The discriminant of a quadratic equation is 225. Describe the nature of the roots.

Among the given answer choices, the correct values for k and j are k = -3 and j = 17. This aligns with the conditions for -7 to be an odd number and 34 to be an even number, respectively.

To determine if -7 is an odd number, we need to check if there exists an integer value for k such that -7 = 2k + 1. By rearranging the equation, we have -7 - 1 = 2k, which simplifies to -8 = 2k. Dividing both sides of the equation by 2, we get k = -4. However, the answer choices do not include k = -4, so this option can be eliminated.

To determine if 34 is an even number, we need to check if there exists an integer value for j such that 34 = 2j. By dividing 34 by 2, we find that j = 17. This satisfies the equation, confirming that 34 is indeed an even number.

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Considering the given probability distribution, we have that there is a 0.349 = 34.9% probability that the left tire has a pressure of at least 25 psi.

The probability distribution for the air pressure of the tires of the car(X right, Y left) is given as follows:

The pressure in the right tire is found to be 22 psi, hence y = 22 and:

The value of K is found considering that the sum of all probabilities has to be 1, hence:

\(\int_{18}^{28} K(x^2 + 484) dx = 1\)

\(\frac{Kx^3}{3} + 484Kx\lbracket|_{x = 18}^{x = 28} = 1\)

Applying the Fundamental Theorem of Calculus:

7317.33K + 13552K - 8712K - 1944K = 1

10213.33K = 1

K = 1/10213.33

K = 0.000098.

The probability that the left tire has a pressure of at least 25 psi is:

\(P(X \geq 25) = \int_{25}^{28} 0.000098(x^2 + 484) dx\)

\(P(X \geq 25) = 0.000098\int_{25}^{28} (x^2 + 484) dx\)

\(P(X \geq 25) = 0.000098\left(\frac{x^3}{3} + 484x\right)_{x = 25}^{x = 28}\)

\(P(X \geq 25) = 0.000098(7317.33 + 13552 - 5208.33 - 12100)\)

\(P(X \geq 25) = 0.349\)

0.349 = 34.9% probability that the left tire has a pressure of at least 25 psi.

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The difference in the average age of the sample and the population is probably due to sampling error

The sampling error in a statistical data is simply an error that arises when a sample that represents the population is not properly selected or analyzed

From the question, we have the following parameters:

\(\bar x = 21.2\) -- the sample average

\(\mu = 19.4\) -- the population average

Notice that:

\(\bar x \ne \mu\)

i.e. sample and the population averages are not equal.

This difference is often as a result of sampling error

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Answer:

its B i think

Step-by-step explanation:

Answer:

with a line accross the points

There is no repeated-measures t statistic for this two-tailed test using the given scores.

The repeated-measures t statistic for a two-tailed test can be calculated using the following formula:

t = (mean difference - hypothesized mean difference) / (standard deviation of the mean difference / square root of sample size)

To calculate the mean difference, subtract the first set of scores (i) from the second set of scores (ii) for each pair:
(3 - 7) = -4
(2 - 6) = -4
(8 - 6) = 2
(7 - 5) = 2

The mean difference is the sum of these differences divided by the sample size:
(-4 + -4 + 2 + 2) / 4 = -4 / 4 = -1

To calculate the standard deviation of the mean difference, first calculate the squared differences between the mean difference and each individual mean difference:
(-1 - (-1))^2 = 0
(-1 - (-1))^2 = 0
(-1 - (-1))^2 = 0
(-1 - (-1))^2 = 0

Then, calculate the sum of these squared differences and divide by the sample size minus 1:
(0 + 0 + 0 + 0) / (4 - 1) = 0 / 3 = 0

Finally, calculate the square root of the result:
sqrt(0) = 0

Now, substitute these values into the formula:
t = (-1 - 0) / (0 / sqrt(4)) = -1 / (0 / 2) = -1 / 0 = undefined

Since the standard deviation of the mean difference is 0, the denominator becomes 0 and the t statistic is undefined.

Therefore, there is no repeated-measures t statistic for this two-tailed test using the given scores.

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The value of the line integral ∫C (P dx + Q dy + R dz) is (√2 - 2 + e^3) with a fraction and e term. This result is obtained by evaluating the integral over each segment of the path C separately and summing them up.

To compute the line integral, we need to parameterize each line segment of C and evaluate the integral over each segment separately.

First, we consider the segment from (0, 0, 0) to (π/2, 0, 0), which moves only in the x-direction. Since y and z remain constant, dy = dz = 0. Thus, the integral over this segment simplifies to ∫(0 to π/2) sin(x) dx. Evaluating this integral gives us -cos(x) evaluated from 0 to π/2, resulting in -(-1 - 1) = 2.

Next, we move from (π/2, 0, 0) to (π/2, 3, 0) in the y-direction. The integral over this segment is ∫(0 to 3) e^3y dy. Integrating this expression gives us (1/3) e^3y evaluated from 0 to 3, resulting in e^9 - 1/3.

