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ra1l [238]
3 years ago
10

Production Rate Suppose the number of items a new worker on an assembly line produces daily after t days on the job is given by

Mathematics
1 answer:
dexar [7]3 years ago
7 0

Answer:

(a) 81 items

(b) 104 items

(c) 155 items

Step-by-step explanation:

Given:

The expression for the number of items produced by a new employee daily after 't' days on the job is given as:

l(t)=45\ln(t+1)

(a) Number of days (t) = 5

Average number of items produced can be obtained by plugging in 5 for 't' in the above expression. This gives,

l(t=5)=45\ln(5+1)\\\\l(t=5)=45\ln 6\\\\l(t=5)=80.6\approx 81

Therefore, nearly 81 items are produced after 5 days.

(b) Number of days (t) = 9

Average number of items produced can be obtained by plugging in 9 for 't' in the above expression. This gives,

l(t=9)=45\ln(9+1)\\\\l(t=9)=45\ln 10\\\\l(t=9)= 103.6\approx 104

Therefore, nearly 104 items are produced after 9 days.

(c) Number of days (t) = 30

Average number of items produced can be obtained by plugging in 30 for 't' in the above expression. This gives,

l(t=30)=45\ln(30+1)\\\\l(t=30)=45\ln 31\\\\l(t=31)=154.5\approx 155

Therefore, nearly 155 items are produced after 30 days.

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Consider two circular swimming pools. Pool A has a radius of 22 feet, and Pool B has a diameter of 13.6 meters. Complete the des
maw [93]

Answers:

13 42 m; B; 0.57 m

Step-by-step explanation:

Data:

Pool A:  r = 22 ft

Pool B: D = 13.6 m  

Calculations:

1. Radius of Pool A

r = 22 ft × (0.305 m/1 ft) = 6.71 m

2. Diameter of Pool A

D =2r = 2 × 6.71 = 13.42 m

The diameter of Pool A is 13.42 m.

3. Compare pool diameters

The diameter of Pool B is 13.6 m.

So, the diameter of Pool <u>B</u> is greater.

4. Compare circumferences

The formula for the circumference of a circle is

C = 2πr or C = πD

Pool A: C = 2π × 6.71 = 42.16 m

Pool B: r =    π × 13.6 = 42.73 m

Pool B - Pool A = 42.73 - 42.16 = <u>0.57 m </u>

The circumference is greater by <u>0.57 m.</u>

8 0
3 years ago
What is the y-value of sin(x) when x= -180°?
Andreyy89

In trigonometry, we start from the point (1,0), so this is the 0-degree point. Then, we start rotating counter clockwise along the unit circle.

Note that rotating 180 or -180 degrees is actually the same, because you travel half the circumference clockwise or counter clockwise. In both cases, you start from the rightmost point of the circle, (1,0), and arrive at the leftmost point, (-1,0).

Now, for every point (x,y) on the unit circle, given by a certain angle \alpha, we have

\cos(\alpha)=x,\quad \sin(\alpha)=y

So, in this case, the angle of -180 is associated with the point (-1,0), and thus we have

\sin(-180)=0

8 0
3 years ago
The measures of the angles of a triangle are ∠A = (2x)°, ∠B = (x+14)°, ∠C = (x−38)° Determine the value of x. Determine A B and
nexus9112 [7]

Answer:

Step-by-step explanation:

Measures of angles are,

m∠A = (2x)°

m∠B = (x + 14)°

m∠C = (x - 38)°

By triangle sum theorem,

m∠A + m∠B + m∠C = 180°

2x + (x + 14) + (x - 38) = 180

(2x + x + x) + (14 - 38) = 180

4x - 24 = 180

4x = 204

x = 51

m∠A = 2(51)° = 102°

m∠B = (51 + 14)° = 65°

m∠C = (51 - 38)° = 13°

4 0
3 years ago
Sarah said that 0.00001 is bigger than 0.001 because the first number has more digits to the right of the decimal point. Is Sara
Ivanshal [37]
No, she is wrong. 0.00001 has 4 zeros in front of the one and behind the decimal, making it 1/100000 or 1/10^5. For 0.001, there are 2 zeros in front, making it 1/1000 or 1/10^3. Since a number gets smaller as the denominator gets larger, and 10^5>10^3, 1/10^5<1/10^3
6 0
3 years ago
Part A:
liubo4ka [24]

Answer:

A)20 apples

B)Can only make 2 pies

C)Yes I think Is very close like probably just a lil bit more sugur but I think yes

D)Ohh so he doesnt have enough sugur I knew he needed a lil bit more sugur lol

Step-by-step explanation:

6 0
3 years ago
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