The entry fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5000 is collected. The number of children attended the fair is___________.

Answer:

A) quantitative

Step-by-step explanation:

A data that can be counted or expressed numerically constitute quantitative data. Quantitative data collection method is capturing statistical data in numbers, figures, or values. Quantitative data collection usually answered the questions of “how many?”, "how much?" and “how often?” are the occurrence of a particular data. These questions are quantitative data collection methods based on numbers and mathematical calculations. Quantitative data collection methods are based on random sampling and structured data collection. Some of the quantitative data collection methods are surveys, questionnaires, quizzes, interviews and direct observation.

Using the mean formula and the data given, the fifth participant’s time to complete the memory task must be 13 seconds to result in a mean (M) of 9 seconds for all five participants.

To find the fifth time recorded when four participants took 7, 8, 8, and 9 seconds to complete a memory task and the mean (M) time is 9 seconds, we need to use the formula for the mean of a sample which is the sum of all values divided by the number of values.

Here's the equation based on the data provided:
(7 + 8 + 8 + 9 + x) / 5 = 9

First, calculate the sum of the times we know:
7 + 8 + 8 + 9 = 32 seconds

Now, insert this sum into the equation and solve for x, where x represents the fifth time:
(32 + x) / 5 = 9
32 + x = 45
x = 45 - 32
x = 13 seconds

The fifth participant must have taken 13 seconds to complete the memory task to have a mean time of 9 seconds.

Answer:

The number of Senators are 120 and number of Representatives are 440.

Step-by-step explanation:

Given,

Total number of members = 560

Solution,

Let the number of Senators be 'x'.

Since, the number of representatives is 160 less than five times the number of senators.

Framing the above sentence in equation form,we get the number of Representative.

So, number of Representative = [tex]5x-160[/tex]

Now, Total number of members is the sum of total number of Senators and total number of representative.

Total number of members = Total number of Senators + Total number of representative

On substituting the values, we get;

[tex]x+5x-160=560\\\\6x=560+160\\\\6x=720\\\\x=\frac{720}{6}\\\\x=120[/tex]

Total number of Senators = 120

So, number of Representative = [tex]5\times120-160=600-160=440[/tex]

Thus the number of Senators are 120 and number of Representatives are 440.

Answer:

h=12, w=24, t=8

Step-by-step explanation:

System of Linear Equations

We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.

We have the following data, being  

w = price of a sweatshirt

t = price of a T-shirt

h = price of a pair of shorts

19.

The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as

[tex]\displaystyle w=2h[/tex]

The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as

[tex]\displaystyle t=h-4[/tex]

The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus

[tex]\displaystyle 3w+2h+5t=136[/tex]

This is the system of equations we need to solve for w,t,h

20.

To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so

[tex]\displaystyle 3(2h)+2h+5(h-4)=136[/tex]

Operating

[tex]\displaystyle 6h+2h+5h-20=136[/tex]

[tex]\displaystyle 13h=156[/tex]

Solving for h

[tex]\displaystyle h=12[/tex]

The other two variables are

[tex]\displaystyle w=2h=24[/tex]

[tex]\displaystyle t=12-4=8[/tex]

if my ans was helpful to u,plz mark my ans as brainliest ans and start following me..

Answer:

Option C.

Step-by-step explanation:

The vertices of triangle PQR are P(3, −6), Q(6, −9), and R(−15, 3).

It is given that triangle PQR dilated by a scale factor of 3 to obtain triangle P′Q′R′.

We know that a figure and its image after dilation are similar. It means triangle PQR and triangle P′Q′R′

If a figure dilated by factor k about the origin then

[tex](x,y)\rightarrow (kx,ky)[/tex]

PQR dilated by a scale factor of 3, so

[tex](x,y)\rightarrow (3x,3y)[/tex]

Using this rule we get

[tex]P(3,-6)\rightarrow P'(3(3),3(-6))=P'(9,-18)[/tex]

[tex]Q(6,-9)\rightarrow Q'(3(6),3(-9))=Q'(18,-27)[/tex]

[tex]R(-15,3)\rightarrow R'(3(-15),3(3))=R'(-45,9)[/tex]

The vertices of image are P'(9,-18), Q'(18,-27) and R'(-45,9).

