22
Liam is trying to remember a 3-digit code.
He knows the rule that
the first digit is a cube number
the second digit is a factor of 16
the third digit is an odd number.
Liam tries at random a code that matches the rule.
Work out the probability that this is the correct code.
[4 marks]

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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Answer:

548

Step-by-step explanation:

First, the sides:

7 × 12 = 84

84 × 2 = 168

7 × 10 = 70

70 × 2 = 140

10 × 12 = 120

120 × 2 = 240

Add:

168 + 140 + 240

 ^         ^

     308  +  240

            548  

Hope this helped.

Answer:

The surface area of the rectangular prism is 548\(ft^{2}\)

Step-by-step explanation:

To find the surface area of the rectangular prism you need to use the formula

A=2(wl+hl+hw)

Answer to question commented:

The surface area of the other rectangular prism is 430\(ft^{2}\)

Hope this helps!

(a)  The net electric field at x = 0 cm is 6.6 × 10⁴ N/C, directed toward the positive x-axis.

(b) The net electric field at x = +6.00 cm is zero.

To find the net electric field at a point on the x-axis, we need to calculate the electric field due to each charge individually and then sum them up.

The electric field due to a point charge is given by the equation:

E = k * (q / r²)

Where:

E is the electric field,

k is the Coulomb's constant (k = 8.99 × 10⁹ N m²/C²),

q is the charge, and

r is the distance between the charge and the point where we want to find the electric field.

Let's calculate the net electric field at the given points:

(a) x = 0 cm:

For this point, we need to calculate the electric field due to both charges and then sum them up.

Electric field due to q1 at x = 0 cm:

r1 = |x1 - x| = |3.00 cm - 0 cm| = 3.00 cm = 0.03 m

E1 = k * (q1 / r1²)

  = (8.99 × 10⁹ N m²/C²) * (5.84 × 10⁻⁶ C / (0.03 m)²)

  = 3.39 × 10⁵ N/C

The direction of E1 is positive (+) since q1 is positive and it points away from the charge.

Electric field due to q2 at x = 0 cm:

r2 = |x2 - x| = |9.00 cm - 0 cm| = 9.00 cm = 0.09 m

E2 = k * (q2 / r2²)

  = (8.99 × 10⁹ N m²/C²) * (-20.9 × 10⁻⁶ C / (0.09 m)^2)

  = -2.73 × 10⁵ N/C

The direction of E2 is negative (-) since q2 is negative and it points towards the charge.

Net electric field at x = 0 cm:

E_net = E1 + E2

      = 3.39 × 10⁵ N/C + (-2.73 × 10⁵ N/C)

      = 0.66 × 10⁵ N/C

      = 6.6 × 10⁴ N/C (to two significant figures)

Therefore, the net electric field at x = 0 cm is 6.6 × 10⁴ N/C, directed toward the positive x-axis.

(b) x = +6.00 cm:

We follow the same procedure as above to calculate the electric field at this point.

Electric field due to q1 at x = +6.00 cm:

r1 = |x1 - x| = |3.00 cm - 6.00 cm| = 3.00 cm = 0.03 m

E1 = k * (q1 / r1²)

  = (8.99 × 10⁹ N m²/C²) * (5.84 × 10⁻⁶ C / (0.03 m)²)

  = 3.39 × 10⁵ N/C

The direction of E1 is positive (+) since q1 is positive and it points away from the charge.

Electric field due to q2 at x = +6.00 cm:

r2 = |x2 - x| = |9.00 cm - 6.00 cm| = 3.00 cm = 0.03 m

E2 = k * (q2 / r2²)

  = (8.99 × 10⁹ N m²/C²) * (-20.9 × 10⁻⁶ C / (0.03 m)²)

  = -3.39 × 10⁵ N/C

The direction of E2 is negative (-) since q2 is negative and it points towards the charge.

