Actual length of the Bridge = 8983.33 feet.
The scale is 1 unit = 19,600.
Height of the postcard is 3.5 inches.
So, original height of the bridge = 3.5 × 19,600 = 68,600 inches
= 5716.67 feet
Width of the postcard is 5.5 inches.
So, original width of the bridge = 5.5 × 19,600 = 107,800 inches
= 8983.33 feet
hope it helps
The correct option is (c) 8980 feet.
What is length ?The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For example - A rectangle, for instance, has length and breadth as its dimensions. Two hours is an example of length for a movie. 12 inches is an illustration of length.Given,length of the Bridge = 8983.33 feet.
The scale is 1 unit = 19,600.
Height of the postcard is = 3.5 inches.
So,
Original height of the bridge = 3.5 × 19,600 = 68,600 inches
= 5716.67 feet
Width of the postcard is 5.5 inches.
So, original width of the bridge = 5.5 × 19,600 = 107,800 inches
= 8983.33 feet
Therefore, the original width of the bridge is 8983.33 feet .
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Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 75 manufacturing companies located in the Southwest. The mean expense is $50.93 million and the standard deviation is $10.80 million. Is it reasonable to conclude the sample data are from a population that follows a normal probability distribution? Advertising Expense ($ Million) Number of Companies 25 up to 35 4 35 up to 45 19 45 up to 55 27 55 up to 65 16 65 up to 75 9 Total 75
Answer:
Step-by-step explanation:
The table can be computed as:
Advertising Expenses ($ million) Number of companies
25 up to 35 4
35 up to 45 19
45 up to 55 27
55 up to 65 16
65 up to 75 9
TOTAL 75
Let's find the probabilities first:
[tex]P(25 - 35) = P \Big(\dfrac{25-50.93}{10.80}<z< \dfrac{35-50.93}{10.80}\Big) \\ \\ =P \Big(\dfrac{-25.93}{10.80}<z< \dfrac{-15.93}{10.80}\Big) \\ \\ =P(-2.4009<z<-1.475) \\ \\ =(0.0694 -0.0082) \\ \\ =0.0612[/tex]
For 35 up to 45
[tex]P(35 - 45) = P \Big(\dfrac{35-50.93}{10.80}<z< \dfrac{45-50.93}{10.80}\Big)=P \Big(\dfrac{-15.93}{10.80}<z< \dfrac{-5.93}{10.80}\Big) \\ \\ =P(-1.475<z<-0.5491) \\ \\ =(0.2912 -0.0694) \\ \\ =0.2218[/tex]
For 45 up to 55
[tex]P(45 - 55) = P \Big(\dfrac{45-50.93}{10.80}<z< \dfrac{55-50.93}{10.80}\Big)=P \Big(\dfrac{-5.93}{10.80}<z< \dfrac{4.07}{10.80}\Big) \\ \\ =P(-0.5491<z<0.3769) \\ \\ =(0.6480 -0.2912) \\ \\ =0.3568[/tex]
For 55 up to 65
[tex]P(55 - 65) = P \Big(\dfrac{55-50.93}{10.80}<z< \dfrac{65-50.93}{10.80}\Big)=P \Big(\dfrac{4.07}{10.80}<z< \dfrac{14.07}{10.80}\Big) \\ \\=P(0.3768<z<1.3028) \\ \\ =(0.9032-0.6480) \\ \\ =0.2552[/tex]
For 65 up to 75
[tex]P(65 - 75) = P \Big(\dfrac{65-50.93}{10.80}<z< \dfrac{75-50.93}{10.80}\Big)=P \Big(\dfrac{14.07}{10.80}<z< \dfrac{24.07}{10.80}\Big) \\ \\ =P(1.3028<z<2.2287) \\ \\=(0.9871-0.9032) \\ \\ =0.0839[/tex]
Chi-Square Table can be computed as follows:
Expense No of Probabilities(P) Expe [tex](O-E)^2[/tex] [tex]\dfrac{(O-E)^2}{E}[/tex]
compa cted E (n*p)
nies (O)
25-35 4 0.0612 75*0.0612 = 4.59 0.3481 0.0758
35-45 19 0.2218 75*0.2218 = 16.635 5.5932 0.3362
45-55 27 0.3568 75*0.3568 = 26.76 0.0576 0.021
55-65 16 0.2552 75*0.2552 = 19.14 9.8596 0.5151
65-75 9 0.0839 75*0.0839 = 6.2925 7.331 1.1650
[tex]\sum \dfrac{(O-E)^2}{E}= 2.0492[/tex]
Using the Chi-square formula:
[tex]X^2 = \dfrac{(O-E)^2}{E} \\ \\ Chi-square \ X^2 = 2.0942[/tex]
Null hypothesis:
[tex]H_o: \text{The population of advertising expenses follows a normal distribution}[/tex]
Alternative hypothesis:
[tex]H_a: \text{The population of advertising expenses does not follows a normal distribution}[/tex]
Assume that:
[tex]\alpha = 0.02[/tex]
degree of freedom:
= n-1
= 5 -1
= 4
Critical value from [tex]X^2 = 11.667[/tex]
Decision rule: To reject [tex]H_o \ if \ X^2[/tex] test statistics is greater than [tex]X^2[/tex] tabulated.
