Another name for the decimal number system that we use every day

Thus, the expected number of calls in one hour is 15.

To find the expected number of calls in one hour, we need to convert the rate of one call every four minutes into calls per hour.

There are 60 minutes in an hour, so we divide 60 by 4 to find the number of four-minute intervals in one hour.

60 minutes / 4 minutes = 15 intervals

Therefore, the rate of one call every four minutes translates to 15 calls per hour.

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To find the missing side of an AAS triangle, use the Pythagorean Theorem and the known lengths of the other two sides to calculate the length of the missing side.

An AAS triangle (angle-angle-side) is a triangle where two angles and one side length are known. To find the missing side, the Pythagorean Theorem must be used. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides must equal the square of the hypotenuse. To use this theorem, the two known sides must be squared and added together. The resulting number must then be equal to the square of the missing side. Once the result is equal, the square root of the result will give you the length of the missing side. For example, if two sides of a triangle are given as 3 and 4, the Pythagorean Theorem can be used to calculate the missing side. Squaring and adding the two sides together (3^2 + 4^2) will result in 25. Taking the square root of this result will give you the length of the missing side, which is 5.

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Answer:

Approximately 9 units.

Step-by-step explanation:

To find the distance between two ordered pairs, we can use the distance formula. The distance formula is:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Let (2,-3) be x₁ and y₁ respectively, and let (-4,4) be x₂ and y₂, respectively.

\(d=\sqrt{(-4-2)^2+(4--3)^2} \\d=\sqrt{(-6)^2+(7)^2} \\d=\sqrt{36+49} \\d=\sqrt{85}\approx9\)

Answer:36

Step-by-step explanation:

Step-by-step explanation:

let, a required negative number be x

then it's cnsecutive odd negative. be x+2

now,

\( x \times ( x + 2) = 35 \\ or \: \: {x}^{2} \: + 2x = 35 \\ {x}^{2} + 2x = 35 \\ {x}^{2} + 2x - 35 = 0 \\ {x}^{2} + 7x - 5x - 35 = 0 \\ x(x + 7) - 5(x + 7) = 0 \\ (x + 7) (x - 5) = 0 \\ \\ now \: \: \: \: \: \: \:either \: \: x + 7 = 0 \\ x = - 7\\ \\or \: \: \: \: \: (x - 5) = 0 \\ x = 5\)

since ,

we have supposed a negative number ,

,

we need negative odd number so,

x = -7

and it's consecutive number will be x+2

so, it is. -7+2 = -5

hence ,

-7 *and -5 are the required answer.

Answer: 73

Step-by-step explanation:

Both sides are exactly the same

Answer:

adult tickets  6.9

children tickets  3.9

Step-by-step explanation:

3x + y = 24.60    L1

5x + 4y = 50.10  L2

5L1 - 3L2

15x +  5y = 123

-15x - 12y = -150.3

-7y = -27,3

y = -27,3/-7

y = 3.9

3x + y = 24.60

3x + 3.9 = 24.60

3x = 24.60 - 3.9

3x = 20.7

x = 20.7 / 3

x = 6.9

5 is d and idk question 5 sorry

Answer:

The proportion of college students who work​ year-round is 58%.

Step-by-step explanation:

The claim made by the education researcher is that 58​% of college students work​ year-round.

A random sample of 400 college​ students, 232 say they work​ year-round.

To test the researcher's claim use a one-proportion z-test.

The hypothesis can be defined as follows:

H₀: The proportion of college students who work​ year-round is 58%, i.e. p = 0.58.

Hₐ: The proportion of college students who work​ year-round is 58%, i.e. p ≠ 0.58. C

Compute the sample proportion as follows:

 \(\hat p=\frac{232}{400}=0.58\)

Compute the test statistic value as follows:

 \(z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0\)

The test statistic value is 0.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

 \(p-value=2\times P(z<0)=2\times 0.5=1\)

*Use a z-table for the probability.

The p-value of the test is 1.

The p-value of the test is very large when compared to the significance level.

The null hypothesis will not be rejected.

Thus, it can be concluded that the proportion of college students who work​ year-round is 58%.

ΔUZE ≅ △NKW ​by angle side angle postultue of congrency.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

As per the given △NKW.

m∠K = m∠Z

Side KW = side ZE

m∠W = m∠E

Thus, by angle side angle theorem both triangles will be congruent.

Hence "ΔUZE ≅ △NKW ​by angle side angle postulate of congruency".

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The complete question is below,

Answer:

Function : 1 input 1 output

not a Function : 1 input more than 1 output

ck12org

Answer:

It seems you forgot to add the picture.....

If you put it in the comments i will try to solve it...

Stay safe and have a Merry Christmas!!!!!!! :D

Answer:

hope it's helpfull...... ;)

If A and B are mutually exclusive, P(A ∩ B) = 0.True.

