Peter has won the lottery. He will receive Kenya Shillings 87325 per month for the next 21 years, a total of Kenya Shillings 22.01

million.

What single deposit (in millions) should the lottery commission make now to fund Peter's annuity. Assume 10.7%
annual interest, compounded monthly

The length of the glass is L = 5.67 cm

Given data ,

Let the length of one glass be "x" cm

According to the given information, the length of 6 glasses is 34 cm.

So, the combined length of 6 glasses is 6x cm, which is equal to 34 cm.

Similarly, the length of 2 glasses is 19 cm.

So, the combined length of 2 glasses is 2x cm, which is equal to 19 cm.

6x = 34 be equation (1)

2x = 19 be equation (2)

Now we can solve these equations to find the value of "x", which represents the length of one glass.

On dividing equation 1 by 6, we get:

x = 34/6

x ≈ 5.67 cm

Hence , the length of one glass is approximately 5.67 cm

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A belt runs a pulley at 80 revolutions per minute.

(a) To find the angular speed of the pulley in radians per second, we can use the formula

ω = 2πf

Where

ω = angular speed in radians per second

f = frequency in Hertz

We know that the pulley rotates at a rate of 80 revolutions per minute. To convert this to a frequency in Hertz, we can divide by 60 seconds per minute

f = 80 rev/min ÷ 60 min/s = 4/3 Hz

Now we can plug in this value for f into the formula

ω = 2πf = 2π(4/3) = 8π/3 rad/sec

Therefore, the angular speed of the pulley is 8π/3 radians per second.

(b) To find the linear speed of the belt in centimeters per second, we can use the formula

v = rω

Where

v = linear speed in centimeters per second

r = radius of the pulley in centimeters

ω = angular speed in radians per second

We know the radius of the pulley is given in centimeters. Let's assume it is r cm. We just found the angular speed to be 8π/3 radians per second. Now we can plug in these values into the formula

v = rω = r(8π/3) = (8π/3)r cm/s

Therefore, the linear speed of the belt is (8π/3)r centimeters per second.

The given question is incomplete and the complete question is ''A belt runs a pulley at 80 revolutions per minute. Find the angular velocity of the pulley in radians per second. (b)Find the linear speed of the belt in centimeters per second''.

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The binomial whose greatest common factor is 7a³ is 14a⁴ + 35a³.

Given, the a³ is not common in A and C.

Now, in 14a⁴ + 35a³

14a⁴ = 2 x 7 x a³ x a

35a³ = 7 x 5 x a³

So, the common factors of 14 and 35 is 7.

Then, 14a⁴ + 35a³

= ( 2 x 7 x a³ x a) + (  5 x 7 x a³)

= 7a³ (2a + 5)

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Answer:

That statement describes an action taken by Keng to add a 3-inch-wide frame around all sides of his canvas, likely for artistic or aesthetic purposes. This would result in the canvas being extended by 3 inches in each direction, effectively increasing its overall dimensions and adding a border or frame around the original artwork. The purpose and effect of adding a frame may vary depending on the artistic intention of the artist, but it is a common practice in art and design to enhance the presentation and visual appeal of the artwork.

Step-by-step explanation:

88% of the students in the school are enrolled in health.

We have,

Students enrolled in health = 440

Students not enrolled = 60

Total students = 500

So, x% of 500 = 440

x/100 (500) = 440

5x = 440

x = 88%

Thus, 88% of the students in the school are enrolled in health.

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The difference between the stratified and systematic random sampling is explained below.

Systematic random sampling is a method where every Kth person of the population is chosen to be part of the sample, whereas stratified random sampling is a method where the population is first divided into subgroups, and then drawing a simple random sample from each subgroup.

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An axon is a long, tubelike structure extending from a neuron's cell body branch-like fiber extending in clusters from a neuron's cell body messenger of the nervous system is true.

We have,

An axon is a long, tubelike structure that extends from a neuron's cell body.

It is a specialized fiber that carries electrical impulses, known as action potentials, away from the cell body and towards the axon terminals.

Axons are covered by a fatty substance called myelin, which insulates and protects the axon and helps to speed up the transmission of signals.

At the end of the axon, there are small branches called axon terminals, which release chemicals called neurotransmitters into the synapse, the small gap between the axon terminals and the dendrites of the next neuron in the circuit.

This allows the electrical signal to be converted into a chemical signal and transmitted to the next neuron, continuing the chain of communication in the nervous system.

Thus,

An axon is a long, tubelike structure extending from a neuron's cell body branch-like fiber extending in clusters from a neuron's cell body messenger of the nervous system is true.

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17. 15 degrees

18. ABC

19. 5.88

20. 11.59

let me know if you'd like an explanation

Answer:

The formula looks like this:

where SA = surface area, l = length, w = width, and h = height. In the rectangular prism net above, l = 8 inches, w = 5 inches, and h = 3 inches. Simply put these numbers into the formula and solve for surface area.