Therefore, the correct option is C.

Answer:

C

Step-by-step explanation:

Answer:

  0.5

Step-by-step explanation:

We assume your function is

  [tex]f(x)=\sqrt{4-x}[/tex]

The distance formula can be used to find the distance from the point on the curve (x, f(x)) to the origin:

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

Written in vertex form, this is ...

  d^2 = (x -1/2) + 3.75

This has a minimum at x=1/2, so that is the x-coordinate of the point closest to the origin.

In the function f(x) = √(4-x), the x-coordinate of the point on the graph that is closest to the origin is x=0 because the function exists in the first quadrant, meaning the shortest distance to the origin is along the y-axis.

The function described is f(x) = √(4-x). We're looking for the x-coordinate of the point on the graph of this function that is closest to the origin. The distance from any point (x, y) to the origin (0, 0) is given by D=√(x²+y²). For this function, y=f(x) = √(4-x), so the distance can be written as D=√(x²+(4-x)²). To find the minimum distance, we take the derivative of this distance function with respect to x, set it equal to zero and solve for x. However, because this function lives in the first quadrant (y is always equal to or greater than 0), the shortest distance to the origin would be along the y-axis. Thus, the solution is x=0, and that is the x-coordinate of the point on the function's graph that is closest to the origin.

https://brainly.com/question/31871004

#SPJ11

Answer:

15 and 25

Step-by-step explanation:

15+25=40

10+20=30+5+5=10+30=40

Answer:one number is 15 and the other number is 25

Step-by-step explanation:

Let x represent one of the numbers.

Let y represent the other number.

There are 2 numbers and the sum of those numbers are 40. This means that

x + y = 40 - - - - - - - -1

The difference of those numbers is 10. This means that

x - y = 10 - - - - - - - - -2

We would eliminate x by subtracting equation 2 from equation 1, it becomes

2y = 50

y = 50/2 = 25

Substituting y = 25 into equation 1, it becomes

x + 25 = 40 - 25 = 15

Answer:

A. 6 188

B. 749 398

C. 6 188

D. 52 975

E. 20 349

F. 11 316

Explanation:

(a) The shop has 6 types of croissants of which a dozen(12) has to be selected

Therefore n=6, r=12

Repetition of croissants is permitted

And C(n+r-1, r)

C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188

(b) The shop has 6 types of croissants of which three dozen(36) has to be selected

Therefore n=6, r=36

Repetition of croissants is permitted

And C(n+r-1, r)

C(6+36-1, 12) = C(41, 36) = 41!÷ 36!(41-36)! = 41!÷36! 5! = 749 398

(c) The shop has 6 types of croissants of which two dozen(24) has to be selected

Let us first select 2 of each kind which 12 croissants in total. Then we still need to select the remaining 12 croissants

Therefore n=6, r=12

Repetition of croissants is permitted

And C(n+r-1, r)

C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188

(d) The shop has 5 types of croissants of which two dozen(24) has to be selected

Therefore n=5, r=24

Repetition of croissants is permitted

And C(n+r-1, r)

C(5+24-1, 24) = C(28, 24) = 28!÷ 24!(28-24)! = 28!÷24! 4! = 20 475

This problem involves calculating the number of combinations with repetition where the order of choosing croissants does not matter and requires applying the combinatorics formula for such scenarios.

The question asked is concerning the number of ways to choose different quantities of croissants from a croissant shop that has six different types. This is a classic example of a combinatorics problem which falls under the category of counting the number of combinations with repetition.

The counting principle states that if there are 'n' ways to do one thing, and 'm' ways to do another, then there are n * m ways to do both. However, when choosing with repetition where the order does not matter, we use the formula for combinations with repetition: (n + r - 1)! / r!(n - 1)!, where 'n' is the number of types and 'r' is the number of items to be chosen.

Answer:angle DAB will be equal to angle CAB

Step-by-step explanation:

AC is a straight line and forms one of the sides of triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.

