Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample. n = 86, p = 0.68: p(54 x 61) 9)

The simplified expression is -3M + 1

To simplify the expression M - (1/6) - 4M + (5/6), we can combine the like terms.

First, let's combine the terms with M:

M - 4M = -3M

Now, let's combine the constant terms:

(1/6) + (5/6) = (1 + 5)/6 = 6/6 = 1

Putting it all together, the simplified expression is:

-3M + 1

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1st piece = x

 2nd piece = 3x-16

x +3x-16 = 136

4x-16 = 136

4x = 152

x = 152/4 = 38

 1st piece = 38 feet

 2nd piece = 136 -38 = 98 feet

Answer:

Option (3) is correct.

The value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]  is 14.

Thus, option (3) is correct.

Step-by-step explanation:

Consider the given expression in the image given,

[tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]

First solve for square term in the denominator,

[tex]3^2=3 \times 3 = 9[/tex]

Expression becomes,

[tex]\frac{-3(7+5)}{9}+9(2)[/tex]

Now solve for numerator,

7 +5 = 12 and -3(12) = -36

Expression becomes,

[tex]\Rightarrow \frac{-36}{9}+9(2)[/tex]

[tex]\Rightarrow -4+9(2)[/tex]

[tex]\Rightarrow -4+18[/tex]

[tex]\Rightarrow 14[/tex]

Thus the value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]  is 14.

Thus, option (3) is correct.

The value of (2a - 2b)/(5a + 5b) can be simplified to c.

To find the value of (2a - 2b)/(5a + 5b) when the equation (a + b)/(a - b) = c is given, we can substitute the value of (a + b)/(a - b) with c. Rearranging the equation, we get:

(2a - 2b)/(5a + 5b) = c

Simplifying the expression, we have:

(2(a - b))/(5(a + b)) = c

So, the value of (2a - 2b)/(5a + 5b) is c.

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Answer:

Perimeter: 2(3x+6)+ 2(2x-4)

X=9

Step-by-step explanation:

In order to create the expression you just have to remember that the perimeter of a rectangle equals 2 bases plus 2 sides, so the expression would be:

Perimeter: 2(heights)+ 2(bases)

Perimeter: 2(3x+6)+ 2(2x-4)

IN order to solve for X we just have to insert the value of perimeter, which is 94:

Perimeter: 2(3x+6)+ 2(2x-4)

94=2(3x+6)+ 2(2x-4)

94= 6x+12+4x-8

94=10x+4

94-4=10x

x=90/10

x=9

So the value of x would be 9.

The norms and the inner product of f and g can be calculated using the given inner product definition and the knowledge that the norm of a vector (here, function) is the square root of its inner product with itself. Then, the cosine of the angle between f and g can be found by dividing their inner product by the product of their norms.

The problem is asking us to compute certain components in the context of a vector space of continuous functions, namely inner product ⟨f,g⟩, norms ‖f‖, ‖g‖, and angle between them for f(x) and g(x). Since the functions are given as f(x)=10x^2-3 and g(x)=6x-9, these can be used in the provided inner product definition ⟨f,g⟩=∫from 0 to 1f(x)g(x)dx.

The norm of a vector, in this case, the function f or g, is the square root of the inner product of the function with itself. The cosine of the angle α between the functions f and g is given by the ratio of the inner product of f and g to the product of their norms.

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The expression 'The quotient of a number and ten increased by eleven' is written as (x/10) + 11 in mathematical terms. Understanding the role of exponents, such as in the expression 10² equals 100, helps in grasping concepts like scientific notation, where large or small numbers are expressed as the product of a number and a power of ten, such as 1.372568 × 10⁶.

The question 'The quotient of a number and ten increased by eleven' translates to a mathematical expression. This expression can be represented as (x/10) + 11, where 'x' is the number in question. It's a simple algebraic expression where you first divide the number by ten and then add eleven to the result.

When discussing multiplication and division by powers of 10, it's important to understand the concept of an exponent. The exponent is a raised number to the right of the 10, indicating the number of factors of 10 in the original number. For example, in the expression 10², the exponent 2 indicates that ten is multiplied by itself once, resulting in 100. This is consistent with the way our numbering system works, with each place value being ten times greater than the one to its right.

The utility of using exponents is highlighted in scientific notation, which simplifies large or small numbers by representing them as a product of a number and a power of ten. This is particularly useful in fields like science and engineering, where very large or very small numbers are common. For example, the number 1,372,568 can be written in scientific notation as 1.372568 × 10⁶, representing the number as a manageable base multiplied by ten raised to the sixth power.

Answer:

D. As a semicircle, a trapezoid and two rectangles.  

Step-by-step explanation:  

Please find the attachment.

We have been given a composite figure. We are asked to decompose our given figure to determine its area.

Upon looking at attachment for our given composite figure, we can see that it consists one semicircle on top, one trapezoid in middle and two rectangles on bottom. So we can decompose our composite figure as a semicircle, a trapezoid and two rectangles.

Therefore, option D is the correct choice.