Find the length of the segment JK in the parallelogram below.

Answer:

170 Degrees.

Step-by-step explanation:

If an interior angle is 170 degrees, that's your best bet.

Answer:

no

Step-by-step explanation:

condition to be a function is that for one x value, only one f(x) can be obtained

Answer:

I think the answer is B.

The amount that Theresa was charged in interest for the billing cycle is $5.30

By using the average daily balance, the amount will be:

= (350 × 12) + (520 × 19) / (12 + 19)

= (4200 + 9880)/31

= 454.19

Therefore, the interest will be:

= (454 × 0.14)/12

= $5.30

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This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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a. A tea bag is considered small if it weighs less than 2.626 grams.

b. The probability that it weighs at least 2.25 grams is 17.07%.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

(a) Let X be the weight of a tea bag. Then X ~ N(3.5, 0.53²). We want to find the value of w such that P(X < w) = 0.052. Using the standard normal distribution, we have:

(P(X < w) - P(X < 3.5)) / 0.53 = z

where z is the 0.052 quantile of the standard normal distribution. Using a standard normal table or calculator, we find that z ≈ -1.645. Substituting the values and solving for w, we get:

(w - 3.5) / 0.53 = -1.645

w - 3.5 = -0.874

w ≈ 2.626

Therefore, a tea bag is considered small if it weighs less than 2.626 grams.

(b) We want to find P(X ≥ 2.25 | X < 2.626), which is the conditional probability that a selected tea bag weighs at least 2.25 grams given that it is small. Using the properties of the normal distribution, we have:

P(X ≥ 2.25 | X < 2.626) = P((X - 3.5) / 0.53 ≥ (2.25 - 3.5) / 0.53 | (X - 3.5) / 0.53 < (2.626 - 3.5) / 0.53)

= P(Z ≥ -2.358 | Z < -1.566)

where Z is a standard normal random variable. Using a standard normal table or calculator, we find that:

P(Z ≥ -2.358) ≈ 0.990

P(Z < -1.566) ≈ 0.058

Therefore, P(X ≥ 2.25 | X < 2.626) ≈ 0.990 / 0.058 ≈ 17.07%.

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The probability that a random person in the GTA will see at least one of the advertisements is 90%. In the second scenario, the probabilities are: a) 1/3, b) 1/3, and c) 2/3. Lastly, the probability of drawing a two from a standard deck is 1/13, and the knowledge that the card is a spade does not change this probability.

Let's denote the probability of reading The Toronto Star as P(TS) = 0.70 and the probability of watching City TV as P(CTV) = 0.60. The probability of doing both (reading The Toronto Star and watching City TV) is P(TS ∩ CTV) = 0.40.

To find the probability that a person will see at least one of these platforms, we can use the principle of inclusion-exclusion. The probability of seeing at least one platform is given by:

P(TS ∪ CTV) = P(TS) + P(CTV) - P(TS ∩ CTV)

            = 0.70 + 0.60 - 0.40

            = 0.90

Therefore, the probability that a person selected at random in the GTA will see at least one of these platforms is 0.90, or 90%.

Moving on to the next question, we have a jar with six red marbles and four green marbles. Two marbles are drawn without replacement. We need to find the probabilities of different events.

a) The second marble is green, given the first is red: Since the first marble is red and not returned to the jar, there are nine marbles left, out of which three are green. Therefore, the probability is 3/9 or 1/3.

b) Both marbles are red: The probability of drawing the first red marble is 6/10, and given that the first marble was not returned, the probability of drawing the second red marble is 5/9. Multiplying these probabilities, we get (6/10) * (5/9) = 1/3.

c) The second marble is red: Given that the first marble was red and not returned, there are nine marbles left, out of which six are red. Therefore, the probability is 6/9 or 2/3.

Lastly, considering a standard deck of 52 cards, the probability of drawing a two is 4/52 or 1/13 since there are four twos in the deck. If we are told that the drawn card is a spade, there are 13 spades in the deck, including one two of spades. Therefore, the probability of the card being a two is now 1/13, which remains unchanged even with the additional information about it being a spade.

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The amount of oil utilized is equal to m/n * 100.

The amount of residual oil is  \(\frac{n - m}{n} * 100\)

Given,

There are n gallons of oil. After m gallons have been used then, in terms of m and n, what percent of oil remains?

To know what percent was used,

The oil used is m

The percentage of oil used is = m/n * 100

The oil remaining is = n - m

The percentage of oil remaining is = \(\frac{n - m}{n} * 100\)

Therefore,

The percentage of oil used is m/n * 100

The percentage of oil remaining is \(\frac{n - m}{n} * 100\)

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Answer:

work is shown and pictured

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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Answer:

Step-by-step explanation:

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

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Answer:

3.75

Step-by-step explanation:

The hundredth is the 2 number after the decimal point so round that up.

