Please any help is greatly appreciated

The required original  number that Peter was thinking about is 18.25.

Let us assume that the original number be x that Peter is thinking about.

Peter adds 6 to the number, therefore the number becomes = (6 + x )

Then doubles the new number therefore it becomes = 2(6 + x) = 12 + 2x

According to question by applying rule of forming equations ( from the information given ) we get,

12 + 2x = 48.5

⇒ 2x = 48.5 - 12

⇒ 2x = 36.5

⇒ x = 36.5/2

⇒ x = 18.25

Hence the original number is 18.25.

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Rectangle ABCD is a square.

Relation between rectangle and square?

Squares and rectangles each have four straight sides. However, a square's and a rectangle's mathematical characteristics are very dissimilar. For instance, a common distinction is that squares have equal sides on each side, whereas only the opposite sides of a rectangle are equal.

Radius of circle R = 4cm

let sides of rectangle is a,b

let rectangle be ABCD in which AB =CD= a , AC=BD=b

ACD is right angled triangle on C.

Then,

\(AD^{2} =AC^{2} +CD^{2} \\\\8^{2} =b^{2} +a^{2} \\\\64=b^{2} +a^{2} \\\\b^{2} =\sqrt{64-a^{2} }\)------(1)

Area of rectangle = Area of ΔACD + ΔABD

                             = \(\frac{1}{2} \times a\times b + \frac{1}{2} \times a\times b\)

Area of rectangle = a×b

by eqn (1)

             Area = \(a\times (\sqrt{64-a^{2} } )\)

For maximum area

\(\frac{dA}{da} =0\\\\a \times \frac{1}{\sqrt{64-a^{2} } } (-a)+(\sqrt{64-a^{2} } )\times(1)=0\)

\(\sqrt{64-a^2} -\frac{a^2}{\sqrt{64-a^2} } =0\\\\\frac{64-a^2-a^2}{\sqrt{64-a^2} } =0\\\\64-2a^2=0\\\\a^2=32\\\\a=\sqrt{32} \\\\In (1) eqn\\b=\sqrt{64-a^2} \\\\b=\sqrt{64-32} \\\\b=32\)

So, a=b

Means Rectangle ABCD is a square.

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Answer:

The minimum number of different rooms for accommodating 390 classes if there are 10 different time periods is 39

Step-by-step explanation:

Number of time periods = 10

Number of Classes = 390

Now, if we have a single room, then we can accommodate 10 classes

if we have 2 rooms, we can accommodate (10)(2) = 20 classes

and so on

so we have the relation,

(number of rooms)(number of time periods) = (number of classes that can be accommodated)

We need to find the number of rooms for 390 classes, given that number of time periods is 10, so we get,

(number of rooms)(10) = 390

number of rooms = 390/10

number of rooms =39

The amount of total distance walked (in miles) has walked by Eric in a man made circular lake is 62.8 miles.

A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.

Let's now discover the components of circumference. The three most crucial components of a circle are those three.

Circumference = D*π

Total distance walked two times = 2.C

=2* D* π

=2x10x3.14

=62.8 miles

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To evaluate which of a set of curves fits the data best, you can use the option "c. R2", also known as the coefficient of determination.

R2 is a statistical measure that helps determine the proportion of variance in the dependent variable explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the curve to the data.

To evaluate which of a set of curves fits the data best, we can use the R2 (coefficient of determination) metric. R2 is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model.

                                         A higher R2 value indicates a better fit of the curve to the data. APE (absolute percentage error), MAPE (mean absolute percentage error), and NPV (net present value) are not appropriate metrics for evaluating the fit of a curve to data. APE and MAPE are typically used to measure forecasting accuracy, while NPV is a financial metric used to determine the present value of future cash flows.

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Dunno what the RACE method is, never heard of it before but.

3x is positive, has a variable.

-3 is negative, has no variable.

-3x^2 is negative, has a variable, and an exponent.

-5x is negaitive, has a variable.

The solution to the system of equations is C = 3 and H = 9.

Let C = Cora's miles last week and H = Hana's miles last week

The equation for Cora's miles is C + 7x = 3, and the equation for Hana's miles is H + 4x = 9, where x is the number of weeks.

The solution to this system of equations is C = 3, and H = 9. This can be determined by solving each equation separately and then checking that the answers satisfy both equations.

For Cora's equation, subtract 7x from both sides to get C = 3 - 7x. Solving for x gives x = (3 - C) / 7. Plugging this into Hana's equation gives H + 4((3 - C) / 7) = 9. Simplifying this equation gives H = 9 - 12 + 4C.