The measure of angle DAB will be congruent to angle CAB if AB and CD are parallel and right angles to AC and AD. The relationship changes as point D moves along AC, with angle DAB diminishing if DE remains parallel to AB.

If point D is placed on AC, the measure of ∠DAB will relate to the measure of ∠CAB based on several geometric principles. If AB is parallel to CD and D moves along AC, with DE remaining constantly parallel to AB, the angle at D (∠DAB) will diminish as D moves away from A. If AB and CD maintain parallels and AC makes equal angles with them, then accordingly ∠DAB will also equal ∠CAB at the point where the two angles are bisected by AC.

Moreover, if AB and CD are right angles to AC and AD, as described by the circle theorem stating that angles inscribed in the same arc are congruent, then ∠DAB will be congruent to ∠CAB.

Answer: Coefficient

Step-by-step explanation:

When solving for an unknown variable that has a number preceding it, you will divide both sides of the equation by this number, which is known as the coefficient.

A coefficient is a number preceding any variable in a function for example, given the function 4x, the variable is 'x' and the number preceding it is 4. This number preceding the variable is what we call 'coefficient' of the variable 'x'

The cost will be the same when 1 shirt is ordered.

Cost Comparison

Option 1: Cost = $41 (setup fee) + $10 (shirt price)

Option 2: Cost = $36 (setup fee) + $15 (shirt price)

Let's assume the number of shirts is 'x'.

Equating the costs of both options:

$41 + $10x = $36 + $15x

$5x = $5

x = 1

Therefore, the cost will be the same for 1 shirt.

https://brainly.com/question/33292944

#SPJ2

Answer:

Step-by-step explanation:

Given

Circle has radius [tex]r=5 in.[/tex]

Area of the sector is given by

[tex]A_s=\frac{\theta }{2\pi }\times \pi r^2[/tex]

if [tex]A_s[/tex] is one-sixth  of area of circle then

[tex]A_s=\frac{\pi r^2}{6}[/tex]

[tex]\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2[/tex]

[tex]\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian[/tex]

If [tex]A_s[/tex] is one-fourth of area of circle then

[tex]A_s=\frac{\pi r^2}{4}[/tex]

[tex]\theta =\frac{2\pi }{4}[/tex]

[tex]\theta =\frac{\pi }{2}[/tex]

I've attached the correct image to this answer, just in case they're scrambled.

To match the equation 5x-4y=20 with its graph, convert it to slope-intercept form to identify a positive slope of 5/4 and a y-intercept of -5. Look for a graph with these features in the provided pictures.

To match the equation with its graph for 5x-4y=20, we first need to rewrite it in slope-intercept form, which is y=mx+b. By isolating y, we get 4y = 5x - 20, or y = (5/4)x - 5. This equation signifies a line with a slope (m) of 5/4, meaning for every increase of 4 units in x, y increases by 5 units. The y-intercept (b) is -5, indicating where the line crosses the y-axis. Now, looking at the provided pictures, we should find a graph with a positive slope of 5/4 and a y-intercept of -5.

The correct graph will rise more than it runs since the slope is greater than 1, and will cross the y-axis below the origin at -5. Without seeing the actual images, we are unable to definitively identify which picture corresponds to the given equation. Typically, you would examine each graph to see which one matches these characteristics.

Answer:

floor

Step-by-step explanation:

price floor is a situation when the price changed is greater or leave than the equilibrium price determined by the force of demand and supply. For a price floor to be effective, the minimum price has to be higher than the equilibrium price. It must be set above the equilibrium price. The opposite of price floor is price ceiling.

Answer:

Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.

Step-by-step explanation:

There is 1 in 600 chance to win the grand price (1/600)

There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)

There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)

We can use these probability to calculate the expected gain from this game

[tex]E_g = 700\frac{1}{600} + 200*\frac{1}{300} + 50*\frac{1}{120} = \$2.25[/tex]

Since the cost to play is $3, the expected net gain from this game is

$2.25 - $3 = -$0.75

So this game is not fair as the player is losing money. The appropriate price should instead be $2.25

The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.

Determining Fairness:

The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.

