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2 years ago

Find the area of the shaded region.

Mathematics

1 answer:

Mila [183]2 years ago

5 0

Answer:

18π cm² ≈ 56.5 cm²

Step-by-step explanation:

The area of the sector can be found using an appropriate area formula.

<h3>Sector area</h3>

When the sector central angle is given in radians, the formula for the area of that sector is ...

A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius

When the angle is in degrees, the formula will include a factor to convert it to radians:

A = 1/2r²θ(π/180) . . . . where angle θ is in degrees

A = (πθ/360)r² . . . . simplified slightly

The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...

A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²

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Shandra's parents put $1,500 in her bank account for college tuition. At an interest rate

gavmur [86]

Answer:

$6,427.99

Step-by-step explanation:

-We first find the effective annual interest rate as follows:

$i_m=(1+i/m)^m-1\\\\=(1+0.0825/2)^2-1\\\\=0.084202$

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3 years ago

A cyclic quadrilateral is shown. x:y=3:7. work out the size of angle z

LekaFEV [45]

Answer:

116 degrees

Step-by-step explanation:

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4 years ago

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with

Ratling [72]

Answer:

$P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)$

And we can find this probability using the complement rule and with excel or the normal standard table:

$P(z>1.61)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(10.5,0.3)$

Where $\mu=10.5$ and $\sigma=0.3$

We are interested on this probability

$P(X>10.983)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)$

And we can find this probability using the complement rule and with excel or the normal standard table:

$P(z>1.61)=1-P(z$

8 0

3 years ago

Can someone help me to find length CD

uysha [10]

Answer:

CD = 3.602019190339

Step-by-step explanation:

CD = DA - CA

DA = DB×Cos(29) = 18.7×cos(29) = 16.355388523507

BA = BA×cos(43) = 18.7×cos(43) = 13.676314220278

CA = BA÷tan(47) = 13.676314220278÷tan(47) = 12.753369333168

Then

CD = 16.355388523507 - 12.753369333168 = 3.602019190339

7 0

4 years ago

The figure below shows a shaded rectangular region inside a large rectangle:

pshichka [43]

Answer:

b. 58%

Step-by-step explanation:

Calculate the area of the entire rectangle using the formula A = lw.

The lowercase "L" is for length.

"w" is for width.

The lighter square is 10 units long by 5 inches wide.

A = lw

A = (10 in)(5 in) Multiply

A = 50 in²

Calculate the area for the shaded rectangle, 7 inches by 3 inches.

A = lw

A = (7 in)(3 in) Multiply

A = 21 in²

Calculate the area for the non-shaded region by subtracting the shaded area from the total area.

50 in² - 21 in² = 29 in²

The chance that a point in the large rectangle will NOT be in the shaded region is 29/50.

Convert this fraction to decimal form by using a calculator. Divide the top number by the bottom number.

29/50 = 0.58

0.58 is in decimal form. To convert it to a percentage, multiply the number by 100.

0.58 = 58%

Therefore the probability that a point chosen inside the large rectangle is not in the shaded region is 58%.

5 0

3 years ago