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BaLLatris [955]

3 years ago

5

One leg of a right triangle measures 6 inches. The remaining leg measures 6 square root of 3 inches. What is the measure of the

angle opposite the leg that is 6 inches long?

1 answer:

soldier1979 [14.2K]3 years ago

4 0

Let
x---------> <span>the measure of the angle opposite the leg that is 6 inches long

we know that
tan x=opposite side angle x/adjacent side angle x
</span>opposite side angle x------> 6 in
adjacent side angle x-------> 6√3 in
<span>so
tan x=6/(6</span>√3)-----> x=1/√3------> √3/3
<span>x=arc tan(</span>√3/3)------> x=30°
<span>
the answer is
30</span>°<span>

</span>

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In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

Marina86 [1]

Answer:

(a) 0.94

(b) 0.20

(c) 90.53%

Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let $p_1$ be the probability that a bearing meets the specification.

So, $p_1=0.9$

Sample size, $n_1=500$ , is large.

Let X represent the number of acceptable bearing.

Convert this to a normal distribution,

Mean: $\mu_1=n_1p_1=500\times0.9=450$

Variance: $\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45$

$\Rightarrow \sigma_1 =\sqrt{45}=6.71$

(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.

So, $X\geq 440.$

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56$ .

So, the probability that a given shipment is acceptable is

$P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062$

Hence, the probability that a given shipment is acceptable is 0.94.

(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.

Denote the probability od acceptance of a shipment by $p_2$ .

$p_2=0.94$

The total number of shipment, i.e sample size, $n_2= 300$

Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, $\mu_2$ , and variance, $\sigma_2^2$ .

Mean: $\mu_2=n_2p_2=300\times0.94=282$

Variance: $\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92$

$\Rightarrow \sigma_2=\sqrt(16.92}=4.11$ .

In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85$ .

So, the probability that a given shipment is acceptable is

$P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977$

Hence, the probability that a given shipment is acceptable is 0.20.

(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).

The area right to the z-score=0.99

and the area left to the z-score is 1-0.99=0.001.

For this value, the value of z-score is -3.09 (from the z-score table)

Let, $\alpha$ be the required probability of acceptance of one shipment.

So,

$-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}$

On solving

$\alpha= 0.977896$

Again, the probability of acceptance of one shipment, $\alpha$ , depends on the probability of meeting the thickness specification of one bearing.

For this case,

The area right to the z-score=0.97790

and the area left to the z-score is 1-0.97790=0.0221.

The value of z-score is -2.01 (from the z-score table)

Let $p$ be the probability that one bearing meets the specification. So

$-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}$

On solving

$p=0.9053$

Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.

8 0

4 years ago

Which relation is a function?

Veseljchak [2.6K]

Answer: B

Step-by-step explanation:

because in A it says 2=3 and 2=2 that is not a function each number has to have an outcome of one possible answer if that is true it is a function.

7 0

4 years ago

Please help with number 39

mr Goodwill [35]

You want to find values of v (number of visors sold) and c (number of caps sold) that satisfy the equation

... 3v + 7c = 4480

In intercept form, this equation is

... v/(1493 1/3) + c/640 = 1 . . . . . divide by 4480

Among other things, this tells us one solution is

... (v, c) = (0, 640)

The least common multiple of 3 and 7 is 21, so decreasing the number of caps sold by some multiple of 3 and increasing the number of visors sold by that same multiple of 7 will result in another possible solution.

The largest multiple of 21 that is less than 4480 is 213. Another possible solution is (0 +213·7, 640 -213·3) = (1491, 1)

We can also pick some number in between, say using 100 as the multiple

... (0 +100·7, 640 -100·3) = (700, 340)

In summary, your three solutions could be

... (visors, caps) = (0, 640), (700, 340), (1491, 1)

7 0

3 years ago

La suma de dos enteros consecutivos es 25

Mkey [24]

X = el entero más pequeño

Entonces, el otro entero = x+1

Y podemos poner estos numeros en la equacion dado:

x + x+ 1 = 25

2x + 1 = 25

2x = 24

x = 12

x+ 1 = 13

Entonces, los enteros son 12 & 13.

5 0

3 years ago

Root 5 times by root 10 add root 2

laiz [17]

6sqrt2

Mark brainliest please

Hope this helps you

7 0

3 years ago