Answer:

C. There were 6,27 times as many people who visited the aquarium on the seventh day as on the first day.

Explanation:

[tex]\displaystyle 1,3^7 = 6,2748517 ≈ 6,27[/tex]

I am joyous to assist you anytime.

Answer:

Option (b) is correct.

The correlation between age and weight  shown in the table is positive.

Step-by-step explanation:

According to the given values, it is found that there is a positive correlation between age and weight.

In this problem, when the age increases, so does the weight, hence they have positive correlation.

More can be learned about correlation coefficients at https://brainly.com/question/25815006

#SPJ2

i got 1.0436 on my calculation hope this helps...

Answer:

The expression representing the Total Cost of the item is  [tex]P + 0.07P[/tex].

Step-by-step explanation:

Given:

Price of Certain item = 'P' dollars

Sales tax =7%

We need to find the expression for Total Cost of the item when tax is applied.

we will first find the Amount deducted in tax;

Amount deducted in Tax is equal to Percentage of sales tax multiplied by Price of Certain item and then divide by 100

Framing in equation form we get;

Amount Deducted in Tax  = [tex]\frac{7}{100}\times P = 0.07P[/tex]

Now Total Cost of the item is equal to sum of Price of Certain item and Amount deducted in tax.

Expressing in expression form we get;

Total Cost of item = [tex]P + 0.07P[/tex]

Hence The expression representing the Total Cost of the item is  [tex]P + 0.07P[/tex].

Answer:

H(160)=150  means that  Kana's height is 150 cm when she is 160 months old

Step-by-step explanation:

According to the model described in the question:

H(t)=X where

Thus H(160)=150 states

Answer:

When Kana was 160 months old, her height was equal to 150 centimeters.

Step-by-step explanation:

Jose will spend 18 minutes on his science homework.

Step-by-step explanation:

Given,

Time Jose have to spend on homework = 5/6 hour

We know that 1 hour = 60 minutes

Therefore;

[tex]\frac{5}{6}\ hour = \frac{5}{6}*60\ minutes\\\\\frac{5}{6}\ hour = 50\ minutes[/tex]

Time Jose have to spend on homework = 50 minutes

Time spent on math home work = [tex]\frac{1}{3}\ of\ his\ time[/tex]

Time spent on math home work = [tex]\frac{1}{3}*50=16.66\ minutes[/tex]

Rounding off to nearest whole minute;

Time spent on math homework = 17 minutes

Time spent on reading homework = 15 minutes

Total time spent = Mathematics + Reading + Science

50 = 17+15+Science

50 = 32 + Science

Science = 50-32 = 18 minutes

Jose will spend 18 minutes on his science homework.

Keywords: addition, fraction

Learn more about fractions at:

#LearnwithBrainly

Step-by-step explanation:

Given data:

Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%.

During the first month, Tran charged $450 and paid $150 of that in his billing cycle.

The expression which will find the amount of interest Tran will be charged after the first month is (0.012)(300)

Here 0.01 because it is 1 month tax.

300 is remaining amount as Tran used $450 but paid $150.

Answer:

its 0.01 [300]

Step-by-step explanation:

Answer:

Credit the buyer $1,776 and debit the seller $1,776.

Step-by-step explanation:

In accounting books the buyer will be credit from $1,776 and seller will be debit from $1,776.

Answer:

1) Credit the buyer $1,776 and debit the seller $1,776.

Step-by-step explanation:

For this, we are to simply understand and follow the calculation of proration. Proration is the allocation or dividing of certain money items at the closing.

The buyer pays:

Total taxes = $ 9540

Total Time Span before closing took place = 2 months and 7 days

Per month charge = [tex]\frac{9540}{12}[/tex] = $795 per month

Charges per day =  [tex]\frac{795}{30}[/tex] =$ 26.5 per day

2 months charge = 795 x 2 = $1590

Charges for 7 days = 7 x 26.5 = $185.5

Total Charges = 1590 + 185.5 = $ 1775.5 ≈ $1776 (Rounding off)

As the property's taxes were paid for by the buyer and the seller was responsible for the day of closing, and buyer paid for the arrears too of the previous 2 months and 7 days, the buyer gets a credit and seller gets a debit. The seller owes the buyer $1776.

