what is the probability that the sample proportion is between 0.70 and 0.80? (round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Answer:

Chris bought the game for 35 after the 30 percent discount  

30 percent of 35 is 10.5

35+10.5 is 40.5

40.5 is the original price before discount!

Step-by-step explanation:

Answer:

(4x - 3)(3x² - 1)

Step-by-step explanation:

12x³ - 9x² - 4x + 3 ( factor the first/second and third/fourth terms )

= 3x²(4x - 3) - 1 (4x - 3) ← factor out (4x - 3) from each term

= (4x - 3)(3x² - 1)

Answer:

4 books

Step-by-step explanation:

We are told that: Hugh bought some magazines that cost 3.95 each

Hugh bought 3 magazines.

Hence, total cost of magazines = 3 magazines × 3.95

= 11.85.

Total cost of magazines = 11.85

From the question, we know that, the total amount Hugh spent = 47.65

Hence, The total cost for books =

Total amount spent - Total cost of magazines

= 47.65 - 11.85

= 35.80

Therefore, the total cost of books = 35.80

We are told in the question that the cost of books is 8.95 each or 8.95 per book.

Hence, the number of books that Hugh bought is calculated as :

35.80/8.95

= 4 books

Therefore, Hugh bought 4 books

True. The Conditional statement is known as the inductive hypothesis.

In mathematical induction, we use this hypothesis to prove that a certain statement or equation is true for all positive integers.

The process involves proving a base case for the smallest possible value of k and then using the inductive hypothesis to prove that the statement is true for the next consecutive value of k.

This process can be repeated infinitely, proving that the statement is true for all positive integers.
Let's say we want to prove that the sum of the first n positive integers is \(n(n+1)/2\) for all positive integers n.

We can start by proving the base case for n=1, which states that \(1(1+1)/2 = 1.\)

Now, assuming that the statement is true for some positive integer k, we can use the inductive hypothesis to prove that it is also true for k+1.

This involves showing that\((k+1)(k+2)/2 = k(k+1)/2 + (k+1)\) which simplifies to the original equation.

By using the inductive hypothesis, we can prove that the statement is true for all positive integers.
Statement "\(P(K) - P(k + 1)\) is true for all positive integers k" is indeed the inductive hypothesis. \(1(1+1)/2 = 1\)

It is an important concept in mathematical induction, allowing us to prove statements and equations for all positive integers.

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Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Step-by-step explanation:

3/5 is the fraction form

3/5×100 is the percentage

0.60 is the decimal

Answer:

a) 3x^2-8x+14

b)x^2-8x-4

c)2x^4-8x+45

Step-by-step explanation:

Answer:

Step-by-step explanation:

b

Answer:

B) \(\$8395.80\)

Step-by-step explanation:

\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)

This is all assuming that r=6% is an annual rate, making t=10/12 years

The given unity feedback system is the type-1 system, which can be observed from the given open-loop transfer function G(s).

Steady state error is the difference between the input and the output as time approaches infinity. It is also the difference between the desired value and the actual output at steady-state.

The steady-state error is calculated using the error coefficient, which depends on the type of the system.Find the steady-state error if the input is 80u(t):The transfer function of the given system can be written as follows;G(s) = 80(8²)/(s+4)(8+6)(8+17)The type of the given system is the type-1 system.

As the input to the system is u(t), the error coefficient is given as,Kp = lims→0sG(s) = 80/4(6)(17) = 5/153The steady-state error can be found out by the following formula;

ess = 1/Kp = 153/5.

Therefore, the steady-state error of the given system if the input is 80u(t) is 153/5.Find the steady-state error if the input is 80tu(t):As the input to the system is tu(t), the error coefficient is given as,Kv = lims→0s²G(s) = 0The steady-state error can be found out by the following formula;ess = 1/Kv = ∞.

Therefore, the steady-state error of the given system if the input is 80tu(t) is infinity.Find the steady-state error if the input is 80t²u(t):As the input to the system is t²u(t), the error coefficient is given as,Ka = lims→0s³G(s) = ∞The steady-state error can be found out by the following formula;

ess = 1/Ka = ∞.

Therefore, the steady-state error of the given system if the input is 80t²u(t) is infinity.

By using the error coefficient formula, we have found that the steady-state error of the given system if the input is 80u(t) is 153/5, steady-state error of the given system if the input is 80tu(t) is infinity and steady-state error of the given system if the input is 80t²u(t) is infinity.

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In programming, an "enclose" statement refers to placing a block of code within a specific construct, such as a loop or function, to control its execution and ensure proper behavior.

When writing code, it's common to encounter exceptions, which are unexpected errors or events that can cause the program to crash or behave in unexpected ways. To handle exceptions, programmers use a construct called a "try-catch" statement, which encloses the code that may throw an exception within a "try" block. If an exception is thrown, the "catch" block will execute, allowing the programmer to handle the exception and take appropriate action.

