There are 18 packets of sweets and 12 boxes of sweets in a carton.
The mean number of sweets in all the 30 packets and boxes is 14
The mean number of sweets in the 18 packets is 10
Work out the mean number of sweets in the boxes.

Answer:

\(\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}\)

Step-by-step explanation:

Given

The above table

Required

The discrete probability distribution

The probability of each is calculated as:

\(Pr = \frac{Frequency}{Total}\)

Where:

\(Total = 2140+ 2853 + 4734 + 4880 + 10715\)

\(Total = 25322\)

So, we have:

\(P(1) = \frac{2140}{25322} = 0.0845\)

\(P(2) = \frac{2853}{25322} = 0.1127\)

\(P(3) = \frac{4734}{25322} = 0.1870\)

\(P(4) = \frac{4880}{25322} = 0.1927\)

\(P(5) = \frac{10715}{25322} = 0.4231\)

So, the discrete probability distribution is:

\(\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}\)

Answer:

I tried figuring out this problem but it is a tad confusing. sorry :/

Step-by-step explanation:

Answer:

121

Step-by-step explanation:

firstly you arrange the numbers in ascending order the number in the middle is considered to be the median

The gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.

The space-time continuum is subject to gravitational waves, which move at the speed of light. They are caused by the acceleration of large objects that distort space-time around them, such as neutron stars or black holes.

The bending of space-time brought on by the existence of mass and energy is what Einstein's theory of general relativity refers to as gravity rather than a force.

The radius of the sphere can be determined using the formula:

R = Distance / Time

For 1.3 billion light years we have:

R = Distance / Time = 1.239 x 10²⁵ meters

Substituting the value in the volume:

V = (4/3) x π x R³ = 3.244 x 10⁷⁴ cubic light-years (approx)

Hence, the gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.

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Answer:

49%

Step-by-step explanation:

84*100=8400

8400/171=49

The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

Step-by-step explanation:

1) 7/23 + 11/23 + 9/23

7+11+9/23

27/23

= 1 4/23

2) 2 5/7 + 9 4/7

11 9/7

= 11.12

3) 9/20 + 3/5

9+12/20

21/20

= 1 1/20 or 1.05

Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Answer:

Step-by-step explanation:

148 people

Answer:

1st Diagram = 72 square units

2nd diagram = 36 square units

heyy 3rd diagram isn't visible properly..please retake the picture.. ;)

Answer:

9-6r

Step-by-step explanation:

9(1−r)+3r

Use the distributive property to multiply 9 by 1−r.

9−9r+3r

Combine −9r and 3r to get −6r.

Answer: 9−6r

Answer:

-6r + 9

Step-by-step explanation:

9( 1 - r ) + 3r

9 - 9r + 3r

9 - 6r

So, the answer is -6r + 9

If the equation be \($\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$\) then the value is 1.22222

The term "numerical evidence" describes information that is expressed in a numerical manner, such as numbers, quantities, or statistical data. It is thought to be objective and quantifiable, and it is used to support a claim or argument.

The quantity of sales made during a specific business quarter is an example of numerical data. Simply put, if the response includes a number, the data is quantitative (numerical).

Let the equation be \($\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$\)

Simplifying the above equation, we get

\($\frac{x^2-x-30}{x^2-3 x-18}= \frac{x+5}{x+3}$\)

\($=\lim _{x \rightarrow 6}\left(\frac{x+5}{x+3}\right)$$\)

Plug in the value x = 6

= (6 + 5)/(6 + 3)

= 11/9 = 1.22222

Therefore, the equation of \($\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$\) be 1.22222.

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Answer:

1.19$ each

Step-by-step explanation:

10.71/9= 1.19

The length of the curve (and thus the total distance traveled by the particle along the curve) is

\(\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt\)

We have

x(t) = 3 sin²(t )   ==>   x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )

y(t) = 3 cos²(t )   ==>   y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )

Then

√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|

and the arc length is

\(\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt\)

Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.

Now,

• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)

• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)

so we split up the integral as

\(\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)\)

which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.

Answer:

A and C

Step-by-step explanation:

Answer:

3. B

4. B

5. C

Step-by-step explanation:

The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically

Given the following expression

23 - √81

The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.

