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vitfil [10]
2 years ago
7

Pings Ice Cream Palace offers a special sundae that contains over 2 kilograms of ice cream plus any number of toppings.

Mathematics
2 answers:
ss7ja [257]2 years ago
5 0

Answer:

,,,

Step-by-step explanation:

Alina [70]2 years ago
4 0
Let "x" represent the weight of the toppings. We know that we can have any number of toppings. This means that one may ask for no toppings at all too.
Now, we have been told that "S" is the weight of the special sundae in kilograms. This definitely included the "mandatory" 2 kilograms of ice cream. Therefore, S will be at-least equal to 2.
Thus, the inequality that describes S, the weight of the special sundae in kilograms at Ping's Ice Cream Palace is given as:
kilograms.
It can be seen that as x increases, S increases too and if an order does not want any toppings in it then the weight of the special sundae will be a minimum of 2 kg which is the weight of the ice cream.
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"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the
STALIN [3.7K]

Answer:

\\ P(z>-2) = 0.97725 or P(x>49) is about 97.725% (or being less precise 97.5% using the <em>empirical rule</em>).

Step-by-step explanation:

We solve this question using the following information:

  1. We are dealing here with <em>normally distributed data</em>, that is "<em>the frequency distribution of the life length data is known to be mound-shaped</em>".
  2. The normal distribution is defined by two parameters: the population mean (\\ \mu) and the population standard deviation (\\ \sigma). In this case, we have that \\ \mu = 55 months, and \\ \sigma = 3 months.
  3. To find the probabilities, we have to use the <em>standard normal distribution</em>, which has \\ \mu = 0 and \\ \sigma = 1. The probabilities for this distribution are collected in the <em>standard normal table</em>, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
  4. For most cases, we need to use the <em>cumulative standard normal table, </em>and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: \\ z = \frac{x - \mu}{\sigma} [1]. A z-score tells us the distance from the mean that a raw score is from it in <em>standard deviations units</em>. If this value is <em>negative</em>, the raw score is <em>below</em> the mean. Conversely, a <em>positive</em> value indicates that it is <em>above</em> the mean.
  5. The <em>cumulative standard normal table </em>is made for positive values of z. Since the normal distribution is <em>symmetrical</em> around the mean, we can find the negative values of z using this formula: \\ P(z [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

<em>First Step: Use formula [1] to find the z-score of the raw score x = 49 months</em>.

\\ z = \frac{49 - 55}{3}

\\ z = \frac{-6}{3}

\\ z = -2

This means that the raw score is represented by a z-score of \\ z = -2, which tells us that it is<em> two standard deviations below</em> the population mean.

<em>Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.</em>

For a z = 2, the probability is 0.97725.  

Then

\\ P(z

\\ P(z2)

\\ P(z2)

But we <em>are not asked</em> for P(z<-2) but for P(z>-2) = P(x>49). This probability is the <em>complement</em> of the previous result, that is

\\ P(z>-2) = 1 - P(z

\\ P(z>-2) = 1 - 0.02275

\\ P(z>-2) = 0.97725

That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is

\\ P(z>-2) = 0.97725 or about 97.725%

A graph below shows this result.

Notice that if we had used the <em>68-95-99.7 rule</em> (also known as the <em>empirical rule</em>), that is, in a normal distribution, the interval between <em>one standard deviation below and above the mean</em> contains, approximately, 68% of the observations; the interval between <em>two standard deviations below and above the mean</em> contains, approximately, 95% of the observations; and the interval between <em>three standard deviations</em> below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last <em>less</em> than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the <em>symmetry of the normal distribution</em>, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0
3 years ago
Help me with this question
MA_775_DIABLO [31]

<em>Answer: C</em>

<em />

<em />

<em>It is C because when there is a line at the top of the number, it is infinite and repeats many times. That number in a shorter was can be written as a fraction over 990. Two of the answer choices has 990 in it which is letters B and C. This eliminates answer choices A and D. The number that is within the dot is your numerator (645) and 990 is your denominator. Overall the answer is 645/990</em>

6 0
3 years ago
Read 2 more answers
Factor the polynomial. 54c3d4 + 9c4d2 A. 9c3d2(d2 + 6c) B. 9c3d2(6d2 + c) C. 9c4d2(d2 + 6) D. 9c4d2(6d2 + 1)
11Alexandr11 [23.1K]
Answer is = 9c^3 d^2 (6d^2 + c)
5 0
3 years ago
Read 2 more answers
Please tell me the final answer and how you got it.
dem82 [27]
It is  484 m^2 ,to my understanding!
5 0
3 years ago
I NEED THIS ASAP 5/8 of 48 is equal to 8/15 of some number. What is this number?
murzikaleks [220]

(5/8) × 48 = (8/15) × n

Multiply by the inverse of the coefficient of n. That inverse is 15/8.

n = (15/8)×(5/8)×48 = (75/64)×48 = 225/4 = 56 1/4

5/8 of 48 is equal to 8/15 of 56 1/4

5 0
3 years ago
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