A glass is 1/3 full then 40cm3 of orange juice is poured in the glass is now 5/7 full what is the total volume of the glass

{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)}, {(−8, −3), (−6, −5), (−4, −2), (−2, −7), (−1, −4)} and {(−6, 4), (−3, −1), (0, 5), (1, −1), (2, 3)} are the sets of ordered pairs considered as a function.

{(−4, −2), (−1, −1), (3, 2), (3, 5), (7, 10)} is not a function.

In mathematics, ordered pair is a pair of numbers that are written in a specific order. They are generally written in (x, y) form. For example (3, 5) is an ordered pair.

The function can also be represented by a set of ordered pairs. A function Is a set of ordered pairs in which no two different ordered pairs have the same value of x coordinate.

Option (a) : {(5, 2),(4, 2),(3, 2),(2, 2),(1, 2)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (b) : {(-4, -2),(-1, -1),(3, 2),(3, 5),(7, 10)}

Two ordered pairs have the same value of x coordinate (3, 2) and (3, 5).

So, it can not be considered a function.

Option (c) : {(-8, -3),(-6, -5),(-4, -2),(-2, -7),(-1, -4)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (d) : {(-6, 4),(-3, -1),(0, 5),(1, -1),(2, 3)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Therefore, Options (a), (c), and (d) are the functions.

Option (b) is not a function.

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Answer: The probability that less than 4 of the 7 adults need correction for their eyesight is approximately 0.1637.

Step-by-step explanation:

This problem can be solved using the binomial distribution, which models the probability of a certain number of successes in a fixed number of independent trials, each with the same probability of success.

Let X be the number of adults among the 7 randomly selected who need correction for their eyesight. Then X follows a binomial distribution with parameters n = 7 (the number of trials) and p = 0.7 (the probability of success in each trial).

We want to obtain  the probability that less than 4 of the 7 adults need correction for their eyesight. This can be written as:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

To calculate each of these individual probabilities, we can use the formula for the binomial probability mass function:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

Using this formula, we can calculate each of the probabilities:

P(X = 0) = (7 choose 0) * 0.7^0 * 0.3^7 = 0.0002

P(X = 1) = (7 choose 1) * 0.7^1 * 0.3^6 = 0.0032

P(X = 2) = (7 choose 2) * 0.7^2 * 0.3^5 = 0.0292

P(X = 3) = (7 choose 3) * 0.7^3 * 0.3^4 = 0.1311

Summing these probabilities, we get:

P(X < 4) = 0.0002 + 0.0032 + 0.0292 + 0.1311 = 0.1637

Therefore, the probability that less than 4 of the 7 adults need correction for their eyesight is approximately 0.1637.

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Answer:

B. 3 hours 30 minutes

Step-by-step explanation:

1 week=7 days

30 minutes each day for 7 days

=30 minutes×7 days

=210 minutes

60 minutes makes 1 hour

210/60=3 hours 30 minutes

Candida has 3 hours 30 minutes from now till her ballet recital to practice

B. 3 hours 30 minutes

Answer:

126°

Step-by-step explanation:

1. We know that 54 degrees and its adjacent are a linear pair, meaning that they add up to 180 degrees. To find the measure of the adjacent angle, we subtract 54 from 180.

2. Now, we know that adjacent of 54 is 126. Also, we know that \(l\) ║ \(m\) ║ n, and x and 126 degrees are corresponding angles. Corresponding angles are congruent within angle measures, so x = 126 degrees.

The expected value of the random variable representing the number of Connecticut residents with type B blood in the sample of 19 is approximately 2.166 residents.

According to the American Red Cross, 11.4% of all Connecticut residents have type B blood. In your question, a random sample of 19 Connecticut residents is taken, and you want to know the expected value of the random variable representing the number of residents with type B blood in the sample.

To find the expected value of this random variable, you can use the following formula:

Expected Value (E[X]) = n * p

where n is the sample size (19 residents) and p is the probability of having type B blood (11.4%, or 0.114 as a decimal).

E[X] = 19 * 0.114 ≈ 2.166

So, the expected value of the random variable representing the number of Connecticut residents with type B blood in the sample of 19 is approximately 2.166 residents.

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The solution of the given initial value problem is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function.

To solve the initial value problem, we start by finding the complementary solution, which satisfies the homogeneous differential equation y'' + y = 0. The complementary solution is given by y_c(t) = A sin(t) + B cos(t), where A and B are constants to be determined.

