Given the two rectangles below. Find the area of the shaded region. 4 4 9 3​

Using the Law of Cosines,

[tex]c^{2}=2^{2}+4^{2}-2(2)(4)(\sin 30^{\circ})\\\\c^{2}=12\\\\c=2\sqrt{3}[/tex]

Using the Law of Sines,

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}\\\\\frac{\sin A}{2}=\frac{\sin 30^{\circ}}{2\sqrt{3}}\\\\\frac{\sin A}{2}=\frac{1}{4\sqrt{3}}\\\\\sin A=\frac{1}{2\sqrt{3}}\\\\A=\boxed{\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]

So, as angles in a triangle add to 180 degrees,

[tex]B=180^{\circ}-30^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)\\\\B=\boxed{150^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]

A triangle is a 2-D shape that has 3 sides and angles. The area of the triangle below is 27 square units

A triangle is a 2-D shape that has 3 sides and angles

In order to determine the area of the shape, we will determine the area of the square circumscribing it first;

Area of the square = 10 * 9 =90 square units

Find the area of the two right triangles

Area of the right triangles = 0.5(10 * 9) + 0.5(9 * 4)

Area of the right triangles = 45 + 18

Area of the right triangles = 63 square units

Take the difference

Area of the given triangle  = 90 - 63 = 27 square units

Hence the area of the triangle below is 27 square units

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The function of the curve is an exponential function. So, the function would be y = e^x.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

Their usual form is specified below. They are written in several such equivalent forms.

For example, [tex]y^x[/tex]

where a is a constant is an exponential function.

We can see that the curve of the function is decreasing constantly.

Thus, the function of the curve is an exponential function. So, the function would be y = e^x.

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The value of the complete equation is 5.1.

We have given the equation,

15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore we have,

[tex]15.3/3=15+0.3 \ tenths/3\\=5+0.1 \ tenths\\=5.1[/tex]

Therefore the value of the complete equation is 5.1.

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Answer:

3.9m x 4.8m

Step-by-step explanation:

1 cm = 1.5m

→ Multiply both sides by 2.6

2.6 cm = 3.9m

→ Multiply from the original statement, both sides by 3.2

3.2 cm = 4.8 m

→ Combine them

3.9m x 4.8m

Answer:

Irrational

Step-by-step explanation:

[tex]\sqrt{9}= 3[/tex]

3 × √3 = 3√3 which is irrational

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Product is multiplication:

√3 x √9 = 3√3 = 5.19615....

Because the fraction does not end, it is not rational.

Answer: Irrational

Answer:

  B.  A pair of intersecting lines

Step-by-step explanation:

The attached image can give you an idea of what you get when a plane perpendicular to the base of a cone intersects the vertex of the cone.

__

In the problem statement here, we assume a double-napped cone with no defined base. That means the lines of intersection with the sides of the cone will meet at the vertex point and extend indefinitely in either direction.

The intersection is a pair of intersecting lines.

Answer:

Step-by-step explanation:

400: 100 you find 1% you multiply it by 20 and you have 20%

400 : 100 * 20 =

4 * 20 =                                    

Answer:

15) 3.2

17) 13.4

Step-by-step explanation:

To find the missing lengths, you need to use the Pythagorean theorem:

a² + b² = c²

In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.

You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".

15)    a = 4.1     c = 5.2

a² + b² = c²                                    <----- Pythagreom Theorem

(4.1)² + b² = (5.2)²                          <----- Plug values in for "a" and "c"

16.81 + b² = 27.04                         <----- Raise numbers to the power of 2

b² = 10.23                                      <----- Subtract 16.81 from both sides

b = 3.2                                           <----- Take the square root of both sides

You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".

17)   a = 4.4      b = 12.7

a² + b² = c²                                      <----- Pythagreom Theorem

(4.4)² + (12.7)² = c²                           <----- Plug values in for "a" and "b"

19.36 + 161.29 = c²                          <----- Raise numbers to the power of 2

180.65 = c²                                      <----- Add

13.4 = c                                            <----- Take the square root of both sides

[tex] {5}^{3} \: \times \: {5}^{ - 5} [/tex]

[tex] {5}^{ - 2} [/tex]

[tex] \boxed{ {a}^{ - n} \: = \: \frac{1}{ {a}^{n} } }[/tex]

[tex] {5}^{ - 2} \: = \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]

[tex]\text{Option C.} \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]

Answer:

(-2, -2)

Step-by-step explanation:

the solution of the system of equation put simply is the point of intersection between the 2 lines

hence, the answer is (-2,-2)

Answer:

The LCM of 16x^2 and 40x^2 is 80x^5

:) Good Luck

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

each times she draws there is 3 blue marbles that she can pick so her chance of picking one blue marble out of the box is 3/8 hope i helped!

Answer: 3/8

Step-by-step explanation:

Step-by-step explanation:

So the question is easy ....The thing that you need to do here is ...You should divide area by length....and you will get your answer....

Area of rectangular parking lot = 7081 m²

length of parking lot = 97 m

Width = ?

Now,

Area = l × b

7081 = 97 × b

7081 / 97 = b

b = 73 m

Hence the width is 73 m....

Answer:

Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of qp where p and q are integers and q =0.

