On Monday, 454 students went on a trip to the zoo. All 9
buses were filled and 4 students had to travel in cars. How many students were
in each bus ?

the limits of integration from 100 to 200 allow you to focus on a particular range and calculate the area under the curve or the accumulated value of a function within that range.

The limits of integration being used, from 100 to 200, define the range over which a function is being integrated. Integration is a mathematical process used to find the area under the curve of a function, or the accumulated value of a quantity over a specified interval.
In this case, the limits of integration are set at 100 and 200, meaning that the integration is being performed over the interval [100, 200] on the x-axis. These limits help to determine the boundaries of the area to be calculated and allow us to focus on a specific part of the function's graph.
The choice of these particular limits may depend on various factors, such as the context of the problem being solved, or the specific properties of the function being integrated. For example, if you are calculating the total distance traveled by a moving object with a known velocity function, the limits of integration would represent the time interval of interest.
By using these limits and performing the integration, you can obtain an accurate representation of the accumulated value of the function over the specified interval.

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Around 50% to 75% of the daffodils on the south side of the building are not between 46cm and 48cm.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

This question asks for the probability that none of the three daffodils selected from the south side of the building are between 46cm and 48cm.

Since the median of the data is 46cm

the third quartile is 48cm,

this means that about 50% to 75% of the daffodils on the south side of the building are between 46cm and 48cm.

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The problem where the professor states that the average age of students in the university is 21 years is an example of statistical inference.

Statistical inference is the process of using data from a sample to make inferences or conclusions about a population. It allows us to draw conclusions about a larger group of individuals or objects based on information from a smaller sample. It is a fundamental part of statistical analysis and is used in many fields, including research, business, and government.

Statistical inference includes two main types: estimation and hypothesis testing.

Estimation: This involves using sample data to make estimates about population parameters. For example, using the sample mean to estimate the population mean or the sample proportion to estimate the population proportion.

Hypothesis testing: This involves using sample data to test a claim or hypothesis about a population parameter. For example, testing the claim that a coin is fair, based on the proportion of heads in a sample of coin flips.

The goal of statistical inference is to use the information from a sample to make informed decisions or predictions about a population. It allows us to draw general conclusions from a specific set of data, and it is an essential tool for making sense of data in many fields.

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Answer: 2 3/10 hope this helps :)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

It would be 2 because it cant have a decimal.2.3 would be a rational number

The Laplace transform of e^(8t) * sin(t) is given by 1 / ((s - 8)(s^2 + 1)).

Theorem 7.4.2 states that if F(s) = ℒ{f(t)} and G(s) = ℒ{g(t)}, then the Laplace transform of the convolution of f(t) and g(t) is given by F(s) * G(s).

Using this theorem, we can evaluate the Laplace transform of e^(8t) * sin(t) by finding the individual Laplace transforms of e^(8t) and sin(t) and then multiplying them together.

The Laplace transform of e^(8t):

ℒ{e^(8t)} = 1 / (s - 8)

The Laplace transform of sin(t):

ℒ{sin(t)} = 1 / (s^2 + 1)

Now, applying Theorem 7.4.2, we can find the Laplace transform of e^(8t) * sin(t):

ℒ{e^(8t) * sin(t)} = ℒ{e^(8t)} * ℒ{sin(t)}

= (1 / (s - 8)) * (1 / (s^2 + 1))

= 1 / ((s - 8)(s^2 + 1))

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Answer: 6

Explanation

If we divide our figure into six, we get the following figure:

As we can see, we are left with 6 equal parts. This can be confirmed by solving the equation:

Answer:

f(x)=8x^3+6

y=8x^3+6 replace y and x

x=8y^3+6

x - 6=8y^3

(x - 6)/8=y^3

Step-by-step explanation:

Answer:

17+7=24

Step-by-step explanation:

I hope this help you

Answer

10

Step-by-step explanation:

Subtract 7 from both sides of the equation.

n=17−7

Subtract 7 from 17.

n=10

BRAINLIEST?

