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Karo-lina-s [1.5K]

3 years ago

14

Pennies are packaged 50 in a roll. A mother gave her son 161 pennies for his bank and she had 39 pennies left over. How many rol

ls of pennies did she use? 6 rolls 5 rolls 7 rolls 4 rolls

2 answers:

Kisachek [45]3 years ago

7 0

She used 4 rolls or pennies.

yulyashka [42]3 years ago

5 0

4 rolls is the answer

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Convert 7 months into days.

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Answer:

212 days are in 7 months

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Identify the like terms.

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The answer is c. 10y and -9y

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3 years ago

Suppose that the probability of a baseball player getting a hit in an at-bat is 0.3089. If the player has 25 at-bats during a we

klio [65]

Answer:

$P(X>9) = 0.3593$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=25, p=0.3089)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

For this case we want this probability:

$P(X >9)$

And we can use the complement rule like this:

$P(X>9) = 1-P(X \leq 8)= 1-[P(X=0) + P(X=1) +....+P(X=8)]$ And we can find the individual probabilities like this:

$P(X=0) =(25C0)(0.3089)^0 (1-0.3089)^{25-0} =0.0000974$

$P(X=1) =(25C1)(0.3089)^1 (1-0.3089)^{25-1} =0.0011$

$P(X=2) =(25C2)(0.3089)^2 (1-0.3089)^{25-2}=0.00584$

$P(X=3) =(25C3)(0.3089)^3 (1-0.3089)^{25-3}= 0.02$

$P(X=4) =(25C4)(0.3089)^4 (1-0.3089)^{25-4}=0.049$

$P(X=5) =(25C5)(0.3089)^5 (1-0.3089)^{25-5}=0.092$

$P(X=6)=(25C6) (0.3089)^6 (1-0.3089)^{25-6} = 0.138$

$P(X=7) =(25C7)(0.3089)^7 (1-0.3089)^{25-7}=0.167$

$P(X=8) =(25C8)(0.3089)^8 (1-0.3089)^{25-8}=0.168$

And in order to do the operations we can use the following excel code:

"=1-BINOM.DIST(8,25,0.3089,TRUE)"

And we got:

$P(X>9) = 0.3593$

4 0

3 years ago

The time it takes for a planet to complete its orbit around a particular star is called the? planet's sidereal year. The siderea

BartSMP [9]

Answer:

(a) See below

(b) r = 0.9879

(c) y = -12.629 + 0.0654x

(d) See below

(e) No.

Step-by-step explanation:

(a) Plot the data

I used Excel to plot your data and got the graph in Fig 1 below.

(b) Correlation coefficient

One formula for the correlation coefficient is

$r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}$

The calculation is not difficult, but it is tedious.

(i) Calculate the intermediate numbers

We can display them in a table.

<u> x </u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>

36 0.22 7.92 1296 0.05

67 0.62 42.21 4489 0.40

93 1.00 93.00 20164 3.46

433 11.8 5699.4 233289 139.24

887 29.3 25989.1 786769 858.49

1785 82.0 146370 3186225 6724

2797 163.0 455911 7823209 26569

<u>3675 </u> <u> 248.0 </u> <u> 911400 </u> <u>13505625</u> <u> 61504 </u>

9965 537.81 1545776.75 25569715 95799.63

(ii) Calculate the correlation coefficient

$r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}$

(c) Regression line

The equation for the regression line is

y = a + bx where

$a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}$

(d) Residuals

Insert the values of x into the regression equation to get the estimated values of y.

Then take the difference between the actual and estimated values to get the residuals.

<u> x </u> <u> y </u> <u>Estimated</u> <u>Residual </u>

36 0.22 -10 10

67 0.62 -8 9

93 1.00 -7 8

142 1.86 -3 5

433 11.8 19 - 7

887 29.3 45 -16

1785 82.0 104 -22

2797 163.0 170 - 7

3675 248.0 228 20

(e) Suitability of regression line

A linear model would have the residuals scattered randomly above and below a horizontal line.

Instead, they appear to lie along a parabola (Fig. 2).

This suggests that linear regression is not a good model for the data.

4 0

3 years ago

14 = 6+z / -2, Solve each equation. Check your solution.

aev [14]

Answer:

-16

Step-by-step explanation:

14=6+z/-2

14-6=z/-2

8=z/-2

z=8*-2

z=-16

5 0

3 years ago