1) * (30C9).Using the formula nCk = n!/k!(n-k)!, we can write it as follows:(20C1) * (30C9) = 20! / 1!19! * 30! / 9!21! = 47152200.

The number of ways to choose a committee of size 10 with exactly 2 men is (20C2) * (30C8). Using the formula nCk = n!/k!(n-k)!, we can write it as follows:(20C2) * (30C8) = 20! / 2!18! * 30! / 8!22! = 47502000. Therefore, the number of ways to choose a committee of size 10 with at least 2 men is:50C10 - 30C10 - (20C1) * (30C9) - (20C2) * (30C8)10272278170 - 30045015 - 47152200 - 47502000 = 961379655  Ways.

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Answer:

40%

Step-by-step explanation:

You can plug in 100 as the price of the radio to see how much the price decreased.

20% off of 100 will make it $80.

Then, with the 25% discount, it will be worth $60.

So, $40 was taken off, and 40÷ 100 is 0.4, so the overall percentage reduction was 40%

Answer:

Step-by-step explanation:

If it asked how many hours he worked per week, then the answer is 37.5 hours

Answer:

37.5 hours!

Step-by-step explanation:

750/20

Answer:

$329.00

Step-by-step explanation:

Let the original price be $x, then

x - 0.30x - 0.10(x - 0.30x) =  207.27

x - 0.30x - 0.10x + 0.03x = 207.27

0.63x = 207.27

x = 329.00.

9514 1404 393

Answer:

  (a) All three pyramids have the same volume

Step-by-step explanation:

The triangular base has an area of ...

  B = 1/2bh . . . . where b is the base of the triangle and h is its height.

The volume of the pyramid is ...

  V = 1/3BH . . . . where B is the area of the base, and H is the height of the pyramid.

Combining these equations gives ...

   V = 1/3(1/2bh)H = 1/6bhH

__

Pyramid 1 volume

  V1 = 1/6(12 m)(2 m)(10 m) = 40 m³

Pyramid 2 volume

  V2 = 1/6(6 m)(4 m)(10 m) = 40 m³

Pyramid 3 volume

  V3 = 1/6(12 m)(4 m)(5 m) = 40 m³

All three pyramids have the same volume.

The given height function y(t) = 80 - 4.9t², we can differentiate it to find dy/dt. Evaluating dy/dt at t = 4 will provide the estimate of the instantaneous velocity of the pebble at that time.

(a) The average velocity of the pebble for a given time period can be calculated by finding the change in height and dividing it by the corresponding change in time.

(i) For a time period of 0.1 seconds, the average velocity is (y(4 + 0.1) - y(4)) / 0.1.

(ii) For a time period of 0.05 seconds, the average velocity is (y(4 + 0.05) - y(4)) / 0.05.

(iii) For a time period of 0.01 seconds, the average velocity is (y(4 + 0.01) - y(4)) / 0.01.

(b) To estimate the instantaneous velocity of the pebble after 4 seconds, we can find the derivative of the height function y(t) with respect to time t and evaluate it at t = 4. The derivative dy/dt represents the rate of change of height with respect to time, which gives us the instantaneous velocity at a specific moment.

Using the given height function y(t) = 80 - 4.9t², we can differentiate it to find dy/dt. Evaluating dy/dt at t = 4 will provide the estimate of the instantaneous velocity of the pebble at that time.

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The two-column proof given below proves that the above statement is true.

For writing a two-column proof, we solve the equation step-by-step, giving an explanation for performing any operation on the equation. This should lead us to the final solution, which can help us check if the given conclusion is true.

        Statement                    Reason          

1. (5x + 1)/2  -  8  = 0              Given

2. (5x + 1)/2 = 8                     Simplification

3. (5x + 1) = 16                       Multiplying both sides with 2

4. 5x = 16 - 1                          Subtracting both sides by 1

5. 5x = 15                              Simplified

6. x = 15/5                             Dividing both sides by 5

7. x = 3                                  Simplified

So, we end up with the result x = 3.

But a solution has to satisfy the equation as well. So by resubstituting,

L.H.S. = [5(3) + 1]/2 - 8

          = [15 + 1]/2 - 8

          = 16/2 - 8

          = 8 - 8

          = 0 = R.H.S.

Thus, we have successfully proved that the given conjecture is correct, by a two-column proof and verification.

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The perimeter of the rectangle is 16.697 meters.

It is given that A rectangle is 30m and 70m. Hence, the area of the rectangle is length × breadth

= 30 × 70 = 2100 square meters.

The fact that a square's area equals a rectangle's area is a given.

Thus the area of the square = 2100. Hence it's side is root of 2100 which is 45.82575 meters.

To find how much the perimeter of the rectangle exceeds the perimeter of the square, we need to find out each perimeter first.

Rectangle perimeter = 2(l + b)

= 2(30 + 70)

= 200 meters.

Square perimeter = 4 * side

= 4 × 45.82575

= 183.303 meters.

Thus it's perimeter exceeds by 200 - 183.303 = 16.697 meters.

It exceeds by 16.697 meters.

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Answer:

Step-by-step explanation:

x=8

Answer: True

Step-by-step explanation:

Isometries include rotation, translation, reflection, glides, etc.