Finally, we move from (π/2, 3, 0) to (π/2, 3, 2) in the z-direction. Since x and y remain constant, dx = dy = 0. Therefore, the integral over this segment simplifies to ∫(0 to 2) z dz, resulting in (1/2) z^2 evaluated from 0 to 2, giving us 2.

Adding up the individual integrals, we get (√2 - 1 + e^3 - 1) as the value of the line integral, which includes a fraction and the term e.

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Answer:

$80.22

Step-by-step explanation:

Answer:

$82.58

Step-by-step explanation:

The total cost of the meal = cost of meal + tip amount - discount amount

We then need to find the tip amount and the discount amount using the given cost of the meal, tip percent, and discount percent.

the tip amount applies to the cost of the meal before the discount. Since the cost of the meal before the discount is $78.65 and the tip percent is 20% then the amount of the tip is: 20% of $78.65=  0.20 x $78.65 = $15.73

Since the cost of the meal before the discount is $78.65 and the discount percentage is 15%, then the amount of the discount is: 15% of $78.65 = 0.15 x $78.65 = $11.80

(Remember that the discount amount needs to be rounded to two decimal places since dollar amounts should be rounded to the nearest cent.)

The total cost is then:

                                            $82.58

Hope this helps!

Reasoning At a butcher shop, Hilda bought beef and pork. She left with     18 8/25 pounds of meat. Express the number of pounds of pork she bought using a decimal.

Hilda bought 18.32 pounds of pork.

Hilda purchased 18.32 pounds of pork, which is a terminating decimal, according to the conversion of an improper fraction to a decimal.

She left behind, in pounds, the following amount of meat:

\(18 \frac{8}{25}\)

Now we have to convert the improper fraction to decimal, which is made adding the decimal fraction to the integer part, that is:

\(18 \frac{8}{25} =18+\frac{8}{25} = 18+0.32 = 18.32\)

Therefore, the number of pounds of pork Hilda bought using a decimal number is 18.32.

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Answer:

5 to 4

Step-by-step explanation:

more like this

I did it on good notes

Answer:

At least 3 min

Step-by-step explanation:

Answer:

3.5 Minutes

Step-by-step explanation:

1. You divide 154 by 44.

2. That is your answer

Answer:

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

Since all numbers are positive, their sum or product can be a positive number but never negative or zero.

6 2/3 ÷ 1/5

20/3 ÷ 1/5

20/3 X 5/1

100/3

33 1/3

Hope this helps! :)

Answer:

33 1/3

First: Convert any mixed numbers to fractions. Then your initial equation becomes: 20/3÷1/5  Applying the fractions formula for division, = 20/3×5/1 = 100/3 Simplifying 100/3, the answer is =33 1/3. I hope this makes sense.

The first number will be \(\frac{11}{2}\) and the second number will be \(-\frac{5}{4}\).

Let the first number be x and the second number be y.

According to the question,

Since seven times the first number plus six times the second number equals 31. So,

\(7x+6y=31.......(1)\)

Similarly,Three times the first number minus ten times the second number is 29.So,

\(3x-10y=29.......(2)\)

Multiplying equation (1) by 3 and equation (2) by 7, we get

\(21x+18y=93\)

\(21x-70y=203\)

Now subtracting both the equations we get,

\(88y=-110\)

\(y=-\dfrac{110}{88}\)

\(y=-\dfrac{5}{4}\)

putting the value of x in equation (1) we get,

\(7x+6\times-\dfrac{5}{4} =31\)

\(7x-\dfrac{15}{2}=31\\\)

\(7x=31+\dfrac{15}{2}\)

\(7x=\dfrac{77}{2}\)

\(x=\dfrac{11}{2}\)

Hence the first number is \(\frac{11}{2}\) and the second number is \(-\frac{5}{4}\).

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Mathematical approaches to aggregate planning involve using quantitative methods to determine the optimal production and resource allocation strategies over a specified planning horizon. These approaches utilize mathematical models to optimize various factors such as production costs, inventory levels, and customer demand.

One mathematical approach to aggregate planning is linear programming, which formulates the planning problem as a linear optimization model. Linear programming considers constraints such as capacity limits, labor availability, and demand variability to find the best allocation of resources and production levels. The objective is to minimize costs or maximize profit while meeting demand requirements.

Another approach is the use of mathematical forecasting techniques to predict future demand. Time series analysis, regression analysis, and other statistical methods can be employed to forecast demand patterns. These forecasts serve as inputs to mathematical models, such as inventory control models or production planning models, which determine the optimal production levels and inventory policies based on the anticipated demand.

Simulation modeling is another mathematical approach where computer-based simulations are used to evaluate different scenarios and make decisions about production levels, inventory levels, and workforce scheduling. These models consider various factors like demand variability, production capacity, and resource availability to simulate the system's behavior and analyze the impact of different planning strategies.

