Verify the identity so that the left side looks like the right side.
[tex]\frac{1-2cos^2(x)}{sin(x)cos(x)}=tan(x)-cot(x)[/tex]

From the given function, the domain of the function is (-∞, ∞) and range of the function is (-∞, -5].

The given function is:

[tex]f(x) = (2/3)(x - 4)^2 - 5[/tex]

The domain of a function is the set of all possible input values (x) for which the function is defined. In this case, there are no restrictions on the input, so the domain is all real numbers:

Domain: (-∞, ∞)

The range of a function is the set of all possible output values (y) that the function can produce. To find the range of the given function, we can complete the square:

[tex]f(x) = (2/3)(x - 4)^2 - 5 \\ = (2/3)(x^2 - 8x + 16) - 5\\ = (2/3)x^2 - (16/3)x + 7.33\\ = (2/3)(x - 4)^2 - 4.67\\[/tex]

Since the term [tex](x - 4)^2[/tex] is always non-negative, the smallest value of the function occurs when [tex](x - 4)^2 = 0[/tex], which happens when x = 4. Substituting x = 4 into the equation gives:

[tex]f(4) = (2/3)(4 - 4)^2 - 5 \\ = -5[/tex]

Therefore, the range of the function is all real numbers less than or equal to -5:

Range: (-∞, -5]

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Answer:

y = 4/3x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (0, -6) and (6, 2)

We see the y increase by 8, and the x increase by 6, so the slope is

m = 8/6 = 4/3

Y-intercept is located at (0, -6)

So, the equation is y = 4/3x - 6

Using the Pythagorean Rule we know that player A is 19.2 ft away from us.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

The Pythagorean Rule can be used to determine the distance between you and Player A since the distances between you, Player A, and Player B are in the shape of a right-angled triangle.

c² = a² + b²

Where;

c = hypotenuse = Distance between you and player A

a = Length of the triangle

b = Height of triangle

Then, calculate as follows:

c² = 12² + 15²

c² = 144 + 225

c = √369

c = 19.2 ft

Therefore, using the Pythagorean Rule we know that player A is 19.2 ft away from us.

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Correct question:

During a basketball game, you want to pass the ball to either Player A or Player B. You estimate that Player B is about 15 feet from you, as shown. How far away from you is Player A?

Answer:

The difference of 1.4 - 0.95 is less than one.

To understand why, we need to calculate the difference between the two numbers:

1.4 - 0.95 = 0.45

Since 0.45 is less than 1, we can conclude that the difference of 1.4 - 0.95 is less than one.

Step-by-step explanation:

Answer:

y=6x-4

Step-by-step explanation:

The slope-intercept form is y=mx+b  

The m in the equation stands for the slope.

The b in the equation stands for the y-intercept.

So you input the y-intercept given to you in the problem, -4, and the slope, 6.

So the equation should be: y=6x-4

Mariya's mistake in solving the inequality and plotting the number line is in step 3.

In mathematics, an inequality is a statement that compares two values or expressions, indicating whether they are equal, not equal, greater than, less than, greater than or equal to, or less than or equal to each other.

Inequalities can be solved by manipulating them in much the same way as equations, but with one important difference: when an inequality is multiplied or divided by a negative number, the direction of the inequality is reversed. For example, if we have the inequality -3x > 12, we can solve for x by dividing both sides by -3, but we also need to reverse the direction of the inequality, giving us x < -4.

The inequality is given as:

[tex]$\frac{a}{-13}\leq-16$[/tex]

Multiply both sides of the inequality by -13

a ≥ 208

The above means that the solution to the inequality are numbers greater than or equal to 208.

