Complete Question
It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample 150 of each gender was selected from recent hospital records, and the following results were obtained.
Men. 43 patients had high blood pressure
Woman. 52 patients had high blood pressure.
Answer:
The 95% confidence interval is
[tex]- 0.1651 < p_m - p_f <0.0451[/tex]
This mean that there is a 95 % confidence that the difference between the true proportions of male and female that are hypertensive is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive
Step-by-step explanation:
From the question we are told that
The sample size for male is [tex]n_1 = 150[/tex]
The number of male that are hypertensive is [tex]m = 42[/tex]
The sample size of female is [tex]n_2 = 150[/tex]
The number of female that are hypertensive is [tex]q = 52[/tex]
The proportion of male that are hypertensive is mathematically represented as
[tex]\r p_m = \frac{43}{150}[/tex]
[tex]\r p_m = 0.287[/tex]
The proportion of female that are hypertensive is mathematically represented as
[tex]p_f = \frac{52}{150}[/tex]
[tex]p_f = 0.347[/tex]
From the question we are told that confidence level is 95%, hence the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =5\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{ \r p_m (1- \r p_m )}{n_1} + \frac{ \r p_f (1- \r p_f )}{n_2} }[/tex]
substituting value
[tex]E = 1.96 * \sqrt{\frac{ 0.287 (1- 0.287 )}{150} + \frac{ 0.347 (1- 0.347 )}{150} }[/tex]
[tex]E = 0.1051[/tex]
The 95% confidence interval is mathematically represented as
[tex](\r p_m - \r p_f ) - E < p_m - p_f < (\r p_m - \r p_f ) + E[/tex]
substituting values
[tex]( 0.287 - 0.347 ) - 0.1051 < p_m - p_f <( 0.287 - 0.347 ) + 0.1051[/tex]
[tex]- 0.1651 < p_m - p_f <0.0451[/tex]
This mean that there is a 95 % confidence that the difference between the true proportion is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive.
I need help please, show work
Answer:
24 and 32 ft or 32 and 24 ft
Step-by-step explanation:
Perimeter of rectangle(p)=2(l+b)
or, 112/2=l+b
Therefore, l+b=56
Now,
diagonal(d)=40
By pythogoras theorem,
h^2=p^2+b^2 (d=h here)
40^2=l^2+b^2
Now,
Square l+b=56
(l+b)^2=56^2
l^2+2lb+b^2=3136
2lb=3136-1600
lb=1536/2
Therefore, lb=768
b=768/l
Now,
Perimeter of rectangle(p)=2(l+b)
l+b=56
l+768/l=56
l^2+768=56l
l^2+768-56l=0
Factoring,
(l - 32) (l - 24) = 0
Either l= 32 or l = 24
When l=32,
l+b=56
32+b=56
b=24
When l=24
l+b=56
24+b=56
b=32
So the dimensions of the dance floor are 24 and 32 ft or 32 and 24 ft.
Answer:
24 ft x 32 ft
Step-by-step explanation:
[tex]2x+2y=112[/tex]
[tex]\sqrt{x^{2}+y^{2} } =40[/tex]
Graph the equations
Find the point where they intersect
Answer is 24 ft and 32 ft
solve for x please help! (show work)
Answer:
x = 3/2
Step-by-step explanation:
4/3 ( 3x+9) -2x= 15
Distribute 4/3
4x+12 -2x =15
Combine like terms
2x+12 = 15
Subtract 12 from each side
2x+12-12 =15-12
2x = 3
Divide by 2
2x/2 = 3/2
x = 3/2
Answer:
4/3(3x+9)-2x=15
4x+12+9-2x=15
2x+21=15
2x=-6
x=-3
Let me know if this helps!
What is the factored form of the binomial expansion x3 + 9x2 + 27x + 27?