We know that the square root of 81 is 9, so we can simplify the expression to:

23 - √81 = 23 - 9

Evaluate the difference

23 - √81 = 14

Therefore, the value of the expression is 14.

In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.

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a) The customs duty on the car would be $1,350,000.

b) The imported price of the bus would be $858,000.

(a) To calculate the customs duty on a car with an imported price of $3,000,000, we can multiply the imported price by the duty rate of 45%:

Customs duty = $3,000,000 * 0.45 = $1,350,000.

(b) To calculate the imported price of a bus if the amount paid, including customs duty, is $1,560,000, we need to determine the portion of the total amount that represents the customs duty. Since the customs duty is 45% of the imported price, we can set up the following equation:

Customs duty = $1,560,000 * 0.45.

Solving for the customs duty:

Customs duty = $702,000.

Now, we can subtract the customs duty from the total amount to find the imported price:

Imported price = $1,560,000 - $702,000 = $858,000.

In summary, the customs duty on a car with an imported price of $3,000,000 would be $1,350,000. On the other hand, if the amount paid for a bus, including customs duty, is $1,560,000, the imported price of the bus would be $858,000.

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Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

Answer:

q=8/3

Step-by-step explanation:

First, add 5/6 to both sides to get rid of -5/6 to get q=16/6 then simplify to q=8/3.

Answer:

\(q=2\frac{2}{3}\)

Step-by-step explanation:

The given equation consists of a fraction and a mixed number.

First, convert the mixed number into an improper fraction by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

\(q-\dfrac{5}{6}=1 \frac{5}{6}\)

\(q-\dfrac{5}{6}=\dfrac{1 \cdot 6+5}{6}\)

\(q-\dfrac{5}{6}=\dfrac{11}{6}\)

Now, add 5/6 to both sides of the equation to isolate q:

\(q-\dfrac{5}{6}+\dfrac{5}{6}=\dfrac{11}{6}+\dfrac{5}{6}\)

\(q=\dfrac{11}{6}+\dfrac{5}{6}\)

As the fractions have the same denominator, we can carry out the addition by simply adding the numerators:

\(q=\dfrac{11+5}{6}\)

\(q=\dfrac{16}{6}\)

Reduce the improper fraction to its simplest form by dividing the numerator and denominator by the greatest common factor (GCF).  

The GCF of 16 and 6 is 2, therefore:

\(q=\dfrac{16\div 2}{6 \div 2}\)

\(q=\dfrac{8}{3}\)

Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:

\(q=2 \; \textsf{remainder}\;2\)

The mixed number answer is the whole number and the remainder divided by the denominator:

\(q=2\frac{2}{3}\)

Answer:

4%

Step-by-step explanation:

Formula for volume of a right rectangular prism is;

V = lwh

Where;

l is length

w is width

h is height

We are given l = 367; w = 24; h = 19

Thus;

Volume is;

V_full = 367 × 24 × 19

V_full = 167352 in³

We are told that Alex filled the aquarium with 6039 in³ of water.

Thus, percentage of the aquarium filled with water is;

(6039/167352) × 100% = 3.61%

Approximating to nearest percent gives; 4%

The length of the rectangle is 10.5 units.

What is perimeter?

Perimeter is the distance of a two-dimensional shape. It is equal to the sum of the lengths of all the sides of the shape. The perimeter is measured in units, such as centimeters, meters, feet, or inches, depending on the unit of measurement used for the dimensions of the shape.

The perimeter of a rectangle is given by the formula:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we know that the perimeter is 34 units, and the width is 6.5 units. So we can substitute these values into the formula and solve for the length:

34 = 2l + 2(6.5)

Simplifying, we get:

34 = 2l + 13

Subtracting 13 from both sides, we get:

21 = 2l

Dividing both sides by 2, we get:

l = 10.5

So the equation to determine the length of the rectangle is:

2l + 2w = P

Substituting the known values, we get:

2l + 2(6.5) = 34

Simplifying and solving for l, we get:

2l + 13 = 34

2l = 21

l = 10.5

Therefore, the length of the rectangle is 10.5 units.

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Complete question: The perimeter of a rectangle is 34 units, its width is 6.5 units. Write an equation to determine the length (l) of the rectangle.