Hence,

The buyer gets a credit of $1,776 and Seller gets a debit of $1,776

Question is incomplete, complete question is given below.

Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 3 cm. B) A rectangle with a length of 20 cm and a width of 10 cm. C) A rectangle with a length of 18 cm and a width of 9 cm. D) A rectangle with a length of 27 cm and a width of 3 cm.

Answer:

A) A rectangle with a length of 9 cm and a width of 3 cm.

Step-by-step explanation:

Given,

Length = 21 cm       Width = 7 cm

[tex]Ratio = \frac{Length}{Width}\\\\Ratio = \frac{21}{7}=3:1[/tex]

For the similarity of rectangle the ratio of length to width of any two rectangles should be equal.

So we have four options given;

A) A rectangle with a length of 9 cm and a width of 3 cm.

[tex]Ratio =\frac{9}{3}=3:1[/tex]

Here the ratio is equal as of rectangle A. So this rectangle is similar to rectangle A.

B) A rectangle with a length of 20 cm and a width of 10 cm.

[tex]Ratio =\frac{20}{10}=2:1[/tex]

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

C) A rectangle with a length of 18 cm and a width of 9 cm.

[tex]Ratio =\frac{18}{9}=2:1[/tex]

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

D) A rectangle with a length of 27 cm and a width of 3 cm.

[tex]Ratio =\frac{27}{3}=9:1[/tex]

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

Thus the correct option is A) A rectangle with a length of 9 cm and a width of 3 cm.

Answer:

Eugene friend will have more pie than Eugene.

Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.

Step-by-step explanation:

Given:

Amount of pie Eugene has = 3

Amount of Pie given to friend  = [tex]1\frac{4}{5}[/tex]

[tex]1\frac{4}{5}[/tex] can be Rewritten as [tex]\frac{9}{5}[/tex]

We need to find who has pie and how much more.

We will first find the amount of pie Eugene is left with.

The amount of pie Eugene is left with is equal to Amount of pie Eugene had minus Amount of pie given to friend.

Framing the equation we get;

The amount of pie Eugene is left = [tex]3-\frac{9}{5}[/tex]

We will take LCM to solve the same.

The amount of pie Eugene is left = [tex]3-\frac{9}{5} = \frac{3\times5}{5}-\frac{9}{5} =\frac{15}{5}-\frac{9}{5} = \frac{15-9}{5} =\frac{6}{5}[/tex]

Now  [tex]\frac{9}{5} = 1.8[/tex] and  [tex]\frac{6}{5} = 1.2[/tex]

Hence  [tex]\frac{9}{5}[/tex] is greater than  [tex]\frac{6}{5}[/tex]

Hence Eugene friend will have more pie than Eugene.

Now we will find amount more pie Eugene friend has.

Amount More Eugene friend has can be calculate by Subtracting Amount of of Eugene has with Amount of pie his friend has.

Amount More Eugene friend has =[tex]\frac{9}{5} - \frac{6}{5} =\frac{9-6}{5}= \frac{3}{5}[/tex]

Hence Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.

Answer:

  8

Step-by-step explanation:

There are two choices for each digit, and 3 digits, so 2^3 = 8 possible numbers. Here's a list:

  222, 225, 252, 255

  522, 525, 552, 555

Answer:

8

Step-by-step explanation:

The first digit has two possibilities; it can either be a 2 or a 5.  

The second digit has two possibilities; it can either be a 2 or a 5.

The third digit has two possibilities; it can either be a 2 or a 5.

2 x 2 x 2 = 8 integers.

