A square pyramid is 6 feet on each side. The height of the pyramid is 4 feet. What is the total area of the pyramid?

60 ft2
156 ft2
96 ft2
120 ft2

Answer:

a) x = 7

b) x = 2

Step-by-step explanation:

* Lets revise some facts in the circle

- If two secant segments are drawn to a circle from a point outside the

 circle, the product of the length of one secant segment and its

 external part is equal to the product of the length of the other secant

 segment and its external part.

# Example:

- If AC is a secant intersects the circle at points A and and B

- If DC is another secant intersects the circle at points D and E

- The two secants intersect each other out the circle at point C

∴ AC × CB = DC × CE , where AC is the secant and CB is its external

  part and DC is the secant and CE is its external part

* Lets solve the problem

a) There are two secants intersect each other at point outside the circle

∵ The first secant is x + 5

∵ Its external part is 5

∵ the second secant is 4 + 6 = 10

∵ Its external part is 6

∴ (x + 5) × 5 = 10 × 6 ⇒ simplify

∴ 5x + 25 = 60 ⇒ subtract 25 from both sides

∴ 5x = 35 ⇒ divide both sides by 5

∴ x = 7

* x = 7

b) There are two secants intersect each other at point outside the circle

∵ The first secant is 5 + 3 = 8

∵ Its external part is 3

∵ the second secant is x + 4

∵ Its external part is 4

∴ 8 × 3 = (x + 4) × 4 ⇒ simplify

∴ 24 = 4x + 16 ⇒ subtract 16 from both sides

∴ 8 = 4x ⇒ divide both sides by 4

∴ 2 = x

* x = 2

Step-by-step explanation:

First, use trig to find the height of the slide.

The slide forms a right triangle.  We know the hypotenuse is 8.80 ft, and the angle opposite of the height is 25.0°.  So using sine:

sin 25.0°  = h / 8.80

h = 3.72 ft

Converting to meters:

h = 3.72 ft × (1 m / 3.28 ft)

h = 1.13 m

Potential gravitational energy is:

PE = mgh

where m is the mass, g is the acceleration due to gravity, and h is the relative height.

At the bottom of the slide, h = 0:

PE = (63.0 kg) (9.8 m/s²) (0 m)

PE = 0 J

At the top of the slide, h = 1.13 m:

PE = (63.0 kg) (9.8 m/s²) (1.13 m)

PE =  700 J

The change is the final potential energy minus the initial potential energy.

ΔPE = 0 J - 700 J

ΔPE = -700 J

Step-by-step explanation:

Let's say the position of the fire is point C.

Bearings are measured from the north-south line.  So ∠BAC = 55°, and ∠ABC = 60°.

Since angles of a triangle add up to 180°, ∠ACB = 65°.

Using law of sine:

190 / sin 65° = a / sin 60° = b / sin 55°

Solving:

a = 181.6

b = 171.7

Station A is 181.6 miles from the fire and station B is 171.7 miles from the fire.

The answers are:

A.

[tex]\frac{5}{6}[/tex] and [tex]\frac{10}{12}[/tex]

D.

[tex]\frac{6}{7}[/tex] and [tex]1\frac{5}{7}[/tex]

To find which of the following pairs of numbers contains like fractions, we must remember that like fractions are the fractions that share the same denominator.

We are given two fractions that are like fractions. Those fractions are:

Option A.

[tex]\frac{5}{6}[/tex] and [tex]\frac{10}{12}[/tex]

We have that:

[tex]\frac{10}{12}=\frac{5}{6}[/tex]

So, we have that the pairs of numbers

[tex]\frac{5}{6}[/tex]

and

[tex]\frac{5}{6}[/tex]

Share the same denominator, which is equal to 6, so, the pairs of numbers contains like fractions.

Option D.