Answer:

3.75

Step-by-step explanation:

the hundreths place is the second number to the left of the decimle, because the number to the left of the hundreths place is less than five. You leave the hundreths place number as it is. This leaves you with your awnser: 3.75

Answer:

3

Step-by-step explanation:

Answer:

9/16

Step-by-step explanation:

║Given║:

Veronica needs to buy 1 3/4 pounds of cheese.

When the clerk places some cheese in a container and weighs it, the scale shows 1 1/4 pounds.

The container weighs 1/16 pound.

║To Solve║:

How many more pounds of cheese should be added to the scale to get the amount that veronica needs? Explain how you solved the problem

║Solving║:

Since, the amount of cubed cheese that Veronica wants to buy = 1 3/4 pounds then turn it into improper fractions.

Which:

 1 3/4                                                                                      = 7/8 pounds

We also knows that:

Weight of the container in which Mr. Sand places the cube = 1/16 pounds

Weight of the cubed cheese and container together = 1 1/4 pounds

               Turn into improper fraction.

Which:

1 1/4                                                                    = 5/4 pounds

Thus,

The amount of cubed cheese placed by Mr. Sands = (5/4 - 1/16) pounds

                                                                           = (20 - 1)/16 pounds

                                                                           = 19/16 pounds

Hence,

The quantity of more cheese that Mr.Sands need to add to the scale is:

(7/4 - 19/16) pounds

= (28 - 19)/16 pounds

= 9/16 pounds.

Base on the solving above we can conclude that need  to add 9/16 pounds of cubed cheese to fullfil the order placed by Veronica.

║ Answer ║

9/16

Kavinsky~

The bank's loan is better because it has a lower APR of 9.2% compared to the dealer's loan with an APR of 34.5%.

Given that, Vin Lin wants to buy a used car that costs $9,780. A 10% down payment is required. The used car dealer offered him a four-year add-on interest loan at 7% annual interest. We need to find the monthly payment.

(a) Calculation of monthly payment:

Loan amount = Cost of the car - down payment

= $9,780 - 10% of $9,780

= $9,780 - $978

= $8,802

Interest rate (r) = 7% per annum

Number of years (n) = 4 years

Number of months = 4 × 12 = 48

EMI = [$8,802 + ($8,802 × 7% × 4)] / 48= $206.20 (approx.)

Therefore, the monthly payment is $206.20 (approx).

(b) Calculation of APR of the dealer's loan:

As per the add-on interest loan formula,

A = P × (1 + r × n)

A = Total amount paid

P = Principal amount

r = Rate of interest

n = Time period (in years)

A = [$8,802 + ($8,802 × 7% × 4)] = $11,856.96

APR = [(A / P) − 1] × 100

APR = [(11,856.96 / 8,802) − 1] × 100= 34.5% (approx.)

Therefore, the APR of the dealer's loan is 34.5% (approx).

(c) APR of the bank's loan is less than the dealer's loan. So, the bank's loan is better for him.

(d) APR of the bank's loan is 9.2%.

APR of the dealer's loan is 34.5%.

APR of the bank's loan is less than the dealer's loan.

So, the bank's loan is better for him. Answer: The bank's loan is better.

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The speed of the truck in km/h at the end of this distance is equal to 81.43 km/h.

The time elapsed is equal to 0.7939 seconds.

In order to determine the speed of the truck in km/h at the end of this distance, we would apply the third equation of motion:

v² = u² + 2as

Where:  

Next, we would convert the value of deceleration in m/s² to km/h² as follows;

Deceleration, a = 6.5 × 60⁴/1000 = -84,240 km/h².

Distance, s = 20/1000 = 0.02 m.

Substituting the given parameters into the third equation of motion, we have;

v² = 100² + 2(-84,240)(0.02)

Speed, v = √(10,000 - 3,369.6)

Speed, v = √6,630.4

Speed, v = 81.43 km/h.

Lastly, we would determine the time by using the first equation of motion:

V = U + at

Time, t = (V - U)/a

Time, t = (100 km/h - 81.43 km/h)/6.5

Time, t = [(100 × 1000/3600) - (81.43 × 1000/3600)]/6.5

Time, t = (27.78 - 22.62)/6.5

Time, t = 5.16/6.5

Time, t = 0.7939 seconds.

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Complete Question:

The driver of a pick up truck going 100 km/h applies the brakes, giving the truck a uniform deceleration of 6.50 m/s^2 while it travels 20.0 m.

a. What is the speed of the truck in km/h at the end of this distance?

b. How much time has elapsed?

The approximate probability that the mean number of siblings in the sample of size 50 is at most 2 is 0.1562 or 15.62%.

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.

To answer this question, we need to use the central limit theorem, which states that the sample mean of a large enough sample from any population with a finite mean and variance will follow a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, we have a sample size of 50, which is considered large enough for the central limit theorem to apply. Therefore, the mean of the sample means will be equal to the population mean, which is 2.2, and the standard deviation of the sample means will be equal to the population standard deviation divided by the square root of the sample size, which is 1.4/sqrt(50) = 0.198.

