Solve for x: −3x + 3 < 6

x > −1
x < −1
x < −3
x > −3

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

(x - 3) and (x - 2)

Step-by-step explanation:

Using the method of long division to divide the polynomial by x + 4

                   x² - 5x + 6

                 -------------------------------

x + 4   |  x³ - x² - 14x + 24

             x³ + 4x²

             ---------------------------

                  - 5x² - 14x + 24

                   - 5x² - 20x

              -------------------------------

                               6x + 24

                               6x + 24

                --------------------------------

                              0        0

The quotient is x² - 5x +  6 = (x - 2)(x - 3)

x³ - x² - 14x + 24 = (x - 2)(x - 3)(x + 4) ← in factored form

          |

Answer:

C. 8 units.

Step-by-step explanation:

The maximum value of the cosine ( cos) function is 1

So, for y = 3cos(2x - 8) + 5

Maximum value  is 3 *1 + 5 = 8.

y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.

Answer:

84.53%

Step-by-step explanation:

total=293

completed=247.7

percentage=247.7/293. ×100%

=84.539%

Answer:

The class sociologist Max Weber formulated a three-component theory of stratification that saw political power as an interplay between “class”, “status” and “group power. ” Weber theorized that class position was determined by a person’s skills and education, rather than by their relationship to the means of production

First and foremost, it is important to note that human skin color is determined by a variety of factors, including genetics, environmental influences, and geographic location. In fact, skin color is the result of the amount and type of melanin pigment produced by specialized cells in the skin called melanocytes.

There are two main types of melanin pigment: eumelanin and pheomelanin. Eumelanin is responsible for producing darker skin colors, while pheomelanin produces lighter skin colors. However, the amount and distribution of these pigments can vary greatly between individuals, resulting in a wide range of skin tones.

Additionally, skin color can also be influenced by factors such as sun exposure, age, and hormonal changes. For example, prolonged sun exposure can lead to darker skin, while aging and hormonal changes can cause changes in skin pigmentation. Furthermore, it is important to note that skin color is not always clearly defined or easily categorized into specific shades. There can be a great deal of variation within a single skin tone, as well as overlap between different skin tones. This is due to the complex interplay of genetic and environmental factors that contribute to skin color.

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Answer:

Area of Triangle is 225 cm^2

Step-by-step explanation:

Let height of triangle be h

Let the base of triangle be b

It is given that the sum of base and height is 45

b + h = 45  ---------(1)

It is also given that the height is twice of base

2b = h ---------------(2)

by substituting (2) in (1)

b + 2b = 45

3b = 45

b = 15 cm

15 + h = 45

h = 30 cm

Area of triangle is given as

1/2 x b x h

= 1/2 x 15 x 30

= 225 cm^2

Answer:

48 cm

Step-by-step explanation:

Here Is a trapezium and a square, The lengths of the parallel sides of the  trapezium are 10 cm and 14 cm, The height of the trapezium is 12 cm. The area of  the square is equal to the area of the trapezium. Work out the perimeter of the  square.

Solution:

The area of the trapezium is given by:

A = (1/2)(a + b)h

where h is the height of the trapezium = 12 cm, a and b are the parallel sides. Given that a = 10 cm, b = 14 cm, hence:

A = (1/2)(10 + 14)12 = 144 cm²

Area of trapezium = Area of square

Area of square = 144 cm²

Area of square = length * length = length²

length² = 144 cm²

length = √144 = 12 cm

Perimeter = 4 * length = 4 * 12 cm = 48 cm

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.

For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:

Margin of error = (critical value) x (standard error)

The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:

Standard error = (standard deviation) / sqrt(sample size)

If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.

Assuming a sample standard deviation of 10, the standard error would be:

\(Standard\  error = \frac{10} { \sqrt{(100)}} = 1\)

Therefore, the margin of error would be:

Margin of error = 1.984 x 1 = 1.984

The confidence interval estimate of the population means examination score would be:

80 ± 1.984, or between 78.016 and 81.984.