Next, we find the particular solution for the given non-homogeneous term δ(t-2π)cos(t). Since the forcing term is a Dirac delta function at t = 2π, we can write the particular solution as y_p(t) = K(t-2π)cos(t-2π), where K is a constant to be determined.

Applying the initial conditions y(0) = 0 and y'(0) = 1, we can solve for the constants A, B, and K. Plugging in these initial conditions into the general solution, we find A = 0, B = 1, and K = 1.

Therefore, the solution of the initial value problem is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function.

The initial value problem with the given conditions is solved by finding the complementary solution and the particular solution. The solution is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function. This solution satisfies the given initial conditions y(0) = 0 and y'(0) = 1.

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Answer:

( + 10)

Hope this helps you out

The cliff divers dive headfirst from the top of cliff. 1/2 or 0.5 second is the time period will the diver's height exceed that of the cliff.

An object that moves along the vertical axis due to gravitational acceleration is called a free-falling object. The free fall position is given by the following equation of motion:

yₜ = y₀ + v₀t + 1/2(at²)

Where y₀--> the initial height of the object

v₀--> the initial velocity

t --> time

a --> the acceleration due to gravity and is equal to a = g = - 32.2 ft²/sec

We have given that,

Initial velocity of divers , v₀ = 8 feet/sec

Initial Height of top of cliff , s₀ = 87 feet

position function, s(t) = - 16t²+ v₀t +s₀

Plugging all known values in above position function,

s(t) = -16 t² + 8t + 87

The the diver's height exceed that of the cliff means, s(t) > 87

=> -16 t² + 8t + 87 > 87

Subtract 87 from both sides, we get

-16t^2 + 8t > 0 , now we solve this inequality by changing it in a equality,

-16 t² + 8t = 0

=> -8 t( 2t - 1) = 0 => -8t = 0 , 2t -1 = 0

=> either t = 0 or t = 1/2

So the first half second, the person is above the height of the cliff.

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Complete question:

Use the position function s(t)-16t2+ vot +so position, t time) to answer the following: Divers in Acapulco, Mexico, dive headfirst at 8 feet per second from the top of a cliff 87 feet above the Pacific Ocean. During which time period will a diver's height exceed that of the cliff? (vo initial velocity, so initial.

An organized group of integers with a shared variance among each succeeding word is known as an arithmetic sequence. Hence, the right response is (b). 1/3, 1/9, 1/15, 1/21, 1/27.

Which collection of numbers doesn't fit the definition of an arithmetic sequence?

The following instances don't constitute arithmetic sequences: 1.) 2,4,8,16 is not true since the first with second terms differ by 2, while the third and fourth terms differ by 4, and the fifth and sixth terms differ by 8. There are no shared differences, hence the sequence is not arithmetic.

Is the number sequence 2 2 2 2 2 arithmetic?

The series cannot be an arithmetic sequence, however it may be defined. It does, nevertheless, have a common ratio across succeeding words, namely 1, which results in its geometric growth.

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(1) Using the Black/Scholes Option Pricing Model, the value of the call option is $7.70.

(2) The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

(3) The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.

(4) If volatility were to decrease, the value of the call would decrease.

(5) If the exercise price would increase, the value of the call would decrease.

(6) If the time to maturity were 3-months, the value of the call would decrease.

(7) If the stock price were $62, the value of the call would be zero.

(8) The maximum value that a call option can take is unlimited.

In the Black/Scholes option pricing model, the value of a call option can be calculated using the formula:

C = S*N(d1) - X*e^(-rT)*N(d2)

where S is the stock price, X is the exercise price, r is the risk-free rate, T is the time to maturity, and σ2 is the variance of the stock's return.

Using the given values, we can calculate d1 and d2:

d1 = [ln(S/X) + (r + σ2/2)T]/(σ2T^(1/2))

   = [ln(74/70) + (0.10 + 0.50/2)*0.5]/(0.50*0.5^(1/2))

   = 0.9827

d2 = d1 - σ2T^(1/2) = 0.7327

Using these values, we can calculate the value of the call option:

C = S*N(d1) - X*e^(-rT)*N(d2)

= 74*N(0.9827) - 70*e^(-0.10*0.5)*N(0.7327)

= $7.70

The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.If volatility were to decrease, the value of the call would decrease. This is because the option's value is directly proportional to the volatility of the stock.

If the exercise price would increase, the value of the call would decrease. This is because the option's value is inversely proportional to the exercise price of the option.

