At a local university the students have been overdosing on caffeine to help them study for exams. However, many students have been getting quite sick from taking too much coffee and cola.
A. How many cups of coffee would be too much and at the dangerous level (3.00 g)? You know that coffee contains 21.5 mg caffeince per ounce and a cup is 8 oz.
B. How many cans of cola would be too much and at the dangerous level? You know that cola contains 4.20 mg per ounce and a soft drink can contain 12.0 oz.

Answer:

[tex]\frac{28}{n}[/tex]

Step-by-step explanation:

9514 1404 393

Answer:

  3885

Step-by-step explanation:

The hundreds digit is 8, and the thousands digit is 5 less, so is 3.

The tens digit is 8 (the largest even digit), and the ones digit is 3 less, so is 5.

The number is ...

  3885

Answer: 7 years

2% = 0.02

3000·0.02=60.00

1 year simple interest = $60.00

420/60=7

7 years

Answer:

The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).

Step-by-step explanation:

We have the standard deviation for the differences, 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 = 8 - 1 = 7

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8946

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.8946\frac{15.9274}{\sqrt{8}} = 10.67[/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 9.582 - 10.67 = -1.088

The upper end of the interval is the sample mean added to M. So it is 9.582 + 10.67 = 20.252

The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).

Answer:

h=2

Step-by-step explanation:

f is translated right 2 units (so h=2) and up 2 units (so k=2)

The value of h is 2.

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

A function f(x) when translated horizontally leads to the function g(x) which is equal to g(x) = f(x ± k) where k is the units to which the function is translated.

And the vertical translation leads to the function g(x) = f(x) ± k, where k is the units to which the function is translated.

Here the original function is, f(x) = 3ˣ.

The point corresponding to x = 0 in f(x) is x = 2 in g(x).

That is (0, 1) is translated to (2, 3).

f(x) is horizontally translated to the right.

3ˣ translates to 3ˣ⁻².

Hence the value of h is 2.

Learn more about Translations here :

https://brainly.com/question/29198392

#SPJ7

Answer:

3x2−2x+6/x2

Step-by-step explanation:

have a great day <33333

Answer:

18

Step-by-step explanation:

1/3 of 27 is 9. 9 times 2 is 18.

Answer:

Peter is a-8 in 9 years, (a-8)+ 9+ a+ 9= 76

Answer:

P = 25

A = 33

Step-by-step explanation:

