How are exponents used for measuring an earthquake? Can you explain?

The measure of each angle of triangle is,

m ∠C  = 46°

m ∠D  = 104°

m ∠DEF = 30°  

What is exterior angle theorem?

In Euclid's Elements, Proposition 1.16, known as the exterior angle theorem, states that the measure of a triangle's exterior angle is greater than either of its remote interior angles. Due to the fact that its proof is independent of the parallel postulate, this is a fundamental result in absolute geometry.

Let the triangle CDE is given.

m ∠D = (10y + 4)°,  m ∠C = (4y + 6)°,  m ∠DEF = 108°

We have to find the measure of each angle of triangle.

By using the Exterior angle theorem,

        m ∠C + m ∠D = m ∠DEF

(4y + 6)° + (10y + 4)° = 108°

                 14y + 10° = 108°

                         14y = 98°

                            y = 7°

⇒ m ∠C = 4y + 6 = 4(10) + 6 = 40 + 6 = 46°

 m ∠D = 10y + 4 = 10(10) + 4 = 100 + 4 = 104°

Since, the measure of three angle of triangle is 180°.

⇒ m ∠C + m ∠D + m ∠DEF = 180°

         46° + 104° + m ∠DEF = 180°

                  150° + m ∠DEF = 180°

                             m ∠DEF = 30°

Hence, the measure of each angle of triangle is,

m ∠C  = 46°

m ∠D  = 104°

m ∠DEF = 30°  

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The correct answer is option B: 60 ft.

To find the length of the model, you can use the formula:

Length of model = (Length of original object) x (Scale factor)

The scale factor in this case is 99 feet / 6 inches = 16.5 feet/inch

So the length of the model = (6 inches) x (16.5 feet/inch) = 60 ft

Answer:

When the bases and exponents are both different, each needs to be evaluated separately:

   5^2 + 3^3 = 25 + 27 = 52

Step-by-step explanation:

1.  When the bases are the same, it is easy.  Just add the exponents:

   (5^2) * (5^4) = 5^6

2.  When the bases are different, but the exponents are the same, multiply the bases first and then use the same exponent:

    (5^3) * (4^3) = (20)^3

3.  When the bases and exponents are both different, each needs to be evaluated separately:

   5^2 + 3^3 = 25 + 27 = 52

A correlation value of -0.8 or lower denotes a significant negative link, whereas one of -0.3 or lower denotes a negligibly weak relationship.

How to interpret a correlation coefficient?

The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls in step with positively associated variables.

Why is correlation coefficient significant? What does it mean?

As a whole, correlation coefficients are used to evaluate the direction and strength of the linear correlations between two sets of variables. When both variables have a normal distribution, use Pearson's correlation coefficient; otherwise, use Spearman's correlation coefficient.

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The score on his next test must be at least 97 to get an average score of at least 85.

Average value of a set of numbers is a single number which represents the whole numbers in the set.

Average value of a set of numbers is calculated by dividing the sum of all the numbers by the number of values in the set.

Here is is given that,

Jerrod had scores of 75, 82, 94 and 77 on his first four history tests.

We need to find the score of his next test such that the average of all is at least 85.

Let x be the score of his next test.

(75 + 82 + 94 + 77 + x) / 5 ≥ 85

75 + 82 + 94 + 77 + x ≥ 85 × 5

328 + x ≥ 425

x ≥ 97

Hence Jerrod must have at least a score of 97.

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When the balloon is released from a height of 6 feet, the equation x = 3y + 6 reflects the balloon's height (y).

Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations.  Algebra is used in many equations. When it comes to arithmetic, algebra is used when it's difficult to compute an exact amount.

given

When a balloon is released, it rises at a constant rate of 3 feet per second from a height of 6 feet.

When the balloon is released from a height of 6 feet, the equation x = 3y + 6 reflects the balloon's height (y).

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On solving the provided question, we can say that the inequality equation here will be The student is no more than 65 inches tall. P(x<  65) = 23.432

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

Mr. Jackson randomly selects a student in Math Club. Use the normal curve from Part A and the empirical rule to find each probability.

the inequality equation here will be

The student is no more than 65 inches tall. P(x<  65) = 23.432

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Answer:

4

Step-by-step explanation:

speed = distance/time

time = distance/speed

time = 4/5 mile / 12 mph

time = 0.0666... hours × (60 minutes)/(1 hour)

time = 4 minutes

Therefore , the solution of the given problem of arithmetic mean comes out to be a5 = 3334.

The group's arithmetic average, often known as the mean, is calculated by multiplying the sum of all the entries in a list by the number of products in that list, then dividing that sum by both. This follows the same mathematical development. The number 3 is the median of the numbers 9, 11, and 7. For instance, the number 7 is obtained by dividing 21 (there are actually three numbers) by the equation 5 + 7 + 9.

