(need help!) A dart is thrown at the board shown. It hits the board at a random point. Find the probability that it will land in the unshaded region. Round to the nearest percent.




20%


33%


17%


25%

The measure of side a is 14.

We have,

We use the trigonometric identites:

Sin function

Now,

Sin A = Perpendicular / Hypotenuse

Sin 34 = a / 25

0.56 = a / 25

a = 0.56 x 25

a =  14

Thus,

The measure of side a is 14.

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The height of cylinder is,

⇒ h = 2.4 inches

We have to given that,

In a cylinder,

Volume = 271.4 inches³

And, Radius = 6 inch

Since, We know that,

Volume of cylinder is,

⇒ V = πr²h

Where, V is volume , r is radius and h is height.

Substitute all the values, we get;

⇒ 271.4 = 3.14 × 6² × h

⇒ 271.4 = 3.14 × 36 × h

⇒ 271.4 = 113.04 × h

⇒ h = 2.4 inches

Thus, The height of cylinder is,

⇒ h = 2.4 inches

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Answer:

B. [tex]x=62[/tex]; [tex]y=30[/tex]

Step-by-step explanation:

We have been given two similar triangles. We are asked to find the value of x and y for the given triangles.

[tex]\Delta SWK\sim \Delta EBT[/tex]

We know that the measure of corresponding angles of two similar triangles are equal.

[tex]m\angle S=m\angle E[/tex]

[tex]m\angle W=m\angle B[/tex]

[tex]m\angle K=m\angle T[/tex]

[tex]110=2x-14[/tex]

[tex]2x-14=110[/tex]

[tex]2x-14+14=110+14[/tex]

[tex]2x=124[/tex]

[tex]\frac{2x}{2}=\frac{124}{2}[/tex]

[tex]x=62[/tex]

[tex]m\angle S=m\angle E[/tex]

[tex]40=m\angle E[/tex]

Using angle sum property, we will get:

[tex]m\angle E+m\angle B+m\angle T=180[/tex]

[tex]40+y+110=180[/tex]

[tex]y+150=180[/tex]

[tex]y+150-150=180-150[/tex]

[tex]y=30[/tex]

Therefore, option B is the correct choice.

Answer:

mean is 578.3 deviation 261.9

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the answer we must use the diagram, we see that among 8 possible results, there's one possible outcome to hit HHH.

So, to find the amount of people that are expected to hit HHH, we just have to  multiply each percentage assigned to the HHH outcome:

[tex](0.7)(0.5)(0.3)=0.105[/tex]

Now, we see that a 10.5% of the people will be expected to hit HHH.

The approximate number of people would be:

[tex]25(0.105) \approx 3[/tex]

Therefore, almost 3 persons are expected to hit HHH.

Final answer:

To find the product of (5.2 · [tex]10^-^6[/tex]) and (8 · 10³), multiply the base numbers and add the exponents. The result is 41.6 × [tex]10^-^3[/tex], which simplifies to 4.16 × 10^-2.

Explanation:

The student asked to find the product of two numbers expressed in scientific notation: (5.2 · [tex]10^-^6[/tex]) and (8 · 10³). When multiplying numbers in scientific notation, you multiply the base numbers and add the exponents.

Step-by-Step Solution:

Simplified Result:

This can further be simplified by writing 41.6 × [tex]10^-^3[/tex]as 4.16 × [tex]10^-^2[/tex], by moving one decimal place to the left in the base number and increasing the exponent by 1 to balance it.

By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)

Function is relation between a set to another set with a property that every element of first set has a unique image in second set.

Here graph of f(x) is given and we have to find the point of intersection of function and it's inverse function

We know that a function and it's inverse function are mirror image of each other with respect to line y=x hence they intersect only at y=x line

By drawing y=x line with the given graph we got that f(x) intersect y=x line at (3,3) hence inverse function will intersect at (3,3)

By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)

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When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect. Therefore, the point of intersection is (x, y).

When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect.

Let's say the point of intersection is (x, y).

This means that both f(x) and f-1(x) have the same x-coordinate, which is x, and the same y-coordinate, which is y.

Therefore, the point of intersection is (x, y).

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The estimated answer would be =14000

We want to make a 4 players team, and there are total 8 players. As we know the order of selection does not matter in a team of players, only the combination of players matters.

So we would use concept of Combinations and It will be choose 4 out of 8 players.

The formula for Combination is given as follows :-

[tex]nCr = \frac{n!}{r!*(n-r)!} \\\\ Choose \;4 \;out \;of \;8 \;players \\\\ 8C4 = \frac{8!}{4!*(8-4)!} = \frac{8!}{4!*4!} \\\\ 8C4 = \frac{8*7*6*5*4*3*2*1}{(4*3*2*1)*(4*3*2*1)} = \frac{8*7*6*5}{4*3*2*1} =\frac{1,680}{24} = 70 \;combinations[/tex]

Hence, Total number of different teams = 70 combinations.

[tex] \displaystyle
|\Omega|=\binom{30}{2}=\dfrac{30!}{2!28!}=\dfrac{29\cdot30}{2}=435\\
|A|=\binom{12}{2}=\dfrac{12!}{2!10!}=\dfrac{11\cdot12}{2}=66\\\\
P(A)=\dfrac{66}{435}=\dfrac{22}{145}\approx15\% [/tex]

Answer:

The new length of the enlarged figure will 18 cm.

Step-by-step explanation:

A scale factor is a number which scales, or multiplies the original figure by some quantity.

In the equation [tex]y = Cx[/tex], C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.

As the given length is 3 cm, so with a scale factor of 6, the length of the enlarged figure will be [tex]3\times 6=18[/tex] cm

Therefore, the new length of the enlarged figure will 18 cm.