In Maryland, The sales tax rate is 6%. What is the tax, in dollars and cents, on a $32.74 purchase? Round your answer to the nearest cent.

Answer:

1mm 1cm 1m 1km

Step-by-step explanation:

1mm shortest

1km longest

Answer:

1mm then 1cm and then 1m and then 1km

Step-by-step explanation:

Calculation of the approximate probability of 35 to 90 tickets given out on a particular day Given: Poisson distribution with μ = 50.The formula of Poisson Distribution is,\(P (x; μ) = (e-μ) (μx) / x!P (35 < X < 90) = P (X < 90) – P (X < 35)P (X < 90) = e-50 * 50⁹⁰ / 90!P (X < 35) = e-50 * 50³⁵ / 35!\)

The approximate probability that between 35 and 90 tickets are given out on a particular day is P (35 < X < 90) = 0.9862.b) Calculation of the approximate probability of the total number of tickets given out during a 5-day week is between 215 and 265 Given: Poisson distribution with μ = 50.The formula of Poisson Distribution is,\(P (x; μ) = (e-μ) (μx) / x!\) Let Y be the number of parking tickets given out during the 5-day week. Therefore, Y has a Poisson distribution with mean E(Y) = 5*50 = 250.The approximate probability is, \(P(215 ≤ Y ≤ 265) = P(Z ≤ 1.5) – P(Z ≤ -3)\) where Z = \((Y - E(Y)) / sqrt(V(Y))and V(Y) = E(Y)\) .Using the formula P(Z ≤ 1.5), we have P(Z ≤ 1.5) = 0.9332 Using the formula P(Z ≤ -3), we have P(Z ≤ -3) = 0.0013 Therefore, \(P(215 ≤ Y ≤ 265) = P(Z ≤ 1.5) – P(Z ≤ -3) = 0.9319c)\)

Calculation of the exact probability that the total number of tickets given out during a 5-day week is between 215 and 265.

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Answer: 83.3

Explanation: tan 73= x/ 27

27 tan 73=x

x=88.313 = 88.3 feet

​

A correlation coefficient is a statistic that tells us the strength and direction of the linear relationship between two variables.

The correlation coefficient is a measure of the degree of association between two variables. It quantifies how closely the data points align along a straight line. The coefficient can range from -1 to +1, where -1 represents a perfect negative linear relationship, +1 represents a perfect positive linear relationship, and 0 indicates no linear relationship.

The sign of the coefficient indicates the direction of the relationship, while the magnitude indicates the strength. A correlation coefficient of 0 does not necessarily imply the absence of any relationship; it only means that there is no linear association between the variables. It is important to note that correlation does not imply causation, as other factors may be influencing the relationship.

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Answer:

A. Yes

Step-by-step explanation:

The contestant has a 50% chance of winning, because they could hit 1 or 3.

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

GCF both of 2

There are 100 integers 'a' satisfying the congruence relation $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$, where $0 \leq a < 100$.

To determine the number of integers 'a' satisfying the congruence relation:

$a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$

First, we can rewrite the congruence as:

$a(a-1)^{-1} - 4a^{-1} \equiv 0 \pmod{20}$

Multiplying both sides by $(a-1)a^{-1}$ (which is the inverse of $(a-1)$ modulo 20) yields:

$a - 4(a-1) \equiv 0 \pmod{20}$

Simplifying further, we have:

$a - 4a + 4 \equiv 0 \pmod{20}$

$-3a + 4 \equiv 0 \pmod{20}$

To solve this congruence relation, we can consider the values of 'a' from 0 to 99 and check how many satisfy the congruence.

For $a = 0$:

$-3(0) + 4 \equiv 4 \pmod{20}$

For $a = 1$:

$-3(1) + 4 \equiv 1 \pmod{20}$

For $a = 2$:

$-3(2) + 4 \equiv -2 \pmod{20}$

Continuing this process for each value of 'a' from 0 to 99, we can determine how many satisfy the congruence relation. However, in this case, we can observe a pattern that repeats every 20 values.

For $a = 0, 20, 40, 60, 80$:

$-3a + 4 \equiv 4 \pmod{20}$

For $a = 1, 21, 41, 61, 81$:

$-3a + 4 \equiv 1 \pmod{20}$

For $a = 2, 22, 42, 62, 82$:

$-3a + 4 \equiv -2 \pmod{20}$

And so on...

Thus, the congruence relation is satisfied for the same number of integers in each set of 20 consecutive integers. Hence, there are 5 sets of 20 integers that satisfy the congruence relation. Therefore, the total number of integers 'a' satisfying the congruence is 5 * 20 = 100.

Therefore, there are 100 integers 'a' satisfying the congruence relation $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$, where $0 \leq a < 100$.

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Answer:

13 Kilometers = 13000 meters

Step-by-step explanation:

Using the conversion:

We can find how much meters are in 13 km.

=> 13 Kilometers = 1000 x 13

=> 13 Kilometers = 13000 meters

Therefore, in 13 kilometers, there is 13000 meters.

Hoped this helped.