When two events A and B do not have any common outcomes, they are referred to as mutually exclusive events. The occurrence of one event implies that the other cannot occur. The probability of their intersection is always zero (P(A ∩ B) = 0).Mutually exclusive events are events that cannot occur at the same time. It's impossible for both events to happen since they don't have any outcomes in common. For example, rolling a six on a die and rolling a three on the same die are mutually exclusive events.The formula for the probability of the union of two events is:P(A ∪ B) = P(A) + P(B) - P(A ∩ B)Where P(A ∩ B) is the probability of their intersection.

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64.77% of a given amount remains after 900 years.

To determine the percentage of radioactive radium remaining after 900 years, we'll use the half-life formula:

Final Amount = Initial Amount * \(1/2^{(time elapsed / half-life)}\)

In this case, the half-life is 1599 years and the time elapsed is 900 years. We want to find the percentage remaining, so let's assume the initial amount is 100%.

Final Amount = 100 * \((1/2)^{(900 / 1599)}\)

Now, we'll calculate the exponent:

Exponent = 900 / 1599 ≈ 0.5635

Then, we'll compute the final amount:

Final Amount ≈ 100 * \((1/2)^{0.5635}\) ≈ 100 * 0.6477 ≈ 64.77%

After 900 years, approximately 64.77% of the initial radioactive radium remains. This percentage was found using the half-life formula, which accounts for the exponential decay of radioactive substances over time.

The formula shows how the remaining amount of a substance decreases as time progresses based on its half-life, which is the time it takes for half of the substance to decay. In this scenario, radium's half-life of 1599 years and the 900-year time frame were used to determine that roughly 64.77% of the initial radium remains.

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Answer:

You need to deposit a minimum of $15.50 to avoid being charged a service fee.

Explanation:

Let x represent the amount needed to be deposited to avoid being charged a service fee.

Given;

Initial balance = 516.46 dollars

Amount on cheque to be withdrawn = 31.96 dollars

Minimum amount to avoid being charged = 500 dollars

So we have;

Therefore, you need to deposit a minimum of $15.50 to avoid being charged a service fee.

To fcalculate the magnitude of the average force exerted on the ball by the club, we can use the equation:

F_av = Δp/Δt

where F_av is the average force, Δp is the change in momentum, and Δt is the time of contact.

Given:

Mass of the ball, m = 65.0 g = 0.065 kg

Time of contact, Δt = 0.00340 s

Final velocity of the ball, v_f = 56.0 m/s

Initial velocity of the ball, v_i = 0 (assuming the ball is initially at rest)

The change in momentum, Δp, can be calculated using the equation:

Δp = m * (v_f - v_i)

Substituting the given values:

Δp = 0.065 kg * (56.0 m/s - 0)

Now we can calculate the magnitude of the average force:

F_av = Δp/Δt

Substituting the values:

F_av = (0.065 kg * 56.0 m/s) / 0.00340 s

Calculating the result gives us:

F_av ≈ 1070 N

Therefore, the magnitude of the average force exerted on the ball by the club is approximately 1070 N.

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The point that is located at the ordered pair (4, -2) is given as follows:

Point B.

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

On the coordinate plane, we have that:

Hence the coordinates for this problem are given as follows:

A(-2, 4), B(4, -2), C(-4, 2) and D(2, -4).

The graph is given by the image presented at the end of the answer.

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Answer:

x = 42.5

Step-by-step explanation:

all triangles inscribed into a circle like in the picture must have a 90 degree angle.

so, 90 = 2x + 5, 85 = 2x, x = 85/2 = 42.5

Answer: \(T= 15 G - 50\)

Step-by-step explanation:

As per given,

Total earning = (profit per game) x (Number of games) -(loss in consul)

Let T be the total amount the company will earn from a customer who buys a consul and G games.

Since,  loss in consul = $50

profit per game = $15

Then required equation will be :

\(T= 15 G - 50\)  , it determines T the total amount the company will earn from a customer who buys a consul and G games.

The Food and Drug Administration should put a stronger warning label on packages of ibuprofen.

To determine whether this proportion of 23 out of 440 users suffered from side effects, it is significant that a hypothesis test can be conducted.

The null hypothesis would be that the proportion of arthritis patients who suffer side effects when using ibuprofen is less than or equal to 3%, while the alternative hypothesis would be that the proportion is greater than 3%.

Using a one-tailed z-test with a significance level of 1%, the calculated z-score is 2.32. This falls in the rejection region, meaning that the null hypothesis can be rejected in favor of the alternative hypothesis.

Therefore, it can be concluded that more than 3% of arthritis patients suffer side effects when using ibuprofen to relieve the pain. As a result, the Food and Drug Administration should put a stronger warning label on packages of ibuprofen.

It is important for patients to be aware of the potential side effects and risks associated with this medication.

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Answer: Choice C  

Mean = 37.1

==================================================

Explanation:

Refer to the table below. The colum labeled "M" is the midpoint for each age interval. To find the midpoint, add up the endpoints and divide by 2. For example, the midpoint of 18 and 24 is (18+24)/2 = 42/2 = 21. Notice how the values of M are increasing by 7 each time.

The column labeled fM refers to multiplying the frequency f with the midpoint M. Example: fM = 6*21 = 126 in the first row.