Answer:

The time would be 4:59

Step-by-step explanation:

The percentage of such groups (of 400) would 150 or fewer improve is 16.60.

The percentage is a relative value indicating the hundredth component of any quantity. One percent (symbolized 1%) is the 100th element; as a result, 100 percent represents the entirety and 2 hundred percent specifies twice the given amount. percentage.

As finding 10% of a variety of means to divide through 10, it is not unusual to assume that to locate 20% of a variety you must divide through 20 and so on. Take into account, to discover 10% of the number of manner dividing through 10 because 10 is going into one hundred ten times. consequently, to discover 20% of various, divide via five due to the fact 20 is going into 100 five times.

In arithmetic, a percentage is a number or ratio expressed as a fraction of one hundred. it's far frequently denoted by the usage of the percentage signal, "%", although the abbreviations "pct.", "pct" and on occasion "computer" also are used. A percent is a dimensionless wide variety; it has no unit of size.

In what percentage of such groups (of 400) would

150

fewer improve?

i. e. PC X ≤ 150)

By using

-continuity correction we have to find.

PCX 150.5)= P "X-M1.6.150.5-160°

9.8

= p[ 2 < -0.97

By using the standard Normal table we get,

0.1660

P(X ≤150)

= 0. 1660 = 16.60 (

16.60 percent of such groups (of 400) would 150

fever improve.

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Answer:

9 1/10th m/s2 :)

Step-by-step explanation:

The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...

Answer:

9 + 1.35 + one-half (3.50 + 1.74)

Step-by-step explanation:

Sally pay

9 - adult ticket

1.35 - drink

1/2 ( 3.50 popcorn + 1.74 veggie cup)

= 9 + 1.35 + 1/2(3.50 +1.74)

Therefore , the solution of the given problem of graph comes out to be function g(x) that has the same shape as f(x), but is scaled down by a factor of 1/4.

Mathematicians utilise graphs to visually depict or chart facts or values in a logical way. Usually, a graph point will show the connection between two or more objects. A graph is a non-linear graph structure made up of nodes, also known as vertices, and lines. The nodes, also referred to as edges, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5.

Here,

Given :

The function f(x) = x² is a parabolic function that opens upward and

passes through the origin (0, 0) on the coordinate plane.

To find the graph of g(x) = 1/4f(x), we need to apply the scaling factor of 1/4 to the function f(x), which will make the parabola narrower and shorter.

To do this, we can multiply the y-coordinate of each point on the graph of f(x) by 1/4.

This will result in a new function g(x) that has the same shape as f(x), but is scaled down by a factor of 1/4.

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The simple interest will be $36 and the amount will be $236

Given, the principal = $200

Rate of interest = 6%

Time = 3 years

Now, on using the formula of Simple Interest,

SI = (P×R×T)/100

SI = (200×6×3)/100

SI = $36

Now, the amount will be

Amount = 200 + 36

Amount = $236

Hence, the simple interest will be $36 and the amount will be $236

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Answer:

it's the 2nd answer.....

Answer:

(7×7×7×7×7)(7×7×7×7×7)(7×7×7×7×7)

Step-by-step explanation:

Properties of exponents state that in this case, the exponents multiply together. So, 5×3 is 15. Now it is \(7^{15}\)

The relative frequency for getting a marble that is either red or blue is equal to 16/25

When we perform an experiment N times, and we get a given outcome K times, the relative frequency of said outcome is:

F = K/N

Here we can see that the experiment was performed 25 times, and the outcomes blue or red appeared 8 times each (so 16 in total)

Then the relative frequency for getting a marble that is either red or blue is:

F = 16/25 = 0.64

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the mathematical statement "a number n increased by 16" is equivalent to the algebraic expression:

n + 16

Here we have a mathematical statement which says "a number n increased by 16"

An "increase" is a sum. So the mathematical expression will just be the addition between a number (which we will denote with the variable n) and 16.

n + 16.