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the

nearest whole number.

To determine the confidence interval estimate of the population mean examination score based on a sample mean

provided to the nearest whole number, we need to know the sample size and the level of confidence.

Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the

confidence interval estimate:

Confidence interval = sample mean +/- (critical value) x (standard error)

The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of

freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.

The standard error is the standard deviation of the sample divided by the square root of the sample size.

For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the

standard error would be 10/sqrt(50) = 1.41.

Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.

Therefore, the confidence interval estimate would be:

75 +/- 1.96 x 1.41 = 75 +/- 2.77

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Answer:

is it 160167

Step-by-step explanation:

hope i helped out

Answer:

88:56 = 11:7

Step-by-step explanation:

Step One

Add the two ratios together 11 + 7 = 18

Now set up a ratio to solve for 11 parts out of 18

11:18 = x:144         Proportion

11 / 18 = x / 144    Equation: Cross mulitiply

11*144 = 18x         Combine the left side

1584   = 18x         Divide by 18

1584 / 18  = x

88 = x

That is the larger amount (11 is larger than 7)

Find the smaller amount

144 - 88 = 56

The two amounts are in the ratio of 11:7

88:56 = 11:7  

I hopes this helps a little  bit

Answer:

56g and 88g

Step-by-step explanation:

7x+11x=144

18x=144

x=144/18

x=8

7x=7*8=56g

11x=11*8=88g

the aggregate demand curve is downward-sloping because, other things being equal, With average price reductions, more people purchase goods and services.

This is known as the law of demand, which states that there is an inverse relationship between the price of a good or service and the quantity of that good or service demanded by consumers. When the price of a good or service goes up, consumers tend to demand less of it, and when the price goes down, consumers tend to demand more of it. Therefore, if all other factors affecting demand remain constant, an increase in price will lead to a decrease in the quantity demanded, and a decrease in price will lead to an increase in the quantity demanded. This is why the aggregate demand curve is downward-sloping.

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Compete Question

the aggregate demand curve is downward-sloping because, other things being equal, ____. FILL IN THE BLANKS

The Robinsons can expect to save approximately $98.10 annually with their new dryer and will need to use it for 10.45 years to make up for the initial cost of $1,025.00.

To calculate the number of years it will take for the new dryer to pay for itself, we need to determine the amount of money the Robinsons will save annually with the new dryer.
The old dryer cost $545 per year to run, while the new dryer will save 18% annually in energy costs.
To find out how much the new dryer will cost to run annually, we can multiply the old cost by (100%-18%) or 82%.
$545 x 0.82 = $446.90
This means that the Robinsons will save $545 - $446.90 = $98.10 annually with the new dryer.
To determine how many years it will take for the new dryer to pay for itself, we need to divide the cost of the new dryer by the annual savings.
$1,025.00 / $98.10 = 10.45 years
Therefore, it will take approximately 10.45 years for the new dryer to pay for itself in energy cost savings.
In conclusion, the Robinsons can expect to save approximately $98.10 annually with their new dryer and will need to use it for 10.45 years to make up for the initial cost of $1,025.00.

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Answer:

steps below

Step-by-step explanation:

sin θ + cos θ / sec θ + cosec θ

= (sin θ + cos θ) / (1/cos θ+1/sin θ)

= (sin θ + cos θ) / ((sin θ + cos θ)/sin θ*cos θ)

= sin θ * cos θ

Answer:

\(\boxed {\boxed {\sf 480\textdegree}}\)

Step-by-step explanation:

First, remember that π radians is equal to 180 degrees. Therefore, to convert from radians to degrees, multiply by 180/π.

The radian measure given is 8π/3

\(\frac {8 \pi}{3} * \frac{180}{\pi}\)

Multiply the fractions. Multiply across the numerator, then across the denominator.

\(\frac{8 \pi *180}{3 * \pi}\)

The pi in the numerator and denominator will cancel out.

