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3 years ago

8

The three angle measures in a triangle are congruent. The angles are equiangular! What is the measurement of one of the angles?

1 answer:

gregori [183]3 years ago

4 0

Answer:

60 degrees per angle.

Step-by-step explanation: a triangle has a total of 180 degrees, and the number of sides determine the number of angles it has. in this case, it's an equilateral triangle. 180/3 = 60. all triangles have 3 sides if you didn't know that ;)

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How to solve question 19<br> thanks

miskamm [114]

Let $X$ be the random variable for the weight of any given can, and let $\mu$ and $\sigma$ be the mean and standard deviation, respectively, for the distribution of $X$ .

You have

$\begin{cases}\mathbb P(X377)=0.025\end{cases}$

Recall that for any normal distribution, approximately 99.7% of it lies within three standard deviations of the mean, i.e. $\mathbb P(\mu-3\sigma$ . This means 0.3% must lie outside this range, $\mathbb P(X\mu+3\sigma)=0.003$ . Because the distribution is symmetric, it follows that $\mathbb P(X$ .

Also recall that for any normal distribution, about 95% of it falls within two standard deviations of the mean, so $\mathbb P(\mu-2\sigma$ , which means 5% falls outside, and by symmetry, $\mathbb P(X>\mu+2\sigma)=0.025$ .

Together this means

$\begin{cases}\mu-3\sigma=347\\\mu+2\sigma=377\end{cases}$

Solving for the mean and standard deviation gives $\mu=365$ and $\sigma=6$ .

6 0

4 years ago

Solve the initial value problem

tigry1 [53]

$9(t+1)\dfrac{\mathrm dy}{\mathrm dt}-7y=14t\implies\dfrac{\mathrm dy}{\mathrm dt}-\dfrac7{9(t+1)}y=\dfrac{14t}{9(t+1)}$

Look for an integrating factor $\mu(t)$ :

$\ln\mu=\displaystyle-\frac79\int\frac{\mathrm dt}{t+1}=-\frac79\ln(t+1)\implies\mu=(t+1)^{-7/9}$

Multiply both sides by $\mu$ :

$(t+1)^{-7/9}\dfrac{\mathrm dy}{\mathrm dt}-\dfrac79(t+1)^{-16/9}y=\dfrac{14}9t(t+1)^{-16/9}$

Condense the left side as the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[(t+1)^{-7/9}y\right]=\dfrac{14}9t(t+1)^{-16/9}$

Integrate both sides:

$(t+1)^{-7/9}y=\displaystyle\frac{14}9\int t(t+1)^{-16/9}\,\mathrm dt$

For the integral on the right, substitute

$u=t+1\implies t=u-1\implies\mathrm dt=\mathrm du$

$\displaystyle\int t(t+1)^{-16/9}\,\mathrm dt=\int(u-1)u^{-16/9}\,\mathrm du$

$\displaystyle=\int\left(u^{-7/9}-u^{-16/9}\right)\,\mathrm du=\frac92u^{2/9}+\frac97u^{-7/9}+C$

$\implies(t+1)^{-7/9}y=\dfrac{14}9\left(\dfrac92(t+1)^{2/9}+\dfrac97(t+1)^{-7/9}+C\right)$

$\implies(t+1)^{-7/9}y=7(t+1)^{2/9}+2(t+1)^{-7/9}+C$

$\implies y=7(t+1)+2+C(t+1)^{7/9}=7t+9+C(t+1)^{7/9}$

Given that $y(0)=12$ , we get

$12=9+C\implies C=3$

$\implies\boxed{y(t)=7t+9+3(t+1)^{7/9}}$

6 0

3 years ago

How long does it take for a car to travel 250 feet at 35 mph?

DedPeter [7]

A little over 7 hours

5 0

3 years ago

Can you help me solve systems of equations by elimination step by step<br> -5x+9y=-12<br> 3x+2y=22

Sergio039 [100]

Answer:

Step-by-step explanation:

First solve -5x+9y=-12 for x:

-5x+9y=-12

-5x+9y-9y=-12-9y

-5x=-12-9

-5x=-9-12

-5x/-5=-9/5-12/-5

x=9/5y+12/6

Substitute x into an equation

3(-9/5y+12/6)+2y=22

37/5y+36/5=22

37/5y+36/5-36/5=22-36/5

37/5y=74/5

37/5y/37/5=74/5/37/5

y=2

Substitute y in x=-9/5y+12/6

9/5(2)+12/6

x=6

Solution Set: (6,2)

xoxo

6 0

3 years ago

2 x + 6 ≤ x + 5 i need help like right noe

MaRussiya [10]

2x+6<u><</u>x+5
subtract x from both sides
x+6<u><</u>5
subtract 6 from both sides
x<u><</u>-1

so x<u><</u>-1

solution set
S={x|x<u><</u>-1}

6 0

4 years ago

Read 2 more answers