Prove that every positive integer can be expressed as the sum of distinct Fibonacci numbers.
For example, 20=2+5+13 where 2,5,13 are Fibonacci numbers. Although we can write 20 = 2+5+5+8, this does not illustrate the result because we have used 5 twice.

Answer:

50 hours

Step-by-step explanation:

Josh = 50 hours

frank worked 50 hours less and twice as many hours as josh did.

Frank = 2(Josh) - 50 hours

= 2(50 hours) - 50 hours

= 100 hours - 50 hours

= 50 hours

Therefore, Frank worked for 50 hours

Answer:

A rectangle is a good, simple shape to begin with. The area of a rectangle is equal to the product of the length of its base and the length of its height. The height is a segment that is perpendicular to the base. For a rectangle, the base and height are often called the "length" and the "width", and sometimes the height is referred to as the "altitude."

Step-by-step explanation

Mark me as brainiest

Answer:

89,680,000

Step-by-step explanation:

236,000×20=4,720,000×19=89,680,000

Answer:36518640

Step-by-step explanation:

The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

The area of the tray is approximately 28.26 square inches.

To find the area of the tray, we need to use the formula for the area of a circle, which is:

Area = π x radius²

Here, π (pronounced "pi") is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Its approximate value is 3.14.

In our case, the radius of the tray is given as 3 inches. So, we can substitute this value into the formula and calculate the area as follows:

Area = π x 3²

= 3.14 x 9

= 28.26 square inches

This means that if we were to cover the tray completely with paint or any other material, it would require 28.26 square inches of that material.

To know more about area here

https://brainly.com/question/14994710

#SPJ1

We can use the analysis of variance procedure to test hypotheses about three or more groups and their mean differences. ANOVA is a powerful tool for testing hypotheses about differences among group means, variability within and between groups, and interaction effects in multifactor studies.

The procedure compares the variability between the groups to the variability within the groups, and determines whether the observed differences in means are statistically significant. This can be used to test hypotheses about the effect of a treatment, the comparison of multiple groups, or the relationship between an independent variable and a dependent variable. Overall, the analysis of variance procedure provides a powerful tool for hypothesis testing in research, and can be used to draw conclusions about the population from a sample of data. The analysis of variance (ANOVA) procedure is a statistical method used to test hypotheses about:

Differences among group means: ANOVA helps to determine if there are significant differences among three or more group means, enabling researchers to compare multiple groups simultaneously. Variability within and between groups: ANOVA compares the variability of data points within each group to the variability between groups. This analysis helps identify if the variation is due to factors of interest or random chance. Interaction effects: In a multifactor ANOVA, the procedure can test for interaction effects between independent variables. This helps to understand if the effect of one factor on the dependent variable is dependent on the levels of another factor.

To know more about hypotheses visit:-

https://brainly.com/question/28269566

#SPJ11

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

For more questions on: compound interest

https://brainly.com/question/31474686

#SPJ8

Number of phone calls the first evening: 17

Number of phone calls the second evening: 88

Number of phone calls on the third evening:​ 22

Given that Lena received a total of 127 phone calls at the call center.

On the third evening, she received 5 more calls than the first evening.

On the second evening, she received 4 times as many calls as on the third evening.

We have to calculate, How many phone calls did she receive each evening?

Let's say on the first day she received x calls

then the number of calls received on the third day = x + 5

number of calls received on second day = 4(x + 5)

Now, x + x + 5 + 4(x + 5) = 127 ( given )

6x + 25 = 127

6x = 102

x = 17

So the number of calls received on the first day = is 17

number of calls received on the second day = 88

number of calls received on the third day = 22

To know more about linear equation follow the given link:

https://brainly.com/question/28307569

Answer:

a. DE < 6This is the correct

answer.Since angle C is larger than

angle F, then the length of the side

of angle C would be greater than

that of angle F. Hope it helps........

✨✨✨

The only conclusion we can make for sure about side DE is that it is longer than side AB.

We can determine the following about side DE: 1. Since we know that < C is larger than < F, we can conclude that side DE is longer than side AB. This is because in a triangle, if an angle is larger, the side opposite that angle is longer.

