area of the base of a pentagonal prism with a volume of 50 cubic centimeters and a height of 7.5 centimeters

Answer:

an ant is about 1/2 a inch long

Step-by-step explanation:

Answer:

What figure lol

Step-by-step explanation:

Answer:

1 is the correct answer

Step-by-step explanation:

Answer:

explain below

Step-by-step explanation:

sin² 90° and sin² (90) has different meaning

The former based on " degree" while the later based on "radians' argument

sin² 90° = 1

sin² (90) = 0.799

Answer:

Step-by-step explanation:

the 1st one is 1735

The 2nd one is 1573

The best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24 are x = 43 and y = 22

From the information given, we have the expressions;

This is represented as;

x - y = -65

x + 3y = 24

Make 'x' the subject from equation 1

x = -65 + y

Now, substitute the expression into equation (2), we get;

-65 + y + 3y = 24

collect the like terms

4y = 24 + 65

Add the like terms

4y = 89

Divide the values by the coefficient of y

y = 89/4 = 22

Substitute the value in eqation3

x = -65 + 22

Add the values

x = 43

Hence, the values are 43 and 22

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Answer:

1) Measure angle QWT and TWX are complementary because their measures add up to 90 degrees.

2) Both measure angles add up to 90 degrees because they're complementary.

3) Angle QWT = 2x and angle TWX = x + 6, and since angles QWT + TWX = 90 then 2x + x + 6 = 90.

4) (Made up?:) Angle measure QWX = 90. The quarter-turn, or the small square, indicates that the angle is 90 degrees.

5) (?)

6) x = 28 because it fulfills the equation, 2x + x + 6 = 90, or 3x + 6 = 90. 90 - 6 is 84, and 84/3 is 28.

Please, tell me if I did anything wrong. I'll gladly edit it.

Answer:

Step-by-step explanation:

2). Definition of complementary angles;

3). Substitution+combine like terms;

4). 3x+ 6 - 6 = 90 - 6   Subtraction Property

5). 3x/3 = 84/3    Division Property  

6). Q.E.D. ("that which was to be demonstrated")

Answer:

400 dollars

Step-by-step explanation:

Answer:

5.8 thats the answer you get when it is simplified and 1 movie ticket=$2 and 1 bag of popcorn= $1

Step-by-step explanation:

The series in question converges.

If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on rising or dropping as the terms of the series go to infinity, it is said to be divergent.

The geometric sequence is as follows:

10 - 4 + 1.6 - 0.64 +...

If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.

The common ratio in this case is

r = -4/10

r = -0.4, or -1 -0.4 1.

The presented series is hence convergent.

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Answer:

A

Step-by-step explanation: because when you say its closer to 0 thats right

Answer:

A

Step-by-step explanation:

Hope this helps anybody <33

(Entered this on my test and it was correct !!)

Answer: You got this

Step-by-step explanation:

use  y2-y1/x2-x1 and find two points then get m

(a) My score was 2.2 standard deviations above the mean. About 2.5% of students did better than I did.

(b) My score was 0.4 standard deviations above the mean. I was easily in the middle of the scores.

(c) My score was 1.8 standard deviations above the mean. I was a little under the 84th percentile on this exam.

(d) My score was 1 standard deviation above the mean. I was around the 84th percentile on this exam.

(e) My score was equal to the mean and equal to the median on this exam.

A z-score is a standard score that represents the number of standard deviations by which a value is above the mean. In other words, a z-score measures the distance of a value from the mean in terms of standard deviations.

Interpretation of z-scores:

(a) My score was 2.2 standard deviations above the mean. Fewer than 5% of students did better than I did.

(b) My score was 0.4 standard deviations above the mean. I was easily in the middle of the scores.

(c) My score was 1.8 standard deviations above the mean. I was a little under the 84th percentile on this exam.

(d) My score was 1 standard deviation above the mean. I was around the 84th percentile on this exam.

(e) My score was exactly the mean and exactly the median on this exam.

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--The question is not readable, answering to the question below--

"Suppose that your statistics professor returned your first midterm exam with only a z-score written on it. She also told you that a histogram of the scores was mound shaped and approximately symmetric. How would you interpret each of the following z-scores?

(a) 2.2

My score was 2.2 standard deviations ____. ____  of students did better than I did.

(b) 0.4

My score was 0.4 standard deviations ____. I was easily in the ____  of the scores.

