Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The eighth term of the sequence is -14

What is common ratio?

The common ratio between consecutive terms in a geometric sequence is constant. Let's denote this common ratio by 'r'. To find 'r', we can divide any term by the preceding term,

r = -448/896 = -1/2

Now we can use the formula for the nth term of a geometric sequence,

[tex]a_n = a_1 \times p^{n - 1}[/tex]

where '

[tex]a_1[/tex] is the first term and 'n' is the index of the term we want to find.

Substituting the values we have,

[tex]a_8 = 896 (-1/2)^{8-1} \\ = 896 \times (-1/2)^{7} = -14[/tex]

Therefore, the eighth term of the sequence is -14.

So, option A is the correct answer.

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Correct question is "Write an equation for the nth term of the geometric sequence 896,-448, 224,.... Find the eighth term of this sequence.

A) -14

B) -18

C) -19

D) 18"

The area of the base of the prism is 6 cm².

To find the area of the base of the trapezoid-based right prism, we need to use the given information about the volume, height of the prism, larger base, and one slanted side of the trapezoid.
Step 1: We know the volume (V) of the prism is 30 cm³ and the height (h) of the prism is 5 cm.

We can use the formula for the volume of a prism:
V = Area of base × h
Step 2: Plug in the values:
30 cm³ = Area of base × 5 cm
Step 3: Solve for the Area of the base:
Area of base = 30 cm³ / 5 cm = 6 cm²

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True. This is because a two-tailed test evaluates both the extreme lower and upper ends of the distribution, allowing for the possibility of a significant difference in either direction.

In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.

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Answer:

So, the correct answer is (30.104, 32.896).

Step-by-step explanation:

To find the 95% confidence interval for the mean number of pounds of trash per person per week, we can use the following formula:

CI = X + Zα/2 * (σ/√n)

σ = population standard deviation = 7.8 pounds

n = sample size = 120

Plugging in the values, we get:

CI = 31.5 ± 1.96 \times(7.8/√120)

CI = 31.5 ± 1.96 \times 0.711

CI = 31.5 ± 1.39

Therefore, the 95% confidence interval for the mean number of pounds of trash per person per week is (30.11, 32.89).

So, the correct answer is (30.104, 32.896).

Answer:

A

Step-by-step explanation:

Since this is a rectilinear angle, we can find x:

x = 180° - 98° = 82°

A. For any number of monthly calls "x" greater than 200, Plan 1 is more economical than Plan 2.

The answer to part a means that if a customer expects to make more than 200 local calls per month, it is more economical for them to choose Plan 1 over Plan 2. For example, if a customer makes 250 local calls per month, Plan 1 would cost $28 while Plan 2 would cost $20 ($12 + $0.08 x 250), so Plan 1 would be the better choice for them. However, if a customer expects to make fewer than 200 local calls per month, then Plan 2 would be more economical for them, as they would pay less than $28 per month.

The break-even point is the number of monthly calls for which the total cost of Plan 1 is equal to the total cost of Plan 2.

This occurs when the inequality $16 < $0.08x is satisfied, which simplifies to 200 < x.

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Answer:

for Identify two-dimensional (2-D)Figures and their positions.

2D stands for 2-dimensional. 2-dimensional shapes are flat and only have two dimensions: length and width. They include squares, rectangles, circles, triangles

Step-by-step explanation:

The solution to the trigonometric equation with sine function is x = 2.5.

Starting with 3√2 sin π/3 (x − 2) + 4 = 7:

First, we can simplify 3√2 sin π/3 to 3, since sin π/3 = √3/2 and 3√2 = 3 x √2 x √2 = 3 x 2 = 6.

6(x - 2) + 4 = 7

6x - 12 + 4 = 7

6x - 8 = 7

6x = 15

x = 2.5

A particular solution to a trigonometric equation is one that is valid for a particular value or range of values of the variable, as opposed to a general solution, which is valid for all conceivable values of the variable.

