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3 years ago

14

Harrison has $9.30 in his coin collection all in pennies and dimes the number of dimes is three times the number of pennies how

many coins of each type does she have

1 answer:

Vsevolod [243]3 years ago

5 0

Answer:

Number of Pennies = 30

Number of Dimes = 90

Step-by-step explanation:

Let the number of pennies be p and number of dimes be d

We can write 2 equations and use substitution method to solve.

<u>Total value of all the coins is 9.30:</u>

We can write:

0.01p + 0.1d = 9.30

Note: value of penny is 0.01 and dime is 0.1, in dollars

<u>Number of dimes is 3 times number of pennies:</u>

We can write:

d = 3p

Now putting 2nd equation in first and solving for p:

0.01p + 0.1(3p) = 9.30

0.01p + 0.3p = 9.30

0.31 p = 9.30

p = 9.30 /0.31

p = 30

Now we know d = 3p, so d = 3 (30) = 90

Hence

Number of Pennies = 30

Number of Dimes = 90

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Answer:

$t=\frac{(810-770)-0}{\sqrt{\frac{67^2}{13}+\frac{56^2}{19}}}}=1.771$

$df=n_1 +n_2 -2=13+19-2=30$

Since is a right tailed test the p value would be:

$p_v =P(t_{30}>1.771)=0.0434$

Comparing the p value with the significance level $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and the mean for group 1 is significantly higher than the mean for the group 2

Step-by-step explanation:

Data given

$\bar X_{1}=810$ represent the mean for sample 1

$\bar X_{2}=770$ represent the mean for sample 2

$s_{1}=67$ represent the sample standard deviation for 1

$s_{2}=56$ represent the sample standard deviation for 2

$n_{1}=13$ sample size for the group 2

$n_{2}=19$ sample size for the group 2

$\alpha=0.05$ Significance level provided

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for category 1 is higher than the mean for category 2, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{2}\leq 0$

Alternative hypothesis: $\mu_{1} - \mu_{2}> 0$

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

And the degrees of freedom are given by $df=n_1 +n_2 -2=13+19-2=30$

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:

$t=\frac{(810-770)-0}{\sqrt{\frac{67^2}{13}+\frac{56^2}{19}}}}=1.771$

P value

Since is a right tailed test the p value would be:

$p_v =P(t_{30}>1.771)=0.0434$

Comparing the p value with the significance level $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and the mean for group 1 is significantly higher than the mean for the group 2

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3 years ago

Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink ha

ICE Princess25 [194]

Answer:

Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

<em></em>

Step-by-step explanation:

Sugar concentration of first drink = 20%

Volume of first soda = 250 ml

Sugar in first soda = 20% of 250 ...... (1)

Sugar concentration of second drink = 45%

Volume of second soda = 250 ml

Sugar in second soda = 45% of 250 ...... (2)

Let $x\%$ be the sugar concentration in resultant mixture.

Volume of mixture = 250 + 250 = 500 ml

Sugar in mixture = $x\%$ of 500 ml ...... (3)

Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):

20% of 250 + 45% of 250 = $x\%$ of 500

$\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%$

Hence, Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

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nirvana33 [79]

$(x-2)^2+(y+2)^2=34$

Step-by-step explanation:

Write the equation of the circle in standard form, where center: (2,-2), point on the circle: (5,3)

The equation of circle in standard form is:

$r^2=(x-h)^2+(y-k)^2$

Where (h,k) is center and r is the radius.

We are given center (2,-2) and we need to find radius r

We know a point on circle (5,3) and center (2,-2)

Finding distance between these points:

$r = d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\r= d=\sqrt{(5-2)^2+(3-(-2))^2}\\r= d=\sqrt{(3)^2+(5)^2}\\r= d=\sqrt{9+25}\\r= d=\sqrt{34}$

So, r = √34

then r^2 = 34

So, equation of circle is:

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7 0

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