Given a quadratic equation px^2 + 8x + 2 does not have real roots. Determine the range of the values of p.
[4 marks]

The required tally table is

Interval     Tally       Frequency

0-4                -                   0

5-9               | |                   2

10-14            | |                   2

15-19            ||||                  4

20-24         ||||| ||||               9

25-29            |||                  3

To create a tally table, follow these steps:

1. Write down the intervals or categories for the data.

2. Create a tally mark (a vertical line) for each observation that falls into that interval/category.

3. After every fifth tally mark, draw a diagonal line across the previous four tally marks to make counting easier.

4. Add up the total number of tally marks in each interval/category to determine the frequency.

Here we have

The data is 20, 27, 5, 6, 29, 7, 17, 11, 18, 5, 15, 17, 20, 27, 22, 13, 6, 28, 27, 23, 24, 17

To make the tally table follow the above steps

Hence, we will get the following tally and frequency table

Interval     Tally       Frequency

0-4                -                   0

5-9               | |                   2

10-14            | |                   2

15-19            ||||                  4

20-24         ||||| ||||               9

25-29            |||                  3

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Answer:

the answer is 15.

Answer:

it is 15

Step-by-step explanation:

The distribution of W, the time in seconds before the 7th count is made, is a gamma distribution with shape parameter 7 and rate parameter 16.

The waiting time W until the 7th count is a random variable that represents the sum of 7 independent and identically distributed exponential random variables with parameter 16. This is because the Poisson process underlying the Geiger counter is memoryless, and the number of counts in any given interval of time is independent of the number of counts in any other interval of time.

Each interval of time between counts follows an exponential distribution with parameter 16, which represents the rate at which alpha particles are emitted from the carbon-14 source.

The sum of n independent exponential random variables with the same rate parameter is a gamma distribution with shape parameter n and rate parameter equal to the rate parameter of each exponential distribution. Therefore, the waiting time W until the 7th count follows a gamma distribution with shape parameter 7 and rate parameter 16.

The mean of this gamma distribution is 7/16, which is equal to the expected waiting time until the 7th count. The variance of the gamma distribution is 7/256, which represents the spread or variability in the waiting times until the 7th count.

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The correct value of \($t^*$\) to be used to create a 90% confidence interval for the true mean number of calls is 1.676

In this scenario, the director of a customer service center wants to estimate the mean number of customer calls the center handles each day. To create a 90% confidence interval for the true mean number of calls, the director needs to use a confidence interval formula that takes into account the sample size, sample mean, and the standard error of the mean.

The standard error of the mean, denoted as \($SE_{\bar{x}}$\), represents the standard deviation of the sampling distribution of the mean. It can be calculated using the formula:

\($SE_{\bar{x}} = \frac{s}{\sqrt{n}}$\)

where\($s$\) is the sample standard deviation and \($n$\) is the sample size.

The director can use the t-distribution to create the confidence interval, as the sample size is relatively small (less than 30). The formula for the 90% confidence interval is:

\($\bar{x} \pm t^* \frac{s}{\sqrt{n}}$\)

where\($\bar{x}$\) is the sample mean, \($s$\) is the sample standard deviation,\($n$\) is the sample size, and \($t^*$\) is the critical value from the t-distribution with (n-1) degrees of freedom and a 90% confidence level.

To determine the value of \($t^*$\), the director needs to consult a t-distribution table or use a statistical software. For a 90% confidence interval and 47 degrees of freedom (48 - 1), the value of \($t^*$\) is approximately 1.676.

Therefore, the correct value of \($t^*$\) to be used to create a 90% confidence interval for the true mean number of calls is 1.676. Using this value, the director can calculate the confidence interval by plugging in the sample mean, sample standard deviation, and sample size into the formula. This will give an estimate of the range of values where the true population mean lies with 90% confidence.

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Answer:

The area of the triangle WYX  = \(\frac{35}{2}\) = 17\(\frac{1}{2}\)

Step-by-step explanation:

The area of the triangle WYX  is \(\frac{1}{2}\)*b*h

We need to find base (b) and height (h)

By counting from the drawing, the base which is horizontal is 7 and the height which is vertical is 5

The area of the triangle WYX  is \(\frac{1}{2}\)*b*h

The area of the triangle WYX  = \(\frac{1}{2}\)*7*5 = \(\frac{35}{2}\) = 17\(\frac{1}{2}\)

The expression for the rectangular prism's base area is 11x² + 7x + 5.