2. However, we cannot determine the exact length of side DE based solely on the information provided. The length of side DE will depend on the specific measurements of angles < C and < F.

3. To determine the exact length of side DE, we would need additional information such as the measurements of angles < C and < F, or the lengths of other sides of the triangle.

4. Therefore, the only conclusion we can make for sure about side DE is that it is longer than side AB, but we cannot determine its exact length without further information.

To know more about length here

https://brainly.com/question/2217700

#SPJ2

Answer:

If x = -0.25 and y = -6 then we have -6(-0.25) = 1.5

Hope this helps!

When the radius is 10 inches and the height is 20 inches

(a) rate change of the volume of the cylinder is 5340.7 inch²/min.

(b) rate of change of the surface area of the cylinder is 1068.14 inch²/min.

Volume and surface area of the closed cylinder both increase with time.

Let r be the Radius and h be the height of the cylinder in inches at time t.

\(\frac{dr}{dt} =5\) inch/min and \(\frac{dh}{dt} =-3\) inch/min

Let V be the volume of the cylinder then

Differentiating with respect to t,

\(\frac{dV}{dt} =2\pi r(\frac{dr}{dt} )h+\pi r^{2} \frac{dh}{dt}\)

At r=10 inch and h=20 inch,

\(\frac{dV}{dt} =1700\pi =\) 5340.7 inch²/min ≈ 5000 inch²/min

Thus, it is increasing with time as it has a positive sign.

Let S be the surface area of a closed cylinder

\(\frac{dS}{dt} =2\pi r(\frac{dr}{dt} )h+2\pi r(\frac{dr}{dt} )+4\pi (\frac{dr}{dt} )r\)

At r=20 inch and h=20 inch

\(\frac{dS}{dt} =340\pi =\) 1068.14 inch²/min ≈ 1000 inch²/min

It is also increasing with time as it is also having a positive sign.

To learn more about Volume and surface area visit:

https://brainly.com/question/28027357

#SPJ4

Answer:

38

Step-by-step explanation:

You need to follow the rule of bodmas.

Brackets first, then multiplication and division, then addition and subtraction.

(4 x 8) + 6 = 32 + 6 = 38

Answer:

38

Step-by-step explanation:

(4 x 8) + 6

32 + 6

38

Answer:

2/3=More

1/4=less

7/8=more

2/6=less

2/4=equal

Step-by-step explanation:

Look at each model that shows each fraction and also look at the denominators and the numerators of each fraction.

#1

Greater than 1/2

#2

Less than 1/2

#3

Greater than 1/2

#4

Less than 1/2

#5

Equal to 1/2

The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

\(15^{3}\)

Step-by-step explanation:

\(15^{3} =(15)(15)(15)=3375\)

Hope this helps

Solving a system by graphing not be the best way to solve it as sometimes it is too time-consuming, and also we cannot solve complex equations with large numbers easily by this.

Solving systems by graphing can be a useful tool, but it is not always the best way to solve a system. Graphs can be difficult to interpret, and it can be difficult to determine if a solution exists based on the graph alone.

Additionally, graphing systems may not be the most efficient way to solve a system, as the process can be time-consuming and require a lot of calculations for larger systems.

Finally, graphing systems can be difficult for systems with large numbers of variables or complex equations, as it can be difficult to accurately draw a graph for such systems.

Learn more about graphs:

https://brainly.com/question/29427540

#SPJ4

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

288

Step-by-step explanation:

32 x 9=288

Answer:

-48

Step-by-step explanation:

the second option, on the second attachment

domain: -6<x<-2 or x>-2

range: -3\(\leq\)y\(\leq\)1 or 4<y<8

Let's calculate the total cost of all the items purchased by the computer club:

Cost of 14 portfolios = 14 * $24.59

Cost of 14 binders = 14 * $12.92

Cost of 14 school sweatshirts = 14 * $14.00

Cost of 14 music cases = 14 * $1.25

Cost of 14 phone cases = 14 * $1.99

Cost of 14 mouse pads = 14 * $2.14

Total cost of all items = Cost of 14 portfolios + Cost of 14 binders + Cost of 14 school sweatshirts + Cost of 14 music cases + Cost of 14 phone cases + Cost of 14 mouse pads

