Simplify the following trigonometric expression. sin(z)+cos(-z)+sin(-z) 1. sin z 2. cos z 3. 2sin z- cosz 4. 2sin z

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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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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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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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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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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The overall average of the weights is 16.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

Given that the average of the first 4 weights is 5.

Avg = Total Sum / Total number of weights

Substituting the value of Avg = 5 and Total number of weights= 4 we have:

5 = Sum(4) / 4

Sum(4) = 20

The average of the next 11 weights was 20 pounds.

Substituting the values, we have:

20 = Sum(11) / 11

Sum(11) = 220

The total sum of the 4 weights and the 11 weights is:

Sum = Sum(4) + Sum(11)

= 20 + 220

= 240

The total number of weights are: 4 + 11 = 15

The overall average weight is:

Avg = Sum/ total number of weights

Avg = 240/ 15

Avg = 16

Hence, the overall average of the weights is 16.

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Answer:

After 5 minutes, Gordon and Erik will each have run 10 laps

Step-by-step explanation:

Let L =lap, M=minute, G=gordon, E=Eric

G=(1L*M)+5

E=(2L*M)+5

Answer:

After 5 minutes, Gordon and Erik will each have run 10 laps

Step-by-step explanation:

Gordon already completed 5 laps and each lap is completed in 1 minute

5 + 5 = 10

Eric completes a lap in 2 minutes

2 x 5 = 10

So after 5 minutes, Gordon and Erik will each have run 10 laps

Hope you get this right :)

A periodic up-and-down motion should be imparted to the nozzle of a garden hose such that the resultant stream of water approximates a sine curve.

A sine curve is a mathematical function that oscillates between a maximum and minimum value in a repeating pattern. To approximate this with a stream of water from a garden hose, the nozzle of the hose should be moved in a periodic up-and-down motion. This motion will cause the water stream to oscillate between a higher and lower height, creating the repeating pattern characteristic of a sine curve. The speed at which the nozzle is moved, as well as the amplitude of the motion, can be adjusted to create a more accurate representation of a sine curve.

Also, the nozzle can be turned to make the water flow in a spiral, which looks even more like a sine curve.

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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

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

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

8x

Step-by-step explanation:

2x x 2x x 2x

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

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

The formula for enlargement = New length = original length × scale factor.

What is enlargement?

A shape's size can be changed by enlarging it. A shape can be made larger by multiplying all of its lengths by the scaling factor. We can calculate how much larger the shape will be by using the scaling factor. For instance, if a shape is scaled up by a factor of 2, all of the sides will lengthen by the same factor.

Here,

We have to determine the formula for enlargement.

We concluded that New length = original length × scale factor.

When we enlarge a shape by a scale factor, the area of the shape is multiplied by the square of the scale factor. When we enlarge a shape by a scale factor, the volume of the shape is multiplied by the cube of the scale factor.

Hence, the formula for enlargement = New length = original length × scale factor.

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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]

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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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

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

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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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 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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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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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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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 solution to the expression 2x²-x will be 45.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 2x²-x. The solution of the expression at x= 5 will be calculated as,

E = 2x²-x

E = 2 x ( 5 )² - 5

E = 2 x 25 - 5

E = 50 - 5

E = 45

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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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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