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3 years ago

Solve the equation. (-7x + 2)^1/3 = (4 + 3x)^1/3

1 answer:

3 0

(-7x + 2)^1/3 = (4 + 3x)^1/3
take the cube of both side to eliminate the 1/3 power
so you get
-7x+2=4+3x
combine like terms
-10x=2
solve for x
x=-1/5

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Nicole bought a piece of property for $12,000. She sold it for $15,000. What is the percent of increase

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The percent of increase is 25 percent

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3 years ago

A researcher wishes to estimate the average blood alcohol concentration (BAC) for drivers involved in fatal accidents who are f

Mnenie [13.5K]

Answer:

A 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .

Step-by-step explanation:

We are given that a researcher randomly selects records from 60 such drivers in 2009 and determines the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.080 g/dL.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean BAC = 0.16 g/dL

s = sample standard deviation = 0.080 g/dL

n = sample of drivers = 60

$\mu$ = population mean BAC in fatal crashes

<em>Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>

So, a 90% confidence interval for the population mean, $\mu$ is;

P(-1.672 < $t_5_9$ < 1.672) = 0.90 {As the critical value of t at 59 degrees of

freedom are -1.672 & 1.672 with P = 5%} P(-1.672 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.672) = 0.90

P( $-1.672 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.672 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.672 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.672 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

<u>90% confidence interval for</u> $\mu$ = [ $\bar X-1.672 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.672 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $0.16-1.672 \times {\frac{0.08}{\sqrt{60} } }$ , $0.16+1.672 \times {\frac{0.08}{\sqrt{60} } }$ ]

= [0.143, 0.177]

Therefore, a 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .

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3 years ago

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harina [27]

Answer:snomwrkgjrmkgernuhierjher8ouynrejyieryjtleyhe9uirojlPOINTSBITHC

Step-by-step explanation:

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3 years ago

the price of milk in 2013 was around $3.28 a gallon. This was eight times as much as you would have probably paid for a gallon o

Jlenok [28]

The cost of the milk is $\fbox{\$\,0.41{\text{ a gallon}}}$ in 1950s.

Further explanation:

The price of milk in 2013 was around $\$3.28$ a gallon.

And it is given that this was eight times as much as one can would have probably paid for a gallon of milk in the 1950s.

It is given that the price of milk in 2013 is $\$3.28$ a gallon.

Assume the price of milk in 1950 be $\$x$ a gallon.

Now, given that 8 times of $x$ is the price of milk in 2013.

Therefore, $8x$ is the price of milk in 2013 and also $\$3.28$ is the price of milk in 2013.

Equating $8x$ and $\$3.28$ equal as both are the price of milk in 2013 as,

$\begin{aligned}8x&=3.28\\x&=\frac{{3.28}}{8}\\x&=0.41\\\end{aligned}$

Here, x is the price of milk in 1950.

Therefore, the cost of the milk is $\fbox{\$\,0.41{\text{ a gallon}}}$ in 1950s.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations in one variable

Keywords: Cost, gallon, milk, linear equation in one variable, polynomials, variables, real numbers, degree of polynomials, equations, expressions, coefficients, zero polynomial, constants, integers, roots of polynomials.

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Answer:

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