s part of a science experiment, Natasha drops a bouncy ball from various heights, h, and observes the height to which the ball rebounds, r. The table shows the results of Natasha's experiment.

Initial height, h (in meters) Rebound height, r (in meters)
0.30 0.24
0.50 0.4
0.80 0.64
1.00 0.8
1.20 0.96

The definite integral in this problem has the value given as follows:

B. 42.

The definite integral in the context of this problem is given as follows:

\(\int_0^2 (x^7 + 5) dx\)

Applying the power of x integral rule, the result of the integral is given as follows:

\(\frac{x^8}{8} + 5x\)

At x = 2, the numeric value of the integral is given as follows:

\(\frac{2^8}{8} + 5(2) = 42\)

At x = 0, the numeric value of the integral is given as follows:

0.

(as both terms involve a multiplication by x and x = 0).

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

42 - 0 = 42.

Hence option B is the correct option in the context of this problem.

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The height of the actual glass is equal to 10 cm.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures such as drinking glasses, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = 2/2.5

For the height of the actual glass, we have:

2/2.5 = 8/x

x = (2.5 × 8)/2

x = 20/2

x = 10 cm.

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The frequency distribution table is shown in image. The frequency distribution of the daily rainfall data is highly skewed to right side, indicating that it does not follow a normal distribution.

Using a lower class limit of 0.00 and a class width of 0.20, the frequency distribution for the given data would be as

To determine if the frequency distribution appears to be roughly normal, we can create a histogram of the data

From the histogram, it is clear that the frequency distribution is not roughly normal. The distribution is highly skewed to right side, with the majority of the rainfall data falling in the lower range of the data set.

The mean of the data set is also much lower than the median, which further supports the conclusion that the data is highly skewed. Therefore, we can conclude that the rainfall data does not follow a normal distribution.

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--The given question is incomplete, the complete question is given

" The data represents the daily rainfall​ (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal​distribution?

data

0.38

0

0.22

0.06

0

0

0.21

0

0.53

0.18

0

0

0.02

0

0

0.24

0

0

0.01

0

0

1.28

0.24

0

0.19

0.53

0

0

0.24

0"--

Bozeman's store has a z-score of -2.5. This indicates that the number of employees in Bozeman's store is 2.5 standard deviations below the mean of 50. The negative sign indicates that it is below the mean.

The z-score measures how many standard deviations an individual data point is from the mean. In this case, we want to find the z-score for Bozeman's store, which has 25 employees.

Using the formula for the z-score, we can calculate it as follows:

z = (x - μ) / σ

z = (25 - 50) / 10

z = -25 / 10

z = -2.5

Therefore, Bozeman's store has a z-score of -2.5. This indicates that the number of employees in Bozeman's store is 2.5 standard deviations below the mean of 50. The negative sign indicates that it is below the mean.

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As a result of answering the given question, we may state that  As a expressions result, the statement "the difference of two positive numbers is always positive" is incorrect.

In mathematics, an expression is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or value. Expressions might be simple, like "3 + 4", or complex, like "(3x2 - 2) / (x + 1)". They may also include functions such as "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and carrying out the mathematical operations in the given order. For instance, if x = 2, the formula "3x + 5" is 3(2) + 5 = 11. In mathematics, expressions are widely used to explain real-world situations, build equations, and simplify complex mathematical issues.

As an example, suppose the two positive numbers are 4 and 7. The difference between these two numbers is 7 - 4 = 3, which is a negative number. As a result, the statement "the difference of two positive numbers is always positive" is incorrect.

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Answer: do PEMDAS and the answer should be 17 I’m not 100%

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

To find the number of tickets not sold, we need to subtract the number of tickets sold from 600. Since it is 50 per hour, the number of tickets sold is -50h, so the equation is n = -50h + 600

Answer:

here you go

Step-by-step explanation:

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number.

Then: divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

The given information on the diagram of the projector and the image can

be used to prove the congruency of the triangles.

∠ABD, ∠BDA, and side \(\overline {AD}\) on ΔABD are congruent to ∠CBD, ∠BDC, and

segment \(\overline {CD}\) on ΔCBD, therefore, ΔABD ≅ ΔCBD, by AAS Theorem

Reasons:

The figure of the projector that casts an image on the screen is attached.

The bisector of the line \(\overline {AC}\) = \(\overline {BD}\)

From the drawing, we have;

∠ABD ≅ ∠CBD by equal number arc mark.