Answer:

See below

Step-by-step explanation:

Sine function would be easiest

  in a right triangle   sin = opposite leg / hypotenuse

sin 57 =   10.8 / x    

then   x = 10.8 / sin 57               then x = 12.88 units

Answer:

2.33

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Given expression: 4x - 7

To determine a numerical value of the provided expression, when x = 4, simply substitute the value of x into the expression and simplify it using the order of operations (PEMDAS). Work has been shown below.

The PEMDAS stands for:

According to the PEMDAS, it is required to simplify the expression using multiplication (M in PEMDAS) firsthand, as there are no parentheses (P in PEMDAS) and exponents (E in PEMDAS). Thus, we get the following:

Please refer to underlined text for simplification of that expression.

Clearly, we can see that division (D in PEMDAS) and addition (A in PEMDAS) is not occurring in the expression. Therefore, we will need to subtract the two terms (16 and 7). Thus, we get the following simplified term:

Therefore, the value of 4x - 7, when x = 4, is 9.

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Answer:

one

Step-by-step explanation:

When a system of equations is graphed, the solution is the coordinate that is plotted at the intersection of the two lines.

If the two lines cross once, there is only one solution.

If the two lines are on top of each other then there are infinitely many solutions.

If the two lines are parallel ( and never touch ) then there are no solutions

By looking at the graph we notice the two lines intersect once. So we can conclude that there is only one solution.

Answer:

√ (p(1-p) / n)

Step-by-step explanation:

Standard Error(SE) of the Sample Proportion: √ (p(1-p) / n). Note: as the sample size increases, the standard error decreases.

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The length of the band in terms of π is given by the expression:

L = 40mm + π*10mm

Remember that for a circle of diameter D, the circumference is:

C = π*D.

Now, if you look at the image, you can see that the length of the band will be equal to 4 times the diameter of the pencils (one time for each side). Plus 4 times one-fourth of the circumference of each pencil (for the four corners).

because the diameter is 10mm, the length of the band will be:

L = 4*10mm + 4*(π*10mm/4)

L = 40mm + π*10mm

This is the length of the band in terms of π.

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Answer:

3.287 Customers

Step-by-step explanation:

Interarrival time (a) = 60 seconds per minute / 190 customers per minute = 0.316 seconds.

Utilization = p / (a × m) = 2 / (0.316 × 8) = 0.792.

Number in queue = Tq / a = 1.038 / 0.316 = 3.287 customers.

The 2nd dot plot in the attachment represents the dot plot that has the same sample mean as the population mean

The dot plot that completes the question is added as an attachment.

Start by calculating the mean of the data plot using:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

Substitute the values on the dot plot

[tex]\bar x = \frac{2*1+3*3+4*2+5+6*3+7*5+8*2+9*4+11*2+12*2}{25}[/tex]

[tex]\bar x = 7[/tex]

This means that the population mean of the dot plot is 7

Next, we create another dot plot that has the same mean as 7.

There are no direct rules to this, so we make use of the trial by error method.

After several attempts, we have the following frequency table:

Data point      Frequency

2                                  1

3                                  2

4                                  0

5                                  4

6                                  5

7                                  2

8                                  5

9                                  0

10                                 2

12                                 3

The mean of the frequency table is:

[tex]\bar x = \frac{2 * 1 + 3 * 2 + 4 * 0 + 5 * 4 + 6 * 5 + 7 * 2 + 8 * 5 + 9 * 0 + 10 * 2 + 12 * 3}{1+2+0+4+5+2+5+0+2+3}[/tex]

Evaluate

[tex]\bar x = \frac{168}{24}[/tex]

Evaluate the quotient

[tex]\bar x = 7[/tex]

This means that the sample mean is 7 (same as the population mean)

Lastly, we represent the frequency table using a dot plot (the 2nd dot plot in the attachment)

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Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we have that the parameters are given as follows:

[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].

The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{35 - 34}{0.4}[/tex]

Z = 2.5

Z = 2.5 has a p-value of 0.9938.

0.9938 = 99.38% probability that the average of these members is less than 35.

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Answer:

16 Tablespoons

Step-by-step explanation:

Using the given information in the diagram, we have proven that sin(B)/b = sin(C)/c

From the question, we are to prove that sin(B)/b=sin(C)/c

Consider the right triangle with sides a, c, and h

Using SOH CAH TOA, we can write that

sin(B) = h/c

∴ h = c × sin(B) --------- (1)

Also,

Consider the other right triangle

Using SOH CAH TOA, we can write that

sin(C) = h/b

∴ h = b × sin(C) ---------- (2)

Equate equations (1) and (2)

That is,

c × sin(B) = b × sin(C)

This can then be expressed as

sin(B)/b = sin(C)/c

Hence, the given expression is proven as shown above

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Answer:

Polynomial

Step-by-step explanation:

⇒ It cannot be option 1 as y does not vary with an exponent

⇒ It cannot be option 2 as y does not relate to any logarithmic values of x

⇒ It cannot be a option 4 as there no irrational numbers under a root

⇒ Therefore it is a polynomial, as it is written in the form : y = ax³ + bx² + cx + d (cubic polynomial)

Answer:

the value of b to 2

The value of b changes to 2.

The correct option is C.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

We have,

Equation: h(x) = -x + 5

Now, using the slope intercept form

y = mx + b

From which we get

m = -1 and b=5

Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get

y = -x+5 -3

y = -x +2.

Here y-intercept is 2.

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