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3 years ago

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The angle between two sides of a triangle is increasing at the rate of 0.03 radians per second. One side of the triangle measure

s 9 inches, and the other is 7 inches. At what rate is the area of the triangle changing when the angle between the sides is `pi/3` ?
`A = 1/2 ab sin theta`
A.
–47.25 in. 2/s
B.
–0.4725 in. 2/s
C.
0.4725 in. 2/s
D.
47.25 in. 2/s

1 answer:

Rainbow [258]3 years ago

5 0

Answer:

its the other won D

Step-by-step explanation:

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Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this informati

KatRina [158]

Answer:

($13,300,$46,900)

Step-by-step explanation:

We are given the following in he question:

Mean, μ = $30,100

Standard Deviation, σ = $5,600

Chebyshev's Theorem:

According to theorem atleast $1 - \dfrac{1}{k^2}$ percent of data lies within 2 standard deviations of mean.
For k = 3,

$1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%$

Thus, 89% of data lies within three standard deviation of mean.

$\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900$

Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)

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3 years ago

The curved surface area of a right circular cylinder of height 14 cm is 88 cm².

Slav-nsk [51]

Answer:

The diameter of the base of the cylinder is 2 cm.

Step-by-step explanation:

<u>GIVEN</u> :

As per given question we have provided that :

➣ Height of cylinder = 14 cm
➣ Curved surface area = 88 cm²

$\begin{gathered}\end{gathered}$

<u>TO</u><u> </u><u>FIND</u> :

in the provided question we need to find :

➠ Radius of cylinder
➠ Diameter of cylinder

$\begin{gathered}\end{gathered}$

<u>USING</u><u> </u><u>FORMULAS</u> :

$\star{\underline{\boxed{\sf{\purple{Csa = 2 \pi rh}}}}}$

$\star{\underline{\boxed{\sf{\purple{d = 2r}}}}}$

➛ Csa = Curved surface area
➛ π = 22/7
➛ r = radius
➛ h = height
➛ d = diameter

$\begin{gathered}\end{gathered}$

<u>SOLUTION</u> :

Firstly, finding the radius of cylinder by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{Csa = 2 \pi rh}}} \\ \\ \qquad{\longrightarrow{\sf{88 = 2 \times \dfrac{22}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{\cancel{7}}\times r \times \cancel{ 14}}}} \\ \\ \qquad{\longrightarrow{\sf{88 =44 \times r \times 2}}} \\ \\ \qquad{\longrightarrow{\sf{88 =88 \times r}}} \\ \\ \qquad{\longrightarrow{\sf{r = \frac{88}{88}}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\pink{r = 1 \: cm}}}}}} \end{gathered}$

Hence, the radius of cylinder is 1 cm.

———————————————————————

Now, finding the diameter of cylinder by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{d = 2r}}} \\ \\ \qquad{\longrightarrow{\sf{d = 2 \times 1}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\red{r = 2 \: cm}}}}}}\end{gathered}$

Hence, the diameter of the base of the cylinder is 2 cm.

$\rule{300}{2.5}$

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2 years ago

Read 2 more answers

What is the measure of x in degrees ?

mr Goodwill [35]

Answer:

x = 35°

Step-by-step explanation:

Same side interior angles are supplementary, or they add up to 180°. So write an equation:

$x+145=180$

Solve for x. Subtract 145 from both sides:

$x+145-145=180-145\\\\x=35$

The value of x is 35°.

:Done

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3 years ago

Determine the term life insurance amount per thousand on a 22-year-old female for a 5-year policy given that the face value of t

VLD [36.1K]

We need to determine the term life insurance amount per thousand on a 22-year-old female for a 5-year policy given that the face value of the policy is $600,000 and the annual premium is $1332.

Since we are supposed to find the term life insurance amount per thousand, therefore, we will use the following formula:

$\text{Term life insurance amount}=\frac{\text{Annual premium}}{\text{Face value of insurance}}*1000$

Upon substituting the values of annual premium and face value of insurance, we get:

$\text{Term life insurance amount}=\frac{\text{1332}}{\text{600000}}*1000\\
\text{Term life insurance amount}=\$2.22$

Therefore, the required life insurance amount is $2.22.

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3 years ago

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A survey of 76 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.55 minutes.

nika2105 [10]

Answer:

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

$2.55-1.96\frac{12}{\sqrt{76}}=-0.148$

$2.55+1.96\frac{12}{\sqrt{76}}=5.248$

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

$\bar X=2.55$ represent the sample mean for the late time for a flight

$\mu$ population mean

$\sigma=12$ represent the population deviation

n=76 represent the sample size

Confidence interval

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

The confidence interval for the true mean is given by:

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

The Confidence level given is 0.95 or 95%, th significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ . If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got $z_{\alpha/2}=1.96$

Replacing we got:

$2.55-1.96\frac{12}{\sqrt{76}}=-0.148$

$2.55+1.96\frac{12}{\sqrt{76}}=5.248$

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

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3 years ago