The two column proof is therefore, presented as follows;

Statement \({}\)                                            Reason

\(\overline {BD}\) is perpendicular bisector of   \({}\)\(\overline {AC}\)   Given

\(\overline {AD}\) = \(\overline {CD}\)   \({}\)                                             Definition of bisected line \(\overline {AC}\)  

∠BDC = 90°       \({}\)                                      \(\overline {BD}\) is perpendicular \(\overline {AC}\)  

∠BDA = 90°                         \({}\)                    \(\overline {BD}\) is perpendicular \(\overline {AC}\)  

∠ABD ≅ ∠CBD \({}\)                                       Given on the diagram

ΔABD ≅ ΔCBD  \({}\)                          by Angle-Angle-Side AAS Congruency rule

The Angle-Angle-Side, AAS, Congruency postulate states that two

triangles are congruent where two adjacent angles and a non included side

on one triangle are congruent to the corresponding two adjacent angles

and a non included side on the other triangle.

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Answer:

Its C

Step-by-step explanation:

Answer:

The answer would be the first choice ; sides jh and tr are congruent

Answer:7?

Step-by-step explanation:

Rise 7

Run. 1

Answer:

-3/9

Step-by-step explanation:

m = 1 - 4/11 - 2 (this is the form it's in: m = y2 - y1/x2 - x1)

m = -3/9

rise: -3

run: 9

(m = slope)

if this doesn't make sense look up "how to find the slope of two points"

hope this helps!

Answer:

pg. 1

teresa: use difference of 2 squares

rico: 6561 is not a perfect square

pg. 2

i think teresa is right and that 6561 can be broken down

problem 1: (x^4-81)^2=(x^2-9)^4=(x-3)^8

problem 2: a. false b. rico

pg. 3

problem 3: a. -1(3x+5)^2 b. teresa is right because it cant still be a perfect square trinomial while having a negative first term.

problem 4: a. (y+3)^2 b. teresa

pg. 4

problem 5: a. (x^n+y^n)(x^n-y^n) b. teresa

teresa got more right, rico is buying pizza

Step-by-step explanation:

apex

3.3.6 Journal PDF answers :)

The length of one leg of a right triangle, a = 8√2

What is pythagoras theorem?

Using pythagoras theorem of triangle:

a² + b² = c²

a² +14² = 18²

a² + 196 = 324

Subtract 196 from both side

a² = 128

Take the square root of both sides

a = √128

a = √(64 * 2)

a = 8√2

Hence, the length of one leg of a right triangle, a = 8√2.

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Answer:

3 feet per minute

Step-by-step explanation:

Find how far the baby gets per minute by multiplying 3/4 by 4:

3/4(4)

= 3

So, the baby crawls 3 feet per minute

a) The probability that exactly 5 aircrafts arrive in a 1-hour period is 0.0378.

b) The probability that at least 5 aircrafts arrive in a 1-hour period is 0.9329.

c) The probability that at least 10 aircrafts arrive in a 1-hour period is 0.4170.

d) The occurrence probability of an aircraft holding event is 0.6082.

e) The occurrence probability of an aircraft holding event in part (d) as a function of the rate of the Poisson process for rates ranging from 10 to 50 is 0.6754

To calculate this probability, we need to use the Poisson distribution formula in this case, k = 5, λ is the rate parameter (10 per hour), e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k. Plugging in the values, we get:

P(X = 5) = (e⁻¹⁰ x 10⁵) / 5! = 0.0378 (rounded to four decimal places)

One way to do this is to use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. Therefore, we can write:

P(X ≥ 5) = 1 - P(X < 5) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)]

Using the Poisson distribution formula, we can calculate each of the individual probabilities and then plug them into the equation above. After some calculations, we get:

P(X ≥ 5) = 1 - 0.0671 = 0.9329

To calculate this probability, we can use the same method as in part (b) but with a different lower limit. Specifically, we need to find P(X ≥ 10). Using the complement rule, we can write:

P(X ≥ 10) = 1 - P(X < 10) = 1 - [P(X = 0) + P(X = 1) + ... + P(X = 9)]

Therefore, we get:

P(X ≥ 10) = 1 - 0.5830 = 0.4170

This gives us a rate of 1.67 arrivals per 10 minutes. Using the Poisson distribution formula again, we can calculate the probability of the number of aircraft arrivals exceeding 2 in a 10-minute period:

P(X > 2) = 1 - P(X ≤ 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

Plugging in the rate parameter of 1.67 and using a calculator, we get:

P(X > 2) = 1 - 0.3918 = 0.6082 (rounded to four decimal places)

Recomputed and plot the occurrence probability of an aircraft holding event in part (d) as a function of the rate of the Poisson process for rates ranging from 10 to 50.

To compute the occurrence probability of an aircraft holding event for different rates, we need to calculate the probability of the number of aircraft arrivals exceeding 2 in a 10-minute period using different rates for the Poisson process. We can write a general formula for this probability as follows:

P(X > 2) = 1 - P(X ≤ 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)] = 0.6754

where X is the random variable representing the number of aircraft arrivals in a 10-minute period, and the Poisson rate parameter λ is equal to (rate/6), where rate is the overall rate of aircraft arrivals per hour.

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The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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To find the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives the probability that a standard normal random variable is less than or equal to a given value. In this case, we need to find the probability that z is less than or equal to 2.67 and subtract the probability that z is less than or equal to -0.15.

Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities:

P(z < 2.67) ≈ 0.9960

P(z < -0.15) ≈ 0.4404

To find the probability of the interval (-0.15 < z < 2.67), we subtract the probability of z < -0.15 from the probability of z < 2.67:

P(-0.15 < z < 2.67) ≈ P(z < 2.67) - P(z < -0.15)

≈ 0.9960 - 0.4404

≈ 0.5556

Therefore, the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution is approximately 0.5556.

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The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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In multivariable calculus, the tangent plane is a plane that "touches" a surface at a given point and has the same slope or gradient as the surface at that point.

To find the equation for the tangent plane at the point P0(2, 1, 2) on the surface 2x^2 + 4y^2 +3z^2 = 24, we need to find the gradient vector of the surface at P0, which gives us the normal vector of the plane. Then, we can use the point-normal form of the equation for a plane to find the equation of the tangent plane.

The gradient vector of the surface is given by:

grad(2x^2 + 4y^2 +3z^2) = (4x, 8y, 6z)

At P0(2, 1, 2), the gradient vector is (8, 8, 12), which is the normal vector of the tangent plane.

Using the point-normal form of the equation for a plane, we have:

8(x - 2) + 8(y - 1) + 12(z - 2) = 0

Simplifying, we get:

4x + 4y + 3z = 20

Therefore, the correct equation for the tangent plane is D. 5x + 4y + 3z = 20.

To find the equations for the normal line, we need to use the direction vector of the line, which is the same as the normal vector of the tangent plane. Thus, the direction vector of the line is (8, 8, 12).

The equations for the normal line can be expressed as:

x = 2 + 8t

y = 1 + 8t

z = 2 + 12t

where t is a parameter that can take any real value.

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Answer:

7 people helped

7/8-3/14

=

(7 × 14) - (3 × 8)

____________

8 × 14

=74/112

74 ÷ 2

_______

112 ÷ 2

=37/56

Step-by-step explanation:

Answer:

84g

Step-by-step explanation:

399÷19=21

21 x 4 = 84

The MAD for this set of data is 0.8.

To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:

Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1

Next, we find the absolute deviation of each age from the mean:

|13 - 10.1| = 2.9

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|11 - 10.1| = 0.9

|9 - 10.1| = 1.1

Then, we find the average of these absolute deviations:

MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8

Therefore,To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:

Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1

Next, we find the absolute deviation of each age from the mean:

|13 - 10.1| = 2.9

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|11 - 10.1| = 0.9

|9 - 10.1| = 1.1

Then, we find the average of these absolute deviations:

MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8

Therefore, the MAD for this set of data is 0.8.

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Answer:

\(y=- \sqrt{\dfrac{1}{2}x}\)

Step-by-step explanation:

Parent functions are the simplest form of a given family of functions.

Transformations of graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

\(\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a \\ & \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a \\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a \end{aligned}\)

\(y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}\)

Given parent function:

\(y=\sqrt{x}\)

Horizontal stretch:

As this is a horizontal stretch, the x variable should be multiplied by a value between zero and 1:

\(\implies y= \sqrt{\dfrac{1}{2}x}\)

Reflected in the x-axis:

To reflect a function in the x-axis, simply make the function negative:

\(\implies y=- \sqrt{\dfrac{1}{2}x}\)

A summary of data that shows the number of observations in each of several non-overlapping bins is called a histogram.

A histogram is a graph used to visualize the distribution of a dataset. The x-axis represents the different ranges of the data being observed, which are usually called bins. The y-axis displays the frequency or count of data values that fall into each bin.

The shape of a histogram can provide valuable insights into the underlying data distribution. For example, if a histogram is bell-shaped, it indicates that the data follows a normal distribution, which is a symmetrical distribution with most values clustered around the mean. If a histogram is skewed to the left, the data has a long tail on the left-hand side and is concentrated on the right-hand side. If a histogram is skewed to the right, the data has a long tail on the right-hand side and is concentrated on the left-hand side. In conclusion, a histogram is a useful tool for summarizing data and providing insights into its distribution.

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Answer:

The answer to the question is b I think

The area of park is 1640.

Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

Given:

Square:

side = 10m

trapezium:

two parallel sides are 38m and 40m

height = 35 m

Now, Area of square

=side * side

=10 *10

=100

and, Area of trapezium

=1/2 * (a + b+10) *h

=1/2 * (38 + 40+10) * 35

=1/2* 88 * 35

=44*35

= 1540

So, the total area of the park is

=100+ 1540

=1640

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The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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Answer:

2355in³

Step-by-step explanation:

3.14(5)²×30=2355 in³

Answer:

Answer:94.2

Answer:94.2Step-by-step explanation:

Answer:94.2Step-by-step explanation:3.14(5)²×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×303.14×5×6

= 94.2

i am sorry if it is not correct