Concluding, the mathematical statement "a number n increased by 16" is equivalent to the algebraic expression:

n + 16

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Answer: No, both statements are false.

Step-by-step explanation: it's logical a square has to have 4 sides no more and no less.

The statements are not logically equivalent because D.) No, both statements are false.

A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and four equal angles. It can also be defined as a rectangle with two adjacent sides of equal length.

A square is a regular polygon with four equal sides and four equal angles of 90° each. A square is a closed two-dimensional shape with four equal sides and four vertices. Its opposing sides are perpendicular to each other. A square can also be thought of as a rectangle with equal length and width.

In this case, a square has four sides. Therefore, the information given about the square is wrong. The correct option is D.

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Answer:

\(\frac{1}{12}\)

Step-by-step explanation:

A full circle consists of 360°, so we can write the fraction of this arc as \(\frac{30}{360}\), which can be simplified to \(\frac{1}{12}\) by dividing the numerator and denominator by 30.

**This content involves simplifying fractions and knowledge on the angle sum of a circle which you may wish to revise. I'm always happy to help!

The answer is that the bird is gaining weight faster when it is weighing 40 grams.

The given problem is a differential equation problem with initial conditions and

\(\frac{dB}{dt}\) = \(\frac{1}{5}\) (100-B)

where B(t) is the solution to the differential equation with initial condition as B(0)=20g.

Now, \(\frac{dB}{dt}\)  at B=40 is    \(\frac{1}{5}\)(60)=12 and at B=70,

\(\frac{dB}{dt}\)  is    \(\frac{1}{5}\)(100-70)= 6.

Since \(\frac{dB}{dt}\) is greater when B=40, therefore the bird gains weight faster when it is weighing 40 grams.

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Answer:

scientific notation:

4.51 × 104

or

4.51x10^4

scientific notation with e:

4.51e4

Step-by-step explanation:

When you write scientific notation of 45100/45.1 thousand, you need to find How do you write 45100/45.1 thousand in scientific notation.

. The 45100 should be written.

Answer:

4.51 * 10^4

Step-by-step explanation:

4.51 * 10^4 = 45100

All you gotta do is move the decimal to the left until you have a number between 1-10. And how ever many spaces you jumped that's the exponent you put on the 10.

Example, 467500

I would jump 5 places to get 4.675

Since I jumped 5 places that's my exponent

4.675 * 10^5

HOpe this helps!!!

In the given figure, we can observe that two triangles are formed: ΔASB and ΔTSC.

It is given that:

Length of ST = 54 ft

Length of TB = 25 ft

Length of SC = 18 ft

To find: The length of SA

The length of TA can be found as follows:

Using the Pythagorean theorem,

In ΔTSC,TS² + SC² = TC²

54² + 18² = TC²

2916 + 324 = TC²

3240 = TC²

TC = 60 ft

Now, in ΔTSA,

TS² + SA² = TA²

60² + SA² = TA²

3600 + SA² = TA²

In ΔTAS,

TA² + AS² = TS²

TA² + AS² = 60²

TA² + AS² = 3600

In ΔASB,

AB² + BS² = AS²

AB² + 25² = AS²

AB² = AS² - 625

In ΔAST,

AS² + ST² = AT²

AS² + 54² = AT²

AS² + 2916 = AT²

From the above equations,

AS² - 625 + 2916 = AT²

AS² + 2291 = AT²

Substituting this value in ΔTAS:

TA² + AS² = 3600

TA² + (AT² - 2291) = 3600

TA² + AT² - 2291 = 36002

TA² = 5891TA² = 2945

TA = 54.23 ft (approx.)

Therefore, the length of SA is

From the above calculation, the length of SA is 43 ft.

In the given figure, two triangles are formed ΔASB and ΔTSC. We are to find the length of segment SA.

For that, we use the Pythagorean theorem to find the length of AT first.

The length of ST is 54 ft, SC is 18 ft and the length of TB is 25 ft. Applying the Pythagorean theorem, we get the length of TC as 60 ft.

