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3 years ago

A metal bar 36 inches long is to be cut into pieces 3/2 inches

Mathematics

2 answers:

Makovka662 [10]3 years ago

6 0

Answer:

Step-by-step explanation:

To make this easier i like to turn my length into a fraction with the same denominator

36/1= 18/2

18/2 divided by 3/2 equals 6

6 total pieces

Hope this was helpful

Please mark brainliest!

Liono4ka [1.6K]3 years ago

4 0

The answer is 6 I hope that helped

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Which is a perfect square?

Leni [432]

Answer:

I believe it's 6^2.

Step-by-step explanation: 6^2 is the same as 6 times 6. Here's a tip, if you see a 2 as an exponent, you can also say x squared. X to the power of 2 is the same as x squared.

7 0

3 years ago

Read 2 more answers

Solve for x. Write the smaller solution first, and the larger solution second.

vekshin1

Answer:

x=-4.73 x=-1.27

Step-by-step explanation:

(x + 3)^2 - 3 = 0

Add 3 to each side

(x + 3)^2 - 3 +3= 0+3

(x + 3)^2 = 3

Take the square root of each side

sqrt((x + 3)^2) =±sqrt( 3)

(x + 3) =±sqrt( 3)

Subtract 3 from each side

x + 3-3 =-3±sqrt( 3)

x = -3±sqrt( 3)

Approximating to 2 decimal places

x=-1.27 x=-4.73

6 0

3 years ago

Read 2 more answers

Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply,

Paladinen [302]

Answer:

Yes

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Dataset given: 70, 201 ,199, 202, 173 ,153

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}=166.33$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=51.075$

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=6 represent the sample size

2) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=6-1=5$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,5)".And we see that $t_{\alpha/2}=2.57$

Now we have everything in order to replace into formula (1):

$166.33-2.57\frac{51.075}{\sqrt{6}}=112.742$

$166.33+2.57\frac{51.075}{\sqrt{6}}=219.918$

So on this case the 95% confidence interval would be given by (112.742;219.918)

Is it reasonable to believe that the mean magnesium ion concentration may be greater than 208?

On this case since the confidence interval contains the value 208 and the values above 208 until 219.918 makes sense the statement.

YES

We can conduct an hypothesis test

We need to conduct a hypothesis in order to check if the mean is less than 208, the system of hypothesis would be:

Null hypothesis: $\mu \geq 208$

Alternative hypothesis: $\mu < 208$

If we analyze the size for the sample is < 30 and 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)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

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

$t=\frac{166.33-208}{\frac{51.075}{\sqrt{6}}}=-1.998$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=6-1=5$

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

$p_v =P(t_{(5)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we fail to reject the hypothesis that the mean is higher or equal than 208 at 5% of significance.

6 0

3 years ago

Tickets to a school play cost $2 if bought in advance and $3 at the door. By selling all 400 tickets, $1030 was collected. First

Marrrta [24]

Answer:

170 tickets.

Step-by-step explanation:

Write formulas for the question.

$N_2+N_3=400$

$2N_2+3N_3=1030$

Then use substitution.

$N_2=-N_3+400$

$2(-N_3+400)+3N_3=1030$

$-2N_3+800+3N_3=1030$

$N_3=230$

So number of $3 tickets sold is 230. But they ask for the tickets bought in advance (i.e. the tickets sold for $2). Use substitution again.

$N_2+230=400\\N_2=400-230\\N_2=170$

6 0

3 years ago

A 4500 kg vehicle and a 3700kg vehicle are both moving at a speed of 85m/s toward east.Calculate the momentum of each veheicle?

lana [24]

The momentum formula is
p = m*v

where,
p = momentum (not sure why p is chosen but many physics books tend to pick this letter)
m = mass in kilograms
v = velocity in meters per second

So let's calculate the momentum for the 4500 kg vehicle
p = m*v
p = 4500*85
p = 382500 kg m/s

And let's do the same for the 3700 kg vehicle
p = m*v
p = 3700*85
p = 314500 kg m/s

8 0

3 years ago