the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths

Answers

Answer 1

Answer:

Length of the rectangle:

[tex]x = \frac{4800}{106} = \frac{2400}{53} [/tex]

Breadth of the rectangle:

[tex]60\%(x) = \frac{60}{100} \times \frac{4800}{106} \: \: \: \: \: \: \: \: \: \: \: \\ =60 \times \frac{48}{106} \\ = \frac{2880}{106} [/tex]

Step-by-step explanation:

Longer side of the rectangle(length) = x

Shorter side of the rectangle(breadth) = (60%)x

Perimeter of the rectangle = 2(l+b) = 96 inches

Hence,

[tex]96 = 2(x + 60\%(x))[/tex]

[tex]96 = 2(x + \frac{6}{100 } x)[/tex]

[tex]96 = 2( \frac{100}{1 00} x + \frac{6}{100} x)[/tex]

[tex]96 = 2( \frac{106}{100} x)[/tex]

[tex]96 = \frac{106}{50} x[/tex]

[tex]96 \div \frac{106}{50} = x[/tex]

[tex]96 \times \frac{50}{106} = x[/tex]

[tex] \frac{4800}{106} = x[/tex]


Related Questions

Simplify 6/x^2−2x/x^2+3.

Answers

Answer:

3x2−2x+6/x2

Step-by-step explanation:

have a great day <33333

SCALCET8 3.9.004.MI. The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 15 cm and the width is 7 cm, how fast is the area of the rectangle increasing

Answers

Answer:

The area of the rectangle is increasing at a rate of 169 cm²/s

Step-by-step explanation:

Given;

increase in the length of the rectangle, [tex]\frac{dL}{dt} = 7 \ cm/s[/tex]

increase in the width of the rectangle, [tex]\frac{dW}{dt} = 8 \ cm/s[/tex]

length, L = 15 cm

width, W = 7 cm

The increase in Area is calculated as;

[tex]Area = Length \times Width\\\\A = LW\\\\\frac{dA}{dt} = L(\frac{dW}{dt} )\ + \ W(\frac{dL}{dt} )\\\\\frac{dA}{dt} = 15 \ cm(8\ \frac{ cm}{s} ) \ + \ 7 \ cm(7\ \frac{ cm}{s} ) \\\\\frac{dA}{dt} = 120 \ cm^2/s \ + \ 49 \ cm^2/s\\\\\frac{dA}{dt} = 169 \ cm^2/s[/tex]

Therefore, the area of the rectangle is increasing at a rate of 169 cm²/s

15. Which of the following is a rational number?
O A.V-
O B. 18
O C. T (3.141592...)
OD.3.59

Answers

Answer:

c

Step-by-step explanation:

non terminating recurring. i think option c must be the answer

Use the value of phi = 1.618 to predict the 23rd number in the Fibonacci sequence. The 22nd number in the sequence is 17,711.

- 10,946

- 17,711

- 22,897

- 28,656

Answers

Given:

[tex]\phi=1.618[/tex]

22nd number in Fibonacci sequence = 17,711

To find:

The 23rd number in the Fibonacci sequence.

Solution:

The nth term of a Fibonacci sequence is:

[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]

Substituting [tex]\phi=1.618, n=21[/tex], we get

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=10941.1724024[/tex]

[tex]f_{21}\approx 10941[/tex]

Now,

[tex]f_{23}=f_{21}+f_{22}[/tex]

[tex]f_{23}=10941+17711[/tex]

[tex]f_{23}=28652[/tex]

It is about 28,656. Therefore, the correct option is D.

Hello can anyone pls help with this multiple choice question

Answers

Answer:

The correct answer is the last one

Step-by-step explanation:


2. If 5 mg in 2 ml of liquid medication, how many mg is in 4 ml of medication?

Answers

Answer:

10mg

Step-by-step explanation:

We have a proportional relationship.

We know that there are 5mg in 2ml of liquid medication.

Now we want to know how many mg there are in 4 ml of medication.

First, we can rewrite it as:

4ml = 2ml + 2ml

And we know that, in every 2 ml of medicine, there are 5mg.

Then if we have two times 2ml of medicine, we have two times 5mg.

