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2 years ago

Given: m∠ATB = 63°, arc AB = 115° Find: arc DC

Mathematics

1 answer:

Flura [38]2 years ago

6 0

Answer:

The measure of arc DC is $11\°$

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

$m\angle ATB=\frac{1}{2}[arc\ AB+arc\ DC]$

substitute the given values

$63\°=\frac{1}{2}[115\°+arc\ DC]$

$126\°=[115\°+arc\ DC]$

$arc\ DC=126\°-115\°=11\°$

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When an apple is dropped from a tower 256 feet high, the function h(t) =-167 +256 models the height of the

DerKrebs [107]

Answer:

around 1.5 sec

Step-by-step explanation:

basically you wanna figure out at what time is the height=0

since h(t) represents height, set it to 0 then solve for t

i believe you might have forgotten the t in the equation so i assumed it was -167t

0=-167t+256

-256=-167t

t=1.53293413174

around 1.5 seconds after it was dropped

alternatively, you could plug the equation into desmos, replacing h(t) with y and t with x and find the x intercept

3 0

2 years ago

6. A wall 12 feet long makes a corner with a wall

kotykmax [81]

Answer:

Yes

Step-by-step explanation:

6 0

2 years ago

A CD usually sells for $17.00. If the CD is 30% off, and sales tax is 6%, what is the total price of the CD, including tax?

Ivan

If it is 30% off, then u r paying 70%

70% of 17 = 0.7(17) = 11.90 ...this is without tax

u have a tax rate of 6%.....

11.90 * 1.06 = 12.614 rounds to 12.61 <== total cost including tax

8 0

2 years ago

Read 2 more answers

Seven Applicants for a Job - F, G, H, I, J, K, and L are each to be interviewed on monday or Tuesday . Each

stiks02 [169]

Answer:

I would guess its D. Because it is the one that makes the most sense.

Step-by-step explanation:

H and L has to be on the same day with no other application so not A, B, or C because there is L in all of them.

Hope I helped!

6 0

2 years ago

g Assume that the distribution of time spent on leisure activities by adults living in household with no young children is norma

OLga [1]

Answer:

"The probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day" is about 0.8749.

Step-by-step explanation:

We have here a random variable that is normally distributed, namely, the time spent on leisure activities by adults living in a household with no young children.

The normal distribution is determined by two parameters: the population mean, $\\ \mu$ , and the population standard deviation, $\\ \sigma$ . In this case, the variable follows a normal distribution with parameters $\\ \mu = 4.5$ hours per day and $\\ \sigma = 1.3$ hours per day.

We can solve this question following the next strategy:

Use the cumulative standard normal distribution to find the probability.
Find the z-score for the raw score given in the question, that is, x = 6 hours per day.
With the z-score at hand, we can find this probability using a table with the values for the cumulative standard normal distribution. This table is called the standard normal table, and it is available on the Internet or in any Statistics books. Of course, we can also find these probabilities using statistics software or spreadsheets.

We use the standard normal distribution because we can "transform" any raw score into standardized values, which represent distances from the population mean in standard deviations units, where a positive value indicates that the value is above the mean and a negative value that the value is below it. A standard normal distribution has $\\ \mu = 0$ and $\\ \sigma = 1$ .

The formula for the z-scores is as follows

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Solving the question

Using all the previous information and using formula [1], we have

x = 6 hours per day (the raw score).

$\\ \mu = 4.5$ hours per day.

$\\ \sigma = 1.3$ hours per day.

Then (without using units)

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{6 - 4.5}{1.3}$

$\\ z = \frac{1.5}{1.3}$

$\\ z = 1.15384 \approx 1.15$

We round the value of z to two decimals since most standard normal tables only have two decimals for z.

We can observe that z = 1.15, and it tells us that the value is 1.15 standard deviations units above the mean.

With this value for z, we can consult the cumulative standard normal table, and for this z = 1.15, we have a cumulative probability of 0.8749. That is, this table gives us P(z<1.15).

We can describe the procedure of finding this probability in the next way: At the left of the table, we have z = 1.1; we can follow the first line on the table until we find 0.05. With these two values, we can determine the probability obtained above, P(z<1.15) = 0.8749.

Notice that the probability for the z-score, P(z<1.15), of the raw score, P(x<6) are practically the same, $\\ P(z$ . For an exact probability, we have to use a z-score = 1.15384 (without rounding), that is, $\\ P(z$ . However, the probability is approximated since we have to round z = 1.15384 to z = 1.15 because of the use of the table.

Therefore, "the probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day" is about 0.8749.

We can see this result in the graphs below. First, for P(x<6) in $\\ N(4.5, 1.3)$ (red area), and second, using the standard normal distribution ( $\\ N(0, 1)$ ), for P(z<1.15), which corresponds with the blue shaded area.

5 0

2 years ago