Answers for number 32 and 31

Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.

Now,

it's vertex is given, I.e (7 , -5)

so, length of semi transverse axis will be equal to distance of vertex from centre, i.e

Now, it's focus can be represented as ;

[tex]\qquad \sf  \dashrightarrow \: (3 + ae, - 5 )[/tex]

so,

and we know, a = 4

[tex]\qquad \sf  \dashrightarrow \: 4e + 3 = 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4e = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: e = \cfrac{3}{2} [/tex]

Now, let's find the measure of semi - conjugate axis (b)

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = {a}^{2} ( {e}^{2} - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{9}{4} - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{9 - 4}{4} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{5}{4} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \sqrt{20} [/tex]

So, it's time to write the equation of hyperbola, as we already have the values of a and b ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {(x - h)}^{2} }{ {a}^{2} } - \cfrac{( {y - k)}^{2} }{ {b}^{2} } = 1[/tex]

[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ ({x-3)}^{2} }{ {16}^{} } - \dfrac{ {(y+5)}^{2} }{ { {20} }^{} } = 1[/tex]

Hello and Good Morning/Afternoon:

Let's solve this problem step-by-step:

Let's find the format of the standard form of hyperbole:

 [tex]\hookrightarrow \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} =1[/tex]

Let's find the value of a, b:

             [tex]a = \sqrt{(7-3)^2+(-5--5)^2} =\sqrt{16} =4[/tex]

           ⇒value of c: distance between focus (9, -5) and center (3, -5)

                  [tex]c = \sqrt{(3-9)^2+(-5--5)^2}=\sqrt{36} =6[/tex]

            ⇒ therefore:

                  [tex]b = \sqrt{c^2-a^2} =\sqrt{6^2-4^2}=\sqrt{20}[/tex]

Let's plug everything into our standard form of the equation:

   [tex]\frac{(x-3)^2}{4^2} -\frac{(y--5)^2}{(\sqrt{20})^2 } =1\\\frac{(x-3)^2}{16} -\frac{(y+5)^2}{20 } =1[/tex] <== Answer

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Answer: tan 1 radians = 1.557, tan 1 degrees = 0.017

The correct answer which represents the quotient of 20√z⁶ ÷ √16z⁷ in simplest radical form is; (5√z)/z.

The quotient given can be evaluated by means of the laws of indices as follows;

20√z⁶ ÷ √16z⁷

= 20√z⁶ ÷ 4√z⁷

= 5 √(z⁶/z⁷)

= 5 √z^(-1)

= 5 × z^(-1/2)

= 5/√z

Hence, by rationalisation; we have;

= (5√z)/z.

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Answer: 2 radians

Step-by-step explanation: You welcome

The pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5

The complete question is added as an attachment

Function 1

f(x) = 5x - 11 and g(x) = (x + 11)/5

Represent 5x - 11 with y in f(x) = 5x - 11

y = 5x - 11

Swap x and y

x = 5y - 11

Add 11 to both sides

x + 11 = 5y

Divide by 5

y = (x + 11)/5

Express as a function

g(x) = (x + 11)/5

From the question, we have:

f(x) = 5x - 11 and g(x) = (x + 11)/5

This means that the function g(x) is an inverse of the function f(x)

Hence, the pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5

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Answer:

100, 25, 50

Step-by-step explanation:

[tex]700: \frac{700}{700} \times 100=100 \\ \\ 175: \frac{175}{700} \times 100=25 \\ \\ 350: \frac{350}{700} \times 100=50[/tex]

The service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

a. Service charge rate

Service charge rate=Budgeted cost/ Budgeted activity base quantity

Help desks:

Service charge rate=$160,000/3,200 calls

Service charge rate=$50 per call

Network center:

Service charge rate=$735,000/9,800 devices

Service charge rate=$75 per device monitored

Electronic mail:

Service charge rate=$100,000/10,000 accounts

Service charge rate=$10 per user or per e-mail account

Local voice support:

Service charge rate=$124,600/8,900 phone extensions

Service charge rate=$14 per phone extension

b.  Help desk charge

Help desk charge =(Number of employees times × Percentage of office employees× Percentage with a computer ×Number of calls)× Service charge rate

