number of boys:number of girls=11:9 there are 124 more boys than girls work out the total number of students

The first five terms of the sequence \(a_n = 3n/(n+4)\) are:

3/5, 3/4, 9/7, 3/2, 15/9.

What is a sequence?

A sequence in A.P stands for "Arithmetic Progression" which is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.

Now the given expression is

To find the first five terms of the sequence \(a_n = 3n/(n+4),\) we need to substitute the values of n from 1 to 5 and solve for \(a_n\).

a1 = 3*1/(1+4) = 3/5

a2 = 3*2/(2+4) = 3/4

a3 = 3*3/(3+4) = 9/7

a4 = 3*4/(4+4) = 12/8 = 3/2

a5 = 3*5/(5+4) = 15/9

Hence, the first five terms of the sequence \(a_n = 3n/(n+4)\) are:

3/5, 3/4, 9/7, 3/2, 15/9.

To learn more about the sequence, visit:

https://brainly.com/question/6561461

#SPJ4

Answer:

V = 130.08

Step-by-step explanation:

To solve we will use the equation V= \(Pe^r^t\)

V= what you are solving for

P= initial number ( 123)

R= rate (2.8%)

-we can convert the rate to a decimal by moving the decimal place 2 spaces to the left.

R= 0.028

T= time (2 years)

The equation should be... \(V=123e^(^0^.^0^2^8^*^2^)\)

To solve we can first multiply 0.028 and 2

This is = 0.056

\(V=123e^0^.^0^5^6\)

Then using a calculator we get...

V = 130.0845

Given, height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial velocity of 48 feet per second is f(t) = −16e′ + 48t + 6.

Rolle's Theorem states that a differentiable function will have at least one point in the interval (a,b) at which the derivative is equal to zero, provided that f(a) = f(b). Now, we have to determine the velocity at some time in the interval (1, 2) according to Rolle's Theorem.Therefore, f(1) = f(2) should be determined first:

f(1) = −16e + 54f(2) = −16e + 102

Since we have already calculated the values of f(1) and f(2), we can now verify whether they are equal or not. f(1) = f(2) is the condition to be checked.

Since the value of f(1) is not equal to f(2), there is no such time at which the velocity is zero in the interval (1, 2).

Thus, Rolle's Theorem cannot be applied here for finding the velocity.

The value of f(1) is equal to -16e + 54 and f(2) is equal to -16e + 102. There is no such time at which the velocity is zero in the interval (1, 2). Thus, the application of Rolle's Theorem cannot be done to find the velocity.

To know more about Rolle's Theorem visit:

brainly.com/question/32056113

#SPJ11

Answer:

2x - 3y = 21

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

Learn more on unit conversion here: https://brainly.com/question/14614674

#SPJ4

We'll solve this equation:

First, let's apply the distributive property:

‎      ‏‏‎5x + 17 = 4(3x - 1)

‎      ‏‏‎5x + 17 = 12x - 4

Now, add 4 to both sides of the equation:

‎      ‏‏‎5x + 17 = 12x - 4

5x + 17 + 4 = 12x - 4 + 4

‎      ‏‏‎5x + 21 = 12x

Substract 5x from both sides:

‎  ‎     ‏‏‎5x + 21 = 12x

5x - 5x + 21 = 12x - 5x

‎      ‏‏‎‎      ‏‏‎‎   21 = 12x - 5x

‎      ‏‏‎‎      ‏‏‎‎   21 = 7x

Now, divide both sides by 7

‎      ‏‏‎‎   21 ÷ 7 = 7x ÷ 7

Therefore, x = 3.

‎      ‏‏‎‎    

Answer:

Option B. One Solution

Step-by-step explanation:

5x+17= 4(3x-1)

5x+17 = 12x-4

17+4 = 12x-5x

21. = 7x

thus, x=3 (one solution)

Answer:

C. Use a compass and draw an arc across both the legs of the given angle.

Step-by-step explanation:

Step-by-step explanation:

t=20/(r-50)t=20/r-50

The volume of the solid is (25/2)π cubic units.