Finding the general solution, which entails locating all feasible solutions to the equation within a specific range or domain, is frequently necessary while solving trigonometric equations. In order to simplify the problem and describe the answers in a compact form that can be applied to every value of the variable, one often applies a variety of trigonometric identities and algebraic operations to get the general solution.

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The value that measures the difference between a sample mean and the population mean on average is the standard error of the mean (SEM).

The value that measures the difference expected, on average, between a sample mean and the population mean is the standard error of the mean (SEM). The SEM is a measure of the variability of sample means around the true population mean, and it quantifies the precision of the sample mean as an estimate of the population mean. In general, the larger the sample size, the smaller the SEM, indicating that larger samples are more likely to provide a more accurate estimate of the population mean.

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Complete question:

when a random sample is selected from a population, the sample mean is not expected to be exactly equal to the population mean. what value measures the difference expected, on average, between a sample mean and the population mean? group of answer choices

A) the standard error

B) the expected value

C) the mean of the population

D) the standard deviation of the population

A cubic polynomial is the one with the highest degree of a variable as 3. The graph for the given cubic polynomial, y = x²- x³ is attached below:

A cubic polynomial is a type of polynomial in which the variable or degree has a maximum power of 3. The format is ax³ + bx² + cx + d. where 'x' is a variable and a,b,c,d are real numbers. Cubic polynomials are used in many areas of mathematics and science, including physics, engineering, and economics. A polynomial is an algebraic expression with variables and constants with integer exponents. A cubic polynomial is a polynomial with the largest exponent of any variable.

Based on the degree, polynomials are classified into four types: zero polynomials, linear polynomials, quadratic polynomials, and cubic polynomials.

The general way of representing a cubic polynomial is p(x) = ax³ + bx² + cx + d, a ≠ 0, where a, b, c are coefficients and d is a constant, all real numbers. Equations involving cubic polynomials are called cubic equations.

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The polynomial with the highest degree of a variable as three is called a cubic polynomial. The cubic polynomial presented in the graph, y = x²- x³ is attached below:

When the variable or degree of a polynomial has a maximum power of three, the polynomial is said to be cubic. The format is as follows: ax³ + bx² + cx + d, where x is a variable and a, b, c, and d are actual values. Physics, engineering, and economics are just a few of the fields in mathematics and science where cubic polynomials are employed. An algebraic expression having variables and constants with integer exponents is called a polynomial. A polynomial with the highest exponent of any variable is said to be cubic.

The four types of polynomials are zero polynomials, linear polynomials, quadratic polynomials, and cubic polynomials. These categories are based on the degree of the polynomial.

A cubic polynomial is typically represented as p(x) = ax³ + bx² + cx + d, a ≠0, where a, b, and c are coefficients and d is a constant, all of which are real values. Cubic equations are equations employing cubic polynomials.

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The average rate of change of the function is:

a) f(x) = 12x^3 + 12 over the interval [5,7] is 1032.

b) f(x) = 12x^3 + 12 over the interval [-4,4] is 507.

a) To find the average rate of change of the function f(x)=12x^3 + 12 over the interval [5,7], follow these steps:

. Evaluate the function at the endpoints of the interval: f(5) and f(7).
  f(5) = 12(5)^3 + 12 = 1532
  f(7) = 12(7)^3 + 12 = 3596

. Subtract the function values: f(7) - f(5) = 3596 - 1532 = 2064.
. Subtract the x-values: 7 - 5 = 2.
. Divide the difference in function values by the difference in x-values: 2064 ÷ 2 = 1032.
So, the average rate of change of the function f(x) = 12x^3 + 12 over the interval [5,7] is 1032.

b) To find the average rate of change of the function f(x) = 12x^3 + 12 over the interval [-4,4], follow these steps:
. Evaluate the function at the endpoints of the interval: f(-4) and f(4).
  f(-4) = 12(-4)^3 + 12 = -2028
  f(4) = 12(4)^3 + 12 = 2028
. Subtract the function values: f(4) - f(-4) = 2028 - (-2028) = 4056.
. Subtract the x-values: 4 - (-4) = 8.
. Divide the difference in function values by the difference in x-values: 4056 ÷ 8 = 507.
So, the average rate of change of the function f(x) = 12x^3 + 12 over the interval [-4,4] is 507.

