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3 years ago

PLZ HELP ASAP LAST SIMMILAR AND CONGRUENT TRIANGLES

Mathematics

1 answer:

JulsSmile [24]3 years ago

4 0

Since Y is the right angle of the triangle LNT, LT is the hypotenuse of that triangle. We are going to use the Pythagorean equation to find the measure of LT:
$LT= \sqrt{LY^2+TY^2}$
$LT= \sqrt{5.2^2+3.9^2}$
$LT=6.5$

We can infer from our picture that triangles LNT and YNT are similar. And remember that in similar triangles the corresponding sides are proportional, so we can establish a proportion between sides LT and NT, and between sides LY and TY:
 $\frac{LT}{NT} = \frac{LY}{TY}$
$\frac{6.5}{NT} = \frac{5.2}{3.9}$
Solving for NT:
 $NT= \frac{(6.5)(3.9)}{(5.2)}$
$NT=4.88$

Now the perimeter of our rectangle LINT will be 2LT + 2NT.
 $2(LT)+2(NT)=2(6.5)+2(4.88)=22.76$ 

We can conclude that the perimeter of the rectangle LINT is 22.76 units

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Mitch mixes 5 parts white paint to 9 parts blue paint. If he has 4 qt of white paint, how much blue paint would he need?

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1. Determine how much blue paint is needed in comparison to white paint

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the length of your stride is 30 inches, if you walk 10,000 steps in a day, how many miles will you walk? Rounded to the nearest

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Answer:

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Step-by-step explanation:

10, 000 steps (stride) * 30 inches per stride = 300,000 inches per day.

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To find number of miles walked in a day, we would need to divide total (300,000) by 63,360 :

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4 years ago

Read 2 more answers

The surface, or rim, of a canyon is at an altitude of 60 m. On a hike down into the canyon, a party of hikers stops for a rest 1

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4 years ago

In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of

Phoenix [80]

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean number of chocolate chips = $\frac{\sum X}{n}$ = 1238.2

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 94.3

n = sample of car drivers = 16

$\mu$ = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.131 < $t_1_5$ < 2.131) = 0.95 {As the critical value of t at 15 degrees of

freedom are -2.131 & 2.131 with P = 2.5%}

P(-2.131 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.131) = 0.95

P( $-2.131 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.131 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.131 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.131 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }$ , $1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }$ ]

= [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

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3 years ago