This is:

2*5mg = 10mg

Question 5 of 10
Select the correct answer.
The graph shows a line of best fit for data collected on the average temperature, in degrees Fahrenheit, during a month and the
number of inches of rainfall during that month.
Average Temp.
90
80
70
60
50
404
30
20
10
1 1 2 3 4 5 6
X
Inches of Rain
The equation for the line of best fit is y = -3.32x + 97.05.
Based on the line of best fit, what would be the prediction for the average temperature during a month with 13.25 inches of rainfall?

Answers

Answer:

53.06°F

Step-by-step explanation:

Given the equation of best fit :

y=-3.32x +97.05.

The average temperature for a month with 13.25 inches of Rainfall

Amount of Rainfall = x

Average temperature = y

To make our prediction ; put x = 13.25 in the equation and solve for y ;

y = -3.32x +97.05

Put x = 13.25

y = -3.32(13.25) +97.05

y = - 43.99 + 97.05

y = 53.06°F

What does point b represent on the graph ?

Answers

You need to add the photo

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation:

Sidney's retirement party costs $28, plus an additional $1 for each guest she invites. What is the maximum number of guests there can be if Sidney can afford to spend a total of $44 on her retirement party?

Answers

Answer:

16 guests

Step-by-step explanation:

Firstly, we know Sidney's retirement party costs a starting amount of $28. We also know that she can only spend $44 on her retirement party. The easiest way to do it in my opinion is subtract 28 from 44, giving you 16. Since we know that each guest is only $1, we know that the maximum number of guests Sidney can afford is 16 guests. I hope this helped and please don't hesitate to ask for clarification!

$44-$28=$16

$16÷$1=16 guests at most

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score less than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789. What is the appropriate conclusion

Answers

Answer:

The p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Step-by-step explanation:

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before.

At the null hypothesis, we test if the two means are equal, that is, the subtraction of them is 0.

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, we test if the two means are different, that is, the subtraction of them is different of 0. So

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789.

Considering a standard significance level of 0.02789, the p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Write the equations for a line parallel to the line:
y=-4/3x-4
That goes through the point (-7,-6)
Write your equation in slope intercept form, using reduced fractions for the slope and intercept if necessary.

Answers

Answer:

y = -4/3x -46/3

Step-by-step explanation:

The question tells us to write an equation that is:

- parallel to the given line

- goes through the point (-7, -6)

Parallel lines will have the same slope, because if the slope was different, they would eventually intersect and not be parallel lines anymore.

We are going to use the point-slope form to find the other line.

Point-slope form uses a point that the graph will cross through and the slope of the graph to find the graph in y = mx + b form (also called slope-intercept form).

(I attached the point-slope form as an image below)

m = slope

x1 = x coordinate of the point

y1 = y coordinate of the point

We are going to substitute our slope into the form first:

y - y1 = (-4/3)(x - x1)

Next let's put in our point (-7, -6):

(Remember! -7 is our x coordinate & -6 is our y coordinate :-) )

y - (-6) = -4/3(x - (-7))

(cancel out the negatives to make them positive)

y + 6 = -4/3 (x +7)

Now solve for x using basic algebra:

y + 6 = -4/3 (x +7)

(distribue the -4/3)

y + 6 = -4/3x - 28/3

(subtract 6 from both sides)

y = -4/3x -46/3

That's your answer!

Hope it helps (●'◡'●)

Answer:

Step-by-step explanation:

y + 6 = -4/3(x + 7)

y + 6 = -4/3x - 28/3

y + 18/3 = -4/3x - 28/3

y = -4/3x - 46/3

A decorative wall in a garden is to be build using bricks that are 3 3/4 inches thick and mortar joints that are 1/4 inch. Use the diagram to find the height of the wall

Answers

Step-by-step explanation:

we cannot see the diagram, so we don't know how many layers of bricks are used. and therefore it is impossible to tell the height of the wall.

Complete the angle addition postulate for the following angle

Answers

Answer:

measurement m<GEM+m<MEO=m<GEO

Find the value for the side marked below.
Round your answer to the nearest tenth.
у
100
49°
y = [?]