P + 8 = A

P + 9 + A + 9 = 76

P + A = 58

~~~~~~~~~~~~~~

P = 58 - A

P = 58 - P - 8

2 P = 50

P = 25

A = 33

Answer:

75

Step-by-step explanation:

She is in the negatives right now so add 40 to get Celicia points equal to 0. Then add an extra 35 points (which is what she ended with). Overall, she gained 75 points to end with 35.

Answer:

n>2 2/3

Draw a filled dot at a little more than 2 1/2 and continue the line to the right.

Step-by-step explanation:

Subtract 1/3 from both sides to get

2 2/3

Flip the inequality

n> 2 2/3

I hope this helps!

Answer:

r= 17.73174

Step-by-step explanation:

calculations

Answer:

[tex]EA = \frac{21 \times 15}{7} = 45 \\ { \tt{ \frac{21}{7} = \frac{x}{45} }} \\ x = 135[/tex]

Answer:

Pizza = 12.35

Chips = 2.75

Step-by-step explanation:

Let :

Pizza = x

chips = y

3x + 4y = 48.05 - - - (1)

5x + 2y = 67.25 - - - (2)

Multiply (1) by 5 and (2) by 3

15x + 20y = 240.25

15x + 6y = 201.75

Subtract :

20y - 6y = 240.25 - 201.75

14y = 38.50

y = 38.50/ 14

y = 2.75

Put y = 2.75 in (1)

3x + 4(2.75) = 48.05

3x + 11 = 48.05

3x = 48.05 - 11

3x = 37.05

x = 37.05 / 3

x = 12.35

Pizza = 12.35

Chips = 2.75

Answer:

1.504

Step-by-step explanation:

0.47×100 = 47

3.2×100 = 320

47×320 = 15040

15040÷10000 = 1.504

Answer:

first thing is y - 35 = 5

then y = 35 + 5 because when = come here - will be + and

then we should do+ y=40 answer

Answer:

Step-by-step explanation:

A circumcircle can be referred to as a circumscribed circle to a triangle. The steps to follow is stated below:

i. Since the triangle is equilateral, draw the triangle with sides 6.5 cm

ii. Bisect any of its two sides. The two bisecting lines would intersect at center, O, of the triangle.

iii. With the center and either radius  OA, OB or OC, draw a circumscribed circle to the triangle.

The construction is attached to this answer for clarifications.

Answer:

aasha here it is.

Step-by-step explanation:

3x−1)(2x+3)

    6x2+7x−3

=6x2+9x−2x−3

=3x(2x+3)−1(2x+3)

=(2x+3)(3x−1)

and hiii

Answer:

-4

Step-by-step explanation:

2t=-1-7

t=-8/2

t=-4

i am not sure also

Answer:

(a) Temperature: Numerical

(b) Traffic congestion: Categorical

Step-by-step explanation:

Required

Determine the variable type

(a) Temperature

Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.

Hence, the variable is numerical

(b) Traffic congestion

From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....

Hence, the variable is categorical

Answer:

Step-by-step explanation:

shape Sides Sum of interior angles Each Angle

Triangle         3 180°         60°

Quadrilateral 4 360° 90°

Pentagon 5 540° 108°

Hexagon         6 720° 120°

Heptagon  7 900° 128.57...°

Octagon         8 1080° 135°

Nonagon 9 1260° 140°

D. 2.3.5 is the correct answer

Answer:

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean diameter of 144 millimeters, and a variance of 49.

This means that [tex]\mu = 144, \sigma = \sqrt{49} = 7[/tex]

Sample of 46:

This means that [tex]n = 46, s = \frac{7}{\sqrt{46}}[/tex]

Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?

Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.

Probability the sample mean is below 142:

p-value of Z when X = 142, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}[/tex]

[tex]Z = -1.94[/tex]

[tex]Z = -1.94[/tex] has a p-value of 0.0262

2*0.0262 = 0.0524

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Answer:

1 71years

Step-by-step explanation:

x+10=81

x=71

2. x+8=49

x=41

3. x+11=100

x=99

Answer:

(Y-3)/(3+12)

(Y-3)/(15)

Y-1/5

so the answer is

(Y-1)

Answer:

[tex]y - 3 \: over \: 3 + 12 \\ y - 3.3 + 12 \\ y - 3.3 + 12 = y + 8.7 \\ y - 33 + 12 \\ y + 8.7[/tex]

Answer:

Step-by-step explanation:

Answer:

That's barely readable!  Anyway the solution is:

7x + 7x +2 +5x +7 = 180 degrees

19x + 9 = 180 degrees

19x = 171 degrees

x = 9

So the angles are:

7x = 63 degrees

7x + 2 = 65

5x + 7 = 52

Double check:

Since ALL 3 triangle sides add up to 180:

63 + 65 + 52 = 180 degrees

Step-by-step explanation:

Answer: Yes it is a function.

This is because any x input leads to exactly one y output.

The graph passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the parabolic curve.

Answer:

Z = 50

Step-by-step explanation:

Given the following data;

Z = 187

x = 64

y = 6

Translating the word problem into an algebraic expression, we have;

Z = k√x/y

First of all, we would find the constant of proportionality, k;

187 = k√64/6

187 * 6 = k√64

1122 = 8k

k = 1122/8

k = 140.25

To find z, when x and y = 9

Z = 140.25√9/9

Z = (140.25 * 3)/9

Z = 420.75/9

Z = 46.75 ≈ 50

Note: The values in the latter part of the question isn't explicitly stated, so I assumed a value of 9 for both x and y.

===============================================================

Explanation:

The given stem and leaf plot leads to this data set

68,68,69,69

71,72,77,77,78,78

80,81

I broke it up to have each tens digit get its own row. That way it's bit more readable.

Unfortunately, the term "average" in math is very vague. It could mean one of the following

To get the mean (specifically the arithmetic mean), we will add up the values and then divide by n = 12 because there are 12 values in the list above. Adding said values gets us

68+68+69+69+71+72+77+77+78+78+80+81 = 888

Dividing that over 12 then leads to 888/12 = 74

The arithmetic mean is 74.

-------------

To get the median, we would first sort the data set. Though that is already done for us. From here, we locate the middle-most item.

Since there are n = 12 items here, the middle item is between slot n/2 = 12/2 = 6 and slot 7

The values in slots 6 and 7 are 72 and 77 respectively. The midpoint of those values is (72+77)/2 = 149/2 = 74.5

The median is 74.5

-------------

The mode is possibly the quickest measure of center or average we can compute. We simply look at the value that shows up the most. In this case, the following values show up twice (which is the most frequent of all the values)

They are all tied for the title of "mode". It's possible to have more than one mode, so we say the mode is the set {68,69,77,78}.

Due to the nature of multiple modes, the mode is often not a good measure of center (but it's still a possibility; especially for categorical data).

In this case, I think the mean or median is a better measure of center.

Since there aren't any outliers, the mean is the best measure of center in this case. Luckily, the mean and median (74 and 74.5 respectively) are fairly close to one another.

-------------

To summarize everything, the term "average" is too vague and it could refer to the mean, median or mode. In this problem, the mean is possibly the best measure of center since there aren't any outliers and the mode isn't one single value.

We found the following:

It's very likely your teacher is wanting the mean.