(x + 3)3
(x - 3)3
(x + 9)3
(X - 9)3
Answer:
A
Step-by-step explanation:
the factored form of the binomial expansion x^3 + 9x^2 + 27x + 27 is (x+3)^3
Write 8x8x88888 as power
Answer:
8[2]×88888
Step-by-step explanation:
[8×8]=8[2]×88888
Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]
Answer:
10.295Step-by-step explanation:
Using the value for calculating the confidence interval as given;
CI = xbar + Z*σ/√n
xbar is the mean = 37.14+42.86/2
xbar= 80/2
xbar = 40
Z is the z-score at the 90% confidence = 1.645
σ is the standard deviation
n is the sample size = 35
Given the confidence interval CI as [37.14, 42.86]
Using the maximum value of the confidence interval to get the value of the standard deviation, we will have;
42.86 = xbar + Z*σ/√n
42.86 = 40 + 1.645* σ/√35
42.86-40 = 1.645*σ/√35
2.86 = 1.645*σ/√35
2.86/1.645 = σ/√35
1.739 = σ/√35
1.739 = σ/5.92
σ= 1.739*5.92
σ = 10.295
Hence, the sample standard deviation of a pair of jeans is 10.295
3-(-4) answer the question
Answer:
7Step-by-step explanation:
[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]
Answer:
7
Step-by-step explanation:
because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7
What is the equation of the line in the following graph?
Answer:
2 . y=-1
Step-by-step explanation:
m=0 (it is a straight line)
use (-6,-1) in y=mx+b
-1=0(-6)+b
-1=b
equation is now
y=0(x)-1
y=-1
If x to the 2nd power equal 60, What is the value of x
Answer:
7.745
Step-by-step explanation:
Square root of 60 equals X.
A pole that is 3 m tall casts a shadow that is 1.23 m long. At the same time, a nearby building casts a shadow that is 42.75 m long. How tall is the building? round your answer to the nearest meter.
Answer:
Hello,
Just using the theorem of Thalès,
Step-by-step explanation:
Let say h the hight of the building
[tex]\dfrac{h}{3} =\dfrac{42.75}{1.23}\\\\h=104.268296...\approx{104(m)}[/tex]
Is u=−12 a solution of 8u−1=6u?
Answer:
No, -12 is not a solution.
Step-by-step explanation:
8u-1=6u
8(-12)-1=6(-12)
-96-1=-72
-97=-72
Untrue, to it’s not a solution
36x7 please EXPLAIN the process of the multiplication plse
36×7
=252
Explaination :
First Multiply 6 and 7 we get 42 !
Write 2 and 4 will be added to the product of 3×7
We get 21 and add 4 here
So we get 252
Answer:
[tex]36 \times 7 = 252[/tex]
Step-by-step explanation:
Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.
Hope it helps u mate
Evaluate:
[tex]{ \int \limits^\pi_{ \frac{1}{4}\pi}{ {e {}^{2 \sigma} (\sqrt{1 - { \sigma}^{2} } ) d \sigma}}}[/tex]
Answer:
hope this answer helps.
Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
The portfolio beta is [tex]\alpha = 1.354[/tex]
Step-by-step explanation:
From the question we are told that
The first investment is [tex]i_1 = \$ 25,000[/tex]
The first beta is [tex]k = 0.8[/tex]
The second investment is [tex]i_2 = \$ 40,000[/tex]
The second beta is [tex]w = 1.7[/tex]
Generally the portfolio beta is mathematically represented as
[tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]
substituting values
[tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]
[tex]\alpha = 1.354[/tex]
In a study of 24 criminals convicted of antitrust offenses, the average age was 60 years, with a standard deviation of 7.4 years. Construct a 95% confidence interval on the true mean age. (Give your answers correct to one decimal place.)___ to____ years
Answer: 56.9 years to 63.1 years.
Step-by-step explanation:
Confidence interval for population mean (when population standard deviation is unknown):
[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].
Given: n= 24
degree of freedom = n- 1= 23
[tex]\overline{x}[/tex]= 60 years
s= 7.4 years
[tex]\alpha=0.05[/tex]
Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:
[tex]t_{\alpha/2}=2.0687[/tex]
A 95% confidence interval on the true mean age:
[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]
Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.