\(\frac{8 *180}{3 }\)

Multiply.

\(\frac{1440}{3}=480\)

The radian measure 8π/3 is equal to 480 degrees.

As per the distributive property, the expression -3x⁴(5x³ - 2x⁶) is equivalent to -15x⁷ + 6x¹⁰

Distributive property:

Distributive property states that the expression has been simplified when you multiply a number by a sum or difference.

Give,

Here we have the expression -3x⁴(5x³ - 2x⁶).

Now, we have to use the distributive property in order to find the equivalent expression.

Based on the distributive property, here we have to multiply the outer term with the individual inner terms, then we get,

=> -3x⁴(5x³ - 2x⁶)

=> (-3x⁴ × 5x³) + (-3x⁴ ×- 2x⁶)

Now we have to multiply the signs and the numbers then we get.

=> -15 (x⁴ × x³) + 6 (x⁴ × x⁶)

As per the rule of exponent, we have to add the exponents of the expression to find the solution,

=> -15x⁷ + 6x¹⁰

Therefore, the equivalent expression is -15x⁷ + 6x¹⁰.

Therefore, the option A is correct.

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Shape C, a complicated shape, needs to be divided into simpler shapes in order to calculate its area. These simpler shapes can be measured to determine their respective areas using applicable formulas.

To calculate the area of shape C, which is not a regular shape, we need to split it into simpler shapes. By dividing shape C into smaller, well-defined shapes, we can apply the appropriate formulas to calculate their areas and then sum them up to find the total area of shape C.

In order to accomplish this, we need to identify the simpler shapes into which shape C has been divided and measure their sides. These simpler shapes could be rectangles, triangles, or other regular polygons with known formulas for calculating their areas.

Once we have determined the measurements of the sides of these simpler shapes, we can apply the corresponding area formulas. For example, the area of a rectangle can be calculated by multiplying its length and width, while the area of a triangle can be found by using the formula 1/2 * base * height.

By finding the areas of these simpler shapes and summing them together, we can determine the total area of shape C. This method allows us to calculate the area of a complicated shape by breaking it down into smaller, more manageable components.

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Answer:

----------------------------------

Given:

Perimeter is:

or

The perimeter is at most 96 cm (not greater than):

The matching choice is A.

Answer:

D

Step-by-step explanation:

4C1*5C1*6C1*8C1

=960

The converted to product four times as much in the CSTR than it was in the PFR that is 400%.

Conversion is a term used to describe the process of transferring a reactant into a product.

In this case, the reactant is being transferred from a 72 l plug flow reactor (PFR) to a 24 l continuous stirred tank reactor (CSTR). The conversion achieved by this process can be determined by calculating the ratio of product to reactant in the CSTR.

Specifically, if the PFR has a conversion of x%, then the conversion achieved in the CSTR will be x/(1-x), where x is the conversion in the PFR.

Therefore, if the PFR has a conversion of 80%, then the CSTR will have a conversion of 80/(1-80) = 400%.

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Answer:

-692784311700

Step-by-step explanation:

Therefore, √128 lies between 11 and 12 on a number line.

To determine the two numbers between which √128 lies on a number line, we can calculate the square roots of consecutive perfect squares that surround 128.

By calculating the square roots, we can find the two nearest whole numbers that √128 lies between.

Calculating the square roots of perfect squares near 128:

√121 = 11

√144 = 12

Since 128 is greater than 121 and less than 144, √128 lies between √121 and √144 on the number line.

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Answer:

3: 23 feet and 4 inches wide

The probability of P(prime) is 1/2.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given you rolled a 6-sided die.

The possible outcomes are {1, 2, 3, 4, 5, 6}.

In the sample space, the prime numbers are 2, 3 and 5.

Number of primes = 3

Total number of outcomes = 6

Probability of getting a prime number = 3/6 = 1/2

Hence 1/2 is the required probability.

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There is no equation for the ellipse with foci (1, 1) and (-1, -1) and a major axis of length 4.