[tex]\frac{6}{7}[/tex] and [tex]1\frac{5}{7}[/tex]

We have that:

[tex]1\frac{5}{7}=1+\frac{5}{7}=\frac{7+5}{7}=\frac{12}{7}[/tex]

So, we have that the pair of numbers

[tex]\frac{6}{7}[/tex]

and

[tex]\frac{12}{7}[/tex]

Share the same denominator, which is equal to 7, so, the pairs of numbers constains like fractions.

Also, we have that the other given options are not like fractions since both pairs of numbers do not share the same denominator.

The other options are:

[tex]\frac{3}{2},\frac{2}{3}[/tex]

and

[tex]3\frac{1}{2},4\frac{4}{4}[/tex]

We can see that both pairs of numbers do not share the same denominator so, they do not contain like fractions.

Hence, the answers are:

A.

[tex]\frac{5}{6}[/tex] and [tex]\frac{10}{12}[/tex]

D.

[tex]\frac{6}{7}[/tex] and [tex]1\frac{5}{7}[/tex]

Have a nice day!

By definition of covariance,

[tex]\mathrm{Cov}(U,V)=E[(U-E[U])(V-E[V])]=E[UV-E[U]V-UE[V]+E[U]E[V]]=E[UV]-E[U]E[V][/tex]

Since [tex]U=2X+Y-1[/tex] and [tex]V=2X-Y+1[/tex], we have

[tex]E[U]=2E[X]+E[Y]-1[/tex]

[tex]E[V]=2E[X]-E[Y]+1[/tex]

[tex]\implies E[U]E[V]=(2E[X]+E[Y]-1)(2E[X]-(E[Y]-1))=4E[X]^2-(E[Y]-1)^2=4E[X]^2-E[Y]^2+2E[Y]-1[/tex]

and

[tex]UV=(2X+Y-1)(2X-(Y-1))=4X^2-(Y-1)^2=4X^2-Y^2+2Y-1[/tex]

[tex]\implies E[UV]=4E[X^2]-E[Y^2]+2E[Y]-1[/tex]

Putting everything together, we have

[tex]\mathrm{Cov}(U,V)=(4E[X^2]-E[Y^2]+2E[Y]-1)-(4E[X]^2-E[Y]^2+2E[Y]-1)[/tex]

[tex]\mathrm{Cov}(U,V)=4(E[X^2]-E[X]^2)-(E[Y^2]-E[Y]^2)[/tex]

[tex]\mathrm{Cov}(U,V)=4V[X]-V[Y]=4a-a=\boxed{3a}[/tex]

Answer:

50% chance

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

There are 3 coins, and each coin has 2 possible outcomes.  So there are a total of 6 possible outcomes.

Of these 6 outcomes, 3 are heads.  Of these 3, only 1 has tails on the opposite face.

So the probability is 1/3.

We can also show this using conditional probability:

P(A|B) = P(A∩B) / P(B)  

Probability that A occurs, given that B has occurred = Probability that both A and B occur / Probability that B occurs

Here, A = tails on opposite face and B = heads.

P(A|B) = (1/6) / (3/6)

P(A|B) = 1/3

Final answer:

The probability of getting exactly one topping on a hamburger, when up to 7 toppings are possible and each choice is unique, is 1 in 8 or 0.125.

Explanation:

When considering the probability of getting exactly one topping on a hamburger when the toppings could range from 0 to 7, and each topping is unique, we apply the concept of theoretical probability. The scenario implies there are 8 different events that could occur - getting no toppings to getting all 7 toppings. We are interested in the event where we get exactly one topping. Since each of these events - from getting 0 toppings to 7 toppings - is equally likely, the probability of getting exactly one topping is 1 in 8 or 0.125, when expressed as a decimal number rounded to four decimal places.

Answer:

Amount of  vinegar. 100% : 20 milliliters

Amount of  Italian dressing: 140 milliliters

Step-by-step explanation:

Let's call A the amount of  vinegar. 100%

Let's call B the amount of  Italian dressing . 12% vinegar

The resulting mixture should have 23%  vinegar, and 160 milliliters.

