John left school with 8.43 he found a quarter on his way home and then stopped to buy an Apple for 0.89 . how much money did he have when he got home

Answer:

Number = 12

Step-by-step explanation:

2n-7=n+5 (+7 to both sides)

2n=n+12 (-n to both sides)

n=12

Answer:

this answer is -1.8

Step-by-step explanation:

because you add and subtract all of them

Answer:

0.9

Step-by-step explanation:

Basic angle =

\(cos { }^{ - 1} ( \frac{4}{5} ) = 36.870 \: degrees \\ \)

Therefore,

\(theta = 180 + 36.870 = 216.87 \: degrees\)

Therefore,

\( \sin( \frac{theta}{2} ) = \sin(108.435 ) = 0.9\)

The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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The probability that three cards chosen at random from a standard 52-card deck that are not all the same color is 3/4.

Total number of combinations of three cards: There are 52 choose 3 = 22,100 ways to choose three cards from a standard deck of 52 cards.

Number of combinations that are not all the same color: There are two possibilities for the colors of the three cards:

a. Two red cards and one black card: There are 26 choose 2 ways to choose two red cards and 26 choose 1 ways to choose one black card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

b. Two black cards and one red card: There are 26 choose 2 ways to choose two black cards and 26 choose 1 ways to choose one red card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

The total number of combinations that are not all the same color is 8,450 + 8,450 = 16,900.

The probability that three cards chosen at random are not all the same color is:

P(not all the same color) = (number of combinations that are not all the same color) / (total number of combinations of three cards) = 16,900 / 22,100 = 3/4.

Therefore, the probability that three cards chosen at random from a standard 52-card deck are not all the same color is 3/4.

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Answer:  \(\bold{2)\ sin\ C=\dfrac{20}{29}\qquad 3)\ tan\ A=\dfrac{8}{15}\qquad 4)\ tan\ Z=\dfrac{4}{3}}\)

Step-by-step explanation:

\(2) \sin C=\dfrac{\text{side opposite of}\ \angle C}{\text{hypotenuse of triangle}}=\large\boxed{\dfrac{20}{29}}\\\\\\3) \tan A=\dfrac{\text{side opposite of}\ \angle A}{\text{side adjacent to}\ \angle A}=\large\boxed{\dfrac{8}{15}}\\\\\\4) \tan Z=\dfrac{\text{side opposite of}\ \angle Z}{\text{side adjacent to}\ \angle Z}=\dfrac{40}{30}\quad \rightarrow \large\boxed{\dfrac{4}{3}}\)

a. Probability calculation for "at most 125 transmission errors occur"Binary communication channels transmit sequences of "bits" (0s and 1s).

Therefore, the probability of each transmitted bit being in error is 0.1.

The distribution of the number of errors in 1000 bits will be a binomial distribution with n=1000 and p=0.1.

Let X be the number of errors in 1000 bits. Then X ~ Bin(1000, 0.1).

Then, to calculate the approximate probability that at most 125 transmission errors occur.

Apply the normal approximation to the binomial distribution.

μ = np = 1000 x 0.1 = 100, σ² = np(1-p) = 1000 x 0.1 x (1 - 0.1) = 90,

P(X ≤ 125) = P(X ≤ 125.5)

Standardize the random variable Z as Z = (X - μ)/σZ = (125.5 - 100) / (sqrt(90))Z = 2.83.

Find the probability that Z is less than or equal to 2.83.

The probability can be found from the standard normal distribution table or using a calculator.P(Z ≤ 2.83) = 0.9977.

The approximate probability that at most 125 transmission errors occur is 0.9977.

b. Probability calculation for "number of errors in the first transmission is within 50 of the number of errors in the second" Suppose send the same 1000-bit message twice, independently of one another.

Let X be the number of errors in the first transmission and Y be the number of errors in the second transmission. Then, X and Y are independent and identically distributed with the same distribution as X ~ Bin(1000, 0.1).

Find the probability thathat the difference in errors between the two transmissions is less than or equal to 50.

Find P(|X - Y| ≤ 50).

Let's introduce a new variable Z = X - Y, then the required probability is P(|Z| ≤ 50) = P(-50 ≤ Z ≤ 50).

This is the sum of probabilities P(Z ≤ 50) - P(Z < -50).

Use the normal approximation to calculate the probabilities.