Answers

Answer:

y = 75.5

Step-by-step explanation:

Reference angle (θ) = 49°

Hypotenuse = 100

Opposite = y

Apply trigonometric function, SOH. Which is:

Sin θ = Opp/Hyp

Plug in the values

Sin 49 = y/100

100*Sin 49 = y

y = 75.5 (nearest tenth)

A senior class of 420 students will rent buses and vans for a class trip. Each bus can transport 50 students and 3 chaperones and costs $1200 to rent. Each van can transport 10 students and 1 chaperone and costs $100 to rent. There are 36 chaperones available (so they can't all go in vans). How many vehicles of each type should be rented in order to minimize the cost

Answers

Answer:

37 buses and 1 van.

Step-by-step explanation:

The cost to rent a van is $1200 for 50 students and 3 chaperones, while a bus for 10 students and a chaperone is $100 .

The cost of renting buses for 50 students is $500

What we do is rent 37 buses and 1 van

37 buses will take in 370 students with empty 2 spaces in 2 buses for chaperones since the chaperones are 36.

Then rent 1 van to take in 50 students and 1 chaperone.

The total cost here will be

$3700 + $1200 = $ 4900

This will help to safe cost.

solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.​

Answers

Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]

Step-by-step explanation:

Given

In equality is [tex]x^3+4x>5x^2[/tex]

Taking terms one side

[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]

Using wavy curve method

[tex]x\in (0,1)\cup (4,\infty)[/tex]

SCALCET8 3.11.501.XP. Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(ln(4)) (b) sinh(4)

Answers

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Which of the following best describes the relationship between angle a and angle bin the image below?

Answers

The answer is angle 2
angle 2 is the answer

3.6 subtract by 1.487 is egual to ______.Pls write in step by step.​

Answers

Answer:

2.113

Step-by-step explanation:

 

               [tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]

what is equivalent to x-2(3x-1)=3x

Answers

Answer:

1/4 = x

Step-by-step explanation:

x - 2( 3x - 1 ) = 3x

Step 1 :- Distribute 2

x - 2 × 3x - 2 × 1 = 3x

x - 6x + 2 = 3x

Step 2:- Combine like terms

-5x + 2 = 3x

Step 3 :- Add 5x to both sides

-5x + 5x + 2 = 3x + 5x

2 = 8x

Step 4 :- Divide both side by 8

2/8 = 8x / 8

1/4 = x

helppp!! 21 - 3y = -18
3x+ y = -5

Answers

Answer:

(-3,4)

Step-by-step explanation:

A system of equations is given to us. The given equations are ,

[tex]\implies 2x - 3y = -18[/tex]

[tex]\implies 3x + y =-5[/tex]

We need to plot the graph and find the solution of the given system . For that refer to attachment . The point at which both the lines of the graph will intersect each other will be the solution of the given system of equations .

From the graph we can see that it intersect at (-3,4) . Therefore the Solution is ,

[tex]\longrightarrow \underline{\underline{ Solution = (-3,4)}}[/tex]

Answer: If you graphing it’s (-6, 13) or (3, 4)

Step-by-step explanation:

21 - 3y = -18- y = 13

3x + y = -5- x = -6

please give full solutions
√8281​

Answers

Answer:

the answer is 91

Step-by-step explanation:

We have the number of emergency room admissions to SWTRHA hospital on 6 different Friday the 13ths along with the number of admissions to the same hospital on the previous Friday the 6th. Is there any difference between admissions on the 6th and the 13th. Conduct a depedent samples t-test to find out. What is the value of your t Stat

Answers

Answer:

Test statistic = - 2.71

Step-by-step explanation:

Table of the sample data is attached below :

Using a dependent sample t test :

H0 : μd = 0

H0 : μd ≠ 0

The difference in the 6th and 13th date data is :

Difference, d = -4, -6, -3, -1, 1, -7

The sample size, n = 6

The mean of d ; μd = Σd/ n = - 3.667

Standard deviation of difference, Sd = 3.011

The test statistic : μd/(Sd/√n)

Test statistic = - 3.33 / (3.011/√6)

Test statistic = - 3.33 / 1.2292356

Test statistic = - 2.709

Test statistic = - 2.71

the sum of the first ten terms of an arithmetic progression consisting of positive integers is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960

Answers

Answer:

The correct answer is = 15.