Help desk charge:

(5,200 employee×25%×96%×1.5)× $50 per call

=$93,600

Network center charge:

[(5,200 employee×25%×96%)+ 600]× $75 per device

=$138,600

Electronic mail:

(5,200 employee×25%×96%×100)×$10 per user or per e-mail account

=$12,480

Local voice support:

(5,200 employee×25%)× $14 per phone extension

=$18,200

Therefore the service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

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Answer: for number 3, x= 6

Step-by-step explanation:

Answer:

15 days

Step-by-step explanation:

5 workers times 12 days is 60 days per worker which gets reduced based on how many workers there are. 60 divide by 4 workers now brings down to 15 days. 5 workers, 12 days. 10 workers 6 days etc.

The area of the small poster is 160 inches square

From the information given, we have the poster to take the form of a rectangle

The formula for area of a rectangle is;

Area = length × width

For the smaller poster created using a scale of factor 2/3

Length = 2/ 3 × 24

Length = 16 inches

Width = 2/ 3 × 15

Width = 10 inches

Substitute into the formula

Area = 16 × 10

Area = 160 inches square

Thus, the area of the small poster is 160 inches square

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Answer:

m∠RQS = 109°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore:

⇒ m∠RQS + m∠SQT = 180°

⇒ (15x + 4) + (10x + 1) = 180

⇒ 15x + 4 + 10x + 1 = 180

⇒ 15x + 10x + 4 + 1 = 180

⇒ 25x + 5 = 180

⇒ 25x + 5 - 5 = 180 - 5

⇒ 25x = 175

⇒ 25x ÷ 25 = 175 ÷ 25

⇒ x = 7

Now that we have found the value of x, substitute this into the expression for m∠RQS:

⇒ m∠RQS = 15(7) + 4

                  = 105 + 4

                  = 109°

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The striped rectangle has a total area of 69,375 cm².

To find the area of the striped rectangle we must carry out the following procedures.

Find the area of each segment of the rectangle, that is, what is the area of each of the 24 squares that make up the rectangle, for that we divide the 111cm² of the total area into 24.

According to the above, we infer that each square has an area of 4.625cm².

On the other hand, to find the area of the striped rectangle we must take into account that it is 5 squares long by 3 squares high, that is, its area is 15 squares.

Finally, each square has an area of 4.625cm², so to find the total area of the striped area we must multiply the area of each square by the number of squares.

15 × 4.625cm² = 69.375cm²

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It will take 6 weeks for the number of infected people to reach 1200

The function is given as:

y equals 15 times 2 to the power of t

Rewrite the function properly as follows

y = 15 * 2^t

When the population is 1200, the equation becomes

15 * 2^t = 1200

Divide both sides by 15

2^t = 80

Take the logarithm of both sides

t * log(2) = log(80)

Divide both sides by log(2)

t = 6.3

Approximate

t = 6

Hence, it will take 6 weeks for the number of infected people to reach 1200

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Answer: 425

Step-by-step explanation:

Think of this problem as 4% of a number equals 17

since in math, the word 'of' usually means multiplication, we can think of it that way.

Also, 4% = 0.04

[tex]x*0.04=17[/tex]

[tex]0.04x=17[/tex]

[tex]\frac{0.04x}{0.04} =\frac{17}{0.04}[/tex]

[tex]x=425[/tex]

According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.

According to the statement

we have given that the mean of 7 hours per day watching TV, and a standard deviation of 1.8 hours.

And we have to find that the At least how many hours of daily TV watching are necessary for a person to be eligible for the interview.

So, For this purpose,

The confidence interval is is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level.

Let us Assume x is the amount of hours that 5% of the persons exceeds.

Then P(z<(x-7)/1.8) = 0.95

From a standard normal table, we know that:

(x-7)/1.8 = 1.6449

x-7 = 2.9607

x = 9.9607

So, According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.

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Answer:

963 hours

Step-by-step explanation:

I subtracted 20 from the 981

The correct answer for the hours elaine spend attending classes is  [tex]817.5[/tex]  hours.

