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3 years ago

Solve: x + 1.5= 5.7 How do I solve this?

Mathematics

2 answers:

slava [35]3 years ago

6 0

Answer: x = 4.2

Explanation: If we're asked to solve for x in the equation x + 1.5 = 7.5, what we're really being asked to do is get x by itself on one side of the equation.

So if we take a look at the left side of our equation, notice that 1.5 is being added to x so in order to get x by itself, we must subtract 1.5 from the left side of the equation. Now remember your first rule of solving equations. If we subtract 1.5 from the left side of the equation, we must also subtract 1.5 from the right side of the equation.

So on the left side our +1.5 and -1.5 cancel out and we're simply left with x. On the right side of the equation,

5.7 - 1.5 simplifies to 4.2 so our answer is x = 4.2.

The nice thing about solving equations is that you can always check your answer by plugging it back in to the original equation.

So here, we're gonna plug a 4.2 back in for x in the original equation and we get (4.2) + 1.5 = 5.7.

Since 4.2 + 1.5 = 5.7 is a true statement, our answer checks and we know that it's right.

Mashutka [201]3 years ago

4 0

Answer:

4.2

Step-by-step explanation:

5.7-1.5=4.2

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An engineer in charge of water rationing for the U.S. Army wants to determine if the average male soldier spends less time in th

lina2011 [118]

Answer:

a) H0: μm = μf versus Ha: μm < μf

b) $t=\frac{(2.68-2.7)-0}{\sqrt{\frac{0.65^2}{66}+\frac{0.5^2}{69}}}}=-0.200$

c) $p_v =P(t_{133}$

d) Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.

Step-by-step explanation:

Data given and notation

$\bar X_{m}=2.68$ represent the mean for the sample male

$\bar X_{f}=2.7$ represent the mean for the sample female

$s_{m}=0.65$ represent the sample standard deviation for the males

$s_{f}=0.5$ represent the sample standard deviation for the females

$n_{m}=66$ sample size for the group male

$n_{f}=69$ sample size for the group female

t would represent the statistic (variable of interest)

Part a

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the average male soldier spends less time in the shower than the average female soldier, the system of hypothesis would be:

Null hypothesis: $\mu_{m}-\mu_{f}\geq 0$

Alternative hypothesis: $\mu_{m} - \mu_{f}< 0$

Or equivalently:

Null hypothesis: $\mu_{m}-\mu_{f}= 0$

Alternative hypothesis: $\mu_{m} - \mu_{f}< 0$

And the best option is:

H0: μm = μf versus Ha: μm < μf

Part b

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

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

And the degrees of freedom are given by $df=n_m +n_f -2=66+69-2=133$

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.

What is the test statistic?

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

$t=\frac{(2.68-2.7)-0}{\sqrt{\frac{0.65^2}{66}+\frac{0.5^2}{69}}}}=-0.200$

Part c What is the p-value?

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

$p_v =P(t_{133}$

Part d

The significance level given is $\alpha =0.1$ since the p value is higher than the significance level we can conclude:

Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.

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