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A) Find the probability that a point chosen randomly inside the rectangle will be in the triangle. Show all calculations. Round answer to the nearest hundred

B) Find the probability that a point chosen randomly inside the rectangle will be in the shaded region. Show all calculations. Round answer to the nearest hundredth. Answer:​

Answer:

30° ; 35°

Step-by-step explanation:

Recall:

Sum of angles in a triangle = 180°

One of the 3 angles = 115

The sum of the other 2 Angles will be :

(180 - 115) = 65°

The other two angles are in the ratio 6:7

Hence,

Each of the two angles can be calculated thus :

Angle 2 :

Sum of ratio = 6 + 7 = 13

(6 / 13) * 65 = 30°

Second angle :

(7 / 13) * 65 = 35°

Answer:

4.5π[tex]cm^2[/tex] will be your answer!

Step-by-step explanation:

Oki... So the area of a circle is radius x radius x π

So.....

Lemme find what the radius's are

4.5 ÷ 2 = 2.25

2.25 - 1.5 = 0.75

2.25 x 2.25 x π = 5.0625π

0.75 x 0.75 x π = 0.5625π

And subtract.

5.0625π - 0.5625π = 4.5π

Answer:

see below

Step-by-step explanation:

9 is the difference of a number n and 7.

Let's break this down.

"is" represents the equal sign.

"the difference" represents subtraction.

9 = n - 7

Now let's solve the equation.

9 = n - 7

Add 7 to both sides.

16 = n

Hope this helps!

Answer:

A

Step-by-step explanation:

The extreme value theorem can be applied on an interval if the function is continuous in the entire interval. Testing the continuity for each function, we get that the correct option is the third option.

Continuity:

A function f is continuous at an interval if all points in the interval are in the domain of the function, and, for each point of [tex]x^{\ast}[/tex], the limit exists and:

[tex]\lim_{x \rightarrow x^{\ast}} = f(x^{\ast})[/tex]

First function:

At [tex]x = 4[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.

Second function:

At [tex]x = 5[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.

Third function:

The only point there can be a discontinuity is at [tex]x = 4[/tex], where the definition of the function changes. First we have to find the lateral limits, and if they are equal, the limits exist:

To the left(-), it is less than 4, so we take the definition for x < 4.

To the right(+), it is more than 4, so we take the definition for x >= 4.

[tex]\lim_{x \rightarrow 4^{-}} h(x) = \lim_{x \rightarrow 4} \frac{9x}{10-x} = \frac{9*4}{10-4} = \frac{36}{6} = 6[/tex]

[tex]\lim_{x \rightarrow 4^{+}} h(x) = \lim_{x \rightarrow 4} x + 2 = 4 + 2 = 6[/tex]

The lateral limits are equal, so the limit exists, and it's value is 6.

The definition at [tex]x = 4[/tex] is [tex]h(x) = x + 2[/tex], so [tex]h(4) = 4 + 2 = 6[/tex].

Since [tex]\lim_{x \rightarrow 4} = h(4)[/tex], the function is continuous over the entire interval, and this is the correct answer.

Fourth function:

There can be a discontinuity at [tex]x = 5[/tex], so we test the limits:

[tex]\lim_{x \rightarrow 5^{-}} h(x) = \lim_{x \rightarrow 5} -x = -5[/tex]

[tex]\lim_{x \rightarrow 5^{+}} h(x) = \lim_{x \rightarrow 5} x^2 - 20 = 5^2 - 20 = 25 - 20 = 5[/tex]

Different limits, so the limit does not exist and the function is not continuous at [tex]x = 5[/tex], and the extreme value theorem cannot be applied.

For more on the extreme value theorem, you can check https://brainly.com/question/15585098

Answer:

0

Step-by-step explanation:

+ 1 + (-1)

1 + (-1)

1 - 1

Answer:

There are 5 choices for the first digit, 5 choices for the second digit, 4 choices for the third digit, 3 choices for the fourth digit, and 2 choices for the fifth digit.

The 30-60-90 triangle is shaped like half of an equilateral triangle.

A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.

The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.

30°-60°-90° Triangle Rule:

In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.

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In linear equation ,The length of waterslide is 12 yards.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Given that,

The length of an object object in feet is equal to 3 times it’s length in yards

The length of wall water side slide is 36 feet

Let "y" be the length of object in yards

From given,

Length in feet = 3 times length in yards

    36 =  3 * y

     3y = 36

    y = 36/3

     y = 12

Thus length of waterslide is 12 yards.