Identifying the Property of Equality
Quick
Check
Identify the correct property of equality to solve each equation.
3+x= 27
X/6 = 5
Answer:
a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication
Step-by-step explanation:
a) This expression can be solved by using the Compatibility of Equality with Addition, that is:
1) [tex]3+x = 27[/tex] Given
2) [tex]x+3 = 27[/tex] Commutative property
3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition
4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property
5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction
6) [tex]x=24[/tex] Modulative property/Subtraction/Result.
b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:
1) [tex]\frac{x}{6} = 5[/tex] Given
2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division
3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication
4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property
5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse
6) [tex]x = 30[/tex] Modulative property/Result
Answer:
3 + x = 27
✔ subtraction property of equality with 3
x over 6 = 5
✔ multiplication property of equality with 6
Factor the trinomial below. x^2 + 5x – 24 A. (x – 8)(x + 3) B. (x – 4)(x + 6) C. (x – 3)(x + 8) D. (x – 6)(x + 4)
Answer:
The answer is option CStep-by-step explanation:
x² + 5x - 24
To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24
That's
x² + 8x - 3x - 24
Factorize x out
That's
x( x + 8) - 3(x + 8)
Factor x + 8 out
We have the final answer as
(x + 8)(x - 3)Hope this helps you
Answer:(x-3)(x+8)
Step-by-step explanation:
Halla x si:
a) 4√5 b) √5 c) 4√3 d) 4 e) 4√2
Answer:
Option A. 4√5
Step-by-step explanation:
To obtain the value of x, we must first obtain the value of y as shown in the attached photo.
The value of y can be obtained by using the pythagoras theory as illustrated below:
In this case y is the longest side i.e the Hypothenus.
y² = 4² + [4√3]²
y² = 4² + [4² × (√3)²]
y² = 4² + [4² × 3]
y² = 16 + [16 × 3]
y² = 16 + 48
y² = 64
Take the square root of both side
y = √64
y = 8
Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.
Note: x is the longest side i.e the Hypothenus in this case.
x² = 4² + 8²
x² = 16 + 64
x² = 80
Take the square root of both side
x = √80
x = √(16 × 5)
x = √16 × √5
x = 4√5
Therefore, the value of x is 4√5.
Suppose a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207]. The population standard deviation used for the analysis is known to be $14,900.
Required:
a. What is the point estimate of the mean salary for all college graduates in this town?
b. Determine the sample size used for the analysis.
Answer: a. $40,800 b. 36
Step-by-step explanation:
Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].
[tex]\sigma= \$14,900[/tex]
a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.
Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]
= 40,800
hence, the point estimate of the mean salary for all college graduates in this town = $40,800
b. Since lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.
Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]
Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.
z-value for 99% confidence level = 2.576
So,
[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]
The sample size used for the analysis =36
The expression $16x^2-106x-105$ can be written as $(8x + a)(2x + b),$ where $a$ and $b$ are integers. What is $a + 2b$?
Answer:
-23
Step-by-step explanation:
16x² - 106x - 105
factoring X
14 x -120 = -1680
14 - 120 = -106
16x² + 14x - 120x - 105
(16x² + 14x) -(120x - 105)
factor out 2 and -15 to get the same expression (8x + 7)
2x(8x + 7) - 15(8x + 7)
(8x + 7)(2x - 15)
a = 7
b = -15
a + 2b
7 + (-15 x 2)
7 + (-30)
= -23
The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.
Answer:
To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.
Hope this helped!
How many 2cm×2cm cubes can be packed in a box 1m long,20cm wide and 4cm deep.
Answer:
1000
Step-by-step explanation:
I guess, something went wrong with the text up there.
