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3 years ago

9

Diedra drew a quadrilateral with 4 right angles and opposite sides of same the same length. Name all the kinds of polygons that

could be Diedra quadrilateral.

1 answer:

Degger [83]3 years ago

7 0

It could be a rectangle or a square

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Cable Strength: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the ca

KatRina [158]

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% 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 breaking weight = 768.2 lb

s = sample standard deviation = 15.1 lb

n = sample of cables = 45

$\mu$ = population mean breaking strength

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

<u>So, 95% confidence interval for the population mean, </u> $\mu$ <u> is ;</u>

P(-2.02 < $t_4_4$ < 2.02) = 0.95 {As the critical value of t at 44 degree

of freedom are -2.02 & 2.02 with P = 2.5%}

P(-2.02 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.02) = 0.95

P( $-2.02 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

<u>95% confidence interval for</u> $\mu$ = [ $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }$ , $768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }$ ]

= [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

3 0

3 years ago

A particle moves in a straight line so that its velocity at time

riadik2000 [5.3K]

Answer:

s(2) = 7.75

Step-by-step explanation:

given the velocity v(t) = t^3

we can find the position s(t) by simply integrating v(t) and using the boundary conditions s(1)=2

$s(t) = \int {v(t)} \, dt\\ s(t) = \int {t^3} \, dt\\s(t) = \dfrac{t^4}{4}+c$

we know throught s(1) = 2, that at t=1, s =2. we can use this to find the value of the constant c.

$s(1) = \dfrac{1^4}{4}+c\\4 = \dfrac{1^4}{4}+c\\c = 4-\dfrac{1}{4}\\c = \dfrac{15}{4} = 3.75$

Now we can use this value of t to formulate the position function s(t):

$s(t) = \dfrac{t^4}{4}+\dfrac{15}{4}\\$

this is the position at time t.

to find the position at t=2

$s(2) = \dfrac{2^4}{4}+\dfrac{15}{4}\\$

$s(2) = \dfrac{2^4}{4}+\dfrac{15}{4}\\$

$s(2) = \dfrac{31}{4} = 7.75$

the position of the particle at time, t =2 is s(2) = 7.75

3 0

3 years ago

A tree was 9 feet tall. One year later, the tree was 16 feet tall. Write an equation and find how many feet f the tree grew

ArbitrLikvidat [17]

Answer:

9 + f = 16

Step-by-step explanation:

So just say 9 + f = 16 since the tree grew to 16, and the f is the amount.

8 0

3 years ago

Read 2 more answers

What 2 numbers add up to 3 and multiply to -18?

prohojiy [21]

6 x (-3) = -18
6 + (-3) = 3
The numbers are 6 and -3

4 0

3 years ago

angle a and b are both supplementary to angle c if the measure of angle a is 12 less than 2 times the measure of c find the meas

castortr0y [4]

Answer:

The measure of a = b = 116 degrees

Step-by-step explanation:

Here, we have value of angles to calculate.

If a and b are both supplementary to c, what this means is that when we add either a or b to c, we get 180

Hence; Mathematically;

a + c = 180 and b + c = 180

What we have here is that a and b must be equal since they are both supplementary to the same angle value

Now, we are told further in the question that the measure of angle a is 12 less than 2 times the measure of c;

Mathematically, this means that;

a = 2c - 12

So we now want to find the measure of b

Let’s substitute for a

2c -12 + c = 180

3c -12 = 180

3c = 180 + 12

3c =192

c = 192/3

c = 64

Thus; a = 2c - 12 = 2(64) -12 = 128 -12 = 116

3 0

3 years ago