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2 years ago

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The tip jar at a sandwich shop has been found to have a dollar value 0.65ℎ +1.25, where ℎ is the number of hours since the shop

opened.
a. By how much is the value of the tip jar increasing
The tip jar is increasing by 65 cents per hour
b. How much is the initial value of the tip jar when the store opens?

1 answer:

DedPeter [7]2 years ago

7 0

Answer:

The intial value is 1.25

Step-by-step explanation:

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An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume t

Neko [114]

Answer:

35.2% probability that the sample mean will be 246 pages or more

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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

In this question, we have that:

$\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61$

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{246 - 245}{2.61}$

$Z = 0.38$

$Z = 0.38$ has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

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2 years ago

Given circle X with radius 10 units and chord AB with length 12 units, what is the length of segment CX, which bisects the chord

andrew-mc [135]

Consider the circle with center X, as shown in the figure.

Draw the diameter of the circle which is parallel to cherd AB, as shown in the figure.

Since the diameter and AB are parallel, then the line segment XC which bisects AB at C, will be perpendicular to AB.

SO triangle XCB is a right triangle. Thus the length of CX, by the Pythagorean theorem is

$\sqrt{ XB^{2}- CB^{2}} = \sqrt{ 10^{2}- CB^{6}}= \sqrt{100-36}= \sqrt{64}=8$ units.

Answer: 8 units

7 0

2 years ago

The cubit is an ancient unit. Its length equals six palms. (A palm varies from 2.5 to 3.5 inches depending on the individual.) W

olasank [31]

Assuminhg the ark has a shoe-box (cuboid) shape it´s volume would be:

$V_{cuboid}=lenght*width*height$

We have this three measurements ( $l=300cubits;w=50cubits;h=30cubits)$ ) and it can be as simple as replacing them in the equation and solving but they are in all in $cubits$ . We will convert them to $ft$ because the problem requires the answer in $ft^{3}$ . In order to do this we will use the given equivalences:

$1cubit=6palms\\1palm=3.10in$

and another one:

$1ft=12in$

First we will convert from cubits to palms:

$l=300cubits*\frac{6palms}{1cubit}=1800palms\\w=50cubits*\frac{6palms}{1cubit}=300palms\\h=30cubits*\frac{6palms}{1cubit}=180palms\\$

now from $palms$ to $in$ :

$l=1800palms*\frac{3.10in}{1palm}=5580in\\w=300palms*\frac{3.10in}{1palm}=930in\\h=180palms*\frac{3.10in}{1palm}=558in\\$

now from $in$ to $ft$ :

$l=5580in*\frac{1ft}{12in}=465ft\\w=930in*\frac{1ft}{12in}=77.5ft\\h=558in*\frac{1ft}{12in}=46.5ft$

We can calculate the Volume now like this:

$V_{ark}=465ft*77.5ft*46.5ft=1675743.75ft^{3}$

The volume of trhe ark would be $1675743.75ft^{3}$

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2 years ago

The probability of flowering plants bearing flowers in January is given the table. If a plant has flowered in January, what is t

ololo11 [35]

Answer:

Probability of a flowering plant bearing flowers in January if it is a peony= 70 %

Step-by-step explanation:

We know that:

Probability =Total favourable outcomes/ Total possible outcomes

Probability of flowering plants bearing flowers in January is given in the table. It means that out of 100 peony 70 peony flowers in January.

There are five kinds of flowers.

We have to select peony and find it's Probability.

As all flowers are independent, their flowering phenomenon does not depend on each other.

So,Probability of a flowering plant bearing flowers in January if it is a peony= 70 %

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1 year ago

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WXYZ is a trapezoid with WX ≅ YZ. Isosceles trapezoid W X Y Z is shown. Sides X Y and W Z are parallel. The length of X Y is 3 a

mash [69]

Answer: 5 units

Step-by-step explanation:

8 0

2 years ago

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