Bob bought some new boots that cost $67.34. He paid 7.5% tax. How much did he pay at the cash register?
A. $3.20
B. $24.78
C. $72.39
D. $33.40

It will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

The current Hours of Service (HOS) rules for truck drivers stipulate that a truck driver cannot drive for more than 11 hours after 10 consecutive hours off duty.

Additionally, the driver is not allowed to drive beyond 14 hours after coming on duty.

The driver's shift includes both driving and non-driving time.

Therefore, it is necessary to consider the total amount of time spent on the job.

The truck driver will have to stop for rest breaks, refueling, or other reasons during the 450-mile journey to Pittsburgh, Pennsylvania. The driver is required to take a 30-minute break after eight hours of driving.

Therefore, the minimum number of clock hours (not driving hours) it will take the truck driver to travel the 450-mile distance from Charlotte, NC to Pittsburgh, PA is calculated as follows:

Time for the trip = (Distance ÷ Average Speed) + Breaks

Time for the trip = (450 ÷ 50) + (30 ÷ 60) × 2

Time for the trip = 9 + 1

Time for the trip = 10 clock hours

Therefore, it will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

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x and x⁴-16x²+56 are the resulting composite functions respectively.

Given the following functions below

f(x) = 7/x

g(x) = x² - 8

We need to determine the composite functions (fof)(x) and (gog)(x)

(fof)(x) = f(f(x))

f(f(x)) = f(7/x)

Replace x with 7/x

f(7/x) = 7/(7/x)

f(7/x) = 7 * x/7

f(7/x) = x

Similarly:

(gog)(x) = g(g(x))

g(g(x)) = (x² - 8)² - 8

g(g(x)) = x⁴-16x²+64 - 8

g(g(x)) = = x⁴-16x²+56

Hence the resulting composite functions of f(f(x) and g(g(x)) are x and x⁴-16x²+56

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Answer:

Maria earns 100 dollars

E=100

Step-by-step explanation:

if E=20h and they want to know how much Maria will make in 5 hours substitute the h for 5. 20 x 5 =100

E=100

Answer:

100

Step-by-step explanation:

The equation is E=20h

E is the amount she earns.

20 is the amount of money she earns per hour.

h is the amount of hours she worked.

She worked 5 hours. h represents hours so plug in 5 where h is in the equation.

E=20h

E=20(5)

E= 20×5

E=100

Answer:

eu singer nuştiu

terog scuză

actual cost is 950+23,500=24450

he sold them for 25000 so his profit is 25000-950-23500=550

Answer:

A cycle + A scooter

= 950 + 23,500

= 24,450

Profit = Sold - cost

= 25,000 - 24,450

= 550

So the profit is $550

Answer:

1

Step-by-step explanation:

Answer:

The first thing to notice with this question is that the volume of the tank is given in cm3 yet the rate at which the water leaks is in litres, so a conversion of units will be neccessary. We know that there are 1000cm3 for every litre so 45000cm3 is equivilent to 45 litres (45,000/1000 = 45). So what do we know now? Well the tank of water contains 45 litres, and every minute 0.75 litres is lost, so our objective is to find out how many miuntes go by before the tank is empty. In other words how many 0.75s go into 45, luckily division can help us out. 45/0.75 = 60 minutes.

Step-by-step explanation:

The time it take for all the water to flow out of the tank is 62.5minutes

The formula for calculating the speed of the water is given as:

Speed = Distance/Time

Given the following parameters

Litres = 4500litres

Speed = 1.2litres/sec

Determine the time (in sec)

Time = Volume/Speed
Time = 4500/1.2
Time = 3750secs

Convert to minutes

Time = 62.5minutes

Hence the time it take for all the water to flow out of the tank is 62.5minutes

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Answer:

24

Step-by-step explanation:

hope this helps :D

Answer:

i think it d

Step-by-step explanation:

Answer:

8, 12 and 18

Step-by-step explanation:

That can form an Obtuse scalene triangle.