This means that we make use of a closed circle

In step 3 of Mariya's solution, the number line uses an open circle

Hence, Mariya's mistake is in step 3

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The complete question is:

Mariya was asked to solve Start Fraction a over negative 13 End Fraction less-than-or-equal-to negative 16 and then graph the solution. Her work is shown below. Step Mariya’s work Start Fraction a over negative 13 End Fraction less-than-or-equal-to negative 16 Step 1 (Negative 13) Start Fraction a over negative 13 End Fraction less-than-or-equal-to negative 16 (negative 13) Step 2 a greater-than-or-equal-to 208 Step 3 A number line going from 205 to 211. An open circle is at 208. Everything to the right of the circle is shaded. In which step, if any, did Mariya make a mistake in her work? Step 1 Step 2 Step 3 No mistake found

The correct answer is ± 5÷2

Answer:

3

Step-by-step explanation:

To estimate the number of students out of the next 10 who will support Julian, we can use the proportion of students who have supported Julian so far.

The total number of students who have been surveyed is:

15 + 9 + 16 + 10 = 50

Out of these 50 students, 15 have supported Julian. Therefore, the proportion of students who have supported Julian so far is:

15/50 = 0.3

To estimate how many of the next 10 students surveyed will support Julian, we can multiply the proportion of students who have supported Julian so far by 10:

0.3 x 10 = 3

Therefore, we can estimate that out of the next 10 students surveyed, about 3 will support Julian.

Answer:

-4x +6y - 8

Step-by-step explanation:

See the attachment below:

The -10 + 6 = -4 not 4

Answer:

Step-by-step explanation:

-10x - 9y + 6x + 15y - 8 =​

-4x+6y -8

False. Calculating standard error is indeed important in statistics, as it serves a different purpose than the regular standard deviation of a single data set.

While standard deviation measures the variability or dispersion within a data set, standard error is used to measure the accuracy of a sample mean as an estimate of the true population mean.
1. Standard deviation measures the dispersion or spread of data points in a single data set. It helps you understand how much the individual data points deviate from the mean (average) of that data set.
2. Standard error, on the other hand, is a measure of how accurate a sample mean is in estimating the true population mean.

It is calculated by dividing the standard deviation of the sample by the square root of the sample size (n).
Standard Error (SE) = Standard Deviation (SD) / √n
3. As the sample size increases, the standard error decreases, indicating that the sample mean becomes a more accurate estimate of the population mean.

This is because larger sample sizes tend to have a smaller sampling error.
4. In hypothesis testing and confidence interval estimation, standard error plays a crucial role.

It helps to determine the margin of error and to assess the significance of differences between sample means.
5. While standard deviation is a useful measure for understanding variability within a single data set, standard error is essential for making inferences about the population based on the sample data.
In conclusion, both standard deviation and standard error are important in statistics as they serve different purposes. Ignoring standard error would lead to inaccurate conclusions about the population mean based on sample data.

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Answer:

C) +18 ÷ +3 = +6

Step-by-step explanation:

The average weekly change in Alvin's training can be calculated by finding the total change in his training over the 3 weeks and then dividing it by the number of weeks. Since he reduced his training by 18 miles per week, his total change over the 3 weeks would be 18 miles/week * 3 weeks = 54 miles.

To represent the average weekly change in his training using an equation, we need to divide the total change by the number of weeks, which gives us:

Average weekly change = total change ÷ number of weeks

Substituting the values we found, we get:

Average weekly change = 54 miles ÷ 3 weeks = 18 miles/week

Solving the equation 2^x + 124 = 5^y for x and, we get x = 0 and y = 5

From the question, we have the following parameters that can be used in our computation:

2^x + 124 = 5^y

Set x = 0

So, that we calculate the of y

Using the above as a guide, we have the following:

2^0 + 124 = 5^y

This gives

1 + 124 = 5^y

Evaluate the like terms

So, we have

5^y = 125

Express 125 as 5^3

So, we have

5^y = 5^3

Evaluate

y = 3

Hence, the solution is x = 0 and y= 3

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The system of equations has two solutions: (0,2) and (-4/5, -6/5).

The substitution method is a way to solve a system of two linear equations with two variables. The method involves solving one of the equations for one of the variables, and then substituting that expression into the other equation in place of the same variable. This process reduces the system of two equations and two variables to a single equation and a single variable, which can then be solved.

We have the system of equations:

4x² + y² = 4 ........(1)

y = x + 2 ........(2)

We can solve this system of equations by substitution.