Then we know that the total amount of mixture will be:

[tex]A + B = 160[/tex]

Then the total amount of pure antifreeze in the mixture will be:

[tex]A + 0.12B = 0.23 * 160[/tex]

[tex]A + 0.12B = 36.8[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

[tex]-A -B = -160[/tex]

[tex]-A -B = -160[/tex]

               +

[tex]A + 0.12B = 36.8[/tex]

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

[tex]-0.88B = -123.2[/tex]

[tex]B = \frac{-123.2}{-0.88}[/tex]

[tex]B = 140\ milliliters[/tex]

We substitute the value of B into one of the two equations and solve for A.

[tex]A + 140 = 160[/tex]

[tex]A = 20\ milliliters[/tex]

Answer:

n = 22

Step-by-step explanation:

We will use the formula for the present value of an ordinary annuity :

[tex]P.V.=P(\frac{1-(1+r)^{-n}}{r})[/tex]

where P = periodic payment

          r = rate per period

          n = number of periods

Given P = PMT = $400, P.V. = $8,000, i = 0.01, and we have to find n.

Now we put the values in the formula

[tex]8000=400(\frac{1-(1+0.01)^{-n}}{0.01})[/tex]

After rearranging we have

[tex]\frac{8000\times 0.01}{400}=1-1.01^{-n}[/tex]

[tex]20\times 0.01=1-1.01^{-n}[/tex]

[tex]1.01^{-n}[/tex] = 1 - 0.2

[tex]1.01^{-n}[/tex] = 0.8

Taking log on both sides

-n log 1.01 = log 0.8

[tex]n=\frac{-log0.08}{log1.01}[/tex] = 22.4257

Therefore, n = 22

So there are total 22 payments

Answer: 0.0433

Step-by-step explanation:

Given: Sample size : n= 133

The number of females in sample = 65

Then the proportion of females : [tex]P=\dfrac{65}{133}[/tex]

The formula to calculate the standard error of the proportion is given by :-

[tex]S.E.=\sqrt{\dfrac{P(1-P)}{n}}[/tex]

[tex]\Rightarrow S.E.=\sqrt{\dfrac{\dfrac{65}{133}(1-\dfrac{65}{133})}{133}}\\\\\Rightarrow\ \Rightarrow S.E.=0.0433444676341\approx0.0433[/tex]

Hence, the standard error of the proportion of females is 0.0433.

The standard error of the proportion of females in the given sample is calculated using the formula SE = sqrt[p * (1-p) / n]. In this case, the proportion (p) is 0.4887 and the sample size (n) is 133, giving a standard error of 0.0432.

The question is asking for the standard error of the proportion of females in the said sample. The standard error (SE) of a proportion is a measure of uncertainty around a proportion estimate. It is calculated using the formula SE = sqrt[p * (1-p) / n], where p is the proportion and n is the sample size.

So, we have a sample size, n = 133, and the proportion of females, p = 65/133 = 0.4887.

Substitute these values into the formula, we get: SE = sqrt[0.4887 * (1 - 0.4887) / 133] = 0.0432 (rounded to four decimal places).

Therefore, the standard error of the proportion of females in this sample is 0.0432.

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Theoretical probability is calculated based on the number of expected outcomes, while experimental probability is based on observed outcomes. They are used in different situations for predictions and estimates, respectively.

Theoretical probability is calculated by dividing the number of times an event is expected to occur by the number of possible outcomes.

For example, if you flip a fair coin, there is one way to obtain heads and two possible outcomes, so the theoretical probability of heads is 1/2 or 0.5.

Experimental probability, on the other hand, is based on observations from an experiment.

If you flip a coin 10 times and get 6 heads, the experimental probability of heads is 6/10 or 0.6.

Both theoretical and experimental probability have their uses in different situations, but theoretical probability is often used to make predictions based on known probabilities, while experimental probability provides a more accurate estimate based on actual observations.