Brainliest please.

Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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Answer: C; 12 miles

Solution:

1) Add the initial Uber cost ($15) and airport toll charge:

$22.95

2) Subtract 22.95 from 45.84

$22.89 to spend on miles

3) Divide 1.84 (cost per mile) from 22.89

≈ 12.44 miles

Round down to 12 miles or option C

The vectors of ||f||. \(f(x, y) = (x^2 + y^2)i + j\) are all of the same magnitude, \(||f|| = \sqrt(2)\), and they all point in the direction of the vector <1,1>, pointing in the northeast direction

The norm of a vector function \(f(x, y) = (x^2 + y^2)i + j\) is given by:

\(||f|| = \sqrt((x^2 + y^2)^2 + 1^2)\)

So in this case, we have:

\(||f|| = \sqrt((x^2 + y^2)^2 + 1)\)

To sketch several representative vectors in the vector field, we can choose some points in the plane and evaluate the function at those points.

For example, we can evaluate the function at the points (1,0), (0,1), (-1,0), and (0,-1), which lie on the unit circle centered at the origin. At these points, we have:

\(f(1,0) = (1^2 + 0^2)i + j = i + j\)

\(f(0,1) = (0^2 + 1^2)i + j = i + j\)

\(f(-1,0) = (1^2 + 0^2)i + j = i + j\)

\(f(0,-1) = (0^2 + 1^2)i + j = i + j\)

So we see that the vectors at these points are all of the same magnitude, \(||f|| = \sqrt(2)\), and they all point in the direction of the vector <1,1>.

We can sketch several of these vectors at different points on the unit circle centered at the origin, and we will see that they all point in the direction of the vector <1,1> and have the same length.

Here is a rough sketch of the vector field:

           ^

            |

          _|__

         /     \

        /   |   \

       /    |    \

      /     |     \

     /__  |___\___>

    /       |       \

   /        |        \

  /         |         \

 /____ |_____\

            |

            |

The vectors are all pointing in the northeast direction, and their magnitude is constant throughout the vector field.

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APR is obtained by dividing the finance charge for the loan by the total amount borrowed, given by this formula APR = ((F / P) x 12) x 100

The formula for APR (annual percentage rate) is given as;

APR = ((F / P) x 12) x 100

Where;

The annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100, is calculated as follows;

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Answer:

172.5

Step-by-step explanation:

The formula for the surface area of a right circular cone (the following shape) is πr( r + √h^2 + r^2). Since the radius (r) is already given (3) and the height (h) is already given (15), you just replace each r with 3 and h with 15. After solving this out, you should get 172.45, which rounds to 172.5 to the first decimal place

Answer:

5n

Step-by-step explanation:

Decision Variables and Objective:

The decision variables in this transportation model are the quantities to be shipped from each plant to each distribution center. Let's denote the quantity shipped from Marietta to Cleveland as X1, from Marietta to Baltimore as X2, and so on. Similarly, let's denote the quantity shipped from Minneapolis to each distribution center as Y1, Y2, and so forth.

The objective of the optimization model is to minimize the total transportation cost. The transportation cost is determined by multiplying the unit cost of shipping between each plant and distribution center by the corresponding quantity shipped and summing up these costs for all combinations.

To enforce the single sourcing constraint, we need to ensure that each distribution center is served from only one plant. This constraint can be represented by adding the following constraint for each distribution center:

X1 + X2 + X3 + X4 = Demand (for each distribution center)

Y1 + Y2 + Y3 + Y4 = Demand (for each distribution center)

These constraints ensure that the total quantity supplied from all plants to a particular distribution center is equal to the demand of that distribution center, effectively enforcing the single sourcing constraint.

Optimization Model and Interpretation of Results:

The optimization model can be formulated as a linear programming problem, where the objective is to minimize the total transportation cost while satisfying the capacity constraints and the single sourcing constraint.

