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maksim [4K]
3 years ago
6

There are 9 more pencils then pens in a container. There are 25 writing utensils in the container in all. How many pens are ther

e in the container?
Mathematics
1 answer:
VashaNatasha [74]3 years ago
3 0
In order to determine the number of pens present in the container, we need to set up equations from the given in the problem statement. We do as follows:

let x the number of pencils
    y the number of pens

From the statement, 9 more pencils then pens in a container,

x = y + 9

From the statement, there are 25 writing utensils in the container in all,

x + y = 25

We use substitution method to calculate for x and y,

y + 9 + y = 25
2y = 16
y = 8
x = 17

Therefore, there are 8 pens in the container and 17 pencils.
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jok3333 [9.3K]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
A policyholder has probability 0.7 of having no claims, 0.2 of having exactly one claim, and 0.1 of having exactly two claims. C
Sladkaya [172]

Answer:

0.89.

Step-by-step explanation:

So, we are given the following data or parameters or information which is going to aid in the solution to this question or problem. So, the data or parameters are;

(1). "probability 0.7 of having no claims, 0.2 of having exactly one claim, and 0.1 of having exactly two claims."

(2). " distributed on the interval [0,60] and are independent."

(3). "The insurer covers 100% of each claim."

So, taking (1) above we will have;

(Total probability= 0.7 + 0.2 + 0.1 = 0.1)

A = { (0.7 × 0)^2 + (0.2 × 1)^2 + ( 0.1 × 2)^2 =( 0.4) +( 0.4) = 0.8.

0.8 + total probability = 0.8 + 0.1 = 0.9.

So, from the question, we are to "Calculate the probability that the total benefit paid to the policyholder is 48 or less."

Hence, P< 48/A = P < 48/0.9 = P < 53.33.

Thus, 53.33/60 = 0.89.

6 0
3 years ago
The Food and Drug Administration (FDA) produces a quarterly report called Total Diet Study. The FDA’s report covers more than 20
pav-90 [236]

Using the normal approximation to the binomial, it is found that:

  • The mean of X is of 52 samples.
  • The standard deviation of X is of 4.2661 samples.
  • 0.0017 = 0.17% probability that less than half without any traces of pesticide.

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

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, with mean given by:  

E(X) = np

And standard deviation of:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution  

Z-score formula is used, which, in a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • Each z-score has an associated p-value, which measures the percentile of measure X.

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

  • 65% of samples had no pesticide, thus p = 0.65
  • 80 samples, thus n = 80

The mean of X is of:

E(X) = np = 0.65(80) = 52

The standard deviation of X is of:

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{80(0.65)(0.35)} = 4.2661

Using the approximation and continuity correction, the probability is P(X < 40 - 0.5) = P(X < 39.5), which is the p-value of Z when X = 39.5. Thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{39.5 - 52}{4.2661}

Z = -2.93

Z = -2.93 has a p-value of 0.0017, thus:

0.0017 = 0.17% probability that less than half without any traces of pesticide.

A similar problem is given at brainly.com/question/24261244

8 0
1 year ago
Lucy’s chocolate bar is 54% cocoa. If the weight of the chocolate bar is 54 grams, how many grams of cocoa does it contain? Roun
Masteriza [31]

Answer:

The chocolate bar contains 29.2 grams of cocoa.

Step-by-step explanation:

Given that Lucy’s chocolate bar is 54% cocoa and the weight of the chocolate bar is 54 grams.

Hence, the amount of cocoa in the chocolate bar is given by

54% of 54 grams

54% percentage means 54/100 = 0.54

Hence, the amount of cocoa in the chocolate bar is

0.54\times54\\=29.16

When rounded to the nearest tenth, 29.16 should be equal to 29.2

Hence, the chocolate bar contains 29.2 grams of cocoa.

4 0
2 years ago
If you are able to help that will be great:)
Schach [20]
1. 14.3-2*5²÷5=14.3-10=4.3
2. Result is Twenty one
7 0
3 years ago
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