Checking the answers, C = 3 - 7(0) = 3, and H = 9 - 12 + 4(3) = 9. Both equations are satisfied by C = 3 and H = 9, so this is the solution to the system of equations.

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The technique often used to prove the correctness of a recursive function is **mathematical induction**.

Mathematical induction is a method of proof used to establish that a property holds for all natural numbers (or a well-ordered set). It consists of two steps:

1. **Base Case**: The base case establishes that the property holds for a specific initial value or base case. It typically involves showing that the property is true for the smallest possible input or base case of the recursive function.

2. **Inductive Step**: The inductive step demonstrates that if the property holds for a specific value, it also holds for the next value. This step involves assuming that the property is true for a certain input, and then proving that it holds for the subsequent input using the recursive definition of the function.

By proving that the base case is true and showing that the inductive step holds, mathematical induction establishes the correctness of a recursive function for all valid inputs.

The other options you mentioned, such as commutativity, diagonalization, and matrix multiplication, are not directly related to proving the correctness of recursive functions. Commutativity refers to the order of operations or elements, diagonalization is a technique used in mathematics and logic, and matrix multiplication is a mathematical operation for matrices. While these concepts may have applications in other areas of mathematics and computer science, they are not specifically used for proving the correctness of recursive functions.

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Answer:

The answer is Dun Dun Duuun 3 {x/4} - 1/2{x/10}

The expression equivalent to 70% of x is,

⇒ 3 (StartFraction x Over 4 EndFraction) minus one-half (StartFraction x Over 10 EndFraction)

⇒ 3 (x/4) - 1/2 (x/10)

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

The expression is,

⇒ 70% of x

Now, We an simplify the expression as;

⇒ 70% of x

⇒ 70/100 × x

⇒ 70x/100

⇒ 7x/10

By option 1;

⇒ 3 (x/4) - 1/2 (x/10)

⇒ 3x/4 - x/20

⇒ (60x - 4x) / 80

⇒ 56x / 80

⇒ 7x/10

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Answer:

A.    (4x+1)(2x squared -2)  you would simply distribute the numbers.

4x(2x squared) + 4x(-2) + 1(2x squared) + 1(-2)

Step-by-step explanation:

In the first case, if iA and B are compact, then it follows that A + B is also compact. In the second case, if A is compact, then both AB and BA are compact. In conclusion, if iA and B are compact operators, then A + B is compact, and if A is a compact operator, then both AB and BA are compact.

1. Assume that iA and B are compact operators. To show that A + B is compact, we need to demonstrate that for any bounded sequence (x_n) in X, the sequence (A+B)(x_n) contains a convergent subsequence. Since iA and B are compact, we can select convergent subsequences from both iA(x_n) and B(x_n). Let (iA(x_{n_k})) and (B(x_{n_j})) be the convergent subsequences of iA(x_n) and B(x_n) respectively. Now, consider the subsequence (A(x_{n_k})) = (iA(x_{n_k})) + (B(x_{n_k})). Since the sum of two convergent sequences is also convergent, (A(x_{n_k})) is a convergent subsequence of (A+B)(x_n). Hence, A + B is compact.

2. Suppose A is a compact operator. To prove that AB is compact, we consider a bounded sequence (x_n) in X. Since A is compact, there exists a subsequence (A(x_{n_k})) that converges in X. Now, for any given epsilon > 0, we can choose a positive integer K such that for k > K, we have ||A(x_{n_k}) - A(x_{n_l})|| < epsilon for all l > K. Since B is a bounded linear operator, B(x_{n_k}) is also a bounded sequence. Therefore, (B(x_{n_k})) contains a convergent subsequence (B(x_{n_{k_p}})). Now, let (AB(x_{n_{k_p}})) be the subsequence of (AB(x_n)). By the properties of convergent sequences, we have ||AB(x_{n_{k_p}}) - AB(x_{n_{k_q}})|| = ||A(x_{n_{k_p}})B(x_{n_{k_p}}) - A(x_{n_{k_q}})B(x_{n_{k_q}})||. Using the properties of norms and the fact that A(x_{n_k}) converges, we can choose K' such that for p, q > K', ||AB(x_{n_{k_p}}) - AB(x_{n_{k_q}})|| < epsilon. Therefore, (AB(x_{n_{k_p}})) is a Cauchy sequence and hence convergent, which proves that AB is compact. Similarly, it can be shown that BA is also compact.

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The probability of at least one is a Samsung in the purchase collection of two independent LED HDTV is equal to 0.376.

Percent of all LED display manufactured by Samsung = 21%

Probability that at least one purchase is Samsung

= 1 - Probability that both purchases are not Samsung

Probability that the first purchase is not Samsung is 1 - 0.21 = 0.79.