Net electric field at x = +6.00 cm:

E_net = E1 + E2

      = 3.39 × 10⁵ N/C + (-3.39 × 10⁵ N/C)

      = 0 N/C

Therefore, the net electric field at x = +6.00 cm is zero.

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Answer:

p = 0.70z

Step-by-step explanation:

p is the food the penguins eat

z is the food the zebras eat

We are told that:  p < z

Then we are told that:  p = 70% of z

This can be written as p = 0.70z

An alternative way this can be written is:  p/z = 0.70  [The ratio of p to z is 0.7]

Answer:

x = 31

Step-by-step explanation:

I will make the explanation easy for you to understand.

Step 1: Subtract 12x from both sides.

13x − 15 − 12x = 12x + 16 − 12x

x − 15 = 16

Step 2: Add 15 to both sides.

x − 15 + 15 = 16 + 15

x = 31

Hope it helps!!!

If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.

An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.

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The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

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The total amount of money spent/ amount of friends

Step-by-step explanation:

52/4

Answer:

4x = 52

Step-by-step explanation:

Let's say the cost of the ticket is represented by the variable x.

If 4 friends each went to the movies, and the tickets cost $52, that means

x + x + x + x = 52

Simplifying this, we get

4x = 52

If you want to solve for the cost of each ticket, divide both sides by 4.

After doing this, we get

x = $13

I hope this helps!

the answer to this question is $250

A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.

This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.

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Using the given digits only once , the four 2 digit prime numbers are 23 , 41 , 59 , 67  and the the sum of the 4 prime numbers is 190 .

Prime Numbers can be defined as numbers that is greater than 1 and whose only factors are 1 and itself .

For Example : 2 is prime number , 11 is a prime number .

In the question ,

9 digits are given as 1, 2, 3, 4, 5, 6, 7, and 9  

we have to form 4 two - digit prime numbers , using each digit only once ,

So , the prime numbers using the given digits using the digits only once is

(i) 23

(ii) 41

(iii) 59

(iv) 67

and the sum of the 4 prime numbers is = 23 + 41 + 59 + 67

= 190

Therefore , the 4 prime numbers are 23 , 41 , 59 , 67 and their sum is 190 .

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Answer:

48

Step-by-step explanation:

4x1/3=4/3

4/3x(-8)=-32/3

-32/3x9=-288/3

-288/3x(-1/2)=288/6

288/6=48

Answer:

48

Step-by-step explanation:

4 x 1/3 x -8 x 9 x -1/2 = 4 x 1 x -4 x 3 x -1 = -16 x 3 x-1 = -48 x -1 = 48

The length of each side of an equilateral triangle is equal to the square root of 3 times the length of its height. So, the length of each side of the sign is about 12.1 feet.

Here's the solution:

Let x be the length of each side of the triangle.

Since the triangle is equilateral, each angle is 60 degrees.

We can use the sine function to find the height of the triangle:

sin(60 degrees) = x/h

The sine of 60 degrees is sqrt(3)/2, so we have:

sqrt(3)/2 = x/h

h = x * sqrt(3)/2

We are given that h = 14 feet, so we can solve for x:

x = h * 2 / sqrt(3)

x = 14 feet * 2 / sqrt(3)

x = 12.1 feet (rounded to the nearest tenth)

(a) The pdf of Y(t) is normally distributed with mean µt and variance t.

(b) The joint pdf of Y(t) and Y(t+s) is a bivariate normal distribution with means µt and µ(t+s), variances t and t+s, and correlation coefficient ρ = t/(t+s).

