Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola?

Answer:

$38.25 US dollars.

Step-by-step explanation:

25 / 1 = 25

To find the number of US dollars that can be exchanged for 25 British pounds, multiply 1.53 by 25 to get $38.25 US dollars.

Hope this helps!

if there is something wrong, just let me know.

Answer:

As x increases, the rate of change of g exceeds the rate of change of f.  

Step-by-step explanation:

Given

[tex]f(x) = 90x^2 + 180x + 92[/tex]

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} \ \end{array}[/tex]

[tex]g(x) = 6^x[/tex]

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} \ \end{array}[/tex]

Required

Which of the options is true?

A. At [tex]x \approx 4.39[/tex], f(x) has the same rate of change as g(x)

Rate of change is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

For f(x)

[tex]f(x) = 90x^2 + 180x + 92[/tex]

[tex]f(4.39) = 90*4.39^2 + 180*4.39 + 92 = 2616.689[/tex]

So, the rate of change is:

[tex]m = \frac{2616.689}{4.39} = 596.06[/tex]

For g(x)

[tex]g(x) = 6^x[/tex]

[tex]g(4.39) = 6^{4.39} = 2606.66[/tex]

So, the rate of change is:

[tex]m = \frac{2606.66}{4.39} = 593.77[/tex]

The rate of change of both functions are not equal at x = 4.39. Hence, (a) is false.

B. Rate of change of g(x) is greater than f(x) with increment in x

Using the formula in (a), we have:

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} & m &\infty & 362 & 406 & 480 & 563 &648.4\ \end{array}[/tex]

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} & m & \infty & 6 & 18 & 72 & 324 & 1555 \ \end{array}[/tex]

From x = 1 to 4, the rate of change of f is greater than the rate of g.

However, from x = 5, the rate of change of g is greater than the rate of f.

This means that (b) is true.

The above table further shows that (c) and (d) are false.

Answer:

Step-by-step explanation:

C

Answer:

27/2 =x

Step-by-step explanation:

We can write a ratio to solve

3             2

-----  = ---------

3+x          11

Using cross products

3*11 = 2(3+x)

33 = 6+2x

Subtract 6 from each side

33-6 = 6+2x-6

27 = 2x

27/2 = 2x/2

27/2 =x

Answer:

Step-by-step explanation:

(-∞,2)

Cost of jacket = $20

No. Of jackets = 1

Let the cost of shirt be x

No of shirts = 5

ATQ

5x + 1(20) = 95

5x + 20 = 95

5x = 95 - 20

5x = 75

x = 75/5

x = 15

Therefore cost of each shirt was $15

Answered by Gauthmath must click thanks and mark brainliest

Answer:

The  proportions of the diameters that are greater than 25.4 millimeters is 5%.

Step-by-step explanation:

Given;

mean of the normal distribution, m = 25.1 millimeters

standard deviation, d = 0.08 millimeter

1 standard deviation above the mean = m + d = 25.1 + 0.08 = 25.18

2 standard deviation above mean =  m + 2d = 25.1 + 2(0.08) = 25.26

3 standard deviation above the mean = m + 3d = 25.1 + 3(0.08) = 25.34

4 standard deviation above the mean = m + 4d = 25.1 + 4(0.08) = 25.42

To obtain a diameter greater than 25.4, we select data after 4 standard deviation above the mean.

Data within 4 standard deviation above the mean is 95%

Data outside 4 standard deviation above the mean is 5%

Therefore, the  proportions of the diameters that are greater than 25.4 millimeters is 5%.

Answer:

x=2

y=1.732

Step-by-step explanation:

we use the formulae.....

SOHCAHTOA

where..Cos 60°=1/x

cos60=0.5

0.5=1/1

X=2

0.8660=y/2

y= 1.732

Answer:

[tex]A). \ \ \frac{(72\pi + 9\pi )}{4} \ in^2[/tex]

Step-by-step explanation:

Given;

radius of the circle, r = 9 inches

the part of the circle cut out = one-forth of the complete circle

the angle of the sector cut out θ= ¹/₄ x 360 = 90⁰

Area of the complete circle = πr² = π x 9² = 81π in²

Area of the sector cut out = [tex]= \frac{\theta }{360} \pi r^2 = \frac{90}{360} \pi (9^2) = \frac{1}{4} \times 81\pi = \frac{81 \pi}{4} = \frac{(72\pi + 9\pi)}{4} \ in^2[/tex]

Therefore, the only correct option is A. [tex]\frac{(72\pi + 9\pi )}{4} \ in^2[/tex]

Answer:

a. 1.44

Step-by-step explanation:

We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%.