Here,

It speaks about sequences where every other term is provided as a rule but needs on a number of the preceding terms, as opposed to implicit series where an expression.

The order is as follows: 

The order is as follows:

=> a1 = 6

=> an= -5a(n-1) + 4

To calculate the value of a5, follow these steps:

=>  a2= -5(6) + 4 = -26

=> a3= -5(26) + 4 = 134

=> a4= -5(134) + 4 = -666

=> a5= -5(-666) + 4 = 3334.

Therefore , the solution of the given problem of arithmetic mean comes out to be a5 = 3334.

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Answer: 24y+46

Step-by-step explanation:

6(4y+8)-2

=24y+48-2

=24y+46

= 2(12y+23)

Answer: 24y+46

Step-by-step explanation:

multiply 6 by 4y = 24y

multiply 6 by 8 = 48

you have left 24y + 48 - 2
subtract 2 from 48 and get 46

The truth values of the statements are:

The complete question is added as an attachment, where we have the following parameters:

Height, h = 2.5 feet

Diameter, d = 4

The base area is then calculated as

Area = п(r²)

So, we have

Area = п(2²)

The volume is then calculated as

Volume = Base area * Height

So, we have

Volume = п(2²) * 2.5

Evaluate

Volume = 31.4

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Yes, 84 is divisible by 3. This can be demonstrated using the modulus operator.

The modulus operator returns the remainder of a division problem. In this case, we can divide 84 by 3 and see what the remainder is.

Calculation

84 ÷ 3 = 28

Remainder

84 % 3 = 0

Since the remainder is 0, this means that 84 is evenly divisible by 3. This can be shown mathematically as 84 = 3 × 28. In other words, 84 is a multiple of 3, meaning it is divisible by 3.

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Answer:

x = -3, y = -5

Step-by-step explanation:

-6x - y = 23 ----------------(1)

y = 4x + 7 -------------------(2)

Put Eq. (2) in (1)

-6x - (4x + 7) = 23

-6x - 4x - 7 = 23

-10x - 7 = 23

-10x = 23 + 7

-10x = 30

Put x = -3 in Eq. (2)

y = 4(-3) + 7

y = -12 + 7

[tex]\rule[225]{225}{2}[/tex]

The equation that best represents the relationship is y = ½x + 2

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

From the values of x and y, let's check if the graph of y against x is linear

taking points x( 2,4) y(3,4)

slope =( 4-3)/4-2

slope = 1/2

therefore the graph is linear and slope is 1/2

the equation of a straight line = y − y 1 = m ( x − x 1 )

= y-3 = m( x- 2)

= y = 1/2(x-2)+3

y = ½x -1+3

y = ½x +2

therefore the equation that best represents the relationship is y = ½x + 2

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f^-1(x) is the inverse of f(x) as the composite functions f(f^-1(x)) and f^-1(f(x)) are both equal to x.

A function is composite when the co- domain of the first mapping is the domain of the second mapping.

We shall evaluate the functions f(f^-1(x)) and f^-1(f(x)) as follows:

f(f^-1(x)) = [(3x+5 / x+1) - 5] ÷ [3 - (3x+5 / x+1)]

changing division to multiplication;

f(f^-1(x)) = [3x + 5 - 5(x + 1)]/(x + 1) × (x + 1)/[3(x + 1) - (3x + 5)]

(x + 1) is common and will cancel out

f(f^-1(x)) = (3x + 5 - 5x - 5)/(3x + 3 - 3x - 5)

f(f^-1(x)) = -2x/-2

f(f^-1(x)) = x

f^-1(f(x)) = [3(x-5 / 3 -x) + 5] ÷ [(x-5 / 3 -x) + 1]

changing division to multiplication;

f^-1(f(x)) = [3(x - 5) + 5(3 - x)]/(3 - x) × (3 - x)/[x - 5 + (3 - x)]

(3 - x) is common and will cancel out

f^-1(f(x)) = (3x - 15 + 15 - 5x)/(x - 5 + 3 - x)

f^-1(f(x)) = -2x/-2

f^-1(f(x)) = x

Therefore, since composite functions; f(f^-1(x)) = x and f^-1(f(x)) = x, then f^-1(x) is the inverse of f(x).

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The slope that is parallel to 3x + y = 9 is -3.

Perpendicular slope is 1/3.

The slope of two lines is considered parallel if the slopes are equal, and the slope of two lines is considered perpendicular if the product of the slopes is -1 or would be negative reciprocals of each other.

Given the equation of a line as 3x + y = 9, rewrite in slope-intercept form to find the slope.