Using a try-catch statement is essential for writing robust and reliable code, as it ensures that unexpected errors are caught and handled gracefully. By enclosing code that may contain an exception within a try block, programmers can prevent their program from crashing or malfunctioning in the event of an unexpected error. Additionally, by handling exceptions appropriately, programmers can provide a better user experience and prevent their users from encountering cryptic error messages or unexpected behavior. Overall, the try-catch statement is a fundamental tool for any programmer, and mastering its use is crucial for writing high-quality code.

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The projectile will reach a vertical position of 213 feet at a time of approximately 1.431 seconds.

In this problem we have the case of a projectile of being launched upward, whose vertical position (s), in feet, is described by a quadratic equation in terms of time (t), in seconds. Herein we must determine the time when the vertical position of the projectile is equal to 213 feet:

- 16 · t² + 126 · t = 213

16 · t² - 126 · t - 213 = 0

Then, by the quadratic formula:

t = - (- 126) / (2 · 16) ± [1 / (2 · 16)] · √[(- 126)² - 4 · (16) · (- 213)]

t = - 63 / 16 ± (1 / 32) · √29508

t = - 63 / 16 ± (1 / 32) · 2√7377

t = - 63 / 16 ± √7377 / 16

t = (- 63 ± √7377) / 16

The only valid solution for the quadratic formula is (- 63 + √7377) / 16 seconds (approx. 1.431 seconds).

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The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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We can write this as:

3 books / 1 week

This tells us that Sanjit reads 3 books per week.

Let's say he read for 3 weeks, we would multiply to find the number of books he read.

3 * 3 = 9 books

So, Sanjit can read 3 books in 1 week.

Best of Luck!

Answer:

3 books/1 week

Step-by-step explanation:

3 books

------------

1 week

c = 4 times h

Linear equation: 1.5c + 2h = 360

Hello!

Your answer should be..

c=4h     ( as there are 4 hours )

1.5c+2h=360

c is 1.50 and h is 2.00 so you must add them to reach 360

Hope this helps! :)

Answer:

-0.16666666666666

Step-by-step explanation:

-.16

Answer:

0.1667

Step-by-step explanation:

The electric charge q of an alpha particle is +2e and the radius f curvature r of the path taken by the alpha particle is 1e+.

Electric charge is a fundamental property of matter, and it is measured in units of elementary charge, denoted by e.

An alpha particle is a type of particle that is commonly encountered in nuclear physics. It consists of two protons and two neutrons bound together, which gives it a net positive charge.

In this explanation, we will determine the electric charge of an alpha particle and the radius of curvature of its path.

The electric charge of a proton is equal to +1e, where e is the elementary charge. Therefore, the electric charge q of an alpha particle is:

q = 2 × (+1e) = +2e

So, an alpha particle has a net positive charge of +2e.

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The three methods for the evaluation of the accuracy of a classifier are Hold-out method, Cross-validation, and Bootstrap. The major differences among the three methods are explained below:a) Hold-out method:This method divides the original dataset into two parts, a training set and a test set.

The training set is used to train the model, and the test set is used to evaluate the model's accuracy. The advantage of the hold-out method is that it is simple and easy to implement. The disadvantage is that it may have a high variance, meaning that the accuracy may vary depending on the particular training/test split.b) Cross-validation:This method involves dividing the original dataset into k equally sized parts, or folds. This process is repeated k times, with each fold used exactly once as the test set.

The advantage of cross-validation is that it provides a more accurate estimate of the model's accuracy than the hold-out method, as it uses all of the data for training and testing. The disadvantage is that it may be computationally expensive for large datasets, as it requires training and testing the model k times.c) Bootstrap:This method involves randomly sampling the original dataset with replacement to generate multiple datasets of the same size as the original. A model is trained on each of these datasets and tested on the remaining data.

In conclusion, the hold-out method is the simplest and easiest to implement, but may have a high variance. Cross-validation and bootstrap are more accurate methods, but may be computationally expensive for large datasets.

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Answer:

True ☑

Step-by-step explanation:

\( - 3 \times - 7 \\ = {}^{ + } 21\)

Answer:

y = -9

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

note that

(a + b)² = a² + b² + 2ab , that is

a² + b² + 2ab = (a + b)² ← subtract 2ab from both sides

a² + b² = (a + b)² - 2ab

           = 5² - 2(3)

           = 25 - 6

          = 19

Answer:

19

Step-by-step explanation:

since value of both a+b and a*b are given

formula for a^2 + b^2 is (a+b)^2-2*a*b

Substituting those value,

a^2+b^2=5^2-2*3

i.e. 25-6

=19

The area of first compound shape is 121 square inches and the area of second one is 128 square inches.

The area of Rectangle is length times of width.

1. The compound figure has a rectangle and a semicircle.

Area of rectangle=12×8

=96 square feet

Area of semicircle=πr²/2

=3.14×4²/2

=3.14×8=25.12 square feet.

Total Area =96+25.12

=121.12 square feet.

2.

Area of rectangle=8×13

=104 square feet.

Now there are two rectangles which has a height of (19-13)=6

Base of 4 inches.