(c) 1.8

My score was 1.8 standard deviations ____. I was a little under the ____ percentile on this exam.

(d) 1.0

My score was 1 standard deviation ____. I was around the ____ percentile on this exam.

(e) 0

My score was ____ the mean and ____ the median on this exam."

The efficiency of the power screw in raising the load is approximately 6976%.

The efficiency of a power screw can be calculated using the formula: Efficiency = (Ideal Mechanical Advantage / Actual Mechanical Advantage) x 100% To find the Ideal Mechanical Advantage (IMA) of the screw, we can use the formula:

IMA = (π / tan(α)) x (π / 2) x (D / P)

Where: π is the mathematical constant pi (approximately 3.14159) tan(α) is the coefficient of friction (given as 0.20) D is the major diameter of the screw (given as 19 mm) P is the pitch of the screw, which can be calculated as (25.4 mm / number of threads per inch) First, let's calculate the pitch: Number of threads per inch = 6

Pitch = 25.4 mm / 6 = 4.23 mm (approximately)

Now, we can substitute the values into the formula to find IMA:

IMA = (π / tan(α)) x (π / 2) x (19 mm / 4.23 mm)

Using the given coefficient of friction, we have:

IMA = (π / 0.20) x (π / 2) x (19 mm / 4.23 mm)

Simplifying the equation, we get:

IMA = 9.87 x 1.57 x 4.49

Calculating IMA, we find:

IMA ≈ 69.76

Now, we need to find the Actual Mechanical Advantage (AMA), which can be calculated using the formula:

AMA = Load / Effort

Where:

Load is the weight being lifted (given as 17.80 kN)

Effort is the force applied to turn the screw

Since the screw is being used to lift the load, the Effort is equal to the load.

AMA = 17.80 kin / 17.80 kin

AMA = 1

Now, we can calculate the efficiency using the formula:

Efficiency = (IMA / AMA) x 100%

Efficiency = (69.76 / 1) x 100%

Efficiency ≈ 6976%

The efficiency of the power screw in raising the load is approximately 6976%.

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Answer:

D. Theoretical

Step-by-step explanation:

The probability is based on the number of marbles in the bag.  It is the theoretical probability.  It is the likelihood that a yellow marble will be picked

20 - 2t = (1/2)t + 28

- 2.5 = 8

t= - 3.2

Answer:

3n+7=16;n=3

20-2t=

Step-by-step explanation:

I just did it

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer:

Ray AC and Ray BC

Step-by-step explanation:

\(\text{Hello! :)}\)

\(\large\boxed{(3x + 4)(x + 8)}\)

\(\text{Factor the polynomial:}\\3x^{2} +28x +32\\\\\text{Find two numbers that multiply into 32 and sum up to 28.}\\\text{Take into account the leading coefficient of 3:}\\\\\text{The numbers 4 and 8 work; arrange them so that they sum up to 28:}\\\\(3x + 4)(x + 8)\)

the measure of the fourth interior angle of the quadrilateral is 68° (Option A)

To find the measure of the fourth interior angle of a quadrilateral, we need to use the fact that the sum of all interior angles of a quadrilateral equals 360°. Given that three interior angles measure 55°, 117°, and 120°, we can find the measure of the fourth angle by subtracting the sum of these three angles from 360°.
First, calculate the sum of the three given angles: 55° + 117° + 120° = 292°.
Next, subtract this sum from 360° to find the fourth angle: 360° - 292° = 68°

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Answer:

No because it does no pass the vertical line test

Step-by-step explanation:

The probability that all letters are mailed to the wrong firm depends on several factors, including the number of firms involved, the number of letters, and the randomness of the selection process.

Assuming that there are only two firms and an equal number of letters are randomly placed in each envelope, the probability that all letters are mailed to the wrong firm is 1/2^n, where n is the number of letters. For example, if there are 4 letters, the probability is 1/16 or 0.0625.

However, if there are more than two firms involved or if the letters are not equally distributed among the envelopes, the probability will be different. The probability can also be affected by factors such as the size of the firms and the likelihood of human error.

Overall, the probability of all letters being mailed to the wrong firm is generally low, but can vary depending on the specific circumstances. It's important to ensure that the selection process is as random and accurate as possible to minimize the chances of such an event occurring.

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(a) To find the mean and variance of the service times, we can use the given discrete distribution.