3x + y = 9

y = -3x + 9

The slope is -3. The negative reciprocal of -3 is 1/3, because it has a product of -1.

Therefore, parallel slope to the line is: -3, while perpendicular slope is 1/3.

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The interest earned at 1.6% for 20 years will be $960.

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used.

Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Given that a new bank customer with ​$3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.6​%.

The interest after 20 years will be calculated as,

SI = ( P x R X T ) / 100

SI = ( 3000 x 1.6 x 20 ) / 100

SI = $960

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In general, if the rectangles are all the same width and if they are placed to the right of the curve, the Riemann sum will be an overestimate of the true area. On the other hand, if the rectangles are placed to the left of the curve, the Riemann sum will be an underestimate of the true.

Another method to determine if a Riemann sum is an overestimate or underestimate, we can compare it to the exact value of the definite integral. If the Riemann sum is larger than the definite integral, it is an overestimate. If the Riemann sum is smaller than the definite integral, it is an underestimate. Additionally, we can also check the sign of the function being integrated and the width of the rectangles. If the function is positive and the width of the rectangles is decreasing, then the Riemann sum will be "an overestimate". If the function is negative and the width of the rectangles is decreasing, then the Riemann sum will be "an underestimate".

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Step-by-step explanation:

-5° < 8°

that is all that is to it. really. you see ? an inequality, meaning that 2 terms or expressions are compared (like on a balance).

they can be totally balanced, that means they are equal, and then we have an equation.

or one can be bigger ("heavier"), and so one side is smaller and the other larger. and that is then not equal. we have an inequality.

[tex](2x^5)^3\implies \left(2^3x^{5\cdot 3} \right)\implies 8x^{15}[/tex]

Answer

192

Step-by-step explanation:

Given :Wendy is arranging books on the bookshelves in the school library. The total number of books she arranges is given by the equation b = 12r, where b is the total number of books and r is the number of rows. Each row contains the same number of books.

To Find: If Wendy arranged 16 rows, she arranged a total of ___ books.

Solution:

Since we are given an expression:

b = 12r

where b = total no. of books she arranged

r denotes the number of rows

Since we are asked  If Wendy arranged 16 rows, she arranged how many books

So, put r = 16 in equation

Thus b = 12*16

b = 192

Thus she arranged 192 books in 16 rows

Answer:

c = 50

Step-by-step explanation:

The given angles are alternate angles and their measures are equal.

We can write the following equation based on this information:

2c - 3 = 97

2c = 100

c = 50

A triangular frame has two edges lengths measuring 18 inches and 12 inches. The possible value of length for the third side is 32 in.

A triangular frame has two side lengths measuring 18 inches and 12 inches. as we know that the sum of any two sides of a triangle is always greater than the third side.

That is, the third side < 18 +12

third side < 30

according to the question, the option that fits perfectly is 32in.

Hence, The possible value of edges for the third side is 32 in.

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Jayla's estimate for food is not a good estimate, given the number of days in a month and the amount she plans on spending.

Jayla has a food budget and does not want to spend more than $2 for breakfast, $8 for lunch, and $8 for dinner. The most spending per day therefore, is:

= 2 + 8 + 8

= $ 18

Given that there are 30 days in a month, the most spending estimate for the month is :

= Cost per day x Number of days

= 18 x 30

= $ 540

Jayla's estimate of $ 60 a month is therefore not good.

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Answer:

y = [tex]\frac{3}{7}[/tex] x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (7, 6) ← 2 points on the line

m = [tex]\frac{6-3}{7-0}[/tex] = [tex]\frac{3}{7}[/tex]

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = [tex]\frac{3}{7}[/tex] x + 3 ← equation of line

In order to determine the volume of the cuboid, we would need to know its length, width, and height in centimeters.

The volume of a cube is given by the formula:

V = s^3

Where V is the volume and s is the length of one side of the cube.

Since this cuboid is made up of centimeter cubes, it means that the length, width, and height are in centimeters.

It is not mentioned the dimension of the cuboid, so it is not possible to determine the volume of the cuboid.

In order to determine the volume of the cuboid, we would need to know its length, width, and height in centimeters.

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A real function, usually referred to as a real-valued function, is one whose domain is the real numbers.  A function from complex numbers to complex numbers is referred to as a complex function.

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8x

Step-by-step explanation:

2x x 2x x 2x

The value of the missing angle x in the triangle is; x = 29 degrees

In a triangle, we know that the exterior angle is always equal to the sum of the interior opposite angles. This property is referred to as exterior angle property. This means that any two triangles will be similar if their corresponding angles tend to be congruent and the length of their sides will be proportional.

From the exterior angle property , when we apply it to the given triangle, we will have;

x + x = 58

2x = 58

x = 58/2

x = 29°

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