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Makovka662 [10]

2 years ago

15

In △ABC m∠CAB = 40° and m∠ABC = 60°. Circle, going through points A and C, intersects sides AB and BC in points D and E respecti

vely. Find all angles in quadrilateral ACED.

1 answer:

Gnom [1K]2 years ago

4 0

Answer:

80, 100

Step-by-step explanation:

180 - (40+60) =

80

That means one of the angles is 80, making an other angle 180-80 = 100 degrees

You might be interested in

A random sample of 25 roundtrip flights between Philadelphia and Dallas has an average airfare of $393.50 with a sample standard

Sauron [17]

Answer:

$393.50+/-$19.72

= ( $373.78, $413.22)

Therefore, the 95% confidence interval (a,b) = ($373.78, $413.22)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $393.50

Standard deviation r = $50.30

Number of samples n = 25

Confidence interval = 95%

z value(at 95% confidence) = 1.96

Substituting the values we have;

$393.50+/-1.96($50.30/√25)

$393.50+/-1.96($10.06)

$393.50+/-$19.7176

$393.50+/-$19.72

= ( $373.78, $413.22)

Therefore, the 95% confidence interval (a,b) = ($373.78, $413.22)

5 0

2 years ago

Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st

Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)

b) n=523 rounded up to the nearest integer

Step-by-step explanation:

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".

$\bar X=530$ represent the sample mean for the sample

$\mu$ population mean

s=70 represent the sample standard deviation

n=48 represent the sample size (variable of interest)

Confidence =95% or 0.995

Part a

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

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

The degrees of freedom are df=n-1=48-1=47

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(0.025,47)".And we see that $z_{\alpha/2}=2.01$

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

$530-2.01\frac{70}{\sqrt{48}}=509.692$

$530+2.01\frac{70}{\sqrt{48}}=550.308$

So on this case the 95% confidence interval would be given by (509.592;550.308)

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

Assuming that $\hat \sigma =s$

And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ , replacing into formula (b) we got:

$n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523$

So the answer for this case would be n=523 rounded up to the nearest integer

3 0

2 years ago

The bagel shop sells special bagel sandwiches for $7 and plain bagels for $2. Last saturday, they sold 100 items and made $385.

zloy xaker [14]

Answer:

Number of special bagel sandwiches = 37

Step-by-step explanation:

Let $x,y$ denote number of special bagel sandwiches and plain bagels respectively.

The bagel shop sold 100 items.

$x+y=100\\y=100-x$

Also, The bagel shop made $385.

$7x+2y=385$

Put $y=100-x$ in $7x+2y=385$

$7x+2(100-x)=385\\7x+200-2x=385\\5x=385-200\\5x=185\\x=\frac{185}{5}\\x=37$

So,

Number of special bagel sandwiches = 37

5 0

2 years ago

-2(x-3y)=18 Solve for y

Inga [223]

Answer:

...The answer is y=3+x/3

7 0

2 years ago

Read 2 more answers

Terry made a plastic birdhouse with the dimensions shown below. How many square inches

xxMikexx [17]

Answer:

376 squared inches for the hole bird house, 60 for the side with the whole.

Step-by-step explanation:

1 side is 60 inches squared, another is 48 inches squared, and another is 80 inches squared, and there are two of each side so you get 120+96+160= 376.

7 0

2 years ago

Read 2 more answers