Using Gaussian elimination followed by back substitution, we get the solution of the system of equations x = -3z - 11, y = 2z + 2, z is free variable The row operations used were: R2 = R2 - 2R1, R3 = R3 + 2R1, R3 = R3 + 7R2. The corresponding elementary matrices were M1 = [1 0 0; -2 1 0; 0 0 1], M2 = [1 0 0; 0 1 2; 0 0 1], M3 = [1 0 0; 0 1 0; 0 7 1]. The product M3M2M1 was found to be  [1 -6 -8; 0 1 2; 0 0 1]. The matrix MA appears as the row-reduced echelon form of A. The matrix U has a triangular form and the matrix L has 1's along the diagonal and values below the diagonal that were used to eliminate the entries in U.

We perform the following row operations

R2 → R2 - 2R1

R3 → R3 + 2R1

R3 → R3 + 7R2

This gives us the following augmented matrix

[1  3  4 |  1]

[0 -1 -2 | -4]

[0  0  0 |  0]

Now, using back substitution, we get

z = any real number

-y - 2z = -4

x + 3y + 4z = 1

So, our solution is

x = -3z - 11

y = 2z + 2

z is free variable

The elementary matrices corresponding to the row operations used in part (a) are

M1 = [1 0 0; -2 1 0; 0 0 1]

M2 = [1 0 0; 0 1 0; 2 0 1]

M3 = [1 0 0; 0 1 0; 0 7 1]

We compute the product of the elementary matrices as

Mk...M2M1 = [1 -6 -8; 0 1 2; 0 0 1]

We have MA = [1 -6 -8; 0 1 2; 0 0 0], which appears during the row reduction process in part (a) when we have arrived at the row echelon form of the augmented matrix.

U is the upper triangular matrix obtained after performing Gaussian elimination on A, while L is the lower triangular matrix obtained from the product of the elementary matrices found in part (c). They have the property that LU = A, and the determinant of U is the product of the pivots of A (in this case, 1*(-1)*0 = 0).

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Answer:

GCF = 5

Step-by-step explanation:

Ignore x as it isn't common between both number. GCF's:

10: 1, 2, 5, 10

25: 1, 5, 25

5 is the greatest common factor between 10 and 25.

Therefore:

GCF of 10x and 25 is 5

Answer:

GCF = 5

Step-by-step explanation:

Ignore x as it isn't common between both number. GCF's:

10: 1, 2, 5, 10

25: 1, 5, 25

5 is the greatest common factor between 10 and 25.

Therefore:

GCF of 10x and 25 is 5

Based on an equation, the number of Cadbury eggs that Teddy bought was 11.5.

An equation is an algebraic statement of the equality of two or more mathematical expressions.

The differentiating factor of an equation from an algebraic expression is the equal symbol (=).

Let the number of eggs Teddy bought = x

Let the number of eggs Elena bought = x + 4

Let the number of eggs Sharon bought = 2x

The total number of Cadbury eggs that the trio bought = 50

Therefore, x + x+4 + 2x = 50

4x + 4 = 50

4x = 46

x = 11.5

Thus, Teddy bought 11.5 eggs, Elena bought 15.5 eggs, while Sharon bought 23 eggs, making a total of 50 eggs.

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Answer:

5/6 = v + 2/7

Step-by-step explanation:

5/6 = v + 2/7  

23/42 - v = 0

5/6 = 1/7 (7 v + 2)

Answer:

23/42 = v

Step-by-step explanation:

5/6=v+2/7

Multiply each side by the common denominator, 42

42( 5/6=v+2/7)

35 = 42v + 12

Subtract 12 from each side

35-12 = 42v

23 = 42 v

Divide each side by 42

23/42 = v

To find the missing sides and angles of a right triangle with side b = 32 and side c = 51, we can use the Pythagorean theorem and trigonometric ratios.

Let's denote the missing side as a and the angles as A and B, with B being the right angle.

Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c):

a^2 + b^2 = c^2

Plugging in the given values, we have:

a^2 + 32^2 = 51^2

a^2 + 1024 = 2601

a^2 = 1577

a ≈ 39.73

Therefore, the length of the missing side a is approximately 39.73.

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Using Tap working problem solving,

when faucet and drain working together, the time to fill up the tub is 60 minutes.

We have the following information about question,

The time taken by faucet to fill up the tub

= 15 minutes

The time taken by drain to empty the tub

= 20 minutes

we have to calculate the time in which the tub is fully fill the tube with drain open.

Rate of fill up the tub by faucet = 1/15 i.e 1/15 th of tub in one minute .

Rate of empty the tub by drain = 1/20 i.e 1/20 th of tub in one minute.

In one minute both are working together and will fill the tub = 1/15 - 1/20 = 1/60 i.e 1/60 th of tub

Since, it takes one minute to fill 1/60th of the tub and it will take 60 minutes to fill the tub.