(a) To find the pdf of Y(t), we need to consider the properties of the Wiener process and the addition of the deterministic term µt. The Wiener process, X(t), follows a standard normal distribution with mean 0 and variance t. The addition of µt shifts the mean of X(t) to µt. Therefore, Y(t) follows a normal distribution with mean µt and variance t. Hence, the pdf of Y(t) is given by the normal distribution formula:

fY(t)(y) = (1/√(2πt)) * exp(-(y - µt)^2 / (2t))

(b) To find the joint pdf of Y(t) and Y(t+s), we need to consider the properties of the joint distribution of two normal random variables. Since Y(t) and Y(t+s) are both normally distributed with means µt and µ(t+s), variances t and t+s, respectively, and assuming their correlation coefficient is ρ, the joint pdf is given by the bivariate normal distribution formula:

fY(t),Y(t+s)(y1, y2) = (1/(2π√(t(t+s)(1 - ρ^2)))) * exp(-Q/2)

where Q is defined as:

Q = (y1 - µt)^2 / t + (y2 - µ(t+s))^2 / (t + s) - 2ρ(y1 - µt)(y2 - µ(t+s)) / √(t(t+s))

The pdf of Y(t) is normally distributed with mean µt and variance t. The joint pdf of Y(t) and Y(t+s) follows a bivariate normal distribution with means µt and µ(t+s), variances t and t+s, and correlation coefficient ρ = t/(t+s). These formulas allow us to analyze the probability distributions of Y(t) and the joint distribution of Y(t) and Y(t+s) in the given context.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given polynomials

One of the zeroes is:

STEP 2: Use synthetic division to divide the polynomials

Write the coefficients of the numerator

The last carry-down value is the remainder and it is 0 (zero)

Since the remainder is a zero, hence, x=-5 is a zero

Step 3: Answer question b

To get the factors, the remainder of the division in step 2 is given as:

The remaining factors of f(x) is:

STEP 4: Answer Question c

The complete factorization will give:

STEP 5: Answer question d

The zeroes of f(x) will be:

zeroes are: -5,4,-5

STEP 6: Plot the graph

Answer:

100 pieces maybe?

Step-by-step explanation:

Answer:

2341

Step-by-step explanation:

(π²/4) = 2.465

(π²/8) = 1.234

√2 = 1.414

√3 = 1.732

1. Least - Greatest

(π²/8), √2, √3, (π²/4)

2. Write as quantities

2, 3, 4, 1

3. Answer

2341

I hope this helps!

Answer:

47

Step-by-step explanation:

Let us assume his son be x

So, the oliver age is x + 33

Now eight years ago, oliver age is 5 more than thrice his son present age

x - 8 = 5 + 3x

So,

33 + x = 5 + 3x

2x =28

x=14

o = 33+14 = 47

The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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Answer:

1.) 160

2.) 40

3.) 200

Step-by-step explanation:

Hoped this helped! =)

Answer:

1/8

Step-by-step explanation:

So if the entire recipe makes 7 loaves and calls for 7/8 of a cup, you would need to split the 7/8 cups flour into 7. 7/8 ÷ 7=1/8.

Option A: 1/8 of a cup

Answer:

(-5,-8)

Step-by-step explanation:

I hope this helps!!! XD

Answer:

A) no

B) yes

C) no

D) yes

E) yes

Step-by-step explanation:

The media theory that can be used to explain the phenomenon of mass media conglomerates reinforcing dominant cultural agendas without accounting for the diversity of lived experiences of ethnic/racial groups in their programming is the cultural hegemony theory.

Cultural hegemony, a concept introduced by Italian Marxist thinker Antonio Gramsci, refers to the dominance of a particular cultural group over others through the imposition of its beliefs, values, and norms as the normative standard. In the context of mass media, this theory suggests that dominant cultural groups, often associated with the ruling elite, shape and control the content that is produced and disseminated to the public.

These media conglomerates, which have significant influence and control over mainstream media platforms, tend to perpetuate and reinforce the ideologies, perspectives, and narratives that align with the interests and agendas of those in power. As a result, the diverse lived experiences and perspectives of ethnic/racial groups, which may challenge or deviate from the dominant cultural norms, are often marginalized, ignored, or misrepresented in mainstream media programming. This perpetuates the exclusion and underrepresentation of these groups, contributing to the reinforcement of dominant cultural agendas.

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To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

?

Step-by-step explanation: