MATHEMATICS COLLEGE

8+9t-3+4 please help me

Answers

Answer 1

Answer:

Answer:

t = -1

Step-by-step explanation:

8 + 9t - 3 + 4

Combine like terms

(8 - 3 + 4) + 9t

9 + 9t

9t + 9

Get t by itself

9t + 9 = 0

-9 -9

9t = -9

Divide both sides by 9 to find t

t = -1

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A cable that weighs 6 lb/ft is used to lift 500 lb of coal up a mine shaft 400 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)

Answers

The work done to lift the coal is 6.8*10^5 ft-lb

Data;

weight of cable = 6lb/ft
weight of coal = 500lb
length of mine shaft = 400ft

Let the distance (ft) below top of the shaft be represented by x

The weight of the coal to be lifted from mine = 500lb

Work Done

The work done to lift the coal is

$work = force * displacement\nw=fx\nforce f(x) = 500 + 6x\nw_i= f(x_i)=[500+6x_i]\delta x\n$

Taking the summation limit

$w = \lim_(0 \to 400) \sum [500+6x_i]\delta x\n \delta w = f(x) \delta x\n$

we can take the integration of both sides where x will the range from 0 to 400.

$\int \delta w = \int f(x) dx\n\int\limits^(400)_0{(500+6x)} \, dx \nw=[500x+3x^2]_0^4^0^0\nw=500(400-0)+ 3(400^2-0^2)\nw= 680000\nw=6.8*10^5 ft-lb$

From the calculations above, the work done is 6.8*10^5 ft-lb

Learn more on work done on a lift here;

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Answer:

8.2 *10^5 ft lb

Step-by-step explanation:

Wcoal = 800*500 = 400000 = 4*10^5 ft lb

$Wrope =\int\limits^(400)_0 {6(400-y)} \, dy$

Using a right Riemann sum

The width of the entireregion to be estimated = 400 - 0 = 400

Considering 8 equal subdivisions, then the width of each rectangular division is 400/8 = 50

F(x) = 6(400-y)

$\left[\begin{array}{cccccccccc}x&0&50&100&150&200&250&300&350 &400\nf(x)&2400&2100&1800&1500&1200&900&600&300&0\end{array}\right]$

Wrope = 50(2100) + 50(1800) + 50(1500) + 50(1200) + 50(900) + 50(600)

+ 50(300) + 50(0) = 420000 = 4.2 * 10^5 ft lb

Note: Riemann sum is an approximation, so may not give a accurate value

work done = Wcoal + Wrope= 4*10^5+ 4.2 * 10^5 = 8.2 *10^5 ft lb

Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Round to the nearest hundredth if necessary. The quotient of a number divided by 6 is 3.5.

Answers

Answer:

$(n)/(6)=3.5$

n= 21

Step-by-step explanation:

The equation is simple, you just have to reason the sentence, the quotient of a number, this means that the result of the division is 3.5, and the number has to be divided by 6, so the equation would end up looiking like this:

$(n)/(6)=3.5$

As 6 is dividing and you want to clear N, you just put it on the other side of the equation multiplying, and you end up with this:

n=6(3.5)

n=21

So your answer for this equation would be n= 6.

n/6 = 3.5
Multiply both sides by 6.
n = 21

The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.07 of the true proportion?

Answers

Answer: 339

Step-by-step explanation:

Since the prior estimate of population proportion is unknown , then we take p= 0.5

Given : Margin of error : E=0.07

Critical value for 99% confidence interval : $z_(\alpha/2)=2.576$

Formula for sample size :-

$n=0.5(1-0.5)((z_(\alpha/2))/(E))^2\n\n=0.25((2.576)/(0.07))^2\n\n=338.56\approx339$

Hence, the minimum sample size required = 339

i.e. they need to survey 339 residents.

Final answer:

To be at least 99% confident that the sample proportion is within 0.07 of the true proportion, the Arizona Department of Transportation needs to survey at least 753 residents.

Explanation:

To determine the minimum number of residents needed to survey in order to be at least 99% confident that the sample proportion is within 0.07 of the true proportion, we can use the formula:

n = (Zα/2)2p(1-p) / E2

Where:

n is the required sample size
Zα/2 is the critical value for the desired confidence level (in this case, 99% confidence)
p is the estimated proportion (we assume 0.5 if no estimate is given)
E is the maximum allowable error (in this case, 0.07)

Plugging in the values:

Zα/2 = 2.576 (from the normal distribution table for a 99% confidence level)
p = 0.5 (since no estimate is given)
E = 0.07

Calculating n:

n = (2.576)2(0.5)(1-0.5) / (0.07)2 = 752.92

Rounding up to the nearest whole number, the Arizona Department of Transportation needs to survey at least 753 residents to be at least 99% confident that the sample proportion is within 0.07 of the true proportion.

Learn more about Sample Size Determination here:

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Sam is getting ready for a big date when he realizes that he has no money. His roommate, Bill, also has no money, but he has a credit card. Knowing that nobody will let Sam use Bill’s credit card, Sam asks Bill to pull out a cash advance for $120.00. Bill agrees under the condition that Sam is responsible for all interest that accrues on the cash advance which is a 30% interest rate, compounded monthly. 5 full years go by before the $120 cash advance is repaid. How much should Bill ask Sam to pay in interest for the cash advance? a.
$3.88
b.
$112.80
c.
$120.00
d.
$232.80

Answers

cash advance = 120

annual interest rate = 30% compounded monthly

term = 5 years

A = P (1 + r/n)^nt

A = future value of the cash advance

P = principal or value of cash advance

r = interest rate

n = times interest is compounded

t = terms or years

A = 120 (1 + 30%/12)^12 * 5

A = 120 (1 + 0.025)^60

A = 120 (1.025)^60

A = 120 (4.40)

A = 528

528 total amount including principal.
528 - 120 = 408 total interest paid
I hope this helps!!

Answer:

I just took the test, the answer is B.) $112.80

Will give brainliest

Answers

Answer:

4a x 2a + 0

Step-by-step explanation:

4a x 2a = 8a

0 + 0 = 0

= 8a, 0

Answer:

brainlyist

Step-by-step explanation:

x=5 y=0

x=0 y=3

The similar triangle is the image of the bigger triangle after a sequence of transformations. What is the value of x?

Answers

Answer:

The value of x is: 2.5 units

Step-by-step explanation:

Two triangles are said to be similar if the ratio of the corresponding sides of the two triangles are equal.

i.e. if two triangles ΔABC and ΔDEF are similar such that the sides of the triangle ABC are a, b and c and the corresponding sides in ΔDEF are d,e and f respectively then we have:

$(a)/(d)=(b)/(e)=(c)/(f)$