The Excel Solver can be used to solve this model, providing the optimal solution for the decision variables and the corresponding minimum cost.

Interpreting the printouts, we can observe the values of the decision variables X1, X2, X3, X4, Y1, Y2, Y3, Y4, which represent the quantities shipped between each plant and distribution center. Additionally, we can see the total transportation cost, which is the objective value obtained by summing the costs of shipping for all combinations.

Pertinent results could include identifying the optimal shipping quantities that meet customer demand while minimizing costs. Interesting results might include identifying any significant differences in shipping costs between the plants and distribution centers. Unusual results could involve finding a scenario where the total transportation cost does not decrease proportionally with an increase in supply capacity or demand.

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Answer:

Step-by-step explanation:

first of all use ^ to indicate exponents

simplify

3ab-a^2=3a^2

subtract a^2 to 3a^2

3ab+2a^2

Answer:

-a(a-2b-3)

Step-by-step explanation:

Step 1: Pull out like-factors.

-a^2+ 2ab+3a

Step 2:

-a^+ -a + a + 2ab + 3a

Step 4:

-a(a-2b-3)

1) The covariance between random variables X and Y can be found using the formula Cov(X,Y) = E[XY] - E[X]E[Y]. Then Cov(X,Y) = -0.015. 2) The correlation between X and Y can be found using the formula Corr(X,Y) = Cov(X,Y) / (SD(X) * SD(Y)), where SD(X) and SD(Y) are the standard deviations of X and Y, respectively. we get Corr(X,Y) = -0.167.

1) Covariance is a measure of the linear relationship between two random variables, indicating how much they vary together. The formula for covariance is Cov(X,Y) = E[XY] - E[X]E[Y], where E[XY] is the expected value of the product of X and Y, E[X] is the expected value of X, and E[Y] is the expected value of Y. To calculate E[XY], we multiply each value of X and Y and sum up the products weighted by their probabilities. Using the joint probability mass function given in the question, we can calculate E[XY] = 2.3. We can also calculate E[X] and E[Y] in a similar way, and get E[X] = 1.85 and E[Y] = 2.2. Plugging in these values into the formula for covariance, we get Cov(X,Y) = -0.015.

2) Correlation measures the strength and direction of the linear relationship between two random variables, and is calculated as the ratio of covariance to the product of their standard deviations. The formula for correlation is Corr(X,Y) = Cov(X,Y) / (SD(X) * SD(Y)), where SD(X) and SD(Y) are the standard deviations of X and Y, respectively. To find SD(X) and SD(Y), we first need to calculate the variance of X and Y using the formula Var(X) = E[X²] - E[X]² and Var(Y) = E[Y²] - E[Y]². Then, we take the square root of the variances to get the standard deviations. Plugging in the values from the joint probability mass function, we get Var(X) = 0.4775, Var(Y) = 0.64, SD(X) = 0.6901, and SD(Y) = 0.8. Finally, we can calculate Corr(X,Y) by dividing Cov(X,Y) by the product of SD(X) and SD(Y), which gives us -0.167. Since the correlation is negative, we can conclude that X and Y are negatively associated, meaning that as X increases, Y tends to decrease and vice versa.

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Here are the vectors **t**, **n**, and **b** at the given point:

* **t** = (-3 sin t, 3 cos t, 0)

* **n** = (-3 cos t, -3 sin t, 3 / cos^2 t)

* **b** = (3 cos^2 t, -3 sin^2 t, -3)

The vector **t** is the unit tangent vector, which points in the direction of the curve at the given point. The vector **n** is the unit normal vector, which points in the direction perpendicular to the curve at the given point. The vector **b** is the binormal vector, which points in the direction that is perpendicular to both **t** and **n**.

