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andreyandreev [35.5K]
3 years ago
13

Peter purchased 14 new baseball cards for his collection. This increased the size of his collection by 35%. How many baseball ca

rds does Peter now have?
Mathematics
1 answer:
Vlad [161]3 years ago
8 0

Answer:

<em>Peter now has 54 baseball cards</em>

Step-by-step explanation:

<u>Percentages</u>

Assume Peter had x baseball cards in his collection. The 35% of his initial collection is

35 * x / 100= 0.35x

We know that those 14 new baseball cards represent a 35% of his previous collection, therefore we can set a simple equation

0.35x=14

When we solve for x, we'll know how many baseball cards Peter had before

x=14 / 0.35 = 40

Peter had 40 cards, he added 14 new baseball cards, so he now has 40+14=54

Peter now has 54 baseball cards

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A ladder leans against the side of a house. The angle of elevation of the ladder is 70 when the bottom of the ladder is 16ft fro
makkiz [27]

46.78

Step-by-step explanation:

you divide 16 by the cos of 70 and it turns out to be 46.78

3 0
3 years ago
(Based on Q1 ~ Q3) According to the Bureau of the Census, 18.1% of the U.S. population lives in the Northeast, 21.9% inn the Mid
vekshin1

Answer:

We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.

Step-by-step explanation:

The null Hypothesis: Geographical distribution of hotline callers could be the same as the U.S. population distribution

Alternative hypothesis: Geographical distribution of hotline callers could not be the same as the U.S. population distribution

The populations considered are the Midwest, South, Northeast, and west.

The number of categories, k = 4

Number of recent calls = 200

Let the number of estimated parameters that must be estimated, m = 0

The degree of freedom is given by the formula:

df = k - 1-m

df = 4 -1 - 0 = 3

Let the significance level be, α = 5% = 0.05

For  α = 0.05, and df = 3,

from the chi square distribution table, the critical value = 7.815

<u>Observed and expected frequencies of calls for each of the region:</u>

<u>Northeast</u>

Observed frequency = 39

It contains 18.1% of the US Population

The probability = 0.181

Expected frequency of call = 0.181 * 200 = 36.2

<u>Midwest</u>

Observed frequency = 55

It contains 21.9% of the US Population

The probability = 0.219

Expected frequency of call = 0.219 * 200 =43.8

<u>South</u>

Observed frequency = 60

It contains 36.7% of the US Population

The probability = 0.367

Expected frequency of call = 0.367 * 200 = 73.4

<u>West</u>

Observed frequency = 46

It contains 23.3% of the US Population

The probability = 0.233

Expected frequency of call = 0.233 * 200 = 46

x^{2} = \sum \frac{(O_{i} - E_{i})  ^{2} }{E_{i} } ,   i = 1, 2,.........k

Where O_{i} = observed frequency

E_{i} = Expected frequency

Calculate the test statistic value, x²

x^{2} = \frac{(39 - 36.2)^{2} }{36.2} + \frac{(55 - 43.8)^{2} }{43.8} + \frac{(60 - 73.4)^{2} }{73.4} + \frac{(46 - 46.6)^{2} }{46.6}

x^{2} = 5.535

Since the test statistic value, x²= 5.535 is less than the critical value = 7.815, the null hypothesis will not be rejected, i.e. it will be accepted. We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.  

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