To find the equation of the ellipse with foci (1, 1) and (-1, -1) and a major axis of length 4, we can use the properties of ellipses.

The major axis is the line segment connecting the two foci, which in this case has a length of 4.

Since the foci are (1, 1) and (-1, -1), the distance between them is 2a = 4, where "a" represents the semi-major axis.

Therefore, the value of "a" is 2.

The distance between each focus and the center of the ellipse is "c". Since the foci are (1, 1) and (-1, -1), the distance between each focus and the center is c = √[\((1 - (-1))^2 + (1 - (-1))^2\)] = √8

Now, we can use the formula for the equation of an ellipse centered at the origin:

\(x^2/a^2 + y^2/b^2 = 1\)

where "a" is the semi-major axis and "b" is the semi-minor axis.

Since the semi-major axis "a" is 2, we have:

\(x^2/2^2 + y^2/b^2 = 1\)

To find the value of "b", we can use the relationship between "a", "b", and "c" in an ellipse, which is given by the equation \(a^2 = b^2 + c^2\).

Plugging in the values, we get:

\(2^2 = b^2 + (\sqrt8)^2\\ 4 = b^2 + 8\\ b^2 = 4 - 8\\ b^2 = -4\)

Since we cannot have a negative value for "\(b^2\)" in this case, it means that there is no real solution for "b".

This indicates that the given parameters do not form a valid ellipse.

Therefore, there is no equation for the ellipse with foci (1, 1) and (-1, -1) and a major axis of length 4.

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Reflection on the relationship between proofs and problem solving reveals both similarities and differences in their approach.

Similarities in Approach:

Logical Reasoning: Both proofs and problem-solving require logical reasoning and systematic thinking to arrive at a solution or conclusion. They both involve analyzing information, identifying patterns, and making logical deductions or inferences.

Clear Definitions and Assumptions: Both proofs and problem-solving benefit from having clear definitions of terms and assumptions. Clarity in understanding the problem or the concepts involved is crucial for formulating a solution or a proof.

Creative Thinking: Both activities often require creativity and thinking outside the box. To solve complex problems or prove challenging theorems, one needs to think creatively, explore different approaches, and consider alternative perspectives.

Step-by-Step Approach: Both proofs and problem-solving typically involve breaking down the task into smaller, manageable steps. They require organizing thoughts and following a structured approach to build a coherent argument or solve a problem systematically.

Differences in Approach:

Objectives: The primary objective of a proof is to establish the truth or validity of a statement or theorem, using logical deductions and rigorous arguments. Problem-solving, on the other hand, aims to find a solution to a specific problem or task.

Context: Proofs are commonly associated with mathematics and formal logic, where the goal is to demonstrate the truth of a statement. Problem-solving, however, applies to a broader range of disciplines and real-life situations, where finding practical solutions is often the objective.

Constraints: Problem-solving often involves dealing with real-world constraints, such as limited resources, time constraints, or practical considerations. Proofs, on the other hand, are more concerned with the logical coherence and validity of the arguments, without being bound by real-world limitations.

Creativity vs. Rigor: While both proofs and problem-solving require creative thinking, the level of rigor is typically higher in proofs. Proofs demand strict adherence to logical rules, axioms, and established mathematical principles, whereas problem-solving may allow for more flexibility and heuristic approaches.

In summary, proofs and problem-solving share similarities in terms of logical reasoning, clear definitions, creativity, and step-by-step approaches. However, they differ in objectives, context, constraints, and the level of rigor required. Both activities contribute to the development of critical thinking skills and the exploration of new ideas and concepts.

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Answer:

21

Step-by-step explanation:

120*7/10= 84  french
15 are chinese
84+15=99
120-99=21

Answer:

21

Step-by-step explanation:

Answer: Look at the variables (letters) and plug them in

Step-by-step explanation: You plug in the variables into the problem, then you separate the other variable that you don't know from your whole number by bringing it to the other side. Then you can divide or whatever you have to do.