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Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.

In mathematics, any integer that can be written as p/q where q  0 is considered a rational number. Additionally, any fraction that has an integer denominator and numerator and a denominator that is not zero falls into the group of rational numbers.

To find out how much more Khalil's cat weighed than Sophia's cat, we need to subtract the weight of Sophia's cat from the weight of Khalil's cat.

Khalil's cat weighed 18 5/6 pounds.

Sophia's cat weighed 10 1/3 pounds.

Subtracting the weights:

18 5/6 - 10 1/3

To subtract mixed numbers, we need to find a common denominator. In this case, the least common multiple of 6 and 3 is 6. So, we can convert the fractions to have a denominator of 6:

18 5/6 - 10 1/3 = 18 5/6 - 10 2/6

Now, we can subtract the whole numbers and the fractions separately:

18 - 10 = 8

5/6 - 2/6 = 3/6

Putting it back together:

8 3/6

We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3 in this case:

8 3/6 = 8 1/2

So, Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.

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Answer:

Answer:

D

Step-by-step explanation:

y = x² - 4x - 5 → (1)

y = x - 9 → (2)

substitute y = x² - 4x - 5 into (2)

x² - 4x - 5 = x - 9 ( subtract x - 9 from both sides )

x² - 5x + 4 = 0 ← in standard form

(x - 1)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

substitute these values into (2) for corresponding values of y

x = 1 : y = 1 - 9 = - 8 ⇒ (1, - 8 )

x = 4 : y = 4 - 9 = - 5 ⇒ (4, - 5 )

Answer: $25.41

Step-by-step explanation:

I think this is right, please correct me if I'm wrong

Step-by-step explanation:

Because a cube has   6    sides ...and a cube has equal side lengths so the area of each side is s x s = s^2    

   then the total is   6 s^2

Enrique must read for at least 12 more minutes to complete his assignment of reading at least 40 pages.

Let's assume that Enrique needs to read for 'm' minutes to complete his assignment of reading at least 40 pages.

Since Enrique reads 2 pages every minute, the number of pages he will read in 'm' minutes will be 2m. Therefore, to satisfy the condition of reading at least 40 pages, we can write the following inequality:

2m + 16 ≥ 40

Simplifying the above inequality, we get:

2m ≥ 24

Dividing both sides by 2, we get:

m ≥ 12

Hence, Enrique must read for at least 12 more minutes to complete his assignment of reading at least 40 pages.

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From the given sample space the probability of P(at least 2 tails) is 68.75%.

Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the occurrence. Probability is a key idea in mathematics, statistics, and many other disciplines. It is used to describe uncertain events. Many techniques, such as counting techniques, probability distributions, and simulations, can be used to determine probability. Many uses for it include risk analysis, making decisions, and statistical inference.

From the given sample space the outcomes with at least 2 tails are:

{TTTT, TTT H, TT HT, T H TT, H TTT, H HTT, HT HT, HTTH, THHT, THTH, THH H}

Now,

P(at least 2 tails) = 11/16 = 0.6875 ≈ 68.75%

Hence, from the given sample space the probability of P(at least 2 tails) is 68.75%.

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Therefore , the solution of the given problem of expressions comes out to be  (x+y) is the LCM of (x+y, x-y).

Utilizing shifting integers that may prove rising, minimizing, or blocking is preferable to using approximations generated at random. Sharing resources, knowledge, or answers to problems was the only way they could assist one another. An equation for a declaration of truth may contain the justifications, components, and mathematical comments for methods like additional disagreement, manufacture, and mixture.

Here,

We must factor each polynomial into its irreducible factors and then take the sum of the highest powers of each irreducible factor to determine the LCM of two polynomials.

Here are the facts:

=> x+y = (x+y)

=> x-y = -(y-x)

We don't need to include the second component separately in the LCM because it is simply the negation of the first factor.