To find the probability that the mean number of siblings in the sample of size 50 is at most 2, we need to calculate the z-score and use the standard normal distribution table or calculator. The z-score can be calculated as:

z = (2 - 2.2) / 0.198 = -1.01

Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score of -1.01 or less is approximately 0.1562.

Therefore, the approximate probability that the mean number of siblings in the sample of size 50 is at most 2 is 0.1562 or 15.62%.

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Option (c) x² + sin x is the correct option.

Given that F(x) = ∫f(t² + sin t) dt

The fundamental theorem of calculus is given as: If f is continuous on [a,b] then F(x) = ∫f(t)dt from a to x is differentiable at x and F'(x) = f(x)Given that F(x) = ∫f(t² + sin t) dt

Differentiating F(x) with respect to x, we get; F¹(x) = f(x² + sin x) * (2x + cos x)Therefore, the value of F¹(z) = f(z² + sin z) * (2z + cos z)

Thus, option (c) x² + sin x is the correct option.

Calculus is a branch of mathematics that deals with the study of change and motion. It is divided into two main branches: differential calculus and integral calculus.

Differential calculus focuses on the concept of derivatives, which measures how a function changes as its input (usually denoted as x) changes. The derivative of a function at a particular point gives the rate at which the function is changing at that point. It helps analyze properties of functions such as their slopes, rates of growth, and optimization.

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Answer:

An absolute value equation with solutions of x = 3 and x = 9 is |x - 6| = 3.

Step-by-step explanation:

Answer:

D (-3, 5)

Step-by-step explanation:

270 counter clockwise is the same as 90 clockwise.

For a 90° clockwise or 270° counter clockwise, take the opposite of the x coordinate then switch the coordinates.

(-5, -3) -----> (5, -3) ------> (-3, 5)

You can also rotate your screen 90° clockwise to see the new coordinates for A.

The radius of the circle  with arc length of 2.4 and subtended angle at the center, 7.1 radians is 0.3

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

length of arc = 2.4

if 7.1 rad is the angle subtended by the intercepts of the arc

But \(\pi\) rad = 180°

so 7.1 rad in degree = \(\frac{7.1}{\pi }\) x 180  which is \((\frac{1278}{\pi } )^{} }\) degree which is \(\alpha\)

Length of an arc = \(\frac{\alpha }{360} * 2\pi r\)

2.4 =  \((\frac{1278}{\pi } )^{} }\) x \(\frac{1}{360}\) x 2 x \(\pi\) x r

The equation reduces to

2.4 = 7.1r

r = 2.4 ÷ 7.1

r = 0.334 which is 0.3

In conclusion the radius of the circle is 0.3

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The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.

It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.

The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.

The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.

A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.

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Answer:

10 times

Step-by-step explanation:

Here, we want to get the number of times the three bells toll together

Now, what we have to do here is to find the number of seconds it will take them to fill together

To find this, we need to get the lowest common multiple of 12, 15 and 18

The lowest common multiple of these three numbers is ;

180

180 seconds

Now, since 60 seconds is 1 minute

The number of minutes in 180 seconds is 180/60 = 3 minutes

So, as we can see, they can sound together once in 3 minutes;

The number of times they will sound together in 30 minutes is 30/3 = 10 times

Using mathematical induction, it can be proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.

Base Case: For n = 2, we have 13 = 3 and 24 = 8. Since 3 <= 8, the inequality holds true.

Induction Hypothesis: Assume that 13...(2k-1) <= 24*...*(2k-2) holds true for some positive integer k >= 2.

Induction Step: We need to show that the inequality also holds for k+1, i.e., 13...(2k+1) <= 24*...(2k).

To do this, we start with the left-hand side of the inequality:

13*...(2k+1) = (13*...(2k-1))(2k+1) <= (24...(2k-2))(2k+1)

(Using the induction hypothesis and the fact that 2k+1 is greater than or equal to 2).

Next, we simplify the right-hand side:

24...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1))

Finally, we can conclude that:

13...(2k+1) <= 24*...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1)) <= 24...*(2(k+1)-2)

(Since k+1 is greater than or equal to 2, we can use the induction hypothesis again.)

Therefore, by the principle of mathematical induction, we have proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.

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Answer:

\(y = \frac{3}{4} x + 10\)

Step-by-step explanation:

no idea how to explain it but just trust. if you test it and say:

\(y = \frac{3}{4}*4 + 10\)

then y would equal 13.

x is 4 on the table and y is 13 below it, so my answer, therefore, is correct.

Answer:

--------------

Average speed equation:

Substitute 350 for d and 5.15 for t:

The average speed must be approximately 68 km per hour.

Answer:

$ 53.33

Step-by-step explanation:

x = original price

.75 * x = 40

x = 40 / .75 = 53.33

Let original price be x

Hence

The dimensions will be 33 , 66 , 51 feet

What in mathematics is a quadratic equation?

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given that:

Let the shortest side be x

Perimeter is 150 feet then then equation will be

x + (2x) + (x+18) = 150

4x + 18 = 150

4x = 150-18

x = 132/4

x = 33

Then the dimensions will be 33 , 66 , 51 feet

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