Step-by-step explanation:

Formula:

The sum of the first n terms of an arithmetic progression with first term a and constant difference d is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]

using this formula in this problem

Solution:

The sum of the first ten terms is

[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]

[tex]S_{10}=5(2a+9d)[/tex]

The sum of the 20th, 21st, and 22nd terms is three times the 21st term:

[tex]3a_{21}=3(a+(21-1)d)[/tex]

[tex]3a_{21}=3(a+20d)[/tex]

[tex]3a_{21}=3a+60d[/tex]

The problem then tells us

[tex]S_{10}=3a_{21}[/tex]

[tex]10a+45d=3a+60d[/tex]

[tex]7a=15d[/tex]

there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is

then, 15, 22, 29, 36, ...

The problem says to find the number of terms n for which the sum is 960:

putting value in the formula

[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]

solving quadratic will give n = 15

thus, the correct answer is 15.

answer please don't skip plz answer

What is the value of x^2

-2xy+y^2

if x-y = 4 ?

please answer ​

Answers

Answer:

16

Step-by-step explanation:

[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]

                   [tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]

The value of x^2-2xy+y^2

will be 16 .

Explanation is in the attachment .

hope it is helpful to you ☺️

What is the meaning proportion between 3 and 27?​

Answers

Answer:

you mean the mean not the meaning right?

The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.

an oil tank, which is a shape of a cylinder, is 3m high and has a diameter of 6m. the oil tank is two-thirds full. find the number of cubic meters of oil in the tank. use 3.14 for pi

Answers

Answer:

Step-by-step explanation:

The key is to find out the entire volume the tank can hold when it is full, then take 2/3 of that amount. The volume of a cylinder is

[tex]V=\pi r^2h[/tex] and filling in:

[tex]V=3.14(3)^2(3)[/tex] (if the diameter is 6 m, the radius is 3) so

V = 84.78 m³ when it is full all the way. If we need the amount that makes up 2/3 of that:

[tex]\frac{2}{3}(84.78)=56.52m^3[/tex]

What is the probability that in a sample of 400 registered voters to at least 290 voted in their most recent local

Answers

Answer:

The probability that in a sample of 400 registered voters at least 290 voted in their most recent local elections is:

= 72.5%

Step-by-step explanation:

Sample of registered voters = 400

Sample of voters that actually voted = 290

Probability = 290/400 * 100

= 72.5%

b) This result above gives the statistic that for every 100 registered voters, 72.5 voters voted.  Probability measures the chance of an event occurring given other events.  Therefore, one can conclude that the voting was at least 72.5%.  Inversely, 27.5% of the registered voters did not participate or cast their ballots in the local elections.

An ordinary fair die is a cube with the numbers one through six on the sides represented by painted that. Imagine that such a die is rolled twice in succession and that the face values of the two goals are added together. This song is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event a: the sun is greater than six

Answers

Answer:

ok so what i think your trying to ask is if we roll two dice that the sum will be more then 6

Two dice

Assuming that the dice are unbiased or not " loaded".

Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.

How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?

These are the possibilities

Case 1.

D1 =1 & D2=5

Or

D1= 5 & D2=1

Case 2.

D1 =2 & D2=4

Or

D1= 4 & D2= 2

Case 3. D1=3, D2=3

P3 =0.027778

Let's say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.

The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.

P1= 0.02778+ 0.02778 =0.055558

P2= 0.02778+0.02778 =0.055558

Same way,

P3=0.027778, when there is only one way to get the sum 6.

So, P = 0.138894

Based on truncating at the sixth decimal place.

A visual representation with two unbiased dice and the possible cases would also give the same result and is a short cut method. I like to derive from the basics.

Hope This Helps!!!

What is the area of triangle ABC? - OP 03 square units 0 7 square units o 11 square units 0 15 square units see pic​

Answers

The answers ir 15 square units

Answer:

7 sq unit

Step-by-step explanation:

Area of triagle ABC = Area of rectangle mnBp - Area of trangle AmC - Are of triangle CnB - Area of triangle ABp

Area of rectangle mnBp = 5x3 = 15 sq unit

Area of trangle AmC = 4x2 /2 = 4 sq unit

Are of triangle CnB = 5x1 /2 = 2.5 sq unit

Area of triangle ABp = 3x1 /2 = 1.5 sq unit

I believe you can work out thd answer from the above

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