Answer:

Given,

The initial population ( on 2010 ) = 40,000,

Let r be the rate of increasing population per year,

Thus, the function that shows the population after t years,

[tex]P(x)=40000(1+r)^t[/tex]

And, the population after 5 years ( on 2015 ) is,

[tex]P(5)=40000(1+r)^{5}[/tex]

According to the question,

P(5) = 50,000,

[tex]\implies 40000(1+r)^5=50000[/tex]

[tex](1+r)^5=\frac{50000}{40000}=1.25[/tex]

[tex]r + 1= 1.04563955259[/tex]

[tex]\implies r = 0.04653955259\approx 0.04654[/tex]

So, the population is increasing the with rate of 0.04654,

And, the population after t years would be,

[tex]P(t)=40000(1+0.04654)^t[/tex]

[tex]\implies 40000(1.04654)^t[/tex]

Since, the exponential function is,

[tex]f(x) = ab^x[/tex]

Hence, by comparing,

a = 40000,

b = 1.04654

Answer:

maryland. (c)

wyoming. (b)

reduced burning of fossil fuels. (b)

Step-by-step explanation:

if you're looking for the answer the question im looking for then those are the answers

Answer:

The logarithmic function modeled by the given table:

f(x) = log₃x

Step-by-step explanation:

Given Table:

x     f(x)

9     2

27    3

81    4

We can see that x increases as powers of 3. And f(x) is the power.

We assume that f(x) = log₃x

Checking using the table:

for x = 9

f(x) = log₃9 = 2

for x = 27

f(x) = log₃27 = 3

for x = 81

f(x) = log₃81 = 4

Hence proved.  

Answer:

[tex]y =( x +9 )\times 4[/tex]

simplified

[tex]y = 4x + 48[/tex]

Step-by-step explanation:

first know that the result would be y or f(x), because it's the function applied to x that makes it y. so its starts with either y= or, f(x)=

increasing by a number is multiplying, the word and is used for addition so

+9 ×4 will be in the equation

used PEMDAS, distribution, and combining like terms to simplify

Answer:

Step-by-step explanation:

Let d represent the number of dimes. Then the number of quarters is 2d-3 and the total value of the coins is ...

  0.10d + 0.25(2d-3) = 7.05

  0.60d -0.75 = 7.05 . . . . . . . simplify

  d = (7.05 +0.75)/0.60 = 13 . . . . add 0.75, divide by 0.60

  2d-3 = 2·13 -3 = 23

Brandon has 23 quarters and 13 dimes.

Answer:

It's B

Step-by-step explanation:

180 - 105 = 75 +55 = 130; the recangle has a sum of 180, hence 180-130 =50

-10x - 3 = -10 - 3x

Bring -10x to the other side by adding it to both sides

(-10x + 10x) - 3 = -10 + (-3x + 10x)

0 - 3 = -10 + 7x

-3 = -10 + 7x

Bring -10 to the oposite side by adding 10 to both sides

-3 + 10 = (-10 + 10) + 7x

7 = 0 + 7x

7 = 7x

Isolate x by dividing 7 to both sides

7/7 = 7x/7

x = 1

Hope this helped!

~Just a girl in love with Shawn Mendes

-10x-3= -10-3x

-10x+10x-3= -10x+10x-3x

-3=-3x

divide by -4 for -3 and -3x

-3/-3= -3x/-3

1=x

x= 1

check answer by using substitution method

-10x-3= -10-3x

-10(1)-3=-10-3(1)

-13=- 13

Answer is x= 1

Answer: Our required linear equation would be [tex]x+48y=148[/tex]

Step-by-step explanation:

Since we have given that

Cost of deep fried bananas on a stick = $1.00

Number of sales reached = 100 per day

Cost of deep fried bananas on a stick becomes = $2.00

Number of sales reached = 52 per day.

Let x is the number of dollars each.

Let y be the number of vendors sale.