P(Z ≤ 50) = P(Z < 50.5) = P((X-Y) < 50.5)P(Z < -50) = P(Z ≤ -50.5) = P((X-Y) ≤ -50.5)

Standardize the random variable Z using the following:

μZ = μX - μY = 0σZ² = σ²X + σ²Y = 2 x 90σZ = sqrt(σZ²) = sqrt(2x90)

Let's compute the standard score for Z:z1 = (50.5 - 0)/13.42 = 3.76z2 = (-50.5 - 0)/13.42 = -3.76

Using the standard normal table,

Find P(Z < 3.76) = 0.9997 and P(Z < -3.76) = 0.0001.

Therefore, P(-50 ≤ Z ≤ 50) = P(Z ≤ 50) - P(Z < -50) = 0.9997 - 0.0001 = 0.9996.

The approximate probability that the number of errors in the first transmission is within 50 of the number of errors in the second is 0.9996.

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Answer:

x=16 ,PQ = 9.5

Step-by-step explanation:

9.

<QRS and <RQT = 180 because they are same-side interior angles (RS parallel to QT)

4x+4+5x+32=180

9x+36=180

9x=144

x=16

10. ST is the midpoint of the trapezoid. Midpoint formula: PQ+NR/2 = ST

name PQ as x.

x+5.5/2 = 7.5

x +5.5 = 15

x = 9.5

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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Answer:

I think that you have to find the length and width of the rectangular

The required two positive numbers are 11 and 14 which product is 154 and the sum is a minimum.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

The product is 154 and the sum is a minimum.

As per the question, the required solution would be as:

product           sum  

1 x 154         1 + 154 = 155

2 x 77          2 + 77 = 79

11 x 14          11 + 14 = 25

7 x 22         7 + 22 = 29

Here, we can arrange these numbers as:

25 < 29 < 79 < 155

This means the sum (11 + 14 = 25) is a minimum.

So the minimum value = 11

And the maximum value = 14

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Answer:

Step-by-step explanation:

Neither

Answer:

=0.0000541

Step-by-step explanation:

\(\frac{0.00541}{10^2}\)
\(\frac{0.00541}{100}\)
\(=0.0000541\)

Answer:0.0000541

Step-by-step explanation:

Firstly, you'll simplify 10².

10²÷0.00541 ---> 100 ÷ 0.00541

Then, you'll divide 100 by 0.00541.

100 ÷ 0.00541 ---> 18484.2883549

Answer:

27 cm²

Step-by-step explanation:

Shaded Area = Area ABCE - Area AED

Answer:

27 sq cm

Step-by-step explanation:

Area of the shaded region

= Area of rectangle - Area of triangle

= 6*6 -1/2(6)(3)

= 36 - 9

= 27 sq cm

The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.

We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.

Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.

Use the distance , in speed/rate formula ,

Rate × Time = Distance

Upstream : (B-S)6 = 258

=> B - S = 43 --(1)

Downstream: (B+S)6 = 330

=> B + S = 55 --(2)

Solve the linear equations by elimination method. Add the two equations.

=> 2B = 98

=> B = 49 km/hr

Substitute this value of B in equation(2) and solve for S, B+S = 55

=> 49+S = 55

=> S = 6 km/hr

So, the rate of the current is 6 km/hr.

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Complete question:

A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.

Answer:

hi

Step-by-step explanation:

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

  The point that divides a line segment into two equal halves is known as the midway.

    We can use a formula that incorporates some of the slope of the line segment to get the point P that partitions the line segment suitably given a line segment AB and a partitioning ratio a/b. P is thus defined as (x1 + c(x2 - x1), y1 + c(y2 - y1)).

  P(x1, y1) and Q are two things to consider (x2, y2). Finding the coordinates of the point R that divides PQ in the ratio m: n is necessary because PR/RQ = m/n. Given the ratio, the point R can either be outside of the segment PQ or between P and Q.

      Two points on a line, for instance, equal one line segment; three points, three segments; five points, ten segments.

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False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Answer:

8056 mm

Step-by-step explanation:

1 m=1000 mm

(8×1000)mm+56 mm

=8000 mm+56 mm

=8056 mm

To construct and store a 4 x 2 matrix filled row-wise with the given values in R, you can use the following code:

# Create the matrix

myMatrix <- matrix(c(4.3, 3.1, 8.2, 9.2, 3.2, 0.9, 1.6, 6.5), nrow = 4, ncol = 2, byrow = TRUE)

This code creates a matrix called "myMatrix" with 4 rows and 2 columns, filled row-wise with the provided values.