Given,

The time spent doing homework was 20% less than the time she spent attending class.

Assume the time Elaine spent attending class is "x" hours.

So, the time spent on these activities is 0.2 * x hours.

Now, the total time  spent attending class, doing homework, or  in extracurricular activities is 981 hours.

The equation representing the total time is:

[tex]x + 0.2x = 981[/tex]

solve for "x":

[tex]1.2x = 981[/tex]

[tex]x= \dfrac{981}{1.2}[/tex]

[tex]x= 817.5[/tex]

Elaine spent approximately [tex]817.5[/tex] hours attending class.

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Explanation:

The probability of getting heads is 1/2 because there's one side we want out of two sides total

The probability of getting less than 3 is 2/6 = 1/3 since we have two sides we want (rolling a "1" or a "2") out of six sides total.

Multiply the two mentioned fractions: 1/2 times 1/3 = 1/6

1/6 can be written as "one sixth", but I prefer the first format better since it's shorter.

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

If you are a visual learner, you can make a table with 2 rows and 6 columns, or vice versa (6 rows and 2 columns). The order doesn't matter.

The two rows represent the events Heads or Tails. The 6 columns show the different outcomes on the number cube. We have 6*2 = 12 different outcomes of rolling a die and flipping a coin.

Of those 12 outcomes, shade in 2 boxes to represent getting heads and either a "1" or "2". Refer to the diagram below.

We have 2 shaded rectangles out of 12 total to get 2/12 = 1/6

The visual representation of a table like this may help show why we multiplied the fractions 1/2 and 1/3 to get the answer. Hint: think of area = length*width.

The probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

A coin is flipped, and a number cube is rolled.

We need to find the probability of getting heads on the coin and a number less than 3 on the number cube.

The probability of getting heads when flipping a coin is 1/2

The probability of getting less than 3 is 2/6 = 1/3 since we have two sides

Now  the probability of getting heads on the coin and a number less than 3 on the number cube

The product of 1/2 and 1/3

1/2×1/3

1/6

Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.

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Answer:

39°

Step-by-step explanation:

Opposite angles of a parallelogram are congruent.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

" The opposite angles of a Parallelogram are always equal to one another "

[tex] \qquad \large \sf {Conclusion} : [/tex][tex] \qquad \large \sf {Conclusion} : [/tex]

Answer: Pr(4.19 ≤ X ≤ 4.81)

Step-by-step explanation:

First of all, let's calculate the mean;

x¯ = (4.3 + 5.1 + 3.9 + 4.5 + 4.4 + 4.9 + 5.0 + 4.7 + 4.1 + 4.6 + 4.4 + 4.3 + 4.8 + 4.4 + 4.2 + 4.5 + 4.4)/17

x¯ = 76.5/17

x¯ = 4.5

We are given standard deviation; s = 0.31

Now, z-value for a 68% Confidence interval is 1

Range in which the data falls is;

Range = x¯ ± zs

Range = 4.5 ± (1 × 0.31)

Range is;

Pr[(4.5 - 0.31) ≤ X ≤ (4.5 + 0.31)]

Pr(4.19 ≤ X ≤ 4.81)

Answer:

Pr (3.57 ≤ X ≤ 5.43)

Step-by-step explanation:

Took the quiz.

The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is $91,669

Share Price, P = 44.29

Premium on the acquisition, p = 20%

Therefore, effective share price for acquisition, P* = P x (1 + p) = 44.29 x (1 + 20%) = $ 53.15

Number of shares outstanding, N = 1,734 MM

Equity value, E = P* x N = 53 x 1,734

= $92,158.63 MM

Net Debt, D = - 496

Hence, the implied enterprise value:

= Equity value + net debt

= 92,158.63 + (- 496)

= $$91,669

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Step-by-step explanation:

=(7x)^2-(y)^2

=(7x+y) (7x-y)

Therefore, a^2-b^3

=(a+b) (a-b)

The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.

The definition of a prime number is a natural number larger than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime.

The only two components in prime numbers are 1 and the number itself.