Answer:

13: (2,3) 14: A. Yes, 90, 180, 270 B. No C. No

Step-by-step explanation:

13. Right: -2+4, Down: 5-2

14. If it can be rotated and be similar, it has rotational.

After two years, Brooklyn will have more money in her savings account than Matthew.

Brooklyn's savings account grows at a slower rate than Matthew's initially but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.

a.

[tex]A = P(1 + r/n)^{nt}[/tex]

where A is the final amount, P is the initial principal (or net pay), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

For Brooklyn saving account,

P = $625, r = 0.025, n = 12 (monthly compounding), and t = 2.

A = $625(1 + 0.025/12)^(12*2) = $686.71

For Matthew saving account,

P = $446, r = 0.04, n = 4 (quarterly compounding), and t = 2.

A = $446(1 + 0.04/4)^(4*2) = $506.84

b.

To graph Brooklyn's equation and Matthew's equation on the same graph, we can use the following equations:

Brooklyn's equation: A = 625(1 + 0.025/12)^(12t)

Matthew's equation: A = 446(1 + 0.04/4)^(4t)

Now,

The resulting graph will show the growth of each saving account over time.

The points of intersection on the graph represent the times when the two savings accounts have the same amount of money.

From the graph, we can see that the two accounts intersect at around 11 months and 23 months.

We can say that Brooklyn's savings account grows at a slower rate than Matthew's initially, but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.

Thus,

After two years, Brooklyn will have more money in her savings account than Matthew.

Brooklyn's savings account grows at a slower rate than Matthew's initially but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.

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The probability of getting exactly zero tails is,

⇒ 1/4

We have to given that;

A fair coin is tossed two times in succession.

And, The set of equally likely outcomes in {HH,HT,TH, TT}.

Hence, a total number of 4 outcomes (denominator) and there in only 1 chance (numerator) that you will not get tails.

Thus, the probability of getting exactly zero tails is,

⇒ 1/4

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Complete question is,

A fair coin is tossed two times in succession. The set of equally likely outcomes in {HH,HT,TH, TT}. Find the probability of getting exactly zero tails.​

You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.

Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.

For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.

Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.

The correct answer is C.

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The solution is, the simplification of the equation is :

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

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

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

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The only equation that represents a direct variation is: y - 3x = 0

Direct Variation is defined as the relationship that exists between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If b is directly proportional to a the equation is of the form b = ka (where k is a constant).

Making y the subject in each of the options gives:

A) y = 4x + 8

B) y = 7x - 2

C) y = 3x

D) y = 5x - 2

Looking at them, the only one where there is a relationship that exists between two variables in which one is a constant multiple of the other is option C

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The domain of the quadratic function in this problem is given as follows:

All real values.

The domain of a function is the set of all the possible input values that can be assumed by the function.

On the graph, the domain of the function is given by the values of x of the function.

A quadratic function has no restrictions on the domain, hence it is defined by all the real values.

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The statement "Angle ∠AEC and ∠DEB are complementary angles" is false.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

Angle ∠AEC and ∠DEB are supplementary angles because the sum is 180 degrees.

Thus, the given statement is false.

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The probability that the first student selects Pennsylvania and the second student selects Virginia to the nearest hundredth of a percent is 0.64%.

The probability that the first student selects Pennsylvania is 1/13. Once Pennsylvania has been drawn, there are only 12 colonies left in the bag, so the probability that the second student selects Virginia is 1/12.

To find the probability that both events occur, we multiply the probabilities:

(1/13) x (1/12) = 1/156

To express this probability as a percentage, we multiply by 100:

(1/156) x 100 ≈ 0.64%

Therefore, the probability that the first student selects Pennsylvania and the second student selects Virginia is approximately 0.64%.

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Answer:

We can start by isolating the variable term on one side of the equation and moving all other terms to the other side.

First, we'll add the square root of 5 to both sides of the equation:

m/2 - sqrt(5) + sqrt(5) = 3 + sqrt(5)

Simplifying:

m/2 = 3 + sqrt(5)

Next, we'll multiply both sides of the equation by 2:

m = 2(3 + sqrt(5))

Simplifying:

m = 6 + 2sqrt(5)

Therefore, the value of m is 6 + 2sqrt(5).

Step-by-step explanation:

To determine which objects hold the same amount of liquid as a 96-fluid-ounce jug, we need to convert each of the given measurements to fluid ounces and then add them up. Here are the conversions:

Two 1-quart bottles = 64 fluid ounces (2 x 32)

Two 1-pint bottles = 32 fluid ounces (2 x 16)

One 1-quart bottle and eight 8-ounce fluid glasses = 96 fluid ounces (32 + 8 x 8)

So, the objects that hold the same amount of liquid as a 96-fluid-ounce jug are:

One 1-quart bottle and eight 8-ounce fluid glasses

Three 1-quart bottles

Therefore, the correct answer is:

one 1−quart bottle and eight 8−ounce fluid glasses

three 1−quart bottles

The value of angle between the two vectors is 86⁰.