The mean can be calculated by taking the weighted average of the service times: Mean = (1 * 0.3) + (2 * 0.3) + (3 * 0.4) = 0.3 + 0.6 + 1.2 = 2.1 minutes
To find the variance, we need to calculate the squared deviations from the mean and then take the weighted average: Variance = [(1 - 2.1)^2 * 0.3] + [(2 - 2.1)^2 * 0.3] + [(3 - 2.1)^2 * 0.4]
      = [(-1.1)^2 * 0.3] + [(-0.1)^2 * 0.3] + [(0.9)^2 * 0.4]
      = 0.363 + 0.003 + 0.324
      = 0.69

(b) The traffic intensity (ρ) is the ratio of the mean service time to the mean interarrival time. In this case, the mean service time is 2.1 minutes, and the mean interarrival time is given as 2.2 minutes. Therefore:

Traffic Intensity (ρ) = Mean Service Time / Mean Interarrival Time
                    = 2.1 / 2.2
                    = 0.9545

(e) The system throughput is the average number of customers served per unit of time. Since the interarrival times are exponentially distributed, the system throughput can be calculated as the reciprocal of the mean interarrival time:

System Throughput = 1 / Mean Interarrival Time
                 = 1 / 2.2
                 ≈ 0.4545 customers per minute

(a) The long-run average waiting time (excluding service time) for each customer can be calculated using Little's Law. Little's Law states that the long-run average number of customers in a stable system is equal to the product of the long-run average arrival rate and the long-run average waiting time. Since the system is single-server, the arrival rate is the same as the throughput. Therefore:

Long-run Average Waiting Time = Average Number of Customers / Throughput
                            = 1 / System Throughput
                            ≈ 1 / 0.4545
                            ≈ 2.2 minutes

(e) The long-run average number of customers in the system can also be calculated using Little's Law. It is equal to the product of the long-run average arrival rate and the long-run average time a customer spends in the system. Since the arrival rate is the same as the throughput, and the service time includes both waiting time and service time, we can subtract the waiting time from the total service time to find the time spent in the system:

Long-run Average Number of Customers = Throughput * (Mean Service Time - Waiting Time)
                                   ≈ 0.4545 * (2.1 - 2.2)
                                   ≈ -0.0454

The negative value indicates that, on average, there are no customers in the system, which suggests that the system is underutilized or not operating at its full potential.

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Answer: Slope

Step-by-step explanation:

Slope is rise over run. It can be calculated by dividing the change in y (rise) over the change in x (run).

The slope of a non vertical line passing through two points is the ratio of the rise to the run.

What is slope of a line?

The slope of a line is a measurement of its steepness and direction.The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.

1. Slope of Parallel Lines :

A set of parallel lines always has the same inclination angle. Assume we possess two parallel lines l1 and l2 in the reference plane, inclined at angles θ1  and θ2 with the x-axis, respectively, such that the, θ2 = θ1.

m1 = m2

Therefore, the slopes of the two given parallel lines are equal.

2. Slope of Perpendicular Lines :

A pair of perpendicular lines always form a 90° angle. Imagine we have two perpendicular lines l2 and l1 in the coordinate plane, inclined at angles θ1 and θ2 with the x-axis, respectively, so that the provided angles follow the external angle theorem, θ2 =  θ1 + 90°

m₁ = tan θ₁

m₂ = tan (θ₁ + 90º) = - cot θ₁

m₁ × m₂ = -1

Therefore, the product of slopes of two given perpendicular lines is equal to -1

Hence , The slope of a non vertical line passing through two points is the ratio of the rise to the run.

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Estimate the product of the numbers 44 and 817 gives 32000

From the question, we have the following parameters that can be used in our computation:

44 and 817

To estimate the number is to approximate the number

Estimating 44, we get 40 and estimating 817, we get 800

This means that the product expression becomes

Estimate = 40 * 800

Evaluate the products

Estimate = 32000

Hence, the estimate is 32000

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The probability of rolling a 3 on the first throw and a 4 on the second throw of a six-sided die is 1/36.

To find the probability of rolling a 3 on the first throw and a 4 on the second throw of a six-sided die, we need to consider the probability of each individual event and multiply them together.

The probability of rolling a 3 on the first throw is 1/6, as there is one favorable outcome (rolling a 3) out of six possible outcomes (numbers 1 to 6 on the die).

Similarly, the probability of rolling a 4 on the second throw is also 1/6.

To find the probability of both events occurring, we multiply the individual probabilities

Probability = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a 3 on the first throw and a 4 on the second throw is 1/36.

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