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The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

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The complete question is this:

What are the factors of 2x^2+7x +3?

Answer:

A . 17/21

B . 14/21

C . 7/14

D. 11/17

Step-by-step explanation:

Answer:

Answer is B: 14 to 21

Step-by-step explanation:

The ratio "2 to 3" was multiplied by 7 to get this ratio. All the other following are incorrect.

Answer:

54

Step-by-step explanation:

63 x 2 = 126

180 - 126 = 54

On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, the equation is -

1200=300+5x

900 = 5x

x=180

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Answer:

36 sq ft

Step-by-step explanation:

The area of a square is equal to the length of one side squared. Therefore, if all sides of a square are 6 feet long, the area of the square is 6 feet * 6 feet = 36 square feet.

Answer:

36

Step-by-step explanation:

you multiply just two of the sides hxw and you get your answer

The wheel will travel 131.8cm in 3 rotations.

The radius of the wheel, r = 7cm

Number of rotations, n= 3

distance covered in 1 rotation= circumference of circle=2πr

distance covered in 3 rotation= 2πr x 3

where π=3.14(fixed)

=2 x 3.14 x 7 x 3

Distance=131.88cm

Therefore, the distance covered in 3 rotations is 131.88cm

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Answer:

132cm

Step-by-step explanation:

use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three

Answer:

we get a required sample size of 122.

Step-by-step explanation:

We can use the following formula to calculate the required sample size:

n = (Z * sigma / e)^2

where:

n is the required sample size

Z is the z-score corresponding to the desired confidence level (e.g. for a 95% confidence level, Z = 1.96)

sigma is the standard deviation of the population

e is the maximum error allowed

Plugging in the given values, we get:

n = (1.96 * 0.6 / 0.08)^2 = 121.6

Rounding up to the next integer, we get a required sample size of 122.

Answer: 14

Step-by-step explanation: 18 x 14 = 252

Answer:

14

Step-by-step explanation:

recall that area of figure, A= length x. breadth

and A=252

and b=18

therefore, 252= 18b

l= 252/18

l= 14

therefore p= 14

Answer:

Step-by-step explanation:

Answer:

What shape? i don't see no shape

Answer:

What shape? Can you add in a picture or something? That would be very helpful in trying to figure out what shape we're dealing with.

Answer:

A. 58 square cm

Step-by-step explanation:

From the composite figure,

A1 = [tex]\frac{1}{2}[/tex] x base x height

   = [tex]\frac{1}{2}[/tex] x 2 x 3

   = 3 [tex]cm^{2}[/tex]

A2 = length x width

     = 8 x 2

     = 16 [tex]cm^{2}[/tex]

A3 = [tex]\frac{1}{2}[/tex] (a + b) h + [tex]\frac{1}{2}[/tex] x base x height

    = [tex]\frac{1}{2}[/tex] (10 + 12) 3 + [tex]\frac{1}{2}[/tex] x 2 x 3

    = [tex]\frac{1}{2}[/tex] (22) 3 + 3

    = 11 x 3 + 3

A3 = 33 + 3

     = 36 [tex]cm^{2}[/tex]

Total area = A1 + A2 + A3

                 = 3 + 16 + 36

                 = 58 [tex]cm^{2}[/tex]

Thanks dude!

Step-by-step explanation:

Can i have brainly?

The 3 horizontal line refers the equivalent relation.

The term horizontal line in math defined as a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

Here have to find the meaning of 3 horizontal line.

As per the definition of horizontal line, the three horizontal line also known as triple line defines the equivalent relation of the term.

Here the equivalent that is not the same as 'equals'

Where the double bar is more common and generally implies equality on the other hand the triple bar or equal sign with three lines means congruent or, more generally, an arbitrary equivalence relation.

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Answer:

A

Step-by-step explanation:

2 boxes has 50 glasses

times by 2 and its equal to A

Answer:  A or B

Step-by-step explanation:

A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.

Part B:

The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.

Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

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Answer:

P = -6

Step-by-step explanation:

y2-y1 / x2-x1 = slope formula

p-2/10-6 =

p-2 over 4

P would be -6 since -6-2 = -8, and -8/4 = -2