The value of angle between the two vectors is calculated as follows;

tan θ = vy/vx

where;

( -8, 9), (-9, -6)

vy = (-6 - 9) = -15

vx = (-9 + 8) = -1

tan θ = ( -15 ) / ( -1 )

tan θ = 15

The value of θ is calculated  by taking arc tan of the fraction,;

θ = tan ⁻¹ ( 15 )

θ =  86⁰

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Answer:

The formula for simple interest is:

I = P * r * t

Where:

I = Interest earned

P = Principal amount (initial amount deposited)

r = Annual interest rate (as a decimal)

t = Time in years

Using the given values, we have:

P = $500

r = 0.04 (4% expressed as a decimal)

t = 6 years

I = P * r * t

I = $500 * 0.04 * 6

I = $120

So the interest earned after 6 years is $120. To find the total amount of money in the account, we add the interest to the principal:

Total = P + I

Total = $500 + $120

Total = $620

Therefore, there will be $620 in the account after 6 years.

Step-by-step explanation:

The value of the Expression is 610, 919.

We have,

Expression : [tex]\sum_{n=0}^{61[/tex] 700 (1.07[tex])^{n+1[/tex]

The expression is a summation formula, representing the sum of a series of values.

Here r= 1.07 and n is number of terms.

So, [tex]\sum_{n=0}^{61[/tex] 700 (1.07[tex])^{n+1[/tex]

= 700 (1) +  [tex]\sum_{n=0}^{61[/tex] 700 (1.07[tex])^{n[/tex]

= 700 + 700 ([tex]r^{61[/tex] - 1)/ (r-1)

= 700 + 700 ([tex](1.07)^{61[/tex]-1)/ (0.07)

= 700+ 700 (871.7428)

= 610, 919

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The rectangular coordinates from the polar coordinates are: (-4√2, -4√2)

The steps to  to convert polar coordinates to rectangular coordinates are:

Step 1: Find the x -coordinate for the rectangular coordinate form of the point by using the equation x = r cos(θ)

Step 2: Find the y -coordinate for the rectangular coordinate form of the point by using the equation y = rsin(θ)

Step 3: Write the rectangular coordinates as (x,y) using the results from steps 1 and 2.

We are given the polar coordinates as (8, 225°)

Thus:

x-coordinate of rectangular coordinate = 8 cos 225 = -4√2

y-coordinate of rectangular coordinate = 8 sin 225 = -4√2

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In a case wherby new bicycle sells for $300 It is on sale for 1/4 off the regular price all the expressions that represent the sale price of the bicycle in dollars are

From the option B)300•3/4, we cam see that (300*3)/4 = 225

From the option C)300•(1-1/4),   (300*3)/4 = 225

From the E.)300 - 1/4•300, 300 - 75 = 225

Therefore, the correct options are the option BCE as listd below because they are seen as the one that gives the  regular price all the expressions hence they are correct.

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The mode of the number of pizzas ordered for all 189 stores is [tex]66[/tex]. The Option D is correct.

Mode refer he most frequent number, that is, the number that occurs the highest number of times. To find mode, we must determine the value that appears most frequently in the sample.

From the given data: [tex]28, 53, 35, 66, 35, 28, 66, 48, 53, 53, 66, 53, 66, 66, 35[/tex]. We see that the value 66 appears 5 times, which is more than any other value.

Therefore, the number 66 is the mode.

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The required solution to the equation 1/5 + s = 32/40 is s = 3/5.

To solve the equation 1/5 + s = 32/40 for s, we can begin by subtracting 1/5 from both sides to isolate s:

1/5 + s = 32/40

s = 32/40 - 1/5

We need a common denominator to combine the fractions on the right side of the equation. The least common multiple of 5 and 40 is 40, so we can convert both fractions to have a denominator of 40:

s = (32/40) - (8/40)

s = 24/40

Simplifying the fraction 24/40 by dividing both the numerator and denominator by their greatest common factor, which is 8, we get:

s = 3/5

Therefore, the solution to the equation 1/5 + s = 32/40 is s = 3/5.

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The conclusion is there is not a significant difference between the preference for the three food containers.

The appropriate statistic to use in this case is a chi-squared test. This test will help us determine if there is a significant difference between the preference of the three food containers.

The critical value for the chi-squared test with 2 degrees of freedom is 5.991.

The chi-squared statistic is calculated as follows:

(74-103)²/103 + (103-123)²/123 + (123-103)²/103

= 3.9/3.9

= 1.0

The chi-squared statistic (1.0) is less than the critical value (5.991). Therefore, there is not a significant difference between the preference for the three food containers.

The statistical results can be presented in the following form:

Chi-squared statistic = 1.0

Critical value = 5.991

Therefore, the conclusion is there is not a significant difference between the preference for the three food containers.

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