The probability that the second purchase is also not Samsung is also 0.79.

Since the purchases are independent,

Multiply these probabilities to get the probability that both purchases are not Samsung,

P(neither is Samsung)

= 0.79 x 0.79

= 0.6241

The probability that at least one purchase is Samsung is,

P(at least one is Samsung)

= 1 - P(neither is Samsung)

= 1 - 0.6241

= 0.3759

Rounding to 3 decimal places, we get,

P(at least one is Samsung) = 0.376

Therefore, the probability that in a collection of two independent LED HDTV purchases, at least one is a Samsung is 0.376.

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Answer:

Width = 160

Length = 110

Step-by-step explanation:

Perimeter is the sum of all the sides

They tell you that the length is 50 m shorter than the width

so L = W - 50

W = W

540 = W + W + W-50 + W-50

540 = 2W + 2(W-50)

540 = 2W + 2W - 100

540 = 4W - 100

640 = 4W

W = 160

L = 160 - 50

L = 110

Answer:

Length: 110 m

Width: 160 m

Step-by-step explanation:

The formula for perimeter of a rectangle is P = 2L + 2W.

We can write the length in terms of width if width is w:

Length: w - 50

Width: w

Plug the values into the formula.

540 = 2(w - 50) + 2w

540 = 2w - 100 + 2w

540 = 4w - 100

640 = 4w

w = 160

find length by subtracting 50 from the width

160-50=110

Therefore, the length is 110 and the width is 160.

If r(x) is a rational function in simplest form where the degree of the numerator is 3 and the degree of the denominator is 1, a)then r(x) has a horizontal asymptote at y=0.

This is because the degree of the denominator is greater than the degree of the numerator, which means that as x gets very large or very small, the denominator will dominate the behavior of the function.

As a result, the function will approach zero, and thus, there is a horizontal asymptote at y=0. If the degree of the numerator were greater than or equal to the degree of the denominator, then the function could have a horizontal asymptote at a nonzero value or no horizontal asymptote at all.

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Answer:

\(y=82\)

Step-by-step explanation:

We know the value of x is -9 so we can plug it in as -9.

\(y=x^2+1\\y=(-9)^2+1\\y=81+1\\y=82\)

Answer:

82=y

Step-by-step explanation:

-9 x -9 = 81

81 + 1 = 82

Answer:

ASA

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

you have to angles on the same segment and one congruent side marked on the other side. this means that the triangles are congruent by AAS

Dr. Jackson has designed a survey to examine the mental health of college students. One measure he includes in the survey is a composite measure of happiness. Which type of reliability should Dr. Jackson be concerned about with this measure.

Dr. Jackson should be concerned with the Internal Consistency Reliability with the composite measure of happiness.Internal Consistency Reliability:Internal consistency reliability measures the degree to which all items in a test measure the same attribute, trait or skill and give consistent scores. It assesses the consistency between items within a test, to see how well they work together to measure the same thing. Internal consistency is usually measured by the Cronbach alpha reliability coefficient.

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1)

\(m = \frac{y - y}{x - x} = \frac{55 - 59}{10 - 0} = \frac{ - 4}{10} = - \frac{2}{5} \)

\(y = - \frac{2}{5} x + b\)

Since the line passes through the point (0,59), the coordinates of this point satisfies the equation of y;

\(59 = - \frac{2}{5} (0) + b\)

\(b = 59\)

Final answer:

\(y = - \frac{2}{5} x + 59\)

Answer:

X=-6

Step-by-step explanation:

Answer:

y=2

Step-by-step explanation:

Both lines will have a slope of 0, as any line where y= a number has a slope of 0. In order for two lines to be parallel, they must have the same slope.

None of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).

The solution of any trigonometric equation represents the value of the parameter which satisfies the given equation. The solution should lie within a given range and it should have the same value as ±π .

To find the solutions to sin x − cos 2x = 0 on the interval [0, 2π), we can start by using the identity cos 2x = 1 - 2sin² x, which gives:

sin x - (1 - 2sin² x) = 0

Simplifying this equation, we get:

2sin² x - sin x + 1 = 0

We can solve this quadratic equation using the quadratic formula:

sin x = [1 ± √(1 - 8)] / 4

sin x = [1 ± √(-7)] / 4

Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, none of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).

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The sets of data for which all the points would be displayed on a scatter plot if the window size on a regression calculator were set to 5 less than or equal to x less than or equal to 15 (5 ≤ x ≤ 15); 25 less than or equal to y less than or equal to 75 (25 ≤ y ≤ 75) is shown in the table below.