The volume of the solid obtained by rotating the region bounded by the curves y=x², 0≤x≤5, y=25, and x=0 about the y-axis can be found using the disk method.

Volume = ∫[0 to 25] π(r² - R²) dy

Step 1: Solve y=x² for x to get x=sqrt(y). The outer radius (r) is the distance from the y-axis to x=5, so r=5. The inner radius (R) is the distance from the y-axis to x=sqrt(y), so R=sqrt(y).

Step 2: Substitute r=5 and R=sqrt(y) into the formula.

Volume = ∫[0 to 25] π(5² - (sqrt(y))²) dy

Step 3: Simplify the equation.

Volume = ∫[0 to 25] π(25 - y) dy

Step 4: Integrate the equation with respect to y.

Volume = π[25y - 1/2y²] | [0 to 25]

Step 5: Evaluate the integral.

Volume = π(625 - 625/2) - π(0) = (25/2)π

To know more about integral click on below link:

https://brainly.com/question/18125359#

#SPJ11

Answer:

Heyyyy!!

The answer is 66.9

please read the explanation... it will help... I promise

Step-by-step explanation:

Okay... Here we go...

The context mentions that the two quadrilaterals are similar... meaning their sides are proportional...

So... you basically have to find the scale factor...

(the math itself is easier than the explanation...

51/16 = 3.1875 (that is the number we multiplied the sides of quadrilateral FGHI to get quadrilateral JKLM...

so to get side JK all you have to do is multiply that scale factor by side FG... which after the use of a calculator results in 66.9 (i rounded, and used a calculator... lol)

but yeah... i hope this helps...

Answer:

68%

Step-by-step explanation:

In normal distribution, the empirical rule (aka 68-95-99.7 rule) describes the approximate proportion of data that falls within certain distances from the mean of a normal distribution. Specifically, the rule states that:

Answer: $11.45

Step-by-step explanation:

Arriving 15minutes late simply means 15/60 = 1/4 of the wages has been lost. We then multiply 1/4 by each person's wage. This will be:

Derek = 1/4 × $10.00

= $2.50

Sam = 1/4 × $11.80

= $2.95

Penny = 1/4 × $11.00

= $2.75

Zachary = 1/4 × $13.00

= $3.25

The amount lost will be:

= $2.50 + $2.95 + $2.75 + $3.25

= $11.45

Answer:

B. (–1, –1)

C. (0, 2)

E. (1, –2)

Step-by-step explanation:

plugged in the answers into (x) and (y)

The points (0, 0), (-1, -1), and (1,-2) inside the conic inequality option (B), (C), and (E) are correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Conic inequality:

8x² – 12x + 4y² + 4y – 20 ≤ 0

After plotting the above inequality on a coordinate plane we will get an ellipse:

From the graph:

The points:

(0, 0), (-1, -1), and (1,-2) inside the conic inequality.

Thus, the points (0, 0), (-1, -1), and (1,-2) inside the conic inequality option (B), (C), and (E) are correct.

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ5

Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

To know more about FCFS :

brainly.com/question/32861141

#SPJ11

Answer:

<

Step-by-step explanation:

First, let's find common denominators:

Multiply 3/4 by 2.

Product is 6/8.

Next, let's compare both fractions:

5/8 ? 6/8

5/8 is less than 6/8.

Therefore 5/8 < 6/8.

The researcher draws a random sample using a Multistage cluster sample

At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.

In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.

Learn more about the Multistage cluster sample here:https://brainly.com/question/14937422

#SPJ4

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

In this scenario, the first expression is the HCF of the two expressions.

If the first expression divides the second expression exactly, then the first expression is a factor of the second expression.

The highest common factor (HCF) of two numbers is the largest number that is a factor of both numbers.

Since the first expression is a factor of the second expression, then the first expression is the HCF of the two expressions.