So, we need to form the linear equation:

As we know the formula for two point slope form:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-1=\dfrac{2-1}{52-100}(x-100)\\\\y-1=\dfrac{1}{-48}(x-100)\\\\-48(y-1)=(x-100)\\\\-48y+48=x-100\\\\-48y=x-100-48\\\\-48y=x-148\\\\x+48y=148[/tex]

Hence, our required linear equation would be [tex]x+48y=148[/tex]

Answer:

Step-by-step explanation:

If you simply need to identify the inequality, it is

n + 5 ≥ 12

since "sum" means to add and "at least" is the inequality sign that is greater than or equal to.

If you are solving it, then the solution set will be

n ≥ 7

Answer:

5 + n ≥ 12.

Step-by-step explanation:

Given  :  sum of five and a number n is at least 12.

To find : Write expression .

Solution : We have given sum of five and a number n is at least 12.

According to given statement :

Sum of 5 and n

5 + n

At least 12 mean the number is 12 or greater than 12

So ,

5 + n ≥ 12.

Therefore, 5 + n ≥ 12.

Answer:

Step-by-step explanation:

What level of math is this?

To determine if H is a subspace, we need to check three properties: the presence of the zero vector, closure under vector addition, and closure under scalar multiplication.

1. Does H contain the zero vector of V? The answer is no, because the zero vector (0,0) does not lie in the second or fourth quadrants.

2. Is H closed under addition? The answer is no. For example, the vectors (-1, 1) from the second quadrant and (-1, -1) from the fourth quadrant would sum to (-2, 0), which is not part of either quadrant.

3. Is H closed under scalar multiplication? The answer is no, as multiplying a vector in H by a negative scalar will place it in the opposite quadrant, which is outside H. For example, the scalar -1 and the vector (-1, 1) will yield the vector (1, -1), which is not in the second or fourth quadrants.

4. Is H a subspace of the vector space V? The answer is no, because it does not meet the required properties mentioned in parts 1-3.

Answer:4,500

Step-by-step explanation:

720 multiple by 25 gives you 18,000 then you find 25% of 18,000 by multiplying 18,000 times 25/100 which gives you 4,500. Or you can find 25%of 25 then multiple the answer by 720

Answer: 4,500.00

Step-by-step explanation:

The probability that the team will win exactly 7 matches over the course of one season is:

                         0.1977

We know that the probability of k successes out of n successes is given by the binomial distribution as:

[tex]P(X=k)=n_C_kp^k(1-p)^{n-k}[/tex]

where p is the probability of success .

Here we are asked to find the probability that the team will win exactly 7 matches over the course of one season.

Since, there are 8 matches over the course of season.

This means n=8

and k=7

and p=0.70

(Since, 0.70 probability of winning a match )

Hence, we get:

[tex]P(X=7)=8_C_7\times (0.70)^7\times (1-0.70)^{8-7}\\\\i.e.\\\\P(X=7)=8\times (0.70)^7\times 0.30\\\\i.e.\\\\P(X=7)=0.1977[/tex]

         Hence, the answer is:

                  0.1977

Final answer:

The probability that a collegiate video-game competition team with a 0.70 chance of winning will win exactly 7 out of 8 matches is approximately 25.41%.

Explanation:

The question asks to calculate the probability that a collegiate video-game competition team, which has a 0.70 probability of winning a match, wins exactly 7 out of 8 matches in a season. This scenario can be modeled using the binomial distribution formula, which is given by P(X = k) = (n C k) * p^k * (1 - p)^(n - k), where 'n' is the total number of trials (matches), 'k' is the number of successful outcomes (wins), and 'p' is the probability of a single success.

To find the probability of winning exactly 7 matches, we set n = 8, k = 7, and p = 0.70. Thus, the calculation becomes P(X = 7) = (8 C 7) * (0.70)⁷ * (0.30)¹. Calculating further, we have P(X = 7) = 8 * (0.70)⁷ * (0.30) = 0.254121. Therefore, the probability that the team will win exactly 7 matches over the course of one season is approximately 25.41%.

Answer:

The length is 78 feet and the width is 30 feet.