A regression line can be defined as a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line refers to a line which best fits a set of data.

A scatter plot is sometimes referred to as scatter diagram, scattergram, or scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association or correlation between the data set.

By critically observing the table (see attachment), you will notice that the least value of x is 6 while the greatest value of x is 14, which is modeled by this domain 5 ≤ x ≤ 15. Similarly, the least value of y is 27 while the greatest value of x is 71, which is modeled by this range 25 ≤ y ≤ 75.

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Answer:

1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71.

The substitution method works by solving one of the equations for one of the variables (you choose the equation and the variable) and then plugging this back into the other equation, substituying for the chosen variable and solving for the other.

For instance, lets solve problem 10. We have the following system:

We can see that the "easiest" way to solve them is by substituting the value of y given in the second equation into the first one. It gives

because y=-3x. Now, we must move -3x to the left hand side as +3x. It yields,

since 6x+3x=9x, we have

Now, if we move -9 to the left hand side as +9, we obtain

then, x=1. Until now, we solved for x. Now. we must subsitute this value into the second equation. It yields,

which gives y=-3. Finally, the answer is x=1 and y=-3.

We can check that this is the correct solution by substituting these values into both equations:

Now, in the second one, we have

Then our answer is corrrect!

Answer:

b = 37

Step-by-step explanation:

3x + 10 = b

(3 x 9) + 10 = 27

27 + 10 = 37

Answer:

b Is 37

Step-by-step explanation:

x Is 9

instead of x you write 9

3x mean 3×X

3×X+10= 3×9+10=27+10=37

Answer:

8?

Step-by-step explanation:

The random variable x as the number of defective cameras in the sample are:

a. P(X =0) = qCn/NCn

                = 2/10

P(X=1) = 2 × (pC1 × qC1)/ NCn

          = 6/10

P(X=2) = pCn/ NCn

           = 2/0

b. The distribution function of:

\(X=[(0,\frac{2}{10} ),(1,\frac{6}{10} ),(2,\frac{2}{10} )]\)

c. The expected number of defective cameras is:

=> 2/3

Probability suggests "possibility" or "chance." When an event is certain to occur, its probability of happening is 1, and when it is definite that it cannot occur, its possibility of occurring is 0.

The given information:

Total number of cameras N = 6

Total number of defective cameras p = 3

Total number of non - defective cameras q = 3

Total number of sample taken n = 2

X can be 0, 1, or 2 . Because, if we pull out 2 cameras, we can have 0, 1, or 2 defective ones.

1) X = number of defective cameras.

We must draw 2 of the 3 non defective cameras and there is a total of ways of drawing 2 cameras out of 6.

P(X =0) = qCn/NCn

            = 3C2/ 6C2

            = 2/10

We must draw 1 out of the 3 non defective cameras and 1 out of the 3 defective cameras.

P(X=1) = 2 × (pC1 × qC1)/ NCn

          = 2 × (3C1 × 3C1) / 6C2

          = 2 × 3/10

          = 6/10

We must draw 2 of the 3 defective cameras

P(X=2) = pCn/ NCn

           = 3C2/6C2

           = 2/10

2) The probability distribution of X is computed as :

The set of order pair

\([x_i,p(x_i);i = 1, 2, 3,...,n,...]\)

specifies the probability distribution function of random variable X. Therefore,

The distribution function of:

\(X=[(0,\frac{2}{10} ),(1,\frac{6}{10} ),(2,\frac{2}{10} )]\)

3) The expected value of X is computed as:

Let \(X_j\) be the indicator random variable that takes value 1 if jth cameras in the sample (of size 2) is defective, and 0 otherwise i.e.,

\(I_j={^1_0\)   if jth camera in the sample is defective otherwise

The no. of defective cameras = \(X_1+X_2\)

Expected no. of defective cameras

\(=E(X_1+X_2)\\=E(X_1)+E(X_2)\\=2E(X_1)\)

Now, \(E(X_1)\) is equal to the probability that the first cameras is defective i.e.,

\(E(X_1)=\frac{2_C_1}{6_C_1}\)

          = 2/6

          = 1/3

Therefore, expected number of defective cameras is:

2 ×  \(E(X_1)\) = 2 × 1/3

                 = 2/3

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The given question is incomplete, So i take similar question:

Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random, with replacement.

a. Define the random variable X as the number of defective cameras in the sample.

b. Write the probability distribution for X.

c. What is the expected value of X?

Answer:

Y=f(x)

Step-by-step explanation:

Answer:

d. reflect triangle abc across line ab

Step-by-step explanation: