Which are the foci of the hyperbola represented by 5y2 – 4x2 – 80 = 0?

(–6, 0) and (6, 0)
(0, –6) and (0, 6)
(0, –5) and (0, 5)
(–5, 0) and (5, 0)

Answer:

C

Step-by-step explanation:

The correct statement is option C.

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, i = √-1 and both a and b are real numbers.

Since we know that

Complex number is of the form a+ib

Where,

a is real number belongs to real axis

And b is also a real number belongs to imaginary axis.

And the value of i = √-1

Thus,

The set of all numbers of the form a+bi, where a and b are any

real numbers and i equals √-1 is the correct statement.

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Answer:

The chain of the length 7 inches weighs 112 ounces.

Step-by-step explanation:

As we know there are 12 inches in a foot and 16 ounces in a pound

That is 1 foot = 12 inches.

and 1 pound = 16 ounces.

Given that the weight of the chain that is 1 foot long = 12 pounds

So weight of the chain per inch is = 12/12

which is equal to 1 pound

and according to the formula 1 pound = 16 ounces

So weight of the chain per inch is =  16 ounces

therefore weight of the chain that is 7 inch long = 7 × 16

that is 112 ounces.

The chain of the length 7 inches weighs 112 ounces.

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We can make 64 different equations using the power of ten.

The power of a number identifies how many times that particular number is multiplied by itself.

Here, let us assume that the different equations = x

Using a power of 10, we have 10x making a total of 640.

Divide both sides by 10

10x/10 = 640/10

x = 64

Therefore, we can conclude that we can make 64 different equations using the power of ten.

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The horizontal distance from the point where it was launched is 7.143.

We have given that,

The path of the marshmallow can be modeled by the quadratic y=−0.07x^2+x+2.2,

x represents the horizontal distance from the point it is launched, in feet.

Horizontal distance means the distance between two points measured at a zero percent slope.

(1) Put x = 7.143 in given equation

y= -0.07(7.143)^2+7.143+2.2

y= 2.2

y= 5.771

We have to determine the what is its horizontal distance from the point where it was launched.

The value of x is called horizontal distance.

Therefore the horizontal distance from the point where it was launched is 7.143.

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Notice that the difference in the absolute values of consecutive coefficients is constant:

|-7| - 1 = 6

13 - |-7| = 6

|-19| - 13 = 6

and so on. This means the coefficients in the given series

[tex]\displaystyle \sum_{i=1}^\infty c_i a^{i-1} = \sum_{i=1}^\infty |c_i| (-a)^{i-1} = 1 - 7a + 13a^2 - 19a^3 + \cdots[/tex]

occur in arithmetic progression; in particular, we have first value [tex]c_1 = 1[/tex] and for [tex]n>1[/tex], [tex]|c_i|=|c_{i-1}|+6[/tex]. Solving this recurrence, we end up with

[tex]|c_i| = |c_1| + 6(i-1) \implies |c_i| = 6i - 5[/tex]

So, the sum to [tex]n[/tex] terms of this series is

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \underbrace{\sum_{i=1}^n i (-a)^{i-1}}_{S'} - 5 \underbrace{\sum_{i=1}^n (-a)^{i-1}}_S[/tex]

The second sum [tex]S[/tex] is a standard geometric series, which is easy to compute:

[tex]S = 1 - a + a^2 - a^3 + \cdots + (-a)^{n-1}[/tex]

Multiply both sides by [tex]-a[/tex] :

[tex]-aS = -a + a^2 - a^3 + a^4 - \cdots + (-a)^n[/tex]

Subtract this from [tex]S[/tex] to eliminate the intermediate terms to end up with

[tex]S - (-aS) = 1 - (-a)^n \implies (1-(-a)) S = 1 - (-a)^n \implies S = \dfrac{1 - (-a)^n}{1 + a}[/tex]

The first sum [tex]S'[/tex] can be handled with simple algebraic manipulation.

[tex]S' = \displaystyle \sum_{i=1}^n i (-a)^{i-1}[/tex]

[tex]\displaystyle S' = \sum_{i=0}^{n-1} (i+1) (-a)^i[/tex]

[tex]\displaystyle S' = \sum_{i=0}^{n-1} i (-a)^i + \sum_{i=0}^{n-1} (-a)^i[/tex]

[tex]\displaystyle S' = \sum_{i=1}^{n-1} i (-a)^i + \sum_{i=1}^n (-a)^{i-1}[/tex]

[tex]\displaystyle S' = \sum_{i=1}^n i (-a)^i - n (-a)^n + S[/tex]

[tex]\displaystyle S' = -a \sum_{i=1}^n i (-a)^{i-1} - n (-a)^n + S[/tex]

[tex]\displaystyle S' = -a S' - n (-a)^n + \dfrac{1 - (-a)^n}{1 + a}[/tex]

[tex]\displaystyle (1 + a) S' = \dfrac{1 - (-a)^n - n (1 + a) (-a)^n}{1 + a}[/tex]

[tex]\displaystyle S' = \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2}[/tex]

Putting everything together, we have

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 S' - 5 S[/tex]

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2} - 5 \dfrac{1 - (-a)^n}{1 + a}[/tex]

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} =\boxed{\dfrac{1 - 5a - (6n+1) (-a)^n + (6n-5) (-a)^{n+1}}{(1+a)^2}}[/tex]

The question is asking you to understand that a population which is raised by a common ratio over a certain time period follows an exponential pattern. See:

After 1 hour, the population is 3*10

After 2 hours, the population is 3*3*10

After 3 hours, the population is 3*3*3*10

.....

