What is 5/12 as a unit fraction?

In the diagram of the park, ADF~ BCF. The crosswalk at point A is about 20 yd long. A bridge across the pond will be built, from

velikii [3]

Since the 2 triangles are similar, their sides are proportional.
You also know AD is 20 yards, since it tells you that is the crosswalk length at A.
So the proportion is :
50 / 120 = 20 / BC
Or
if you flip it over,
120 / 50 = BC / 20
Then you can solve for BC.
120 / 50 = BC / 20
(20)(120/50) = BC
BC = 48

6 0

3 years ago

Which graph has the same end behavior as the graph of f(x) = –3x^3 – x^2 + 1?

ololo11 [35]

To find out end behavior, we always look at the largest exponent (3 in this case) and the sign of the term with the largest exponent (negative in this case). We can rule out the first two choices because since it is a cubic graph (exponent of 3) the graph will be pointing in opposite directions. Then, the negative tells us that as the x values approache infinity, the y values will approach negative infinity. So the correct answer is the last choice.

Hope this helps

4 0

3 years ago

From 19 measurements of a pressure controller, the mean operating pressure is 4.97 kPa with a standard deviation of 0.0461 kPa.

Semenov [28]

Answer:

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

Step-by-step explanation:

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".

$\bar X =4.97$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.0461 represent the sample standard deviation

n=19 represent the sample size

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:

$df=n-1=19-1=18$

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(0.025,18)".And we see that $t_{\alpha/2}=2.10$

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

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

5 0

2 years ago

For which operations is the set {0, 1} closed?

velikii [3]

0 × 0 = 0
0 × 1 = 0
1 × 1 = 1

Which means multiplication is closed under {0, 1}

1 ÷ 1 = 1
0 ÷ 1 = 0

Division is not closed under {0, 1}

1 + 1 = 2

Addition is not closed under {0, 1}

0 - 1 = -1

Subtraction is not closed under {0, 1} either

So it's only A. Multiplication which is closed under {0, 1}

5 0

3 years ago

Tia's teacher asked her to find the product of 8 and 207 in her head. Which of the following describes the best way for Tia to m

Alex

The correct answer is B

4 0

2 years ago