At the null hypothesis, it is tested if the proportion is of at most 40%, that is:

[tex]H_0: p \leq 0.4[/tex]

At the alternative hypothesis, it is tested if the proportion is of more than 40%, that is:

[tex]H_1: p > 0.4[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that [tex]p = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]

A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A.

This means that:

[tex]n = 200, X = \frac{90}{200} = 0.45[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.45 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}[/tex]

[tex]z = 1.44[/tex]

Thus the correct answer is given by option a.

Answer:

look at the value of f(x) carefully when we put 7 from x the x take 2 value

Step-by-step explanation:

And g(x) function take 4 value. please look at the first option it has extra 2 so 2 plus 2 equal to 4 this means that the answer might be A. But look at D option it multiply by 2 so D option might be correct answer but we need some info and I want to continue. When I put 1 from x f(x)=1 and g(x)= 2 but when we look at the first option it is 1+2 equal to 3 but it must be 2 so the correct answer is not A and the correct answer is D

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

Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

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

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.

Answer:

answer is 12

Step-by-step explanation:

gcf = 3

lcm = 180

let 45 be y

let unknown be X

to get x

X=( lcm * gcf) / y

X=(180*3)/45

X=(540)/45

X=12

the other number is 12

Answer:

False

Step-by-step explanation:

To find the inverse of a function, switch the variables and solve for y.

The inverse of f(n)=-(n+1)^3:

[tex]y=-(n+1)^3[/tex]

[tex]n=-(y+1)^3[/tex]

[tex]\sqrt[3]{n} =-(y+1)[/tex]

[tex]\sqrt[3]{n} =-y-1[/tex]

[tex]\sqrt[3]{n} +1=-y[/tex][tex]-(\sqrt[3]{n} +1)=y[/tex]

[tex]-\sqrt[3]{n} -1=y[/tex]

Answer:

False

Step-by-step explanation:

Answer:

-14 is the answer for the second term (?)

Answer:

Step-by-step explanation:

Let's begin calculating the MPH for Fran.: Joanne's MPH is 250 / 2.5 = 100 MPH.

Now I'm going to subtract the 100 MPH by Fran. going 10 MPH less: 100 - 10 = 90.

I can't see the bottom part of the graph, so based on the MPH, it might be X, if you could put a better picture it would be better!

Answer:

3x ( x+2)(x^2−2x+4)

Step-by-step explanation:

3x^4 + 24x.

Factor out the greatest common factor

3x*x^3 + 3x*8

3x(x^3+8)

Then factor the cubic term

The sum of cubes is a^3+b^3=(a+b)(a^2−ab+b^2)

3x ( x+2)(x^2−2x+4)

The time it takes to wash has the probability density function,

[tex]P(X=x) = \begin{cases}\frac1{17-8}=\frac19&\text{for }8\le x\le 17\\0&\text{otherewise}\end{cases}[/tex]

The probability that it takes between 14 and 16 minutes to wash the dishes is given by the integral,

[tex]\displaystyle\int_{14}^{16}P(X=x)\,\mathrm dx = \frac19\int_{14}^{16}\mathrm dx = \frac{16-14}9 = \frac29 \approx \boxed{0.22}[/tex]

If you're not familiar with calculus, the probability is equal to the area under the graph of P(X = x), which is a rectangle with height 1/9 and length 16 - 14 = 2, so the area and hence probability is 2/9 ≈ 0.22.

Answer:

b

Step-by-step explanation:

i had it

Answer:

nada está bien gana bien.

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

Answer:

B: kept the same to make an experiment a faith test

Answer:

35

Step-by-step explanation:

The pattern is adding powers of 2.

4+1=5 (exception)

5+2=7

7+4=11

11+8=19

19+16=35

Answer:

35

Step-by-step explanation:

4 + 1 = 5

5 + (1 × 2) = 5 +2 =7

7 + (2×2) = 7 + 4 = 11

11 +(4×2) = 11 + 8 = 19

19 + (8×2) = 19 + 16 = 35

Answer:

35 lbs is the final weight

Step-by-step explanation:

20 +23 = 43 lbs

Then they had to remove 8 lbs

43 - 8 =35

35 lbs is the final weight

Answer:

no solution

Step-by-step explanation:

multiply 2 and get 2x^2+18-4=0

combine like terms

2x^2+14=0

subtract 14

2x^2=-14

there can't be a square root of a negative number so there's no solution

Answer:

x = ±i sqrt(7)

Step-by-step explanation:

2(x^2+9)-4=0

Add 4 to each side

2(x^2+9)-4+4=0+4

2(x^2+9)=4

Divide by 2

2(x^2+9)/2=4/2

(x^2+9)=2

Subtract 9 from each side

x^2 +9-9 = 2-9

x^2 = -7

Taking the square root of each side

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

x = sqrt(-1 *7)

x = ±i sqrt(7)

Answer:

"125 callers" is the right answer.