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Answer:

-3.75

-0.55

-0.5

-0.3

-0.2

Step-by-step explanation:

-3% = -0.3

-1/2 = -0.5

-1/5 = -0.2

-3.75

-0.55

Arlene buys a phone case and charging cord for 15% off

Discount on case and cord = 15%

Original cost of case = $18

Total discount amount = $4.20

Let the original cost of charging cord = x

So, Arlene buys a phone case and charging cord for 15% off = 15% of cost of cord and case

15% of cord and case = 15% of (x + 18)

as the discount amonut ins $18

15% of cord and case = 15% of (x + 18)

15% of cord and case = 4.20

15% of (x + 18) = 4.20

So, the expression is : 15(x + 18) = 420

Simplify the expression for x :

15(x + 18) = 420

15x + 270 = 420

15x = 420 - 270

15x = 150

x = 150/15

x = 10

So, the cost of charging cord is $10

Answer : equation : 15(x + 18) = 420

$10

Answer: 26.47%

Step-by-step explanation:

Given the following :

markup based on cost = 36%

Assume a cost of $50

$50 × 1.36 = $68

Now, markup based on the selling price ;

$68 - $50 = $18

Therefore, ratio of cost price to selling price :

18 / 68 = 26.47%

Answer:

The values that have 2 significant figures are;

A. 0.0056

D. 4500

Both A and D are correct

Explanation:

We want to find which of the values have 2 significant figures.

From the opthoins;

0.0056 -----------2 significant figure

0.356 ------------3 significant figure

1200.1 -------------5 significant figure

4500 --------------2 significant figure

Therefore, the values that have 2 significant figures are;

A. 0.0056

D. 4500

Both A and D are correct

Option B. $9,255.75, Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of

To find the present value of an infinite stream of cash flows, we can use the formula:

PV = CF / r

where PV is the present value, CF is the cash flow per period, and r is the interest rate per period.

In this case, CF = $100 (received at the end of each year forever) and r = 10%.

Plugging in the numbers, we get:

PV = $100 / 0.10 = $1,000

So the present value of the infinite stream of cash flows is $1,000.

However, we need to adjust for the fact that the cash flows are received at the end of each year, not at the beginning. To do this, we can use the formula:

PV = CF / (r - g)

where g is the growth rate of the cash flows, which in this case is 0 (since the cash flows are constant).

Plugging in the numbers, we get:

PV = $100 / (0.10 - 0) = $1,000

So the present value of the infinite stream of cash flows received at the end of each year is also $1,000.

Therefore, the answer must include the present value of an infinite stream of cash flows. Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of cash flows.

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Answer:

30hours

Step-by-step explanation:

complaints/ hours

13/2=195/h

h=30

First pump can fill the tank in 4 hours. So, In 1 hour it fill 1/4 of the tank.

Second pump 1/3

Third one, 1/4

If three pumps are used at the same time, then in 1 hour they will fill

1/4 + 1/3 + 1/4 = 5/6

Therefore tank will be full = 1 ÷ 5/6 = 1.2 hours or 1 hour and 12 minutes

Answer:

\((xy+1)(xy-1)\)

Step-by-step explanation:

x²y²-1

=(xy)²-(1)²

=(xy+1)(xy-1)

Answer:

x= -4

Step-by-step explanation:

Answer:

x=-4

Step-by-step explanation:

6x-2x=-7-9

4x=-16

x=-16/4

x=-4

Answer: y=2x-3

Step-by-step explanation:

It will cross the y axis at -3 and the x axis at 3/2

Answer:

h=97

Step-by-step explanation:

38+45=83

180-83=97

Answer:

\(\sqrt{65}\)

Step-by-step explanation:

the absolute value of the complex number a + bi is

| a + bi | = \(\sqrt{a^2+b^2}\)

then

| 4 + 7i | = \(\sqrt{4^2+7^2}\) = \(\sqrt{16+49}\) = \(\sqrt{65}\)

The margin of error for the confidence interval is approximately 0.014, indicating that the estimate of the proportion of dissatisfied customers could be off by approximately plus or minus 0.014. This means that we can be 95% confident that the true proportion of dissatisfied customers falls within the range of the estimated proportion ± 0.014.

(a) To find the sample size needed to achieve a margin of error of about 0.015 with a 95% confidence level, we can use the formula for sample size calculation for proportions:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = critical value (corresponding to the desired confidence level)

p = estimated proportion of the population

E = margin of error

In this case, the estimated proportion of dissatisfied customers is 0.17, and the desired margin of error is 0.015. Since we want a 95% confidence level, the critical value can be obtained from a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.

Plugging these values into the formula, we have:

n = (1.96^2 * 0.17 * (1-0.17)) / 0.015^2

n ≈ 1901.63

Therefore, the sample size needed is approximately 1902.

(b) If 25% of the sample say they are not satisfied, we can calculate the margin of error using the following formula:

MoE = Z * sqrt((p * (1-p)) / n)

Where:

MoE = margin of error

Z = critical value (corresponding to the desired confidence level)

p = proportion of the sample

n = sample size

Using the same critical value of 1.96 for a 95% confidence level and plugging in the values:

MoE = 1.96 * sqrt((0.25 * (1-0.25)) / 1902)

MoE ≈ 0.014

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The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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