Subtract 7 from each side.Divide each side by 3.Add 7 to each side.Multiply each side by 3.

Answer: 84

Step-by-step explanation:

4 x 21 is 84 a fraction can be simplified and be a whole number so if 84 divided by 4 it will be 21 if you want to write it as a fraction it will be 21/1 which is equal to 21

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Answer:

Step-by-step explanation:

Product means multiply.

-300

Answer:

The 99% confidence interval of the  standard deviation of the pulse rates of men is  

       \([ 7.949 \  \ , \  14.387 ]\)

Step-by-step explanation:

From the question we are told that

  The  sample size is  n  =  40

  The mean is  \(\= x = 67.3 \ beats \ per \ minute\)

  The standard deviation is  \(s = 10.3 \ beats \ per \ minute\)

Generally the degree of freedom is mathematically represented as

     \(df = n- 1\)

=>  \(df = 40- 1\)

=>  \(df = 39\)

From the question we are told the confidence level is  99% , hence the level of significance is    

      \(\alpha = (100 - 99 ) \%\)

=>   \(\alpha = 0.01\)

Generally from the chi distribution table the critical value  of   at a degree of freedom of is  

   \(X^2 _{\frac{\alpha }{2} , 39} =  65.476\)

Generally from the chi distribution table the critical value  of   at a degree of freedom of is  

   \(X^2 _{1- \frac{\alpha }{2} , 39} =  19.996\)

Generally the 99% confidence interval of the standard deviation of the pulse rates of men is mathematically represented as

  \(s \sqrt{\frac{n- 1}{X^2_{1- \frac{\alpha }{2} , n-1} } }\  \ , \ s \sqrt{\frac{n- 1}{X^2_{\frac{\alpha }{2} , n-1} } }\)

=>  \(10.3 \sqrt{\frac{40- 1}{65.476} }\  \ , \ 10.3 \sqrt{\frac{40- 1}{19.996} }\)

=>  \([ 7.949 \  \ , \  14.387 ]\)

Given:

The coordinates of the point K, (x1, y1)= (-8, 2).

The coordinates of the point L, (x2, y2)=(10, 2).

The distance between points K and L can be calculated as,

Therefore, the distance between point K and L is 18 units.

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

5km

Step-by-step explanation:

A - her office

E - her home

AB = 1km; BC = CE = 4km

AE - the shortest disctance between her office and home.

ADE - right triangle, where AD = 4km, ED = 3 (EC - CD) =>

According to the Pythagorean theorem , we make up the equation:

AE = √ED^2 + AD^2 = √25 = 5km

Answer:

C

Step-by-step explanation:

Plugged into calculator

Vertical asymptotes: x=-2

Horizontal asymptotes: y=0

No oblique asymptotes

The factorization of the quadratic expression 25x² - 4 gives us (x + 6)(x - 7) where; x = -6 or 7

We are given the quadratic equation as;

x² - x - 42

Now, this quadratic equation can be written as;

x² + 6x - 7x  - 42

We can group this using algebra properties to get;

(x² + 6x) - (7x + 42)

Collecting like terms gives us;

x(x + 6) - 7(x + 6)

Thus, the factorization is;

(x + 6)(x - 7)

Thus, the values of x would be;

x + 6 = 0

x = -6

x - 7 = 0

x = 7

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Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

Answer:

10 milligrams

Step-by-step explanation:

Answer:

1 milligrams

milligrams

Answer: yes true or false

Step-by-step explanation: 7 true, 8 true, and 9 false

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

Length of equator = 40212.39 km

Step-by-step explanation:

Hope this helps! Please mark brainliest for you can! :)

Answer:

  40,000 km

Step-by-step explanation:

The circumference is given by the formula ...

  C = 2πr

For the given values of π and radius, the circumference is ...

  C = 2·3.14·6400 km = 40,192 km

Rounded to the nearest 10,000, the length of the equator is 40,000 km.

_____

Additional comment

The original definition of the meter was 1/10,000,000 of the distance from the north pole to the equator, through Paris. Essentially, the polar circumference of the earth was defined as about 40,000 km. The polar distance in the southern hemisphere will differ from that in the northern hemisphere, and apparently, the chosen longitude also makes a difference. All of these are different from the equatorial circumference. That definition has long been superseded.

Answer:

horizontal line

Step-by-step explanation:

The slope formula is m=(y2-y1)/(x2-x1)

-6+6/-4-1

y2-y1 = 0

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)

from the graphs n f (x) and g( x) are 1 and 5 .

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h = hours till they're 58 miles apart

Check the picture below.

so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.

Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}\)

The percentage population increase from 2001 to 2011 is 50%.

To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.

The formula to calculate the percentage increase is:

Percentage Increase = ((New Value - Old Value) / Old Value) * 100

Plugging in the values:

Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%

Therefore, the percentage population increase from 2001 to 2011 is 50%.

Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.

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The standard form of the equation is (x - 1)² - (y - 1)² + (z + 2)²  = 3

The equation is given as:

x² -y² + z² - 2x + 2y + 4z + 1 = 0

Subtract 1 from both sides

x² -y² + z² - 2x + 2y + 4z = -1

Rewrite the equation as:

x² - 2x -y² + 2y + z² + 4z = -1

Next, we complete the square on each variable term.

Using a graphing calculator, we have:

(x - 1)² - (y - 1)² + (z + 2)²  = -1 + 1 + 4 - 1

Evaluate the sum and difference

(x - 1)² - (y - 1)² + (z + 2)²  = 3

x^2 - 2x + 2 - (y^2 - 2y + 2) + z^2 + 4z + 4 = 3

Hence, the standard form of the equation is (x - 1)² - (y - 1)² + (z + 2)²  = 3

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The amount he would pay is $46.40.

Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.