Any whole number greater than one is a prime number.

It has exactly two factors—1 and the actual number.

There is just one 2-digit even prime number.

Every pair of prime numbers is always a co-prime.

The product of prime numbers can be used to represent any number.

Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960

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The time at which the break started is 10 : 30 am.

The first step is to convert the time between  10:00 a.m. - 11:15 a.m. to minutes.

The time  between  10:00 a.m. - 11:15 a.m. is 1 hour 15 minutes

In order to convert hours to minutes, multiply hour by 60

1 x 60 = 60 minutes

60 minutes +  15 minutes =  75 minutes

The second step is to subtract the time from the break from the duration of the golf lesson

75 minutes -  15 minutes = 60 minutes

The third step is to divide 60 minutes into equal halves by dividing 60 by 2

60 / 2 = 30 minutes

The last step is to add 30 minutes to the time the lesson started : 10 : 00 am + 30 minutes = 10 : 30 am

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Answer:

35,000 - 8000=27,000 altitude

Answer: Either Rohmbus or Parallelogram...

Step-by-step explanation: Your picture is a bit small, sry

Answer:

b

Step-by-step explanation:

b

The probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

Given that graduation rate is 95.2%.

We are required to find the probability that out of 12 selected candidates atleast 11 should be graduated.

Probability is basically the chance of happening an event among all the events possible. It cannot be negative. It lies between 0 and 1.

Probability=Number of items/ Total items.

Probability that atleast 11 will be graduated out of 12 selected candidates is as under:

It will be a binomial distribution.

So,

P(X>=11)=[tex]12C_{11}(0.925)^{11} (0.075)^{1} +12C_{12}(0.925)^{12} (0.075)^{0}[/tex]

=12*0.4241*0.075+1*0.3923

=0.3816+0.3923

=0.7739

Hence the probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

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If the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.

Given sample size of 1488, percentage of those polled own a home be 69% and confidence level be 99%.

We are required to find the approximate margin of error.

Margin of error is the difference between calculated values and real values.

n=1488

p=0.69

Margin of error=z*[tex]\sqrt{p(1-p)/n}[/tex]

Z score when confidence level is 99%=2.576.

Margin of error=2.576*[tex]\sqrt{0.69(1-0.69)/1488}[/tex]

=2.576*[tex]\sqrt{(0.69*0.31)/1488}[/tex]

=2.576*[tex]\sqrt{0.2139/1488}[/tex]

=2.576*[tex]\sqrt{0.0001437}[/tex]

=2.576*0.01198

=0.03088

Hence if the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.

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Answer:

0.031

Step-by-step explanation:

Plato/Edmentum

Answer:

[tex]\textsf{A)} \quad (x-40)^2=-100(y-16)[/tex]

B)  Focus = (40, -9)

    Directrix:  y = 41

    Axis of symmetry:  x = 40

Step-by-step explanation:

The x-intercepts of a parabola are the points at which the curve intercepts the x-axis (when y = 0).

The x-coordinate of the vertex of a parabola is halfway between the x-intercepts.

The y-coordinate of the vertex if the minimum or maximum height of the parabola.

A jumping spider's movement is modeled by a parabola.

Define the variables:

From the information given:

Standard form of a parabola with a vertical axis of symmetry:

[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute the vertex (40, 16) and one of the x-intercept points (0, 0) into the formula and solve for p:

[tex]\implies (0-40)^2=4p(0-16)[/tex]

[tex]\implies 1600=-64p[/tex]

[tex]\implies p=-25[/tex]

Substitute the vertex and the found value of p into the formula:

[tex]\implies (x-40)^2=4(-25)(y-16)[/tex]

[tex]\implies (x-40)^2=-100(y-16)[/tex]

Given:

Substitute the given values into the formulas for focus, directrix and axis of symmetry:

Focus

⇒ (h, k+p)

⇒ (40, 16 + (-25)))

⇒ (40, -9)

Directrix

⇒ y = (k-p)

⇒ y = (16 - (-25))

⇒ y = 41

Axis of symmetry

⇒ x = h  

⇒ x = 40