To find the vectors **t**, **n**, and **b**, we can use the following formulas:

```

t(t) = r'(t) / |r'(t)|

n(t) = (t(t) x r(t)) / |t(t) x r(t)|

b(t) = t(t) x n(t)

```

In this case, we have:

```

r(t) = (3 cos t, 3 sin t, 3 ln cos t)

r'(t) = (-3 sin t, 3 cos t, 3 / cos^2 t)

```

Substituting these into the formulas above, we can find the vectors **t**, **n**, and **b** as shown.

The vectors **t**, **n**, and **b** are all orthogonal to each other at the given point. This is because the curve is a smooth curve, and the vectors are defined in such a way that they are always orthogonal to each other.

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The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.

To find the vectors t, n, and b at the given point, we need to calculate the first derivative, second derivative, and third derivative of the position vector r(t).
Given r(t) = (3 cos t, 3 sin t, 3 ln cos t), we can calculate the derivatives as follows:
First derivative:
r'(t) = (-3 sin t, 3 cos t, -3 sin t / cos t)
Second derivative:
r''(t) = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 sin^2 t / cos t)
       = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 tan^2 t)
Third derivative:
r'''(t) = (3 sin t, -3 cos t, 6 cos t / cos^3 t - 6 sin t / cos t)
        = (3 sin t, -3 cos t, 6 sec^3 t - 6 tan t sec t)
At the given point (3, 0, 0), substitute t = 0 into the derivatives to find the vectors:
r'(0) = (0, 3, 0)
r''(0) = (-3, 0, 3)
r'''(0) = (0, -3, 6)
Therefore, at the given point, the vectors t, n, and b are:
t = r'(0) = (0, 3, 0)
n = r''(0) = (-3, 0, 3)
b = r'''(0) = (0, -3, 6)
These vectors represent the tangent, normal, and binormal vectors, respectively, at the given point.
The tangent vector (t) represents the direction of motion of the curve at that point. The normal vector (n) is perpendicular to the tangent vector and points towards the center of curvature.

The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.
Remember to check your calculations and units when applying this method to different functions.

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Answer:

36 degrees

Step-by-step explanation:

180 - 58 = 122 degrees

122 - 90 = 32 degrees

32 + 4 = 36 degrees

Answer:

s = 36

Step-by-step explanation:

These lines is 180° in total and the one that is a right triangle has 90° and there is 58° on one so, 180 - 90 - 58 = 32.

32° = s - 4°

32 + 4 = s

36° = s°

Answer:

2/21.

Step-by-step explanation:

\(\frac{2}{7}\) ÷ 3 = (2 / 7) * (1 / 3) = (2 * 1) / (7 * 3) = 2 / 21 = 0.0952380952.

Hope this helps!

Write 3 as 3/1

Now you have 2/7 / 3/1.

When you divide by a fraction change the divide to multiply and flip the second fraction over

Now you have 2/7 x 1/3 now multiply top by top and bottom by bottom to get

2/21

A common distribution used for modeling time-to-failure is the "Weibull distribution."

The Weibull distribution has two parameters: shape (k) and scale (λ).
The shape parameter (k) determines the behavior of the failure rate. If k > 1, the failure rate increases over time, which indicates that the item is more likely to fail as it gets older. If k < 1, the failure rate decreases over time, which means that the item becomes less likely to fail as it gets older. If k = 1, the failure rate is constant over time, indicating a random failure.

The scale parameter (λ) represents the characteristic life of the item, which is the point where 63.2% of the items have failed.

To determine the specific parameters for a given situation, you would need to analyze the historical data on the time-to-failure and perform a statistical fit to estimate the values for the shape (k) and scale (λ) parameters.

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Answer:

d=-4

Step-by-step explanation:

-7d - 5 = 23

-7d = 28

d = -4

Answer:-6d-3f+5

Step-by-step explanation:

Answer:

A) The correct inequality is: -18 < 53

B) The correct description is: Eduardo sent fewer text messages during May than April

Step-by-step explanation:

Month     Number of message

April        53

May         -18

A) The correct inequality is: -18 < 53

Reason:

We need to choose the correct inequality, negative number is less than positive number so the inequality will be -18 < 53

B) The correct description is: Eduardo sent fewer text messages during May than April

Reason:

Negative values shows that he has messaged under the allotted limit, while positive values shows the number of messages he was over the limit.

