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2 years ago

If a: b = 2:3, b: c = 4:3, and c: d = 7: 8, find a: d.

Mathematics

1 answer:

Taya2010 [7]2 years ago

3 0

Answer:

a:d=7:9

Step-by-step explanation:

We have a system with 3 equation:

$\frac{a}{b}=\frac{2}{3}\\\frac{b}{c}=\frac{4}{3}\\\frac{c}{d}=\frac{7}{8}$

If we multiply all of these equations, then we have:

$\frac{a}{b}*\frac{b}{c}*\frac{c}{d}=\frac{2}{3}*\frac{4}{3}*\frac{7}{8}\\\frac{a*b*c}{b*c*d}=\frac{2*4*7}{3*3*8}\\\frac{a}{d}=\frac{56}{72}$

If we simplify this fraction dividing by 9, then:

$\frac{a}{d}=\frac{56:9}{72:9}=\frac{7}{9}$

Therefore, a:d=7:9

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2 years ago

Danielle made 13 out of 18 free throw shots. About how many out of 7 free throw shots would you expect her to make?

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3 years ago

Can i please help me I don't understand

Step2247 [10]

There are two ways for finding p, here is one way:

1/2 = 4p

Multiply both sides by 2:
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3 years ago

Read 2 more answers

Select the equivalent expression.

Free_Kalibri [48]

Answer:

$\frac{7^{15}}{3^{30}}$

Step-by-step explanation:

The given expression is:

$(\frac{3^{-6}}{7^{-3}})^{5}$

Moving the expression to the other side in the fraction changes its sign to opposite. A numerator with negative exponent, when written in denominator will have the positive exponent. Using this rule, we can write:

$(\frac{3^{-6}}{7^{-3}})^{5}\\\\ = (\frac{7^{3}}{3^{6}} )^{5}$

The exponent 5 can be distributed to both numerator and denominator as shown:

$(\frac{7^{3}}{3^{6}} )^{5}\\\\ = \frac{(7^{3})^{5}}{(3^{6})^{5}}$

The power of a power can be written as a product. i.e.

$\frac{(7^{3})^{5}}{(3^{6})^{5}}\\\\ =\frac{7^{15}}{3^{30}}$

So, the expression similar to the given expression and with positive exponents is: $\frac{7^{15}}{3^{30}}$

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2 years ago

Read 2 more answers

The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has under

Ann [662]

Answer:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

Step-by-step explanation:

Data given and notation

$\bar X=1.20$ represent the sample mean given

$\sigma = 0.14$ represent the population standard deviation

$n=49$ sample size

$\mu_o =1.25$ represent the value that we want to test

t would represent the statistic (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean for the gasoline prices is lower than 1.25, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1.25$

Alternative hypothesis: $\mu < 1.25$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Calculate the statistic

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

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

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3 years ago