Conclusion: Since [tex]X^2 = 2.0942[/tex] is less than critical value 11.667. Then we fail to reject [tex]H_o[/tex]
Jonathan went shopping for a new pair of pants. Sales tax where he lives is 4.75%. The price of the pair of pants is $20. Find the total price including tax. Round to the nearest cent.
Answer:
20.95$
Step-by-step explanation:
To find the total price we need to find 4.75% of the 20 and to do that we need to multply 20 with 4.75 and divide it by 100
20 × 4.75 ÷ 100 = 0.95
20$ + 0.95$ = 20.95$
Solve for x and round to the nearest tenth
9514 1404 393
Answer:
88.9
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(77°) = 20/x
x = 20/cos(77°)
x ≈ 88.9
If x varies inversely as y and x=16 when y=5, find x when y=20.
9514 1404 393
Answer:
x = 4
Step-by-step explanation:
The inverse variation means that when y goes up by a factor of 20/5 = 4, the value of x goes down by the same factor.
x = 16/4
x = 4
What is the volume of a sphere with the diameter = 10 cm and the height = 200 cm
Find a fraction with a demominator of 30 that is equivalent to 1/3
Answer:
10/30
Step-by-step explanation:
First, multiply the denominator by 10 to make 30.
Then, since we multiplied the denominator, we multiply the numerator. 1 x 10= 10
Therefore the answer is 10/30.
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-1,4) and (8, 2)
Answer:
9.2 ([tex]\sqrt{85[/tex][tex]\sqrt{85}[/tex])
Step-by-step explanation:
square root of (8-(-1))^2 + (2-4)^2) which is square root of 85 which is approximately 9.2 rounded to the nearest tenth
Answer:
9.2
Step-by-step explanation:
f(x) = 2 x + 5, g(x) = x - 1
asked = f(x) • g(x)
please help..
Answer:
2x² + 3x - 5
Step-by-step explanation:
(2x + 5)(x - 1)
2x² - 2x + 5x - 5
2x² + 3x - 5
i-Ready
Equivalent Linear Expressions - Instruction - Level G
3
-2 +1+
4
2
) Write an expression that is equivalent to
2
3
1
20.
2
2
1
3
-2 +1+ 2
4
4
1
2
2
2 +
?
3
Answer:
LEavel ^ 9-8=1
Step-by-step explanation:
The variable x varies directly as y and x varies inversely as z. What is the value is y when x=20 and z=-2, if y=30 when z=3 and x=5?
Answer:
Y=-80
Step-by-step explanation:
X=Ky/z
5=30k/3
30k=15
K=1/2
20=Ky/(-2)
Ky =-40
1/2y=-40
Y=-80
At a furniture store, the employees earn a 2.5% commission on every sale they make. If Ginny made $8850 in sales one week, how much did she earn in commission?
help please :( 100 points
Answer:
She earned 221.25 in commission
Step-by-step explanation:
2.5% of 8850 is 221.25
What are some random numbers that add up to 50?
Answer:
25+25, 40+10, 35+15 If that's your question, not sure. But if you mean what's divisible by 50, maybe 10, 5
Step-by-step explanation:
what is the probability if you randomly select comedy book replace it and another comedy book?
(if your going to answer pls explain )
Please answer look at pitot
Answer:
z = 7
Step-by-step explanation:
Based on the midsegment theorem of a triangle, the length of the midsegment of the triangle (z) = ½ of the length of the 3rd side of the triangle (14)
Thus:
z = ½(14)
z = 7
Natalie budgets $146 for yoga training. She buys a yoga mat for $10 and spends $9 per day on yoga classes. Which inequality represents the number of days, d, that Natalie can take classes and stay within her budget?