The interquartile range of the given data is 35.

The given set of data is,

{85, 50, 34, 56, 82, 78, 40, 50}

To find the interquartile range,

calculate median of the given data set.

Now arrange the data into ascending order,

34, 40, 50, 50, 56, 78, 82, 85

The median is the middle value, which is 56.

The median of the lower half of the data set (34, 40, 50, 50).

The median of the lower half is (40 + 50) / 2 = 45.

Finally, find the median of the upper half of the data set (56, 78, 82, 85). The median of the upper half is (78 + 82) / 2 = 80.

The interquartile range is the difference between the median of the upper half and the median of the lower half.

Hence,

Interquartile range = 80 - 45 = 35.

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Var(aX + bY) = (e^(a²σ_X² + b²σ_Y²) - 1)e^(2(aμ_X + bμ_Y) + a²σ_X² + b²σ_Y²). If X and Y are independent lognormal random variables with means μ_X and μ_Y and variances σ_X² and σ_Y², respectively, then aX + bY is also a lognormal random variable with mean μ = aμ_X + bμ_Y and variance σ² = a²σ_X² + b²σ_Y². The expectation of a lognormal random variable is given by e^(μ + σ^2/2), so

E(aX + bY) = e^(aμ_X + bμ_Y + (a²σ_X² + b²σ_Y²)/2)

The variance of a lognormal random variable is given by (e^σ^2 - 1)e^(2μ + σ²), so:

Var(aX + bY) = (e^(a²σ_X² + b²σ_Y²) - 1)e^(2(aμ_X + bμ_Y) + a²σ_X² + b²σ_Y²)

Note that the expectation and variance of a lognormal random variable are not directly computable from the expectation and variance of the underlying normal random variable, due to the non-linear transformation involved in taking the exponential.

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To test the candy company's claim about the percentage of blue candies, a hypothesis test can be conducted using a significance level.

The null hypothesis would assume that the claimed percentage is true, while the alternative hypothesis would state that the claimed percentage is not true. The significance level will determine the threshold for rejecting the null hypothesis based on the observed data.

In hypothesis testing, the null hypothesis (H₀) represents the claim being tested, which in this case is that the percentage of blue candies is equal to a specific value. The alternative hypothesis (H₁) contradicts the null hypothesis and suggests that the claimed percentage is not true. Let's assume the claimed percentage is p. The test statistic used for comparing observed data with the null hypothesis is typically the z-score.

The next step is to determine the significance level, denoted as α. This value represents the probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 (5%) and 0.01 (1%). Once the significance level is chosen, a critical region is established, which defines the range of values that would lead to rejecting the null hypothesis. The critical region is determined based on the chosen significance level and the distribution of the test statistic (in this case, the standard normal distribution).

Finally, the observed data is collected and analyzed. The test statistic is calculated using the observed proportion of blue candies, and it is compared to the critical values. If the test statistic falls within the critical region, the null hypothesis is rejected, indicating that there is evidence to support the claim that the percentage of blue candies is different from the claimed value. If the test statistic does not fall within the critical region, the null hypothesis is not rejected, suggesting that the claim made by the candy company is plausible.

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Step-by-step explanation:

there are 12 months in a year, and therefore 2×12 = 24 "half-months" and therefore semimonthly payments.

that means each paycheck is

72,000 / 24 = $3,000

there are 52 weeks per year.

that means they're are 52/2 = 26 biweekly periods and therefore payments.

each paycheck is therefore

72,000 / 26 = $2,769.23

so, Alice receives 2 more paychecks (26 to 24) in a year.

the difference between the 2 types of payment is

3000 - 2769.23 = $230.77

The correct answer is 138 students.

x = .24 * 575

x = 138 students

Therefore, the correct answer is 138 students.