If the time to maturity were 3-months, the value of the call would decrease. This is because the option's value is inversely proportional to the time to maturity of the option.If the stock price were $62, the value of the call would be zero. This is because the intrinsic value of the call is zero when the stock price is less than the strike price.

The maximum value that a call option can take is unlimited. This is because the value of a call option is directly proportional to the stock price. As the stock price increases, the value of the call option also increases.

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Answer:

12cm long

Step-by-step explanation:

Given data

Volume of cube= 1728cm^3

We know that the expression for the volume is

V=l^3

substitute and solve for l

1728=l^3

cube root both sides

l=∛1728

l=12cm

Hence the edge is 12cm long

Answer:

A) 66cm³

Step-by-step explanation:

Using the Pythagorean Theorem, the base of the triangle is 4.  The area of a triangle is 1/2 base times height.  Then you multiply times 11 to get the volume.

1/2(3)(4)(11)=66

Answer:

k<-62/7

Step-by-step explanation:

I hope it helps.

Answer:

k> 56

Step-by-step explanation:

-35 -k + 6< -85

-29-k < -85

+29        +29

_______________

-k> -56

/-1

k> 56

Answer:

a)-3>-7

b)3>-4 The symbol was preserved.

c)-6<8 The symbol was reversed.

Step-by-step explanation:

Hope this helps! :)

In a normal distribution, the mean represents the center of the distribution and the standard deviation represents the spread of the distribution.

The higher the standard deviation, the more spread out the data is. The probability of a specific outcome occurring is given by the area under the curve of the normal distribution that corresponds to that outcome.

For example, if we wanted to find the probability of x being between 45 and 55, we would find the area under the normal curve between those two values. This can be done using a table of standard normal probabilities or by using a calculator or statistical software.

In general, if we know the mean and standard deviation of a normally distributed random variable, we can use that information to find probabilities for specific outcomes or ranges of outcomes.

you'll need to provide a specific range or value of X. Once you have that, you can use the Z-score formula or a standard normal distribution table to determine the probability.

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Answer:

=> membership fee = $50

=> monthly fee = $55

=> First month = 105$

=> 50 + 55(x)

=> 50 + 55 (15)

=> 50 + 825

=> 875

Workout gym

=> membership fee = $200

=> monthly fee = $45

=> First month = 245$

=> 200 + 45(x)

=> 200 + 45(15)

=> 200 + 675

=> 875

Answer:

Step-by-step explanation:

The number of views make a GP since increase 20% or 1.2 times per day

The first term is t = 1090 and common ratio is r = 1.2

Find the sum of the first 21 terms

Answer: 245278 views

Series built : 1090, 1308, 1569.6, 1883.52, 2260.224, 2712.2688,...

As every term increases by 1.2, This is a geometric progression sequence.

\(\sf Geometric \ Sequence: a_1 \ x \ \dfrac{r^n - 1}{r -1}\)

Identify Variable's:

a1 = 1090

r = second term ÷ first term = 1308 ÷ 1090 = 1.2

n = 21

Explanation:

\(\rightarrow \sf 1090 \ x \ \dfrac{(1.2)^{21} - 1}{(1.2) -1}\)

\(\rightarrow \sf 245277.9035\)

\(\rightarrow \sf 245278 \ \ \ \ \ (rounded \ to \ nearest \ integer)\)

Answer:

\( 4,220.16 \: {units}^{3} \)

Step-by-step explanation:

Diameter of cone = 24 units

Radius of cone (r) = 24/2 = 12 units

Height of cone (h) = 28 units

\(V_{cone} = \frac{1}{3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \times 3.14 \times {(12)}^{2} \times 28 \\ \\ = \frac{1}{3} \times 3.14 \times 144 \times 28 \\ \\ = 3.14 \times 1,344 \\ \\ = 4,220.16\: {units}^{3} \)

Answer:

Danielle burns calories at a higher rate

Step-by-step explanation:

Alex: 650/75=8 2/3 calories per minute

Danielle: 420/45=9 1/3 calories per minute

Answer:

5 2/3

Step-by-step explanation:

So because it is a mixed number that means you want to have a whole plus a fraction. You keep the 5 as the whole and because 2/3=.666666. You add them together making 5 2/3.

Answer:

its always C trush me on this one

Step-by-step explanation:

Answer:

Its y=-x-3

Step-by-step explanation:

x+y=-3

You would subtract the x to make it a y equals statement

y=-x-3

the -3 stays the same all thats different is the x which you will subtract over since its added to the y.