The LCM is just (x+y) because x+y is already indivisible.

Consequently, (x+y) is the LCM of (x+y, x-y).

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Given that ABCD is a parallelogram:

Opposite sides of a parallelogram are parallel and congruent. Therefore, AB = DC.

Diagonals of a parallelogram bisect each other. Therefore, the midpoint of AC is the same as the midpoint of BD. Let M be the midpoint of AC, and N be the midpoint of BD.

By the midpoint theorem, BM = DM and BN = AN.

Since BM = DM and BN = AN, we can conclude that quadrilateral ABCD is a parallelogram in which BC || AD and CD || AB.

Therefore, we have shown that AB = CD and BC = AD in parallelogram ABCD.

The minimum amount of cloth Carl needs to cover the entire box is 272 square inches.

A prism is a three-dimensional geometric shape that consists of two identical polygonal bases that are connected by a set of parallelogram faces. The shape of the prism is determined by the shape of its bases. For example, if the bases are triangles, the prism is called a triangular prism. Similarly, if the bases are squares, the prism is called a square prism, and so on.

Prisms have a number of interesting properties. The faces that connect the bases are always parallelograms, and the opposite faces are congruent and parallel. The altitude of a prism is the perpendicular distance between its bases, and its lateral faces are all rectangles or parallelograms. The volume of a prism can be calculated by multiplying the area of its base by its altitude. The formula for the volume of a prism is V = Bh, where V is the volume, B is the area of the base, and h is the altitude.

Given:

Length of the rectangular prism, l = 12 in

Height of the rectangular prism, h = 2 in

Width of the rectangular prism, w = 8 in

Carl needs to cover the total surface area of the prism, which is minimum he needs to cover.

Total surface area of rectangular prism= 2(lh+hw+lw)

TSA= 2(12 × 2 + 2×8 + 12 × 8)

      = 2(24 + 16 + 96)

      = 272 square inches

Minimum cloth required = 272 square inches.    

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The complete question is:

Answer: x=23

Step-by-step explanation:

Set the two equal to each other:

5x=3x+46

2x=46

x=23

What the polynomial said when it sat down for dinner is "I've got a lot of roots" (sounds like "I've got a lot of fruits") as a polynomial equation can have multiple roots.

Polynomial equations are equations in which the variables and coefficients are combined using the mathematical operations of addition, subtraction, and multiplication, but not division by a variable.

The degree of a polynomial equation is determined by the highest power of the variable in the equation.

Polynomial equations can have one or more variables and are often used in mathematical modeling to represent real-world phenomena. The solutions to polynomial equations can be found by factoring, using the quadratic formula, or using numerical methods.

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Step-by-step explanation:

We are given:

Sample size (n) = 35

Sample mean ($\bar{x}$) = 36 seconds

Population standard deviation ($\sigma$) = 8 seconds

Confidence level = 95%

We can find the margin of error using the formula:

Margin of Error = z*(σ/√n), where z is the z-score for the given confidence level, σ is the population standard deviation, and n is the sample size.

For a 95% confidence level, the z-score is 1.96 (from the z-table or calculator).

Putting the values in the formula, we get:

Margin of Error = 1.96*(8/√35) ≈ 2.68

The confidence interval is given by:

Lower Limit = $\bar{x}$ - Margin of Error

Upper Limit = $\bar{x}$ + Margin of Error

Substituting the values, we get:

Lower Limit = 36 - 2.68 ≈ 33.32

Upper Limit = 36 + 2.68 ≈ 38.68

Therefore, the 95% confidence interval for the mean time that all half-hour local TV news broadcasts devote to U.S. foreign policy is (33.32, 38.68).

Since the Lear Center's claim of the average time being 38 seconds falls within this interval, we can say that the sample data supports the Lear Center's claim at a 95% confidence level.

20.4 seconds separate the lowest 24% of the means.

Look up the z-scores for the given percentages (24% and 76%) using the z-table.

Since the green lights' lengths are normally distributed with a mean of 45 seconds and a standard deviation of 15 seconds, calculate the number of seconds corresponding to the z-scores.

For the highest 76%, the number of seconds is 45 + (0.68 * 15) = 45 + 10.2 = 55.2 seconds.
Now, subtract the lowest 24% of the means (34.8 seconds) from the highest 76% (55.2 seconds) to find the difference in seconds.

So, 20.4 seconds separate the lowest 24% of the means from the highest 76% in the state transportation study's sampling distribution of 75 traffic lights.

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To find the percent change, we need to use the formula:

percent change = (new value - old value) / old value * 100%

In this case, Max's old value is 73 and his new value is 96. So:

percent change = (96 - 73) / 73 * 100%

percent change = 23 / 73 * 100%

percent change = 0.3151 * 100%

percent change = 31.51%

Therefore, Max's percent change is 31.51%, rounded to the nearest whole percent, it is 32%.

The probability that the random variable has a value between 0.1 and 3.3 is 0.0256. Option b is correct answer.

Since the area under the density curve represents the total probability, we need to find the area between the vertical lines at x = 0.1 and x = 3.3, and under the curve.

First, we need to find the y-coordinates of the two horizontal lines. The line passing through (0, 125) and (8, 125) is parallel to the x-axis, so it has a constant y-coordinate of 125. The line passing through (8, 0) and (8, 125) is parallel to the y-axis, so it has an undefined slope and is a vertical line.

Therefore, we do not need to find its y-coordinate.

Next, we need to find the equation of the density curve. Since it is a uniform density curve, the height of the curve is constant over its entire length.

To find the height, we need to find the total area under the curve, which is given by the rectangle formed by the vertical lines at x = 0 and x = 8, and the horizontal lines at y = 0 and y = 125.

The width of the rectangle is 8, and the height is 1/125 (since the total area is 1 and the width is 8). Therefore, the height of the curve is 1/125 over its entire length.

Now, we can find the area between the vertical lines at x = 0.1 and x = 3.3, and under the curve.

The width of this area is 3.3 - 0.1 = 3.2, and the height of the curve is 1/125. Therefore, the area is:

3.2 × (1/125) = 0.0256

Therefore, the probability that the random variable has a value between 0.1 and 3.3 is 0.0256.

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The question is -

Using the following uniform density curve,

What is the probability that the random variable has a value between 0.1 and 3.3?

A) 0.5875 B) 0.0256 C) 0.3750 D) 0.2125

Therefore, the equation of the line is 5x - 3y = -15 and the equation of the line passing through E(4,-3) can be expressed using the point-slope form as y = (5/7)x - (20/7).

a) We can rewrite the provided line in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, to determine the slope.

y + 1 = (5/7)(x - 4) (x - 4)

y = (5/7)x - (20/7) - 1

y = (5/7)x - (27/7)

This line and the one we're looking for are parallel, thus their slopes are the same (5/7). Hence, the equation of the line passing through E(4,-3) can be expressed using the point-slope form:

y - (-3) = (5/7)(x - 4) (x - 4)

y = (5/7)x - (20/7)

b) The intercept form of the equation of a line with an x-intercept of 3 and a y-intercept of 5 is:

x/(-3) + y/5 = 1

The result of multiplying both sides by -15 (the least frequent multiple of -3 and 5) is as follows:

5x - 3y = -15

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The sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given: A city official would like to estimate the mean age of all residents of Stuart. The standard deviation of the ages of all residents of Stuart is known to be 16 years.

σ = 16 ..Population SD

The margin of error, E = 3.4

c = 90% = 0.90 ...confidence level

a = 1 - c = 1 - 0.90 = 0.1

a/2 = 0.1/2 = 0.05

Using the Z table,

z = 1.64

Now, sample size (n) is given by,

= (za/E)²

= (1.64×16/3.4)²

=59.56

Hence, the sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

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Answer:

please see the attached I put the answer.

Step-by-step explanation:

I put the steps I did, to graph it.