Learn more on HCF :https://brainly.com/question/21504246

#SPJ1

Compared with the graph of the parent function, an equation which shows only a vertical compression by a scale factor of 1/3 and a shift downward of 4 units is: A. y = 1/3∛x - 4.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (1/3x, 1/3y)

Where:

In this scenario, the only equation that is vertically compressed by a scale factor of 1/3 and translated (shifted) downward by 4 units is given by:

y = 1/3∛x - 4.

Read more on function and scale factor here: https://brainly.com/question/11778962

#SPJ1

Answer:

The first part is A

and second part is D

Step-by-step explanation:

100% on edge 2023

Answer:

ST/XY

Step-by-step explanation:

(RT/RX)/(RS/RY)= ST/XY

if the shapes are equal  and the same then the ratio are equal

if RT is corresponds to RX and RS is corresponds to RY then TS corresponds to TS

The sound level β in decibels of a sound with an intensity of i is calculated in relation to the threshold of human hearing I₀ by this equation.
β= 10log (I/ I₀)

The threshold of human hearing is 10⁻¹² watts/ meter²

The sound level of a jet plane is approximately 140 db. The intensity of a sound of a jet plane is approximately 100 db.

One tenth of a bel is equivalent to one decibel, which is a relative unit of measurement. It uses a logarithmic scale to express the ratio of two values of a power or root-power quantity. The power ratio of two signals with a one decibel difference in levels is 101/10, or a root-power ratio of 10¹⁄²⁰

A dishwasher or a washing machine can be heard at 70 dB. It makes a fair amount of noise. Noise levels of 70 dB are not regarded as damaging to human hearing. Extended exposure to noise levels exceeding 55-60 dB, however, may be deemed unsettling or irritating.

Learn more about decibels here brainly.com/question/26848451

#SPJ4

Answer:

12/37

Cos D = 12/37

Answer:

The lines are parallel

Step-by-step explanation:

When lines are parallel they travel side-by-side without ever crossing paths.

Answer: Parallel

Step-by-step explanation:

Two parellel lines have the same slope, thus will never cross, regardless of how far in each direction you go. This is true of the image attached, thus the lines are parallel.

118.4 - 6.4 = 112

314.944 - 3.7 = 311.244

1,840.5072 + 23.56 = 1864.0672

325 - 2.5 = 322.5

196 + 3.5 = 199.5

405 + 4.5 = 409.5

3,437.5 +5.5 = 3443

393.75 +5.25 = 399

2,625 + 6.25 = 2631.25

231 + 8.25 = 239.25

92 + 5.75 = 97.75

196 + 12.25 = 208.25

117 - 6.5 = 110.5

936 + 9.75 = 945.75

305 + 12.2 = 317.2

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

To learn more about trigonometric functions visit:

brainly.com/question/25618616  

#SPJ11

Answer:

144

Step-by-step explanation:

first you gotta do 3x4 which is 12 then 12x12. and then you get 144.

Robert will run a total of 144 miles during the 12 weeks.

Given:

Robert runs 3 times a week for 12 weeks.

So, total number of runs will be:

= 3 runs/week * 12 weeks

= 36 runs

Since each run is 4 miles, multiply the total number of runs by the distance per run:

= 36 runs * 4 miles/run

= 144 miles

Therefore, Robert will run a total of 144 miles.

Learn more about Unitary Method here:

https://brainly.com/question/28276953

#SPJ6

Step-by-step explanation:

a no. is divisible by 4 if the last two digits are a mutiple of 4

Answer:

(i), (iii), (v).

Step-by-step explanation:

If a number is divisible by 4 then its last 2 digits are divisible by 4.

For example 23408 is because 08  is divisible by 4.

Answer: You just have to multiply the percent and divide it by the weight.

Step-by-step explanation:

90%*40%= 3600

3600/600= 6 grams

Answer: Refer to Step-by-step explanation

Step-by-step explanation:

To find the MAD

Step 1 Find the mean of the data.

Step 2 Find the distance between each data value and the mean.

Step 3 Add the distances together from Step 2

Step 4 Divide the sum in Step 3 by the total number of values in the data.

1) MAD = 21.36

2) Mean = 56

MAD = 3.75

3) Mean = 57

MAD = 16.67