Using this value, we apply the Pythagorean theorem again to find the length of AT, which comes out to be 54.23 ft (approx.).

Now that we have the length of AT, we apply the Pythagorean theorem in the triangle ΔTAS.

We find that the value of TA² is 2945. Substituting this value in the equation, we get that the length of SA is 43 ft.

Therefore, the length of line segment SA is 43 ft.

Therefore, from the above calculation, the length of line segment SA is 43 ft.

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Given:

The equation of the parabola is:

\(y=x^2+6x\)

To find:

The y-intercept of the parabola.

Solution:

We have,

\(y=x^2+6x\)

Putting \(x=0\) in the given equation, we get

\(y=(0)^2+6(0)\)

\(y=0+0\)

\(y=0\)

Therefore, the y-intercept of the parabola is 0. It means the y-intercept of the given parabola is at point (0,0).

The solution to the given system of equations for x only is x = 7.

Given system of equations can be represented as:

X = (x, y, z)

A =    5  3 -1
      1 -1  0
      5  4  0

B = 5  3
       3  -1
      0  -4

Using the formula of Cramer's rule, the value of x can be calculated as below:

X = (x, y, z)

A =    5  3 -1
      1 -1  0
      5  4  0

B = 5  3
       3  -1
      0  -4

x = | B1| / |A|,

where B1 is the matrix obtained by replacing the first column of A with B and |A| is the determinant of A.

Similarly, the values of y and z can be obtained by replacing the second and third columns of A with B respectively.

The determinant of matrix A can be obtained as follows:

|A| = 5(-1 * 4 - 0 * 4) - 3(1 * 4 - 0 * 5) + (-1 * 5 - 3 * 5)

= -20 - (-12) - 20

= -8

Substituting values of B and A in the formula of Cramer's rule, the value of x can be obtained as:

x = |B1| / |A|, where

B1 =    5  3 -1
       3 -1  0
       0  4  0

|B1| = 5(-1 * 4 - 0 * 4) - 3(3 * 4 - 0 * (-1)) + (-1 * (3 * 0) - 0 * (-1) * 5)

= -20 - 36

= -56

Therefore, x = -56 / -8

= 7

Using Cramer's rule, x is calculated as 7.

So, the solution to the given system of equations for x only is x = 7.

Hence, the conclusion is that the solution to the given system of equations for x only is x = 7.

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The sum of the relative frequencies for all classes will always equal (c) one

To start with, the relative frequency of a class is the frequency of the class divided by the total frequency of the of all classes

Mathematically, this is represented as

Relative frequency of class A = Frequency of class A/Total frequency of all classes

When the relative frequencies are summed up, they will always equal to 1

This is so because they have a part-whole ratio

Hence, the correct option is (c) one

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Note that the perpendicular bisector to line PQ is constructed and attached accordingly. Here is how to do it.

Note that the first stage is to draw a line PQ. But this has already been done.

Next is to place the compass on P as shown in the image above. If you allow you compass (locked at the same degree) to rotate about point P, you will get a circle. However, that is not the objective.

If you also place your compass on point Q, locked to the same degree as when it was on P, and take a rotation around point Q, you will also get a circle.

At some point, you will notice that both circles intersect at two point, which we can call AB₁ and AB₂.

Now you are done with the compass. Take up your ruler, and place it such that it meet both AB₁ and AB₂ but allowing you space to mark a line connecting both points.

Next, using your live or online pencil tool, draw the line from AB₁ to AB₂. Now you have the Perpendicular bisector which you can call AB₁₂.

Note that a perpendicular bisector is a line or plane that intersects a line segment at its midpoint, forming a right angle and dividing the segment into two equal parts.

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Day 6/11 = $6,920

Day 6/15 = $6,505

Day 6/20 = $6,305

She withdrew $279 to buy clothes

Therefore her final balance= $6,920

Therefore, her balance is

= $6,920 - $415

= $6,505

Therefore her balance is

= $6,505 - $200

= $6,305

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