I assume it should say 2cm×2cm×2cm cubes. right ? because a cube has 3 dimensions, not just 2.
otherwise an infinitely large number of "just squares" would fit into the box ...
so, the box is
1m×20cm×4cm = 100cm×20cm×4cm = 8000 cm³
a single cube would be
2cm×2cm×2cm = 8 cm³
therefore,
8000 / 8 = 1000 cubes can be packed into that box, since the dimensions of the box in relation to the dimensions of the cubes do not force to have some empty left over space. the box can be packed tightly.
A model rocket is launched with an initial velocity of 240 ft/s. The height, h, in feet, of the rocket t seconds after the launch is given by
h = −16t2 + 240t.
How many seconds after launch will the rocket be 390 ft above the ground? Round to the nearest hundredth of a second.
s (smaller value)
s (larger value)
Answer:
About 1.85 seconds and 13.15 seconds.
Step-by-step explanation:
The height (in feet) of the rocket t seconds after launch is given by the equation:
[tex]h = -16t^2 + 240 t[/tex]
And we want to determine how many seconds after launch will be rocket be 390 feet above the ground.
Thus, let h = 390 and solve for t:
[tex]390 = -16t^2 +240t[/tex]
Isolate:
[tex]-16t^2 + 240 t - 390 = 0[/tex]
Simplify:
[tex]8t^2 - 120t + 195 = 0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]
In this case, a = 8, b = -120, and c = 195. Hence:
[tex]\displaystyle t = \frac{-(-120)\pm \sqrt{(-120)^2 - 4(8)(195)}}{2(8)}[/tex]
Evaluate:
[tex]\displaystyle t = \frac{120\pm\sqrt{8160}}{16}[/tex]
Simplify:
[tex]\displaystyle t = \frac{120\pm4\sqrt{510}}{16} = \frac{30\pm\sqrt{510}}{4}[/tex]
Thus, our two solutions are:
[tex]\displaystyle t = \frac{30+ \sqrt{510}}{4} \approx 13.15 \text{ or } t = \frac{30-\sqrt{510}}{4} \approx 1.85[/tex]
Hence, the rocket will be 390 feet above the ground after about 1.85 seconds and again after about 13.15 seconds.
20 POINTS ANSWER QUICK
Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)? left 13 units, down 2 units right 13 units, down 2 units left 13 units, up 2 units right 13 units, up 2 units
Answer:
Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function
g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)?
left 13 units, down 2 units
right 13 units, down 2 units
left 13 units, up 2 units
right 13 units, up 2 units
A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3. Assuming the distribution is bell-shaped and we randomly select a measurement:
a) What percentage of measurements are between 71 and 89?
b) What is the probability a person's blood systolic pressure measures more than 89?
c) What is the probability a person's blood systolic pressure being at most 75?
d) We should expect 15% of patients have a blood pressure below what measurement?
e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.
Answer:
Explained below.
Step-by-step explanation:
Let X = systolic blood pressure measurements.
It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].
(a)
Compute the percentage of measurements that are between 71 and 89 as follows:
[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]
[tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of measurements that are between 71 and 89 is 99.73%.
(b)
Compute the probability that a person's blood systolic pressure measures more than 89 as follows:
[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.
(c)
Compute the probability that a person's blood systolic pressure being at most 75 as follows:
Apply continuity correction:
[tex]P(X\leq 75)=P(X<75-0.5)[/tex]
[tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]
Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.
(d)
Let x be the blood pressure required.
Then,
P (X < x) = 0.15
⇒ P (Z < z) = 0.15
⇒ z = -1.04
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]
Thus, the 15% of patients are expected to have a blood pressure below 76.9.
(e)
A z-score more than 2 or less than -2 are considered as unusual.
Compute the z score for [tex]\bar x[/tex] as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]
The z-score for the mean blood pressure measurement of 3 patients is more than 2.
Thus, it would be unusual.
What is the range of possible sizes for side z?
Pro
Pro
Tea
2
4.1
1.3
Stuck? Watch a video or use a hint.