Step-by-step explanation:

The perimeter of a rectangle can be calculated with this formula:

[tex]P=2l+2w[/tex]

Where "l" is the length and "w" is the width.

Since we know that the perimeter of the playing field is 216 feet and its length is 48 feet longer than the width ([tex]l=w+48[/tex]), we can substitute them into the formula and solve for "w":

[tex]216=2(w+48)+2w\\\\216=2w+96+2w\\\\216-96=4w\\\\\frac{120}{4}=w\\\\w=30\ ft[/tex]

Finally, substitute the width into [tex]l=w+48[/tex] to find the length. This is:

[tex]l=30+48\\\\l=78\ ft[/tex]

Final answer:

To find the dimensions of the playing field, we identify the width as w feet and the length as w + 48 feet. By using the perimeter formula and solving the resulting equation, we determine that the width is 30 feet and the length is 78 feet.

Explanation:

The student is asking to find the dimensions of a rectangle given its perimeter and the relationship between its length and width. The perimeter of the rectangle is known to be 216 feet, and the length is specified to be 48 feet longer than the width.

Let's call the width w feet. Then, the length would be w + 48 feet. Since the perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width, we can set up the following equation:

2(w + w + 48) = 216

Solving this equation, we find:

4w = 120

Therefore, the width of the playing field is 30 feet. To find the length, add 48 feet to the width:

Length = w + 48 = 30 + 48 = 78 feet.

The dimensions of the playing field are 30 feet in width and 78 feet in length.

let's recall that a rational whose numerator and denominator are of the same degree, has a horizontal asymptote at the fraction provided by the leading term's coefficients.

so we can simply pick any two polynomials, make them the same degree and give their leading term 2 and 9 respectively.

hmmmm say for the numerator x⁴ - 3x³.... and the denominator hmm say x⁴ + 7x, so then let's give them 2 and 9 respective... so

[tex]\bf \cfrac{\stackrel{\stackrel{\textit{leading term}}{\downarrow }}{2x^4}-3x^3}{\underset{\underset{\textit{leading term}}{\uparrow }}{9x^4}+7x}\implies \stackrel{\textit{horizontal asymptote}}{y=\cfrac{2}{9}}[/tex]

Answer: 90.5%

Step-by-step explanation:

Given: Mean : [tex]\mu = 1\text{ inch}[/tex]

Standard deviation : [tex]\sigma = 0.003\text{ inch}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 0.995

[tex]z=\dfrac{0.995-1}{0.003}=-1.66666666667\approx-1.67[/tex]

The P Value =[tex]P(z<-1.67)=0.0474597[/tex]

For x= 1.005

[tex]z=\dfrac{1.005-1}{0.003}=1.66666666667\approx1.67[/tex]

The P Value =[tex]P(z<1.67)= 0.9525403[/tex]

[tex]\text{Now, }P(0.995<X<1.005)=P(X<1.005)-P(X<0.995)\\\\=P(z<1.67)-P(z<-1.67)\\\\=0.9525403-0.0474597=0.9050806[/tex]

In percent ,

[tex]P(0.995<X<1.005)=0.9050806\times100=90.50806\%\approx90.5\%[/tex]

the probability that an elevator rail will meet the specifications is about 90.5%, which is 0.9525 - 0.0475.

The student is asking for the fraction of all elevator rails produced by Smalltown Elevator that will meet the given specifications, assuming that the diameter of an elevator rail follows a normal distribution with a mean of 1 inch and a standard deviation of 0.003 inches. To meet specifications, the diameter must be between 0.995 inches and 1.005 inches.

The z-score for the lower specification limit (0.995 inches) is calculated as: (0.995 - 1) / 0.003. This gives us a z-score of -1.67. The z-score for the upper specification limit (1.005 inches) is calculated as: (1.005 - 1) / 0.003. This gives us a z-score of 1.67.

Using the standard normal distribution table, we find that the cumulative probability for a z-score of 1.67 is approximately 0.9525, and for -1.67 is approximately 0.0475. Thus, the probability that an elevator rail will meet the specifications is about 90.5%, which is 0.9525 - 0.0475.