(Here are the numbers listed out):

222

225

252

255

522

525

552

555

Answer:

A) 14 cm² per sec

B) 0 cm per sec

C) -28 cm per sec

Step-by-step explanation:

We know that,

If l = length of a rectangle and w = width of the rectangle

A) Area of a rectangle,

[tex]A=l\times w[/tex]

Differentiating with respect to t ( time )

[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex]

We have,

[tex]l=12\text{ cm}, w=5\text{ cm}, \frac{dw}{dt}=2\text{ cm per sec}, \frac{dl}{dt}=-2\text{ cm per sec}[/tex]

[tex]\frac{dA}{dt}=12\times 2+5\times -2[/tex]

[tex]\frac{dA}{dt}=24-10[/tex]

[tex]\frac{dA}{dt}=14\text{ square cm per sec}[/tex]

B) Perimeter of the rectangle,

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

Differentiating with respect to t ( time ),

[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})=2(-2+2)=0[/tex]

C) Length of the diagonal,

[tex]D=\sqrt{l^2+w^2}[/tex]

[tex]D^2 = l^2 + w^2[/tex]

Differentiating with respect to t ( time ),

[tex]2D\frac{dD}{dt}=2l\frac{dl}{dt}+2w\frac{dw}{dt}[/tex]

Since, if l = 12 cm, w = 5 cm,

[tex]D=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\text{ cm}[/tex]

[tex]\implies 2\times 13 \frac{dD}{dt}=2(12)(-2)+2(5)(2)[/tex]

[tex]26\frac{dD}{dt}=-48+20=-28\text{ cm per sec}[/tex]

Using implicit differentiation, it is found that:

a) The rate of change of the area of the rectangle is: 14 cm²/sec.

b) The rate of change of the perimeter of the rectangle is: 0 cm/sec.

c) The rate of change of the lengths of the diagonal of the rectangle is: [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.

Item a:

The area of a rectangle of length l and width w is given by:

[tex]A = lw[/tex]

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt}[/tex]

For this problem, the values are:

[tex]w = 5, \frac{dl}{dt} = -2, l = 12, \frac{dw}{dt} = 2[/tex]

Then:

[tex]\frac{dA}{dt} = 5(-2) + 12(2)[/tex]

[tex]\frac{dA}{dt} = 14[/tex]

The rate of change of the area is of 14 cm²/sec.

Item b:

The perimeter is given by:

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

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dP}{dt} = 2\frac{dl}{dt} + 2\frac{dw}{dt}[/tex]

Then

[tex]\frac{dP}{dt} = 2(-2) + 2(2) = 0[/tex]

The rate of change of the perimeter is of 0 cm/sec.

Item c:

The diagonal is the hypotenuse of a right triangle in which the sides are the length and the width, then, applying the Pythagorean Theorem:

[tex]d^2 = l^2 + w^2[/tex]

The value of the diagonal is:

[tex]d^2 = 5^2 + 12^2[/tex]

[tex]d^2 = 169[/tex]

[tex]d = \sqrt{169}[/tex]

[tex]d = 13[/tex]

The rate of change is:

[tex]2d\frac{dd}{dt} = 2l\frac{dl}{dt} + 2w\frac{dw}{dt}[/tex]

Then

[tex]26\frac{dd}{dt} = -48 + 20[/tex]

[tex]26\frac{dd}{dt} = -28[/tex]

[tex]\frac{dd}{dt} = -\frac{14}{13}[/tex]

The rate of change of the lengths of the diagonals of the rectangle  is of [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.

A similar problem is given at https://brainly.com/question/24158553

Answer:

The three questions about the given triangle has been answered below.

Step-by-step explanation:

We are given a right angled triangle whose sides are of length 20, 21 and 29.

(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]

              = [tex]\frac{21}{29}[/tex]

              = 0.72

(2) sin(A) = [tex]\frac{20}{29}[/tex]

     sin(A)  = 0.689

     ∠CAB = [tex]sin^{-1}(0.689)[/tex]

     ∠CAB = 43.551°

(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.

From the given options the angles that satisfy this are 55 , 66 and 75.

45 is not included as then sinA = cosA and that condition is not there.

We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

A: The ratio equivalent to sin(B) is:

[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]

B: The measure of angle ∠CAB is calculated as:

[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]

C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:

55, 65 and 75:

The reason for the angles possible are 55, 66 ,75 is that:

[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]

Thus, we have:

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

Learn more about trigonometric ratios here:

https://brainly.com/question/95152