A 146 ≤ 9d + 10
B 146 ≥ 9d + 10
C 146 ≤ 10d + 9
D 146 ≥ 10d + 9
Answer:
The answer should be letter D (146 ≥ 10d + 9)
Step-by-step explanation:
Function operations
Find the area of each figure. A = _ in²
Answer:
1824in^2
Step-by-step explanation:
area of rectangle:
L x W = A
32 x 48 = 1539
area of triangle:
(L x W) / 2 = A
(48 x 12) / 2 = 288
add:
1539 + 288 = 1824in ^2
please answer this thanks
Answer:
try using an online calculator, it might help
Asanji stands at the edge of the top of a tall building and lobs a watermelon up into the air then proceeds to watch it fall to the street below (luckily it's empty because everybody is at home). The equation below represents the height, off the ground in meters, of the watermelon t seconds after Asanji has thrown it.
h = -4.9t^2 + 9.8t + 28
Approximately, how long does it take the watermelon to hit the ground? Round to the nearest tenth of a second.
9514 1404 393
Answer:
3.6 s
Step-by-step explanation:
This is nicely solved by a graphing calculator. It takes about 3.6 seconds to hit the ground.
__
We notice that the vertical velocity is a multiple of the leading coefficient, so we can solve this by completing the square.
0 = -4.9(t^2 -2t) +28 . . . . . for h = 0
28 +4.9 = 4.9(t^2 -2t +1) . . . . . rearrange, add 4.9 to both sides
32.9/4.9 = (t -1)^2
1 +(1/7)√329 = t ≈ 3.5912. . . . . square root and add 1
It takes about 3.6 seconds for the watermelon to hit the street.
if Mike Burns 220 calories in 20 minutes and 275 calories is in 25 minutes 385 calories in 35 minutes how much calories did he burn in 29 minutes
Answer:
319 calories
Step-by-step explanation:
Steps to answering this question :
Determine the amount of calories burnt per minute Multiply the answer gotten in the above step by 29 minutes to determine the total calories burnt in 29 minutesCalories burnt per minute = total calories / minutes
220 / 20 = 11 calories
275 / 25 = 11 calories
385 / 35 = 11 calories
11 calories is burnt per minute
Total calories burnt in 29 minutes = calories burnt per minute x 29 minutes
11 x 29 = 319 calories
319
The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?
Answer:
formula for the area A of a circle in terms of its radius r:
A = πr2
It is important to remember that both r, and hence, A are functions of time, t. Take the derivative of both sides with respect to t and obtain
dA/dt = 2πr(dr/dt)
Note that we are using implicit differentiation here, since A and r are (implicit) functions of t. Now we can find the required answers.
r = 5 inches.
Substitute r = 5 and dr/dt = 3 to get
dA/dt = 2π5·3 = 30π ≅ 95.25
(the units are in2/min.)
r = 22 inches
dA/dt = 2π22·3 = 132π ≅ 414.69
Hope that helps.
What is the arc measure of major arc \stackrel{\large{\frown}}{ACB}
ACB
⌢
A, C, B, start superscript, \frown, end superscript on circle PPP in degrees?
Answer:
286°
Step-by-step explanation:
A circle is the locus of a point such that its distance from a fixed point (known as the center) is always constant. This distance is known as the radius of the circle.
A major arc is an arc larger than a semicircle, therefore its measure is greater than 180°. A minor arc is an arc smaller than a semicircle, therefore its measure is less than 180°.
The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=angle\ about\ a\ point-\stackrel{\large{\frown}}{AB}[/tex]
The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=360-74=286^o\\[/tex]
What is the unit digit of 3^(25) + 325 ? (Please show work and I will mark brainlist)
A. 1
B. 3
C. 5
D. 6
E. 8
Unit digit of [tex]3^{25} + 325[/tex] is 8.
Thus option E is correct .
Given , expression [tex]3^{25} + 325[/tex]
To identify the unit digit firstly the cyclicity of 3 ,
Cyclicity of 3 :
[tex]3^1 = 3\\\\3^2 = 9\\\\3^3 = 27\\\\3^4 = 81\\\\3^5 = 243\\\\3^6 = 729\\\\3^7 = 2187[/tex]
[tex]3^8 = 6561[/tex]
Here the cyclicity of 3 is 4 that is the unit digit of exponent of 3 will be repeating after every fourth power.
Here, the exponent of 3 is 25.