The acceptance angle of a right-angle prism made from glass (n=1.5) is approximately 41.8 degrees. The acceptance angle of a corner reflector made from glass (n=1.5) is approximately 90 degrees.

(a) For a right-angle prism, the acceptance angle (2θ_out) is the angle at which the incident light ray inside the prism reaches the critical angle and undergoes total internal reflection. The critical angle can be determined using Snell's law, which states that sin(θ_c) = 1/n, where n is the refractive index of the medium (in this case, n=1.5 for glass). Solving for θ_c, we find θ_c = sin^(-1)(1/n). Since the incident angle inside the prism is equal to the critical angle, the acceptance angle is 2θ_c. Substituting n=1.5, we find 2θ_out ≈ 2 * sin^(-1)(1/1.5) ≈ 41.8 degrees.

(b) A corner reflector is formed by three mutually perpendicular plane mirrors, such as those in a prism. In a corner reflector made from glass (n=1.5), each mirror surface will have an acceptance angle equal to the critical angle. Using the same formula as in (a), we find θ_c = sin^(-1)(1/1.5). Since each mirror is perpendicular to the others, the total acceptance angle of the corner reflector is the sum of the acceptance angles of the individual mirrors, which results in 2θ_out ≈ 2 * sin^(-1)(1/1.5) ≈ 90 degrees.

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The amount of each deposit is $210000

Compound interest is when you reinvest your income. Compound interest distinctively means "interest on interest" and is the reason so many investors are so successful.

The computation of the each deposit is shown below:

Given that

Future value be $70,000

Time period = 10 × 2 = 20

And, the rate = 9% ÷ 2 = 4.5%

Now the formula is as follows

= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1

= ($70,000 × 4.5) ÷ (1 + 0.025)²⁰⁻¹

= $315,000 ÷ 1.5

= $210000

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Answer:

To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:

(-3+1)+(-4-i) = -2 + (-4-i)

Next, we can simplify the addition of -2 and -4 by adding their numerical values:

-2 + (-4-i) = -6 - i

Therefore, (-3+1)+(-4-i) simplifies to -6-i.

Step-by-step explanation:

Answer:

Step-by-step explanation:

3(a^2 + a - 6)

3(a + 3)(a - 2)

answer is D

Answer:

28.79 cm.

Step-by-step explanation:

The perimeter of a semicircle is equal to the sum of the diameter (which is twice the radius) and half of the circumference of the circle.

The diameter of the semicircle is 2 × 5.6cm = 11.2cm.

The circumference of a full circle with radius 5.6cm is 2π × 5.6cm = 11.2π cm.

Therefore, the circumference of the semicircle is 1/2 of the circumference of the full circle, which is 1/2 × 11.2π cm = 5.6π cm.

The perimeter of the semicircle is the sum of the diameter and the circumference, which is:

11.2cm + 5.6π cm ≈ 28.79cm (rounded to two decimal places)

Therefore, the perimeter of the semicircle is approximately 28.79 cm.

Answer:

pi ( 5.6 ) + 11.2 or approximately 28.79291 cm

Step-by-step explanation:

The outside of the semicircle or the perimeter is 1/2 of the circumference and the length that closes the circle is the diameter.

Perimeter = 1/2 C + d

                 = 1/2 *pi*d + d

The diameter is 2 times the radius.

                 = 1/2 ( pi) * (2r) + 2r

                  = pi r + 2 r

                   = pi ( 5.6 ) + 11.2

Approximating pi, we get approximately 28.79291

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Answer:

$210

Step-by-step explanation:

(January - March) charge last year :

Unit consumed = 2000

Bill = $250

(July - September) charge last year:

Unit consumed = 600 units

Bill = $138

Billing :

Fixed charge + rate per unit ;

Let fixed charge = c ; rate per unit = m

Billing can be represented by the equation :

mx + c = y

x = unit consumed ; y = total charge

Expensive quarter:

2000x + c = 250 - - - (1)

Least expensive quarter:

600x + c = 138 - - - (2)

From (2)

c = 138 - 600x ; plug into (1)

2000x + 138 - 600x = 250

1400x = 250 - 138

1400x = 112

x = 0.08

0.08 = x = rate per unit

From ; c = 138 - 600x

c = 138 - 600(0.08)

c = 90

Fixed charge = 90

Billing equation :

y = 0.08x + 90

If insulation will reduce unit consumption by 25%

Then, consumption in most expensive quarter will be :

(100 - 25)% * 2000

0.75 * 2000 = 1500 units

Charge will be :

(0.08*1500) + 90

= $210