Answer:

We have, 80% × x = 100

or,

80/100×1 x = 100

Multiplying both sides by 100 and dividing both sides by 80,

we have x = 100 × 100/80

x = 125

If you are using a calculator, simply enter 100×100÷80, which will give you the answer.

Using Stokes' Theorem F · dr equals zero, the line integral ∫F · dr evaluates to zero.

To evaluate the line integral ∫F · dr using Stokes' Theorem, we need to compute the surface integral of the curl of F over the surface S bounded by the curve C. Stokes' Theorem states that:

∫F · dr = ∬(curl F) · dS

First, let's calculate the curl of F:

F(x, y, z) = z i + y + 422 + y^2 k

The curl of F is given by:

curl F = (∂F₃/∂y - ∂F₂/∂z) i + (∂F₁/∂z - ∂F₃/∂x) j + (∂F₂/∂x - ∂F₁/∂y) k

Let's calculate the partial derivatives of F:

∂F₁/∂z = 0

∂F₂/∂x = 0

∂F₃/∂y = 1 + 2y

Now we can determine the curl of F:

curl F = (0 - 0) i + (0 - 0) j + (1 + 2y) k = (1 + 2y) k

Next, we need to find the outward unit normal vector n to the surface S. Since S is defined as the part of the paraboloid above the xy-plane with z = 4 - 2x - y, we can write it as:

z = 4 - 2x - y

We rearrange the equation to express it explicitly in terms of x and y:

2x + y + z = 4

Comparing this equation with the general form of a plane equation Ax + By + Cz = D, we have:

A = 2, B = 1, C = 1, D = 4

The coefficients A, B, and C give us the components of the normal vector n = (A, B, C):

n = (2, 1, 1)

Since C is oriented counterclockwise when viewed from above, we take the outward normal direction, which is n = (2, 1, 1).

Now, let's calculate the surface area element dS. In this case, dS will be the projection of the differential area element in the xy-plane onto the surface S. Since the surface S is parallel to the xy-plane, the surface area element dS is simply dxdy.

Now we can apply Stokes' Theorem:

∫F · dr = ∬(curl F) · dS

Since the surface S is bounded by the curve C, we need to find the parametrization of C to evaluate the surface integral. The curve C lies on the part of the paraboloid where z = 4 - 2x - y. We can parameterize C as:

r(t) = (x(t), y(t), z(t)) = (t, y, 4 - 2t - y), where 0 ≤ t ≤ 2.

The tangent vector dr is given by:

dr = (dx/dt, dy/dt, dz/dt) dt = (1, 0, -2) dt

Substituting the parameterization into F, we have:

F(x(t), y, z(t)) = (4 - 2t - y) i + y j + (4 - 2t - y)^2 k

Now, let's calculate F · dr:

F · dr = (4 - 2t - y) dx + y dy + (4 - 2t - y)^2 dz

= (4 - 2t - y) dt + (4 - 2t - y)(-2) dt + y(-2) dt

= (4 - 2t - y - 4 + 2t + y)(-2) dt

= 0

Therefore, ∫F · dr = 0 using Stokes' Theorem.

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The expression i⁵ when evaluated is √-1 or i

From the question, we have the following parameters that can be used in our computation:

i⁵

The above expression is a complex numbers expression

As a general rule, complex numbers are numbers that consist of both a real part and an imaginary part.

A complex number can be written in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Using the above as a guide, we have the following:

i⁵ = i⁴ * i

So, we have

i⁵ = (√-1)⁴ * i

Evaluate the exponent

i⁵ = 1 * i

So, we have

i⁵ = i or i⁵ = √-1

Hence, the solution to the expression i⁵ is √-1 or i

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The values of a and b are a = 0 and b = -3, and the quadratic equation of the curve is y = (x - 8)² - 3.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

In this case, the vertex is (8, -3).

So we have -

y = a(x - 8)² - 3

To find the value of a, we need one more point on the parabola.

Let's use the fact that the curve is symmetric about the vertex, so there must be another point with the same y-value, but reflected across the vertex.

Since the vertex is at (8, -3), the reflection would be at (8 - 2a, -3).

So we have -

-3 = a(8 - 2a - 8)² - 3

Simplifying -

0 = a(2a)²

0 = 4a³

So either a = 0 or a is undefined (i.e. the parabola is a horizontal line). But we know the curve has a minimum, so it can't be a horizontal line.

Therefore, a must be 0.

Substituting this into our equation, we get -

y = 0(x - 8)² - 3

y = (x - 8)² - 3

Therefore, a = 0 and b = -3, and the equation is y = (x - 8)² - 3.

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Answer:

4 * pi

Step-by-step explanation:

Given r = 10

Formula for the circumference of this full circle is:

2 * r * pi

2 * 10 * pi = 20 * pi

Given one (biggest) part = 16 * pi of this circle.

The other (smaller) part must therefore be:

20 * pi - 16 * pi

4 * pi

Answer:

ok listen when looking at the graph the answer is easy its b

Step-by-step explanation:

Answer:

it is B

Step-by-step explanation:

because G and K , g is 2.5 and k -3/2