Plugging in the given values:

Total cost of all items = (14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14)

Now, the computer club will pay for 40% of the total cost. To calculate this, we can multiply the total cost by 40% (or 0.40):

Club's payment = 0.40 * Total cost of all items

The remaining cost will be divided equally among the 14 members:

Remaining cost per member = (Total cost of all items - Club's payment) / 14

Plugging in the values and calculating:

Club's payment = 0.40 * ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14))

Remaining cost per member = ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14) - Club's payment) / 14

So, each member of the computer club will owe the calculated value for "Remaining cost per member".

Hope this is good

The process that generates more values that are more than 2 standard deviations from the mean is called a "fat-tailed" distribution.

In a fat-tailed distribution, the probability of extreme values occurring is higher compared to a normal distribution.

To understand this concept, let's consider two processes: Process A and Process B.

Process A generates a dataset with a normal distribution, while Process B generates a dataset with a fat-tailed distribution.

In a normal distribution, the majority of the data falls close to the mean, with fewer values farther away.

The probability of values more than 2 standard deviations from the mean is relatively low.

On the other hand, in a fat-tailed distribution, there is a higher likelihood of extreme values occurring.

This means that the probability of values more than 2 standard deviations from the mean is higher.

For example, let's say we have two datasets: Dataset A generated by Process A and Dataset B generated by Process B.

We calculate the mean and standard deviation for both datasets.

In Dataset A, if the mean is 50 and the standard deviation is 5, then values more than 2 standard deviations away from the mean would be greater than 60 or less than 40.

In Dataset B, if the mean is 50 and the standard deviation is also 5, then values more than 2 standard deviations away from the mean would have a wider range.

These values could be significantly higher than 60 or lower than 40, depending on the specific distribution of Dataset B.

Therefore, if Process B generates a fat-tailed distribution, it is more likely to produce values that are more than 2 standard deviations from the mean compared to Process A and its normal distribution.

In summary, the process that generates more values that are more than 2 standard deviations from the mean is a fat-tailed distribution, which has a higher likelihood of extreme values occurring.

To know more about deviations visit:

https://brainly.com/question/31835352

#SPJ11

Answer:

-2(-6+3y-1) = -6y+14

Step-by-step explanation:

Answer:

that answer is A plusjsh

Answer:

x+8*2=57.4

x=41.4

Step-by-step explanation:

Peter is thinking about a number. So, let's represent that number by x. So, he adds 8 to that number. x+8 so far. Then he doubles the result. x+8*2  to get an answer of 57.4. x+8*2=57.4. Ok, now in order to solve for x we would take 8*2 and get 16. 57.4-16=41.4. Now we know that x is 41.4. Substitute x into the equation. 41.4+8*2=57.4. 57.4=57.4. Have a great day! :)))))

The height of the tree is 20 feet.

Cross-multiplying is a mathematical operation that is used to solve equations that involve fractions or ratios. It involves multiplying both sides of an equation by the product of the denominators of the fractions in the equation.  

Let's call the height of the tree h.

Then, we have two similar triangles: John's shadow triangle and the tree's shadow triangle.

The height of the tree corresponds to the height of the tree's shadow triangle, and the height of John corresponds to the height of John's shadow triangle.

The ratio of the height of the tree's shadow triangle to the length of its base (the length of the tree's shadow) is the same as the ratio of the height of John's shadow triangle to the length of its base (the length of John's shadow).

So, we can set up the following proportion:

h/30 = 6/(30-21)

Simplifying this equation, we get:

h/30 = 6/9

h = (6/9) × 30

h = 20

Therefore, the height of the tree is 20 feet.

To know more about perimeter, visit:

https://brainly.com/question/7067665

#SPJ9

The complete question is:

John, who is exactly 6 feet tall, wants to measure the height of a tree using similar triangles. He measures the shadow of a tree to be 30 feet long. He then walks from the end of the shadow, towards the tree, until the tip of his shadow exactly overlaps the tip of the trees shadow . At that point he is 21 feet from the tree. What is the height of the tree?