Area of triangle=ab/2

=4×6/2

=12 square inches

As there are two right angle triangles.

2(12)=24

Now total Area is 24+104

128 square inches.

Hence, the area of first compound shape is 121 square inches and the area of second one is 128 square inches.

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The sum of first 10 terms is 72.

Concept: Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

Arithmetic Progression Formula

= an - a. nth term of an AP: an = a + (n - 1)d. Sum of n terms of an AP: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the arithmetic progression.

Given:

Eighth term is 8.2

Common difference is 0.4

a(8) = 8.2

a + 7d = 8.2

Since d = 0.4

a + 7(0.4) =8.2

a = 5.4

Sum of 10 terms = n/2 (2a+(n-1)d)

= 5(2*5.4 + 9*0.4)

=5(10.8 +3.6)

Sum=72

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Answer:

x = 120

Step-by-step explanation:

Assuming you require to find the value of x

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

Sum the interior angles and equate to 720

140 + 150 + 90 + x + 130 + 90 = 720 , that is

x + 600 = 720 ( subtract 600 from both sides )

x = 120

Answer:

41 cents for each apple

The estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

To calculate an estimate of the mean length of the insects Ciara found, we need to find the weighted average of the lengths using the given frequencies.

Let's denote the lower limits of the length intervals as L1 = 0, L2 = 10, and L3 = 20.

Similarly, denote the upper limits as U1 = 10, U2 = 20, and U3 = 30.

Next, we calculate the midpoints of each interval by taking the average of the lower and upper limits.

The midpoints are M1 = (L1 + U1) / 2 = 5, M2 = (L2 + U2) / 2 = 15, and M3 = (L3 + U3) / 2 = 25.

Now, we can calculate the sum of the products of the frequencies and the corresponding midpoints.

This gives us (5 \(\times\) 5) + (6 \(\times\) 15) + (9 \(\times\) 25) = 25 + 90 + 225 = 340.

Next, we calculate the sum of the frequencies, which is 5 + 6 + 9 = 20.

Finally, we divide the sum of the products by the sum of the frequencies to find the weighted average, which is 340 / 20 = 17.

Therefore, the estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

Thus, the mean length of the insects Ciara found is approximately 17 millimeters (mm).

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Answer:

3, 4, and 5

Step-by-step explanation:

To put it simply, 3 + 4 + 5 = 12 and the numbers are consecutive, next to each other.

The method:

The three consecutive numbers could be called x, x + 1, and x + 2 and we know that x + x + 1 + x + 2 = 12

This can be simplified to 3x + 3 = 12. Next, subtract 3 from both sides to get 3x = 9. Now, divide both sides by 3 to get x = 3.

This means that the first number is 3 and the other numbers are 4 (3 + 1) and 5 (3 + 2).

Hope this helps!

Answer:

Step-by-step explanation:

Let's name the three consecutive number x, x + 1, and x + 2.

Now, just substitute the value of x into all the numbers to get your answers.

Hence, the numbers are 3, 4 and 5.

The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49). The probability of X being greater than 10 is very small, less than 0.001%.

In this communication system, the signal Θ is a Gaussian distributed random variable with a mean of 0 and standard deviation of 1. The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49).

The receiver observes X, which is the sum of 2Θ and W. Since Θ and W are independent, we can calculate the mean and variance of X as follows:

E[X] = E[2Θ + W] = 2E[Θ] + E[W] = 0 + 0 = 0

Var[X] = Var[2Θ + W] = 4Var[Θ] + Var[W] = 4(1) + 49 = 53

Therefore, X is also a Gaussian distributed random variable with a mean of 0 and standard deviation of √53 = 7.2801.

To find the probability of X taking a certain value, we can use the formula for the Gaussian probability density function:

f(x) = (1/√(2πσ^2)) * e^(-(x-μ)^2/(2σ^2))

where μ is the mean and σ is the standard deviation. For example, the probability that X is equal to 0 can be calculated as:

f(0) = (1/√(2π*53)) * e^(-(0-0)^2/(2*53)) = 0.0494

To find the probability of X being greater than a certain value, we can use the cumulative distribution function (CDF) of the Gaussian distribution. For example, the probability that X is greater than 10 can be calculated as:

P(X > 10) = 1 - Φ((10 - μ)/σ)

where Φ is the standard normal CDF. Substituting the values for μ and σ, we get:

P(X > 10) = 1 - Φ((10 - 0)/7.2801) = 0.00002

So the probability of X being greater than 10 is very small, less than 0.001%.
In the given communication system with Gaussian noise, the signal Θ is a Gaussian distributed random variable Θ∼N(0,1), and the noise W is also a Gaussian distributed random variable W∼N(0,49), independent of the signal. The receiver observes X = 2Θ + W. To provide accurate information, answers should be given to at least 4 decimal places.

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Answer:

C

Step-by-step explanation:

Jason- Two bags 6 tiles each = 1 bag 12 tiles

2/12 for a 5. 2 for 36.