To overwrite the second column of the matrix with the numbers 8, 9, 11, and 17 in that order, you can use the following code:

# Overwrite the second column

myMatrix[, 2] <- c(8, 9, 11, 17)

This code selects the second column of the matrix using the indexing notation [, 2] and assigns the new values using the c() function. The second column is replaced with the numbers 8, 9, 11, and 17.

Finally, to save the updated matrix to an object named "BruceLee", you can use the following code:

# Save the updated matrix

BruceLee <- myMatrix

Now the updated matrix with the overwritten second column is stored in the object "BruceLee" for further use.

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Answer:17

Step-by-step explanation:

Number them in order from lowest to highest and find the median it will help with finding the Q1

Answer:

\(a_{n}\) = 2n - 3

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

given a₁ = - 1 and a₅ = 7 , then

a₁ + 4d = 7 , that is

- 1 + 4d = 7 ( add 1 to both sides )

4d = 8 ( divide both sides by 4 )

d = 2

then

\(a_{n}\) = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

\(a_{n}\) = 2n - 3

Answer:

72,072

Step-by-step explanation:

To determine the number of different ways the committee can be formed, we need to calculate the combination of selecting 5 teachers out of 10 and 3 students out of 13.

The number of ways to choose 5 teachers out of 10 is given by the combination formula:

C(10, 5) = 10! / (5! * (10 - 5)!) = 252

Similarly, the number of ways to choose 3 students out of 13 is:

C(13, 3) = 13! / (3! * (13 - 3)!) = 286

To find the total number of ways the committee can be formed, we multiply the number of ways to choose teachers by the number of ways to choose students:

Total number of ways = 252 * 286 = 72,072

Therefore, there are 72,072 different ways the committee can be formed.

Answer:

7.6

Step-by-step explanation:

-3 multiple by y and -3 multiple by 2 resolve to 7.6....

The measure of angle c is 70 degrees.

If angle a and angle b are complementary, it means that the sum of their measures is equal to 90 degrees.

Given:

Measure of angle a = 10x + 10

Measure of angle b = 20

We can set up the equation:

(10x + 10) + 20 = 90

Simplifying the equation:

10x + 30 = 90

Subtracting 30 from both sides:

10x = 60

Dividing both sides by 10:

x = 6

Now, we have found the value of x to be 6.

To find the measure of angle c, we can substitute the value of x into the equation for angle a:

Measure of angle a = 10x + 10

Measure of angle a = 10(6) + 10

Measure of angle a = 60 + 10

Measure of angle a = 70

As a result, angle c has a measure of 70 degrees.

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50 miles because of the miles

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

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The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( \(e^{(-λ)\) * \(λ^k\)) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = (\(e^{(-72.8)\)* \(72.8^(70)\)) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

\(Z = (X - mean) / \sqrt{(variance)\)

Fοr X = 70, we have:

Z = (70 - 1.4) / \(\sqrt{(1.4)\) ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

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Evaluating this expression will give us the value of f(3).

To find the value of f(3), we need to integrate the second derivative of f(x) twice and use the given initial conditions to determine the constants of integration.

Step 1: Integrate the second derivative f''(x) with respect to x to find the first derivative f'(x):

∫(f''(x)) dx = ∫(9x + 5sin(x)) dx

f'(x) = (9/2)x^2 - 5cos(x) + C1

Step 2: Use the given initial condition f'(0) = 2 to find the constant C1:

f'(0) = (9/2)(0)^2 - 5cos(0) + C1

2 = 0 - 5 + C1

C1 = 7

Step 3: Integrate f'(x) with respect to x to find the function f(x):

∫(f'(x)) dx = ∫[(9/2)x^2 - 5cos(x) + 7] dx

f(x) = (9/6)x^3 - 5sin(x) + 7x + C2

Step 4: Use the given initial condition f(0) = 3 to find the constant C2:

f(0) = (9/6)(0)^3 - 5sin(0) + 7(0) + C2

3 = 0 - 0 + 0 + C2

C2 = 3

Now we have the function f(x):

f(x) = (9/6)x^3 - 5sin(x) + 7x + 3

To find f(3), substitute x = 3 into the function:

f(3) = (9/6)(3)^3 - 5sin(3) + 7(3) + 3

Therefore, Evaluating this expression will give us the value of f(3).

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