Reportage
Answer:
2.8 < x < 5.4
Step-by-step explanation:
Given the triangle with two known sides, 4.1 and 1.3, the range of possible values of the third side, x, can be ascertained by considering the triangle inequality theorem.
According to the theorem, when you add any two of the angles in a triangle, it should give you a value greater than the third side.
If a, b, and c are 3 sides of a triangle, the theorem implies that:
a + b > c.
Therefore, a - b < c < a + b
We can use this logic to find the possibly values of x in the given triangle above.
Thus,
4.1 - 1.3 < x < 4.1 + 1.3
2.8 < x < 5.4
Range of possible sizes of x is 2.8 < x < 5.4
The temperature dropped 15 degrees in an hour. If the starting temperature was 10 degrees, What was the final temperature?
Answer:
Step-by-step explanation:
15-10=5 degrees
The image of (5,-4) reflected across the y-axis is
A. (-5, 4)
B. (-5, 4)
C. (5, 4)
D. (5, 4)
The image of (3,-2) reflected across the line x - 1 is
A. (-1, -2)
B. (3,0)
C. (0, -2)
D. (-2, -1)
Answer:
Number 1: A
Number 2:D
Step-by-step explanation:
Will give brainliest answer
Lena is comparing offers from two banks on checking accounts that include debit cards. Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions. Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
Suppose Lena makes 35 transactions in a given month.
How much would she pay at each bank for the given month?
Bank A
Bank B
For the given month, which bank is cheaper and by how much?
Bank A. is cheaper than Bank B by $
or
Bank B is cheaper than Bank A by $
Answer:
Bank A spending= $20
Bank B spending= $22.5
Bank A is cheaper with $2.5
Step-by-step explanation:
Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions.
Sheade 35 transactions.
Total charges from bank A
= $20 monthly
Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
She made 35 transactions.
Total charges on bank B= $5 + (0.5)35
Total charges on bank B= $5+17.5
Total charges on bank B= $22.5
A television screen has a length to width ratio of 8 to 5 and a perimeter of 117 inches. What is the diagonal measure of the screen (to the nearest tenth of an inch)?
Answer:
[tex]D = 42.5\ inch[/tex]
Step-by-step explanation:
Given
[tex]L = Length[/tex] and [tex]W = Width[/tex]
[tex]L:W = 8: 5[/tex]
[tex]Perimeter = 117[/tex]
Required
Determine the Diagonal
First, the dimension of the screen has to be calculated;
Recall that; [tex]L:W = 8: 5[/tex]
Convert to division
[tex]\frac{L}{W} = \frac{8}{5}[/tex]
Multiply both sides by W
[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]
[tex]L = \frac{8W}{5}[/tex]
The perimeter of a rectangle:
[tex]Perimeter = 2(L+W)[/tex]
Substitute [tex]L = \frac{8W}{5}[/tex]
[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]
Take LCM
[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]
[tex]Perimeter = 2(\frac{13W}{5})[/tex]
Substitute 117 for Perimeter
[tex]117 = 2(\frac{13W}{5})[/tex]
[tex]117 = \frac{26W}{5}[/tex]
Multiply both sides by [tex]\frac{5}{26}[/tex]
[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]
[tex]\frac{5 * 117}{26} = W[/tex]
[tex]\frac{585}{26} = W[/tex]
[tex]22.5 = W[/tex]
[tex]W = 22.5[/tex]
Recall that
[tex]L = \frac{8W}{5}[/tex]
[tex]L = \frac{8 * 22.5}{5}[/tex]
[tex]L = \frac{180}{5}[/tex]
[tex]L = 36[/tex]
The diagonal of a rectangle is calculated using Pythagoras theorem as thus;
[tex]D = \sqrt{L^2 + W^2}[/tex]
Substitute values for L and W
[tex]D = \sqrt{36^2 + 22.5^2}[/tex]
[tex]D = \sqrt{1296 + 506.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = 42.4529150943[/tex]
[tex]D = 42.5\ inch[/tex] (Approximated)