Step-by-step explanation:

Given values:

Arrival calls rate,

= 25 per minute

Talking time,

= 4 minutes

Hold time,

= 1 minute

The flow time will be:

= [tex]1 \ minute \ + 4 \ minutes[/tex]

= [tex]5 \ minutes[/tex]

Flow rate,

= [tex]Arrival \ calls \ rate[/tex]

= [tex]25 \ per \ minute[/tex]

By using the Little's law,

⇒ [tex]WIP = Flow \ rate\times Flow \ time[/tex]

By substituting the values, we get

            [tex]= 25\times 5[/tex]

            [tex]=125[/tex]

Thus the above is the correct approach.

Answer:

-4y^2 + 4x +4

Step-by-step explanation:

add -y^2 and -3y^2 = -4y^2

add 2x + 2x = 4x

add 3+1 = 4

and then rearrange

Answer:

100

Step-by-step explanation:

We have the sum of first n terms of an AP,

Sn = n/2 [2a+(n−1)d]

Given,

36= 6/2 [2a+(6−1)d]

12=2a+5d ---------(1)

256= 16/2 [2a+(16−1)d]

32=2a+15d ---------(2)

Subtracting, (1) from (2)

32−12=2a+15d−(2a+5d)

20=10d ⟹d=2

Substituting for d in (1),

12=2a+5(2)=2(a+5)

6=a+5 ⟹a=1

∴ The sum of first 10 terms of an AP,

S10 = 10/2 [2(1)+(10−1)2]

S10 =5[2+18]

S10 =100

This is the sum of the first 10 terms.

Hope it will help.

[tex]\sf\underline{\underline{Question:}}[/tex]

If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.

$\sf\underline{\underline{Solution:}}$

$\space$

$\sf\underline\bold\red{||Step-by-Step||}$

$\sf\bold{Given:}$

$\space$

$\sf\bold{To\:find:}$

$\space$

$\sf\bold{Formula\:we\:are\:using:}$

$\implies$ $\sf{ Sn=}$ $\sf\dfrac{N}{2}$ $\sf\small{[2a+(n-1)d]}$

$\space$

$\sf\bold{Substituting\:the\:values:}$

→ $\sf{S6=}$ $\sf\dfrac{6}{2}$ $\sf\small{[2a+(6-1)d]}$

→ $\sf{36 = 3[2a+(6-1)d]}$

→$\sf{12=[2a+5d]}$ $\sf\bold\purple{(First \: equation)}$

$\space$

$\sf\bold{Again,Substituting \: the\:values:}$

→ $\sf{S16}$ $\sf\dfrac{16}{2}$ $\sf\small{[2a+(16-1)d]}$

→ $\sf{255=8[2a + (16-1)d]}$

:: $\sf\dfrac{255}{8}$ $\sf\small{=31.89=32}$

→ $\sf{32=[2a+15d]}$ $\sf\bold\purple{(Second\:equation)}$

$\space$

$\sf\bold{Now,Solve \: equation \: 1 \:and \:2:}$

→ $\sf{10=20}$

→ $\sf{d=}$ $\sf\dfrac{20}{10}$ $\sf{=2}$

$\space$

$\sf\bold{Putting \: d=2\: in \:equation - 1:}$

→ $\sf{12=2a+5\times 2}$

→ $\sf{a = 1}$

$\space$

$\sf\bold{All\:of\:the\:above\:eq\: In \: S10\:formula:}$

$\mapsto$ $\sf{S10=}$ $\sf\dfrac{10}{2}$ $\sf\small{[2\times1+(10-1)d]}$

$\mapsto$ $\sf{5(2\times1+9\times2)}$

$\mapsto$ $\sf\bold\purple{5(2+18)=100}$

$\space$

$\sf\small\red{||Hence , the \: sum\: of \: the \: first\:10\: terms\: is\:100||}$

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