The amount paid = list price of the first shirt + [list price of the second shirt x ( 1 - percentage discount)]

$29 + [$29 x (1 - 0.4)]

$29 + ($29 x 0.6) = $46.40

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Answer:

Profit when producing 70 items = $3,050

Profit when producing 80 items = $1,350

Step-by-step explanation:

To find the profit when producing a certain number of items, we need to subtract the cost from the revenue:

Profit = Revenue - Cost

Let's calculate the profit for producing 70 items:

Revenue when producing 70 items:

R(70) = -0.5(70-120)^2 + 7,200 = $6,800

Cost of producing 70 items:

C(70) = 50(70) + 250 = $3,750

Profit when producing 70 items:

Profit = Revenue - Cost = $6,800 - $3,750 = $3,050

Similarly, let's calculate the profit for producing 80 items:

Revenue when producing 80 items:

R(80) = -0.5(80-120)^2 + 7,200 = $5,600

Cost of producing 80 items:

C(80) = 50(80) + 250 = $4,250

Profit when producing 80 items:

Profit = Revenue - Cost = $5,600 - $4,250 = $1,350

We can see that the profit is less when producing 10 more units because the cost of producing those additional units exceeds the revenue generated from selling them. In other words, the marginal cost (the cost of producing one additional unit) is greater than the marginal revenue (the revenue generated from selling one additional unit) beyond a certain point.

This is an example of the law of diminishing returns, which states that as we increase the quantity of inputs while keeping other inputs constant, the marginal product (output per unit of input) eventually decreases.

Hope this helps!

Answer: 28 cm

Step-by-step explanation:

x - the length of the shorter piece

2x - the length of the longer piece

Together they are 42 cm long.

Compose te equation:

2x + x = 42

3x = 42

x = 14 cm

The shorter piece is 14 cm, the longer piece is twice longer, 2x, or 2( 14 ).

Two times longer than 14 is 28. The longer piece is 28 cm.

It could be assembled a rectangular prism

and

Answer:

10:4

35:14

55:22

Answer:

D) 3 i

    \(\frac{Z_{1} }{Z_{2} } = 3 i\)

Step-by-step explanation:

Step(i):-

Given  Z₁ = 9 Cis ( 5π/6) = 9 ( Cos (5π/6) +i Sin (5π/6))

          Z₂ = 3 Cis ( π/3) = 3 ( Cos (π/3) +i Sin (π/3))

  Now  Cos (5π/6) = cos (150°) = cos(90°+60°)   = -sin 60 = \(\frac{-\sqrt{3} }{2}\)

           Sin (5π/6) = Sin (150°) = Sin(90°+60°)   = Cos 60 = \(\frac{1 }{2}\)

    Z₁  = 9 ( Cos (5π/6) +i Sin (5π/6))

          \(= 9(\frac{-\sqrt{3} }{2} + i\frac{1}{2} )\)

   Z₂ = 3 ( Cos (π/3) +i Sin (π/3))    

       \(= 3(\frac{1 }{2} + i\frac{\sqrt{3} }{2} )\)

Step(ii):-

\(\frac{Z_{1} }{Z_{2} } = \frac{ 9(\frac{-\sqrt{3} }{2} + i\frac{1}{2} )}{3(\frac{1 }{2} + i\frac{\sqrt{3} }{2} )}\)

\(\frac{Z_{1} }{Z_{2} } =\frac{3 (-\sqrt{3}+i) }{1+i\sqrt{3}) }\)

Rationalize with 1 - i √3 and we get

\(\frac{Z_{1} }{Z_{2} } =\frac{3 (-\sqrt{3}+i) }{1+i\sqrt{3}) } X\frac{1-i\sqrt{3} }{1-i\sqrt{3} }\)

on simplification , we will use formulas

i² = -1 and    (a+b)(a-b) = a² - b²

\(\frac{Z_{1} }{Z_{2} } =\frac{3(-\sqrt{3} + 3 i + i +\sqrt{3} )}{1 - i^{2} (\sqrt{3} )}\)

\(\frac{Z_{1} }{Z_{2} } =\frac{3(4 i )}{1 - i^{2} (\sqrt{3} )^{2} }\)

\(\frac{Z_{1} }{Z_{2} } =\frac{3(4 i )}{1 - i^{2} (\sqrt{3} )^{2} } = \frac{3(4 i)}{1-(-3)}= \frac{3(4 i)}{4}\)

\(\frac{Z_{1} }{Z_{2} } = 3 i\)

Final answer:-

\(\frac{Z_{1} }{Z_{2} } = 3 i\)

Answer: D. 3i

Step-by-step explanation: I got this right on Edmentum.

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

Answer:

As  \({x \to \infty}, \,\,{f(x) \to -\infty\)  and as  \({x \to -\infty}, \,\,{f(x) \to \infty\)

Step-by-step explanation:

Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards  minus infinity).

As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)

Answer:

The GCF (Greatest Common Factor) of two numbers is the largest number that divides both of them. In this case, the GCF of 36 and 60 is 12.

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A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.

A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.

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Answer:

The length of CD is 6

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

Answer:

6 units.

Step-by-step explanation:

Got it correct on khan academy:

Answer:

\( \frac{60}{7} \)

Based on the concept of fraction, the 8 4/7 as an improper fraction is written as 60/7

Improper fraction is a mathematical term that is used to describe the type of fraction where the numerator is greater than or equal to the denominator.

For example, 6/2 and 9/5, are improper fractions.

In this case, to convert 8 4/7 into an improper fraction we need to multiply the whole number (8) by the denominator of the fraction (7) and then add the numerator (4).

8 * 7 = 56

56 + 4 = 60

Therefore, in this case, it is concluded that 8 4/7 as an improper fraction is 60/7.

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