Given;

The volume of rectangular prism = 33x³ + 43x² + 29x + 10

The height of the prism = 3x + 2

We know that, the area of the prism = length * breadth

where as, volume = length * breadth * height

So, area = volume / height

Using synthetic division, dividing volume by height, we get;

3x+2  ) 33x³ + 43x² + 29x + 10 ( 11x² + 7x + 5

            33x3 + 22x2

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

                        21x² + 29x

                        21x² + 14x

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

                                  15x + 10

                                   15x + 10

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

                                       x

Quotient is 11x² + 7x + 5 which is equal to expression for the area of the base of the rectangular prism.

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Answer:

8.15 miles

Step-by-step explanation:

Monday: 1 1/10 miles = 1.1

Multiply by 10 to get to 100

Wednesday: 4 4/5 miles = 4.8

Multiply by 20 to get to 100

Friday: 2 1/4 miles = 2.25

Multiply by 25 to get to 100

1.1 + 4.8 + 2.25 = 8.15 miles

Answer:

120

Step-by-step explanation:

80 is 2/3 of Drew's book

80 divided by 2 is 40

divided by 2 to find 1/3 of the book

40 * 3 = 120

3 is the whole

120 is the total amount of pages in the book

Answer:

yes

Step-by-step explanation:

2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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The total interest that is deposited when interest is compounded annually at a rate of 2% is $3,121.20.

Divide the total by the risk premium, this same length of time, and certain other factors that arrive at simple interest. Simple revenue = initial + interest + hours is the commercial formula. This method allows it easiest to determine interest. Its most typical manner to figure out payment is as a portion of the outstanding amount. He will only collect his share of the 100percent interest, for example, if he borrows $100 from just a friend and offers to pay it back with 5% interest. $100 (0.05) = $5. When you borrow, you must pay interest, and when you give it out, you must make payments. Interest is often determined as an annual percentage of the loan total.

given

compound interest = FV = P*(1+R/N)^(N*T),

= 3000* ( 1 + 2/1 )^ ( 1*1)

= $3,121.20

The total interest that is deposited when interest is compounded annually at a rate of 2% is $3,121.20.

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Answer:

A

Step-by-step explanation:

Bulldogs PitBulls Dogs the answer is A

Answer:

$16,557

Step-by-step explanation:

The computation of the amount after four years is shown below:

As we know that

Future value = Present value × (1 + rate of interest)^number of years

=  £15,000 × (1 + 2.5%)^4

=  £15,000 × 1.025^4

= $16,557

area of rectangle= length × width

= 19×33

= 627 sq units

The foil method is an effective method because you are able to successfully remember the other at which you multiply the brackets to open them using F.O.I.L, so its not only easy to remember but very good to use for quadratic, cubic and to an extent, polynomials.

The FOIL Method stands for First Outer Inner Last. This is a standard method for multiplying two binomials together. It is also a valid method for solving quadratic equations and simplifying expressions.

The FOIL method is a valid method because it helps to simplify complicated expressions, and it is easy to use. It is used to multiply two binomials together.

By following the steps, the user can easily find the product of two binomials. The steps are as follows:

The FOIL method is valid because it helps to simplify expressions by breaking them down into smaller parts. This makes it easier to see how the parts relate to each other and how they combine to create the final expression. It is a straightforward method, and it is easy to use.

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Answer:

0.67 = x

Step-by-step explanation:

to solve the value of x we need to : (x,9)

y = 3x + 7

9 = 3x + 7

9 - 7 = 3x

2 = 3x

2/3 = x

0.67 = x

From the given point (x , 9) let's plug the value of its y - coordinate of into Equation - y = 3x + 7 and solve for x :

hence, value of x = 2/3

The given statement "If A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have AX · AY = X · Y" is proved.

Given that A is a n * n order matrix.

And X, Y ∈ Rₙ so,

|X - Y|² = (X - Y) * (X - Y)

|X - Y|² = |X|² - 2 * X * Y + |Y|²

2 * X * Y = |X|² + |Y|² - |X - Y|²

Since A is orthogonal matrix so,

2 * (AX * AY) = |AX|² + |AY|² - |AX - AY|²

2 * (AX * AY) = |X|² + |Y|² - |X - Y|²

2 * (AX * AY) = 2 * X * Y

(AX * AY) =  X * Y

Hence the statement is proved.