Substitute (2) into (1) to eliminate y:

4x² + (x + 2)² = 4

Simplify and solve for x:

4x² + x² + 4x + 4 = 4

5x²+ 4x = 0

x(5x + 4) = 0

x = 0 or x = -4/5

If x = 0, then from equation (2), y = 2. So one solution is (x,y) = (0,2).

If x = -4/5, then from equation (2), y = -6/5. So the other solution is (x,y) = (-4/5, -6/5).

Therefore, the system of equations has two solutions: (0,2) and (-4/5, -6/5).

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Answer:

ans:88.18cm

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be  result of rounding 3.90287605 to the closest thousand is 0.

Instead of using estimates produced at random, it is better to use shifting integer variables that can be rising, reducing, or blocking. They could only help one another by sharing tools, information, or solutions to issues. The justifications, elements, and mathematical remarks for techniques like additional disapproval, manufacture, and mixture may be included in a statement of truth equation.

Here,

It is necessary to look at the digit in the thousands place, which is 0,

when rounding the number 3.90287605 to the closest thousand.

We round down and maintain the same value in the thousands place because this digit is less than 5.

Thus, zero is the figure that has been rounded to the nearest thousand.

The result of rounding 3.90287605 to the closest thousand is 0.

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Answer:

1. 36

2. 28

Step-by-step explanation:

You are just counting how many sides are showing.  

The right side, you see 6 green sides.  Although you cannot see the other side, you know that it must be 6 also.  You count the orange and blue.  That is 12.  The bottom is 6.  the back is 6.

6 + 6 + 12 + 6 + 6  = 36

Helping in the name of Jesus.

The graph of this inequality is located at x = 4 and is represented using a solid line with shaded region to the right of the line.

Using a mathematical symbol like (less than), > (greater than), (less than or equal to), or (less than), an inequality statement compares the values of two expressions (greater than or equal to). When two expressions are compared, an inequality means that they are not equal and that one expression is either greater or smaller than the other.

For instance, the inequality 5 < 7 denotes that the number 5 is lower than the number 7, whereas the inequality 2x + 3 > 7 denotes that the number 2x + 3 is higher than the number 7. Algebra, calculus, and optimisation are just a few of the areas of mathematics where inequalities are frequently employed to describe connections between numbers and to solve issues.

The given inequality is x + 10 ≥ 14.

Simplifying the expression we have:

x ≥ 14 - 10

x ≥ 4

The graph of this inequality is located at x = 4 and is represented using a solid line with shaded region to the right of the line.

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The sampling interval for this account balance is $12,000.

To calculate the sampling interval, we will use the following formula:
Sampling interval = Population value (Book value) / Sample size
Student question: For an account balance with a book value of $1.5 million, the sample size is 125.

Given this information, the sampling interval will be:
Sampling interval = $1,500,000 / 125
Sampling interval = $12,000.

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Answer:

Step-by-step explanation:

It 3. cause you want to expand the number outside to every number or variable in the inside of the brackets

Answer:

not know but know formula

Step-by-step explanation:

8y + y-2

Using the inverse variation formula, p × q = k, where k is a constant, we can solve for q when p is equal to 2, given that p and q vary inversely and p is 24 when q is 23 when p is equal to 2, q is equal to 276.

When two variables vary inversely, as one variable increases, the other variable decreases proportionally, and vice versa. In this problem, p and q vary inversely, which means that if we multiply p by some constant, we need to divide q by the same constant to maintain the inverse variation.

First, we need to find the value of k using the given information:

p × q = k

24 × 23 = k

k = 552

Now that we have the value of k, we can use it to solve for q when p is equal to 2:

p × q = k

2 × q = 552

q = 276

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The calculated radius of the cylidner when approximated is 8.0 meters

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, h is the height, and π is a constant approximately equal to 3.14.

To find the radius of a cylinder with volume 1607 m³ and height 8 m, we can rearrange the formula as:

r^2 = V / (πh)

Substituting the given values, we get:

r^2 = 1607 / (3.14 x 8)

r^2 ≈ 63.973

Taking the square root of both sides, we get:

r ≈ 8.0

Therefore, the radius of the cylinder is approximately 8.0meters.