This can be generalised as a function of t, the time in hours:

f(t) = (3^t) * 10

Since the function determines the population at a given time, it is more prudent to replace f(t) with P, the population after time t:

P = (3^t) * 10

Since 20 minutes is equal to (1/3) hours, t can be substituted for (1/3) in order to calculate the population size after 20 minutes:

P = (3^(1/3)) * 10 = 14.4224957031 ≈ 14

Therefore the population after 20 minutes is 14.

Answer:

yes

Step-by-step explanation:

I'll use the method of transformations.

If [tex]f_X(x)[/tex] denotes the PDF of [tex]X[/tex], and [tex]y=g(x)=x^3 \iff x=g^{-1}(y) = y^{1/3}[/tex], we have

[tex]f_Y(y) = f_X\left(g^{-1}(y)\right) \left|\dfrac{dg^{-1}}{dy}\right|[/tex]

[tex]\dfrac{dg^{-1}}{dy} = \dfrac13 y^{-2/3}[/tex]

[tex]\implies f_Y(y) = f_X\left(y^{1/3}\right) \left|\dfrac13 y^{-2/3}\right| = \boxed{\begin{cases} \dfrac53 y^{2/3} & \text{if } 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}}[/tex]

The linear equation that satisfy the data in the table is: A. y = −4x − 4.

Given the table attached below, find the slope (m) = change in y / change in x using two pairs of values, say, (-1, 0) and (0, -4):

Slope (m) = (-4 - 0)/(0 - (-1)) = -4/1 = -4

Find the y-intercept (b), which is the value of y when x = 0. From the table, when x = 0, y = -4.

b = -4.

Substitute m = -4 and b = -4 into y = mx + b

y = -4x + (-4)

y = -4x - 4

The equation that satisfy the data is: A. y = −4x − 4.

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Answer:

600/100*20=6*20=120

600-120=480$

The correct answer is option A which is the number of cars sold for the price range of $4000 to $4999 will be 15.

A histogram is a graph for the representation of the data on the plot of the rectangular boxes. It has the data sets on the horizontal and the vertical axes.

As we can see from the histogram data we will conclude that the price range of $4000 to $4999 is shown by the third block and this third block reaches the height of 15.

Therefore the correct answer is option A which is the number of cars sold in the price range of $4000 to $4999 will be 15.

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Answer:  The equation is   y = 4x+3

Slope = 4

y intercept = 3

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

Explanation:

Let's start off by finding the slope.

[tex]A = (x_1,y_1) = (0,3) \text{ and } B = (x_2,y_2) = (4,19)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{19 - 3}{4 - 0}\\\\m = \frac{16}{4}\\\\m = 4\\\\[/tex]

The slope is 4.

The y intercept is 3 because of the point (0,3)

We go from y = mx+b to y = 4x+3

m = slope

b = y intercept

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

Check:

Plug in x = 0 and we should get to y = 3

y = 4x+3

y = 4(0)+3

y = 0+3

y = 3

That works out. Now try x = 4. It should lead to y = 19

y = 4x+3

y = 4(4)+3

y = 16+3

y = 19

The answer is confirmed.

The solution to all the answers are given below.

The complete question includes

Grades on a standardized test are known to have a mean of 1,000 for students in the Delhi. 453

randomly selected Delhi students take the test, yielding sample mean of 1,013 and sample standard

deviation (s) of 108.

It is given by

Confidence Interval for 95% confidence Interval is given by

[tex]\rm Z = X \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]

(a) Construct a 95% confidence interval for the mean test score for Delhi students.

The confidence interval is given by

[tex]\rm 1,013 \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\rm 1,013 \pm 1.96 \dfrac{108}{\sqrt{453}}[/tex]

1013 ± 5.07

so the interval is  [1003.06,1022.94]

(b)Yes, since the null of no difference is rejected at the 5% significance level (interval excludes Delhi sample mean of 1,013)

(c) Another 503 Delhi students are randomly selected to take a 3-hour prep course and then give the test. Their average score is 1,019 with a standard deviation of 95.

The standard deviation now is

[tex]\rm \sqrt{\dfrac{95^2}{453} + \dfrac{108^2}{503}}[/tex]

= 6.61

The interval is given by

[tex](1,019-1,013) \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]

= [-7,+19]

(d) No, the interval includes 0, the null difference between the two populations

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Answer:

3.160

Step-by-step explanation:

You can solve for x using logarithm.