Overall, mathematical approaches to aggregate planning provide a systematic and quantitative way to optimize production and resource allocation decisions, considering factors such as demand, capacity, costs, and constraints. These approaches help organizations make informed decisions to meet customer demand efficiently while minimizing costs and maximizing operational performance.

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Answer:

144 codes are possible

Step-by-step explanation:

Okay for the first digit, we shall be selecting one out of 3,4,5,6.

Meaning we are selecting one out of four choices

The number of ways this can be done is 4C1 ways = 4 ways

For the second digit, we have 5,6,7 or 8, we are still selecting 1 out of 4 selections and the number of ways we can do this is also 4 ways

And lastly , we can choose any digit for the last number expect 5 , so from 0 to 9, we are removing 1 which means we are left with 9 choices

So the number of different area codes possible are ; 9 * 4 * 4 = 144 codes

Answer:

= 12.5% decrease

Step-by-step explanation:

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

Therefore, the answer is 12.5% decrease

To find the Taylor series for a function centered at a specific point, we need to calculate the function's derivatives at that point. Let's find the Taylor series for the function h(x) centered at x = 3.

(a) Taylor series for h(x) centered at x = 3:

Step 1: Find the value of the function and its derivatives at x = 3.

h(3) = 4 (value of h(x) at x = 3)

h'(x) = 2x (first derivative of h(x))

h''(x) = 2 (second derivative of h(x))

Step 2: Write the Taylor series using the function's derivatives.

h(x) = h(3) + h'(3)(x - 3) + (h''(3)/2!)(x - 3)^2 + ...

The first five terms of the Taylor series for h(x) centered at x = 3 are:

h(x) ≈ 4 + 2(x - 3) + 2/2!(x - 3)^2

(b) Graph of the function and approximating polynomials:

To graph the function h(x) along with the approximating polynomials P2 and P4, we'll substitute the values into the respective polynomials.

P2(x) = h(3) + h'(3)(x - 3) + (h''(3)/2!)(x - 3)^2

= 4 + 2(x - 3) + 2/2!(x - 3)^2

= 4 + 2x - 6 + (1/2)(x - 3)^2

= 2x - 2 + (1/2)(x - 3)^2

P4(x) = P2(x) + (h'''(3)/3!)(x - 3)^3 + (h''''(3)/4!)(x - 3)^4 + ...

= P2(x) (since we have only calculated up to the second derivative)

Now, we can plot the graph of h(x), P2(x), and P4(x) to visualize the approximations.

Note: Without the specific equation for h(x), it's not possible to plot the function and its approximating polynomials accurately.

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Step-by-step explanation:

what do we need to do ?

just calculate the value of the expression by using the given values for the variables ?

what's the problem ? this is just basic calculation.

8/4 + 7×9 = 2 + 63 = 65

remember (please, for your life !) that multiplication and division always happens before any addition or subtraction (except for the case, where brackets force us in a different direction).

I believe the answer is 48.3

Step-by-step explanation:

sorry if I'm wrong

Answer:

5,400

Step-by-step explanation:

do the exponent which is 10x10=100 then add it to 5,300

Answer:

question three 8488

question four 288

Step-by-step explanation:

Answer:

3. 8448

4. 288

Step-by-step explanation:

Paying a bill amount through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

1. Paying a bill amount through the mail without check is a convenient and secure way of making payments.

2. It allows for payment to be made without having to visit a physical location to do so.

3. It also allows for payment to be made without having to use a credit or debit card.

4. Therefore, an advantage of paying a bill through the mail without check is that it is convenient and secure.

Paying a bill through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

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The correct option is b. The form of logic evident in this scenario is a statistic.

In this scenario, the logic being used is based on a statistic. A statistic is a numerical value or measure that represents a specific characteristic or trend within a population. In this case, the statistic is derived from the experiences of the five friends who have had a great experience with their Chevrolet purchases. By observing their positive experiences, you are using this statistic to make an inference about the overall quality or satisfaction associated with Chevrolet vehicles.

It's important to note that the logic being used here is based on a sample size of five friends, which may not necessarily represent the entire population of Chevrolet buyers. The experiences of these friends can be seen as a form of anecdotal evidence. While their positive experiences are valuable and can provide some insight, it is always advisable to consider a larger sample size or gather additional information before making a purchasing decision. So, while the form of logic evident here is a statistic, it is essential to exercise caution and gather more data to make a well-informed decision.

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Answer:

105

Step-by-step explanation:

symmetrical angles and 105+105+75+75=360

The zeroes of the function are the values of x which make it equal to zero

Since f(x) = (2x + 6)(x - 4)

Then to find the zeroes of f, equate f(x) by 0

Equate each bracket by 0 to find x

Subtract 6 from each side

Divide both sides by 2

Add 4 to each side

The zeroes of the function are x = -3 and x = 4

The answer is C