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Answer:   10.75

Step-by-step explanation: 1: Based on the given conditions, formulate: 4.3 x 2.5

2: Calculate 4.3 x 2.5 = 10.75.

Therefore, the answer is 10.75.

The expression that we need to add to 5x + 7 to make it equivalent to 9(x + 1) is -2x + 2.

To make the expressions 5x + 7 and 9(x + 1) equivalent, we need to find the expression that, when added to 5x + 7, will give us 9(x + 1).

First, we can simplify 9(x + 1) by distributing the 9:

9(x + 1) = 9x + 9

Now we can see that we need to find an expression that, when added to 5x + 7, will give us 9x + 9:

5x + 7 + ? = 9x + 9

To find the missing expression, we need to isolate the variable on one side of the equation and the constant terms on the other side:

5x - 9x = 9 - 7

Simplifying this expression, we get:

-4x = 2

Dividing both sides by -4, we get:

x = -1/2

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Question:-

What expression would be added to 5x + 7 to make it equivalent to the expression 9(x + 1)?

88 is the measure of arc BC.​

What is arc ?

In general, an arc is any smooth wind joining two points. The length of an arc is known as its arc length. In a graph, a graph arc is an ordered brace of conterminous vertices. In particular, an arc is any portion( other than the entire wind) of the circumference of a circle.

                       An arc is the term used to describe the convex area of a circle that curves away from an angle like this, between two line segments or rays. A circle's circumference, or outside border, is known as the arc's circumference, and it is this area that is measured when an arc is drawn along it.

DE ≅ BC

  3x + 22 = 4x

      4x - 3x = 22

          x = 22

BC = 4X = 4 * 22

              =    88

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The percent of those interviewed said they like orange juice for breakfast is 58%.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent.

The percent of those interviewed said they like orange juice for breakfast will be:

= Orange juice taker /  Total respondent

= 29/50

= 0.58

= 58%

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Gas company charges are typically not linear due to the use of fixed fees, variable charges, and tiered pricing structures. While it is possible for a company to adopt a linear rate structure, it is not common in practice.

The charges levied by gas companies can vary depending on a variety of factors, including the amount of gas used, the location, the season, and other factors. However, when considering a particular rate structure, we can analyze whether the charges are linear or not.

A linear rate structure implies that the cost of gas usage is directly proportional to the amount of gas consumed. In other words, if you use twice as much gas, you would be charged exactly twice as much.

In practice, most gas companies use non-linear pricing structures that incorporate fixed charges, variable charges, and tiered pricing structures. For instance, a gas company may charge a fixed monthly fee for the gas supply, regardless of the amount of gas used. Additionally, there may be variable charges that depend on the amount of gas consumed, with different rates applying to different usage levels. Finally, some companies may apply tiered pricing structures, where the price per unit of gas increases as consumption levels increase.

For example, suppose a gas company charges a fixed fee of $10 per month for the gas supply, and then $0.10 per cubic foot of gas for the first 500 cubic feet used in a month, and then $0.15 per cubic foot for all additional usage. In this case, the pricing structure is not linear, as the rate per cubic foot of gas changes depending on the amount consumed.

It is also important to note that gas companies may adjust their pricing structures from time to time in response to market conditions, regulatory changes, or other factors. Therefore, it is important for consumers to review their bills regularly to ensure that they understand the charges and are not being overcharged.

In conclusion, gas company charges are typically not linear due to the use of fixed fees, variable charges, and tiered pricing structures. While it is possible for a company to adopt a linear rate structure, it is not common in practice.

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Answer:

6

Step-by-step explanation:

Answer:

[C] $28.39

Step-by-step explanation:

As given that-

Question to answer -

Solve-

Thus,

                              = 0.062 × 457.88

                              = 28.38856

                              = $ 28.39 (Approx)

Answer-

Hence, the Social Security tax deducted from  gross pay will be $28.39 .

Which means the correct answer is [C] $28.39

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