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mamaluj [8]
3 years ago
13

A copy machine makes 32 copies per minute. How many copies does it make in 3 minutes and 15 seconds?

Mathematics
1 answer:
Bas_tet [7]3 years ago
5 0

3 minutes will be 3*32 = 96 copies
15 secs is 1/4hrs, so 32/4 = 8 copies
That’ll be a total of 104 copies
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A random sample of 121 students from the University of Oklahoma had a sample mean ACT score of 23.4 with a sample standard devia
Grace [21]

Answer:

(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 121

Sample mean = 23.4

Sample standard deviation = 3.65

Level of significance = 0.05

Degree of freedom

= n - 1 = 120

95% Confidence interval:  

\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}  

Calculation of critical value:

t_{critical}\text{ at degree of freedom 120 and}~\alpha_{0.05} = \pm 1.9799  

Putting the values, we get,  

23.4\pm 1.9799(\dfrac{3.65}{\sqrt{121}} )\\\\ = 23.4 \pm 0.6569\\\\ = (22.7431 ,24.0569)\approx (22.74,24.06)  

(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.

5 0
3 years ago
Jorden leaves home for school on his bike everyday at 6:00 AM, traveling at 32 km/h. one day he forgot his homework, which his m
densk [106]

Answer:

She caught up with Jordan at 6:39 AM

Step-by-step explanation:

We solve this question making linear functions for the distances that Jorden and his mom have driven, and then we equalize them to find the moment they caught up.

Jorden leaves home for school on his bike everyday at 6:00 AM, traveling at 32 km/h.

Her mom will have left 15 minutes after he left, when he will already have traveled \frac{15*32}{60} = \frac{32}{4} = 8\text{km}

So, his position after t minutes can be modeled by the following function:

J(t) = 8 + 32t

His mom

His mom goes after him starting from home, so the initial position is 0, with a velocity of 52 km/h. So her position can be modeled by the following function:

M(t) = 52t

At what time did she catch up with Jorden,

She catches up t minutes after 6:15 AM.

t is found when

M(t) = J(t)

So

8 + 32t = 52t

20t = 8

t = \frac{8}{20}

t = 0.4

0.4 of an hour is 0.4*60 = 24 minutes.

So she catched up with Jordan after 6:15 AM + 24 minutes = 6:39 AM

4 0
2 years ago
to download movies off the internet, you must pay 1.99 per movie,plus one time fee of 5.50 write an expression to show the total
Oksanka [162]
1.99x+5.5= total cost
8 0
3 years ago
Read 2 more answers
V = u + at<br> u = 2<br> a = -5<br> t = 1/2 (0.5)
Vsevolod [243]

v = 2 + ( - 5 \times 0.5) \\ v = 2  - 0.5 \\ v = 1.5
8 0
3 years ago
Y=2x^2+12x+14 in vertex form
balandron [24]

Answer:

y = 2(x + 3)² - 4

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Using the method of completing the square

y = 2x² + 12x + 14 ← factor out 2 from the first 2 terms

  = 2(x² + 6x) + 14

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 6x

y = 2(x² + 2(3)x + 9 - 9 ) + 14

  = 2(x + 3)² - 18 + 14

  = 2(x + 3)² - 4 ← in vertex form

4 0
3 years ago
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