MATHEMATICS COLLEGE

Julio has $2.75 in his pocket in nickels and dimes. The number of dimes is 10 less than twice the number of nickels. Find the number of each type of coin.

Answers

Answer 1

Answer:

Answer: Dimes= 20, Nickels= 15

Step-by-step explanation:

Since we are looking for the amount of coins, we can use system of equations to solve for the amount of coins.

Equation 1:

0.1x+0.05y=2.75

This equation comes from the total cost. x stands for dimes and y stands for nickels. 0.1 is the worth of a dime and 0.05 is the worth of a nickel.

Equation 2:

x=2y-10

This equation comes from 10 less than twice the number of nickels.

We can use substitution to find x and y.

0.1(2y-10)+0.05y=2.75

0.2y-1+0.05y=2.75

0.25y-1=2.75

0.25y=3.75

y=15

There are 15 nickels.

Now that we have y, we can plug it back into the equation to find x.

x=2(15)-10

x=30-10

x=20

There are 20 dimes.

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HELP ASAP WILL MARK BRAINLY

Answers

Answer:

$(61)/(99)$

Step-by-step explanation:

let x = 0.616161 (etc.)

make a second equation because you multiply by 100:

100x = 61.616161 (etc.)

subtract from each other

100x = 61.616161

x = 0.616161

you get

99x = 61

solve for x

$(61)/(99)$

What is 5 88/100 - 1 94/100

Answers

Answer:

197/ 50 or in decimal 3.94

Answer

197/ 50 or in decimal 3.94

Step-by-step explanation:

How much is 4+2x(10-5)

Answers

4+20x-10x
4+10x
10x+4
hope this helps!!!

These two trapeziums are similar.Calculate the area of trapezium G.
If your answer is a decimal, give it to 1 d.p.

Answers

Check the picture below.

so let's firstly get the corresponding side of "a".

$\textit{Area of a Trapezoid}\n\n A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\n a,b=\stackrel{parallel~sides}{bases~\hfill }\n[-0.5em] \hrulefill\n h=5\n b=16\n A=70 \end{cases} \implies 70=\cfrac{5(a+16)}{2} \n\n\n 140=5(a+16)\implies \cfrac{140}{5}=a+16\implies 28=a+16\implies 12=a \n\n[-0.35em] ~\dotfill$

$\cfrac{12^2}{30^2}~~ = ~~\cfrac{70}{A}\implies \left( \cfrac{12}{30} \right)^2 =\cfrac{70}{A}\implies \left( \cfrac{2}{5} \right)^2=\cfrac{70}{A}\implies \cfrac{4}{25}=\cfrac{70}{A} \n\n\n 4A=1750\implies A=\cfrac{1750}{4}\implies \boxed{A=437.5~cm^2}$

The time needed for all college students to complete a certain paper-and-pencil maze follows a normal distribution with a population mean of 30 seconds and a population standard deviation of 3 seconds. You wish to see if the mean time μ (where μ stands for population mean) is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. It takes them an sample average of 31.2 seconds to complete the maze. Use this information to test the hypotheses:

H0: μ = 30,

Ha: ≠30

at the significance level of 0.01.

You conclude:

a) There is not enough evidence to support the claim.

b) There is enough evidence to support the claim.

Answers

Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 30\ seconds$

The standard deviation is $\sigma = 3 \ seconds$

The sample size is n = 9

The null hypothesis is $H_o: \mu = 30$

The alternative hypothesis is $H_a : \mu \ne 30$

The level of significance is $\alpha = 0.01$

The sample mean is $\= x = 31.2$

Generally the test statistics is mathematically represented as

$z = ( \= x - \mu )/( (\sigma)/(√(n) ) )$

=> $z = ( 31.2 - 30)/( (3)/(√(9) ) )$

=> $z = 1.2$

From the z table the area under the normal curve to the right corresponding to 1.2 is

$P(Z > 1.2) = 0.11507$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > 1.2)$

=> $p-value = 2 *0.11507$

=> $p-value = 0.230$

From the value obtained w can see that

$p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is there is not enough evidence to support the claim

Final answer:

To test the hypotheses, use a one-sample t-test to compare the sample mean to the population mean. Calculate the t-value and compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Explanation:

To test the hypotheses, we can use a one-sample t-test since we know the population standard deviation and the sample size is small. The null hypothesis (H0) is that the population mean (μ) is equal to 30 seconds, while the alternative hypothesis (Ha) is that the population mean is not equal to 30 seconds.

Using the given information, we can calculate the t-value by using the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Once we have the t-value, we can compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, we reject the null hypothesis. If not, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.