Divide 25 by the cyclicity of 3.
25/4
Remainder = 1
Hence the unit digit of [tex]3^{25[/tex] will be 3.
Unit digit of 325 is 5.
Add 5 + 3
= 8
Hence the unit digit will be 8.
Option E is correct .
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Study each equation, then solve.
18) 5 + r = 6 - r
Answer:
5+r=6-r
-5 -5
r=1-r
+r +r
2r=1
÷2 ÷2
r=1/2
1. you invest $10,000 for 5 years at 4% interest. To the nearest cent, find the amount of money in the account after 5 years if:
a) The interest is simple interest.
b) The interest is Compound annually
c) The interest is Compound monthly
d) The interest is compound daily
2. After 20 years, the total amount in an investment earning 3.5% interest compounded quarterly was $16,061.05. To the nearest dollar, how much money was originally invested?
3. After 5 years, the total amount in an investment earning 4% interest compounded daily was $12,213.89. To the nearest dollar, how much money was originally invested?
Answer:
See explanation
Step-by-step explanation:
1.
a) simple interest = PRT/ 100
I = 10,000 * 4 * 5/100
I =$ 2000
A = $10,000 + $ 2000
A =$ 12,000
b) A = P(1 + r/n)^t*n
Where;
A = amount
P = principal
r = rate per year
n = number of time the interest is compounded in a year
t = time in years
A = 10,000(1 + 0.04)^5/1
A = $ 12,166.5
c) A = P(1 + r/n)^t*n
A = 10,000(1 + 0.04/12)^5*12
A =$ 12,210
d) A = P(1 + r/n)^t*n
A = 10,000(1 + 0.04/365)^5*365
A=$ 12,213.90
2.A = P(1 + r/n)^t*n
$16,061.05 = P( 1 + 0.035/4) ^20*4
$16,061.05 = P (2.0076)
P = $16,061.05/2.0076
P= $8000
3.
A = P(1 + r/n)^t*n
12,213.89 = P(1 + 0.04/365)^5*365
12,213.89 = P(1.221)
P = 12,213.89/1.221
P = $10,003.2
Use the models above to explain why a 5×2/3 equals 10×1/3
Answer:
I kind of need the models to help with this one
Find the degree of the polynomial – 3x + x² +3.
Answer:
Step-by-step explanation:
Degree means highest exponent. got it?
Larry has a cylinder shaped pictures that is 13 inches long and radius of 4 inches. Sandra has a cylinder shaped pitcher that is 8 inches long and radius of 6 inches. The volume of Larry’s picture is approximately __. The volume of Sandra’s pitcher is approximately __?
The volume of Larry’s picture is approximately 653in³
The volume of Sandra’s pitcher is approximately 905in³
How to determine their volumeThe formula for calculating the volume of a cylinder is expressed as;
V = πr²h
Such that the parameters are;
V is the volumer is the radiush is the heightNow, substitute the values, we have;
Larry's cylinder
Volume = 3.14 × 4² × 13
Find the square value and multiply the expression
Volume = 653in³
Sandra's cylinder
Volume = 3.14 × 6² × 8
Find the square value and multiply the expression
Volume = 905in³
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1
message
The value of your iphone starts to depreciate/decrease as soon as you purchase it. If the function y= -200x + 1200, represents the estimated value of a certain phone after x years of ownership, what does the slope (-200) most likely represent?
The value of the phone decreases 200 dollars every year.
The current value of the phone.
The price it originally costs.
The value of the phone increases 200 dollars every year.
Answer:
-200 represents the price it orignally cost??
Step-by-step explanation:
The Environmental Protection Agency (EPA) publishes fuel economy values that are known to be good estimates of the fuel economy a typical driver will achieve under average driving conditions. One of the fuel economy values the EPA publishes is a combined estimate, which represents a combination of city driving (55%) and highway driving (45%). A large car rental company has 16 Ford Explorers in their fleet. They collected fuel economy data from these cars and calculated the sample mean to be 23.29 mpg and sample standard deviation as 0.78 mpg.
Required:
The car rental company is willing to assume that the conditions are met for constructing a confidence interval. Use the collected data to construct a 90% confidence interval for the mean combined fuel economy for Ford Explorers.
Answer:
The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7531
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7531\frac{0.78}{\sqrt{16}} = 0.34[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 23.29 - 0.34 = 22.95 mpg
The upper end of the interval is the sample mean added to M. So it is 23.29 + 0.34 = 23.63 mpg
The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.