Add up everything in the column labeled fM and you should get 1484. Divide this over the sum of the frequencies (40) and the mean is 1484/40 = 37.1

Answer:

c is the right answer

Step-by-step explanation:

hope i helped

The confidence interval for the population proportion is [0.4667, 0.5217] at a 95% confidence level.

A. The best point of estimate of the population proportion p, is given by the formula :p=542/1096=0.4942Therefore, the point estimate of p is approximately equal to 0.4942.

B. Margin of error: The margin of error E, for a 95% confidence level is given by the formula: E = 1.96√[(p(1-p))/n]Where n is the sample size, and p is the sample proportion E=1.96 * √[(0.4942 * (1 - 0.4942))/1096]E=0.0275

Hence, the margin of error is approximately equal to 0.0275.

C. Confidence Interval: A confidence interval is a range of values, derived from a data sample, that is used to estimate an unknown population parameter such as the mean, standard deviation, or population proportion. The formula for the confidence interval for proportion is given by :p±E Where, p is the sample proportion and E is the margin of error at a 95% confidence level p±E=0.4942 ± 0.0275

The lower bound is given by: p - E = 0.4942 - 0.0275 = 0.4667 The upper bound is given by: p + E = 0.4942 + 0.0275 = 0.5217

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A. The best point estimate of the population of proportion is given as the values of \($\hat{p}$\) and E calculated earlier;$$0.4942-0.0261

A. The best point estimate of the population of proportion is given as the values,

\(\hat{p}=\frac{x}{n}=\frac{542}{1096}\\\\=0.4942B\)

For a 95% confidence level, the value of the margin of error E can be determined using the formula;

\($$E=z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$\)

Where \($\alpha =1-0.95=0.05$\),

so \($\alpha/2=0.025$\) (for a two-tailed test).

From the normal distribution table, \($z_{\alpha/2}=1.96$\).

Therefore, the margin of error E is given by;

\($$E=1.96\sqrt{\frac{(0.4942)(1-0.4942)}{1096}}\approx0.0261$$\)

Rounded to four decimal places, the value of the margin of error E is 0.0261.C.

The 95% confidence interval is given by;

\($$\hat{p}-E< p <\hat{p}+E$$\)

Substituting the values of \($\hat{p}$\) and E calculated earlier;$$0.4942-0.0261

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Each matrix can be multiplied by the identity matrix to convert all entries to integers.

Let A' = A + 2I = [3 0 0; 0 2 1] as an example.

B' = B + I = [1 1 0; 0 1 1]

A' and B' are now integer matrices, although they still have the same null space and column space as A and B. As a result, A = [3 0 0; 0 2 1]

B = [1 1 0; 0 1 1]

These matrices share the same null space and column space and are not multiples of one another.

The elements of a matrix are usually denoted by a symbol, such as a, b, c, etc., and are arranged in a specific order. Matrices are used in many areas of mathematics, including linear algebra, calculus, and geometry.

Matrices are represented by enclosing the elements in brackets or parentheses. For example, a 2x3 matrix A can be represented as:

A = [ a11, a12, a13 ]

[ a21, a22, a23 ]

Here, a11, a12, and a13 are the elements of the first row, and a21, a22, and a23 are the elements of the second row. The columns are denoted by the subscript numbers.

Matrices are used to represent many mathematical concepts, such as systems of linear equations, transformations, and data sets. They can be added, subtracted, multiplied, and transposed to obtain new matrices with different properties.

Some common operations on matrices include:

Matrix addition: Adding two matrices of the same size element-wise.

Matrix multiplication: Multiplying two matrices to produce a new matrix.

Transpose: Flipping a matrix across its main diagonal to produce a new matrix.

Determinant: A scalar value that can be calculated for a square matrix and provides information about its properties.

Matrices are widely used in computer graphics, physics, and engineering, among other fields. They provide a powerful tool for modeling and manipulating complex systems and data sets, and they have numerous applications in real-world problem-solving.

In summary, a matrix is a rectangular array of numbers or symbols arranged in rows and columns. matrices are used to represent mathematical concepts and can be added, multiplied, and transposed to obtain new matrices with different properties. They have numerous applications in fields such as computer graphics, physics, and engineering.

To find integer matrices A and B such that Nul(A) = Nul(B) and Col(A) = Col(B), we can start with any two non-multiples of each other matrices with the same nullspace and column space, and then modify them slightly to make them integers.

For example, let:

A = [1 0 0; 0 0 1]

B = [0 1 0; 0 0 1]

Both A and B have nullspace {(0, t, 0) | t is a scalar} and column space spanned by the two columns of the matrices, which are linearly independent. However, these matrices are not integers, since they contain non-integer entries.

To modify them, we can add a multiple of the identity matrix to each matrix, such that all entries become integers. For example, we can let:

A' = A + 2I = [3 0 0; 0 2 1]

B' = B + I = [1 1 0; 0 1 1]

Both A' and B' have the same null space and column space as A and B, but they are now integer matrices. Therefore, we have:

A = [3 0 0; 0 2 1]

B = [1 1 0; 0 1 1]

These matrices are not multiples of each other, and they have the same null space and column space.

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