Answer:

We need to find the domain, range, x-intercept and y-intercept of the following function:

[tex]f(x) = 1.6x^{-2} + 1[/tex] ⇒ [tex]f(x)=\frac{1.6}{x^{2} }+1[/tex]

To find the y-intercept, we have to make 'x=0'

[tex]f(x) = \frac{1.6}{x^{2} } + 1[/tex] ⇒ [tex]f(x) = \frac{1.6}{0}  + 1[/tex]. Given that divisions by zero are not possible, we conclude that there's no y-intercept. In other words, the function does not cross the y-axis,

To find the x-intercept, we have to make 'y=0'

[tex]f(x) = \frac{1.6}{x^{2} } + 1[/tex]  ⇒ [tex]\frac{1.6}{x^{2} } + 1 = 0[/tex]

⇒ [tex]x^{2} = -1.6[/tex]

Given that we cannot take the square rooth of a negative number, we can conclude that there's no x-intercept. In other words, the function does not cross the x-axis.

The domain is all the possible values that the independent variable 'x' can take. Given that we can not divide by zero, the domain is all real numbers except zero. In set notation: ℝ - {0}.

The Range is all the possible values that the dependent variable 'y' can take. Solving the expression for 'x' we have:

[tex]\frac{1.6}{x^{2} } + 1 = y[/tex]  ⇒ [tex]\frac{1.6}{x^{2} }= y-1[/tex]

⇒ [tex]\sqrt{(\frac{1.6}{y-1 })}= x[/tex]

Given that square roots can not be negative, and the denominator can't be equal to zero, the range is y>1. In set notation: Range: (1, +∞)

Answer:

a_n=-\frac{1}{4 a_{n-1}

Step-by-step explanation:

The recursive formula for the geometric sequence is given by:

a_n = a_{n-1} \cdot r

where,

r is the common ratio terms

-16, 4, -1, ...

This is a geometric sequence.

Here,  and

Since,

ans so on .....

Substitute the given values we have;

⇒

Therefore, the recursive formula for the following geometric sequence is,

Answer:

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

Step-by-step explanation:

Formulate the recursive formula for the following geometric sequence.

{-16, 4, -1, ...}

Here the common difference of two terms are not same.

LEts find the common ratio. To find common ratio, divide the second term by first term

[tex]\frac{4}{-16} =\frac{-1}{4}[/tex]

[tex]\frac{-1}{4} =\frac{-1}{4}[/tex]

So common ratio is -1/4

Recursive formula is

[tex]A_n= A_{n-1} (r)[/tex]

'r' is the common ratio.

Recursive formula becomes

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

Answer:

481/600

Step-by-step explanation:

Since the delay is exactly 10 min, or 600 seconds, the delay must be more than 480. Taking this, the probability of it not being 480 seconds or less becomes 481/600. (Since you can't have 480)

The probability is 481/600

Since the delay is exactly 10 min, or 600 seconds, the delay must be more than 480. Taking this, the probability of it not being 480 seconds or less becomes 481/600. (Since you can't have 480)

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Answer:

A) 4/33 hour

Step-by-step explanation:

This is a distance = rate * time problem

We are given the distance and the rate, now we need to solve for the time:

[tex]\frac{4}{7}=4\frac{5}{7}t[/tex]

Let's change that mixed fraction into an improper one:

[tex]\frac{4}{7}=\frac{33}{7}t[/tex]

Now to solve for t we can multiply the 33/7  by its recirocal:

[tex](\frac{7}{33})\frac{4}{7}=\frac{33}{7}(\frac{7}{33})t[/tex]

Multiplying a fraction by its reciprocal = 1, so that leaves only a t on the right:

[tex](\frac{7}{33})\frac{4}{7}=t[/tex]

The 7's cancel out on the left and that leaves you with

[tex]t=\frac{4}{33}hr[/tex]