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The question is incomplete. The complete question will be -

"Suppose that A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have

AX · AY = X · Y"

The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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As we know that circumference of circle is 2πr but here radius is R so it will be 2πR

Hope it helps u

Answer:

4.86 people/sq.miles

Step-by-step explanation:

the area of the state of Wyoming =

360 × 280 = 100,800 sq. miles

so, the population density =

490,408 ÷ 100,800

= 4.86 people/sq.miles

Answer:

x = 58.47

Step-by-step explanation:

Use SOH CAH TOA

Sin(16) = 20/x

x = 58.47

In this problem, the total amount that Linda and Rob were overcharged is $9.00

Let the amount that Linda and Rob was supposed to be charged be A and the amount that the waitress charged be B. Therefore, from the question,A = $67.44 (original bill)B = $76.44 (wrongly charged bill)They were overcharged = (B - A) = $76.44 - $67.44 = $9.00We know that the credit card has an 18% APR and this is the annual interest rate charged on borrowed money. So, the monthly interest rate is given by (18/12)% = 1.5%.Since Linda and Rob noticed this later that month, this means they borrowed the extra $9 for the remaining part of the month.

Therefore, the interest charged on this extra amount borrowed for the remaining part of the month is given by:

Interest charged = Principal × rate × time .In this case, Principal = $9.00,Rate = 1.5% per month,Time = (30 - number of days in the month they received their statement) / 30We don't know the number of days in the month they received their statement. But let's assume they received their statement on the 15th day of the month. This means the number of days in the month they received their statement is 15. So, the time is given byTime = (30 - 15) / 30 = 1/2Therefore,Interest charged = 9 × 1.5% × 1/2= 0.0675= $0.07 (approx.)Therefore, the total amount they were overcharged was $9.00 + $0.07 = $9.07.

Therefore, conclusion is that Linda and Rob were overcharged a total of $9.07.

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Answer:

0.0069444444

Step-by-step explanation:

Answer:

Answer: $457,835

Step-by-step explanation:

I just took the test :)

Answer:

We have ordered pairs (60,360), (120,720), (180,1080), (240,1440), and (300,1800) as the answer.

Step-by-step explanation:

The table would look like this:

Under minutes you would place 60, 120, 180, 240, and 300.

Under calories you would place 360, 720, 1080, 1440, and 1800.

y = 6x

Multiply 60, 120, 180, 240, and 300 by 6 for 6 calories.  This gives us the ordered pairs above.  

The sum of first 10 terms is 72.

Concept: Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

Arithmetic Progression Formula

= an - a. nth term of an AP: an = a + (n - 1)d. Sum of n terms of an AP: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the arithmetic progression.

Given:

Eighth term is 8.2

Common difference is 0.4

a(8) = 8.2

a + 7d = 8.2

Since d = 0.4

a + 7(0.4) =8.2

a = 5.4

Sum of 10 terms = n/2 (2a+(n-1)d)

= 5(2*5.4 + 9*0.4)

=5(10.8 +3.6)

Sum=72

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Answer:

25 minutes.

Step-by-step explanation:

11:19 to 11:44 is 25 minutes.

The probability that one die is a 3 is  0.167.

The concept of the conditional probability formula is one of the quintessential concepts in probability theory. The conditional probability formula gives the measure of the probability of an event, say B given that another event, say A has occurred.  

The Bayes' theorem is used to determine the conditional probability of event A, given that event B has occurred, by knowing the conditional probability of event B, given that event A has occurred, also the individual probabilities of events A and B.

Note: In case P(B)=0, the conditional probability of P(A | B) is undefined.  (the event B did not occur).

Number of ways to roll out two dice =  6 x 6 = 36

Let A be the event in which the sum of the two dice is 7.

∴ P(A) = 6/36

Let B be the event in which one die is 3.

∴ P(B) = 10/36

Let P(B∩A) be the event in which the sum of the dice is 7 and one die is 3.

P(B∩A) = 1/36

Applying the formula of conditional probability,

P (B|A) = P (A ∩ B)⁄P (A)

= 1/36 * 6/36 = 1/6 = 0.167

Thus, the probability that one die is a 3 is  0.167.

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The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

What is a normal distribution?

A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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