Rewrite in logarithm form

[tex]log_{6}4=2x\\\\x=\frac{log_64}{2}\\x=\frac{\frac{log4}{log6}}{2}\\x=\frac{log4}{log6} * \frac{1}{2}\\x=\frac{log4}{log6 * 2}\\x\approx0.386852807\\36^{6(0.386852807)-2} \approx3.160[/tex]

The inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

a(n) =  3n - 30

To find make subject n and solve

a(n) + 30 = 3n

[tex]\rm n = \dfrac{a(n) + 30}{3}[/tex]

Plug n = n(a) and a(n) = a

[tex]\rm n(a) = \dfrac{a + 30}{3}[/tex]

Thus, the inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.

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[tex]\angle P = \angle S \Rightarrow \angle S = 42 &^\circ\\\angle Q = \angle T \Rightarrow \angle S = 86 &^\circ\\\angle R = \angle U\\[/tex]

Sum of all angles in a triangle equals 180:

[tex]\angle R = 180 - (86 + 42) = 180 - 128 = 52[/tex]

Answer:

[tex]U = 52 &^ \circ[/tex]

Answer:

the answer for this problem is A, big

The result follows from the fundamental theorem of calculus.

[tex]\displaystyle \int_a^b f(x) \, dx = F(b) - F(a) = 2022 - 10 = \boxed{2012}[/tex]

Answer:

it's 1,1 is the correct ans

Step-by-step explanation:

Because my teacher told its absolutely correct answer I got the same question in exam

Answer:

the answer should be the 2 one

Step-by-step explanation:

I got it right just had it.

Answer:

[tex](a) \: 3.1563 \times {10}^{6} = 31563 \times {10}^{6} \times {10}^{ - 4} = 31563 \times {10}^{6 - 4} = 31563 \times {10}^{2} = 3156300[/tex]

__o__o__

[tex](b) \: 5.65 \times {10}^{ - 4} = 565 \times {10}^{ - 4} \times {10}^{ - 2} = 565 \times {10}^{ - 4 - 2} = 565 \times {10}^{ - 6} = 0.000565[/tex]

The function in this graph is increasing in the interval   –2 ≤ x ≤ 3 , Option D is the right answer.

A function is a mathematical statement used to relate a dependent and an independent variable.

From the graph it can be seen that the graph is increasing in the interval

–2 ≤ x ≤ 3

The graph is said to be increasing when the value of y is getting more and more positive

As  –2 ≤ x ≤ 3 , y varies from -3 to +3

Therefore Option D is the right answer.

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Answer:

–2 ≤ x ≤ 3

Step-by-step explanation:

Answer:

radius ≈ 15.5

Step-by-step explanation:

the radius is RS

the angle between a tangent and the radius at the point of contact is 90°

then Δ RST is a right triangle

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

RS² + ST² = RT² ( substitute values )

RS² + 7² = 17²

RS² + 49 = 289 ( subtract 49 from both sides )

RS² = 240 ( take square root of both sides )

RS = [tex]\sqrt{240}[/tex] ≈ 15.5 ( to 1 dec. place )

Answer: 925

Step-by-step explanation:

This is an arithmetic series with first term 1 and last term 3(25)-2=73, with a total of 25 terms.

Using the sum of an arithmetic series formula, we get the sum is:

[tex]\frac{25}{2}(1+73)=\boxed{925}[/tex]

Only Set B  is a partition of set N of natural numbers .

Numbers starting from 1 to infinity comes under Natural Numbers.

It is asked in the question that to determine whether or not each of the following is a partition of set N of natural numbers

A  ) {{n | n > 5}, {n | n < 5}]

It is not a set of natural numbers as it does not include 5.

B  )  [{n | n ≥ 6}, {1, 3,5} , {2, 4}]

{1,3,5} {2,4}and {n|n≥6} include all the natural numbers

Therefore , it forms a partition of N.

C ) {{n | n^2 > 11}, {n | n^2 < 11}

Every natural number n must satisfy either n^2 > 11 or n^2 < 11

This cannot be possible , therefore it is not the partition of Natural Numbers.

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The  values of x and y would make the following expression represent a real number is 4 and -5 respectively

The standard form of writing a complex number is given asl

z= x + iy

where

x is the real part

y is the imaginary part

Given the expression below;

(4 +5i)(x + yi)

Expand

4x + 4yi + 5ix + 5y(-1)

4x + 4yi + 5ix - 5y

Hence the  values of x and y would make the following expression represent a real number is 4 and -5 respectively

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Answer:

According to the given function, the value of h(-1) is -1, h(-0.5) is 0 and h(1) is 1.

Step-by-step explanation:

The given function says that:

If the range of the values of x is x∈(-2,-1], then the value of the function is -1.

If the range of the values of x is x∈(-1,0], then the value of the function is 0.

If the range of the values of x is x∈(0,1], then the value of the function is 1.

If the range of the values of x is x∈(1,2], then the value of the function is 2.

In the first case, we have x = -1. This satisfies the first condition. So accordingly, the value that the function will give is -1.

In the second case, we have x = -0.5. This satisfies the second condition. So accordingly, the value that the function will give is 0.

In the third case, we have x = 1. This satisfies the third condition. So accordingly, the value that the function will give is 1.

So, h(-1) = -1, h(-0.5) = 0 and h(1) = 1.

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Answer:

It appears to already be solved. What do you need help with?

Step-by-step explanation: