What is the surface area of a rectangular prism with dimensions 14 inches by 8 inches by 3 inches?

367 in2
356 in2
183.5 in2
135 in2

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

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Answer:

x=35

Step-by-step explanation:

because the angles are next to each other they are supplementary, which makes the total of the angle 180 degrees.

the equation would be:

180=x+14 +4x -9

add the like terms

180=5x =5

then subtract 5 from both sides

175=5x

then divide five from both sides

x=35

Answer:

no

Step-by-step explanation:

using the converse of Pythagoras' identity

If the square of the longest side is equal to the sum of the squares of the other 2 sides then the triangle is right.

longest side = 12 , then 12² = 144

7² + 10² = 49 + 100 = 149

since 149 ≠ 144 then the triangle is not right

Adding two numbers combines their values

Subtracting one number from another finds the difference between the two values

Multiplying two numbers gives the product of their values

Dividing one number by another gives the quotient of their values

By performing the same operations on both sides, to maintain the balance and validity of the equation.

Arithmetic Operations with Whole Numbers, Integers, Fractions, and Decimals:

1. Addition: Adding two numbers combines their values. For example,

2 + 3 = 5.

This operation is commutative, meaning the order of numbers doesn't affect the result.

2. Subtraction: Subtracting one number from another finds the difference between the two values. For example,

5 - 3 = 2.

This operation is not commutative since changing the order of numbers will yield a different result.

3. Multiplication: Multiplying two numbers gives the product of their values.

For example, 2 * 3 = 6.

This operation is commutative.

4. Division: Dividing one number by another gives the quotient of their values. For example,

6 / 2 = 3.

Division is not commutative, and it's important to note that division by zero is undefined.

When solving equations, what is done to one side of the equation must also be done to the other side. This is because an equation represents a balance or equality between two expressions. The goal is to isolate the variable on one side of the equation and keep the equation balanced.

By performing the same operation on both sides of the equation, maintain equality. If  only performed an operation on one side, the equation would become unbalanced, and the equality would be lost.

For example, let's solve the equation 2x + 5 = 11 for x:

1. Start with the equation:

2x + 5 = 11.

2. To isolate the term with x, subtract 5 from both sides:

2x + 5 - 5 = 11 - 5.

  This simplifies to:

2x = 6.

3. Finally, divide both sides by 2 to solve for x:

(2x) / 2 = 6 / 2.

  This gives the solution:

x = 3.

If only subtracted 5 from one side of the equation, the equality would be broken, and the solution would be incorrect. By performing the same operations on both sides, maintain the balance and validity of the equation.

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Answer:

6.7

Step-by-step explanation:

Answer:

Radius = 2.1 in.

Step-by-step explanation:

Pythagorean Theorem

•a²+4²=4.5²

•a²+16=20.25

•Subtract 16 from both sides

•a²=4.25

•Remove the square root

•√a²=√4.25

•a=2.06155

To give a 96% confidence interval for a population mean μ, the critical value to use is z* = 2.054. This corresponds to option (b).

In statistics, confidence intervals provide a range of values within which we can be reasonably confident that the true population parameter lies. The critical value is determined based on the desired level of confidence. For a 96% confidence interval, we need to find the critical value that leaves 2% of the area in the tails of the standard normal distribution.

By looking up the z-score in the standard normal distribution table, we find that the critical value z* for a 96% confidence level is approximately 2.054. Therefore, to give a 96% confidence interval for a population mean μ, the critical value to use is z* = 2.054, as stated in option (b).

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The solution is shown below:

In addition to two-way selection, most programming languages provide another selection concept known as multiway selection. Multiway selection chooses among several alternatives. C has two different ways to implement multiway selection: the switch statement and else-if construct.

Given condition:

adds 1 to minors if age is less than 18, adds 1 to adults if age is 18 through 64 and adds 1 to seniors if age is 65 or older.

if age < 18:

   minors += 1

else if age < 65:

   adults += 1

else:

   seniors += 1

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A real image is an image that is formed by the actual convergence of light rays, it can be projected onto a surface, located in the front or behind the lens, and can be inverted or upright depending on the properties of the lens or mirror used to form the image.

A real image is an image that is formed by the actual convergence of light rays. Real images can be projected onto a surface, such as a screen or a wall, and can be captured by a camera or viewed directly by an observer.

Real images can be produced by both converging and diverging lenses and can be located either in front of or behind the lens or mirror that forms them.

In the case of a converging lens, real images are located on the same side of the lens as the object, whereas in the case of a diverging lens, real images are located on the opposite side of the lens as the object.

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Answer:

The answer is C

Step-by-step explanation:

Answer:

Its c

Step-by-step explanation:

got it right on edge

Answer:

south america and north america

Step-by-step explanation:

By applying the distributive property of multiplication, the students that are correct in their approach to solving the problem are: Nico, Raj and Sandra.

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 5/2 as follows:

2/5(5 + x) = 8

Multiplying both sides by 5/2, we have:

5/2 × 2/5(5 + x) = 8 × 5/2

5 + x = 40/2

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 1/2 and then 5 as follows:

2/5(5 + x) = 8

Multiplying both sides by 1/2, we have:

1/2 × 2/5(5 + x) = 8 × 1/2

1/5(5 + x) = 4

Multiplying both sides by 5, we have:

5 × 1/5(5 + x) = 4 × 5

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would apply the distributive property of multiplication:

2/5(5 + x) = 8

2/5 × 5 + 2/5 × x = 8

2 + 2x/5 = 8

Subtracting 2 from both sides, we have:

2 - 2 + 2x/5 = 8 - 2

2x/5 = 6

Multiplying both sides by 5/2, we have:

5/2 × 2x/5 = 5/2 × 6

x = 30/2

x = 15.

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There are 52 cards in the deck and so the probability of guessing the card right is 1/52.

Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

We can find this probability by seeing that

=1/4×1/13

=1/52

Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.

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Answer:

The transformation is 5 units left and 4 units down

It is described as the rule:

or

830.72 sq in of wrapping paper does Tiana need to buy.

What is surface area of a cylinder?

The formula for the surface area of a cylinder is

 SA = 2πr^2 +2πrh = 2πr(r +h)

To find the total area of wrapping paper needed for one box, Tiana needs to add up the area of each of the six sides. The area of the top and bottom is,

22.2 inches * 4.8 inches = 106.56 square inches.

The area of each of the four sides is 14 inches * 22.2 inches = 308.8 square inches.

So, the total area of wrapping paper needed for one box is,

106.56 + 308.8 = 415.36 square inches.

Since, Tiana needs to wrap 2 boxes, she needs to buy twice that amount, which is 2 * 415.36 = 830.72 square inches.

Rounding to the nearest hundredth, Tiana needs to buy 830.72 sq in of wrapping paper.

Hence, 830.72 sq in of wrapping paper does Tiana need to buy.

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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To sketch the graph of the function `f(x) = - 5 sin 6 5 4 3 2 -&t -7n -65-4n -3n-2n - j -2 -3 -4 -5 -6 + - (a) 27 3 4 5 \ / 67 8`, we first need to identify its key features, which are:Amplitude = 5

Period = 2π/6

= π/3

Phase Shift = 2

The graph of the function `f(x) = - 5 sin 6x + 2` can be obtained by starting with the standard sine graph and making the following transformations:Reflecting it about the x-axis by multiplying the entire function by -1.

Multiplying the entire function by 5 to increase the amplitude.

Shifting the graph to the right by 2 units.For the specific domain provided in the question, we have:27 < 6x + 2 < 67 or 25/6 < x < 65/6.

This gives us a range of approximately 4.17 ≤ x ≤ 10.83.

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Answer: A :)

Step-by-step explanation:

Answer:

f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12

Step-by-step explanation:

Notice that the year data are evenly spaced. Check the first differences between the total number or units to see if the data set is linear.

First Differences

41 − 18 = 23

67 − 41 = 26

82 − 67 = 15

69 − 82 = −13

17 − 69 = −52

Because the first differences are not constant, a linear model is not the best model of the data. Check the second differences to see if the data set can be modeled by a quadratic function.

Second Differences

26 − 23 = 3

15 − 26 = −11

−13 − 15 = −28

−52 − (−13) = −39

Because the second differences of the independent variable are not constant, a quadratic model is not the best model of the data. Check the third differences to see if the data set can be modeled by a cubic function.

Third Differences

−11 − 3 = −14

−28 − (−11) = −17

−39 − (−28) = −11

The third differences are approximately the same so we will use a cubic function to represent the data.

Enter the data into a calculator. Plot the data and find the cubic regression equation that best models the data.

f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12

The statement that 99% of all confidence intervals with a 99% confidence level should contain the population parameter of interest is false.

A confidence interval (CI) is essentially a range of estimates for an unknown parameter in frequentist statistics. The most frequent confidence level is 95%, but other levels, such 90% or 99%, are infrequently used for generating confidence intervals.

The confidence level is a measurement of the proportion of long-term associated CIs that include the parameter's true value. This is closely related to the moment-based estimate approach.

In a straightforward illustration, when the population mean is the quantity that needs to be estimated, the sample mean is a straightforward estimate. The population variance can also be calculated using the sample variance. Using the sample mean and the true mean's probability.

Hence we can generally infer that the given statement is false.

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Answer: 105.3 m

Step-by-step explanation:

Given

Applied force is \(F=1.12\times 10^4\ N\)

Work done is \(W=1.18\times 10^6\ J\)

Work done is given by the displacement done by the force.

\(\Rightarrow W=F\cdot s\\\Rightarrow 1.18\times 10^6=1.12\times 10^4\cdot s\\\\\Rightarrow s=1.05\times 10^2\\\Rightarrow s=105.3\ m\)

Answer:

105

Step-by-step explanation:

the answer is 105

Answer:

1 and 5/10 or 1 and 1/2

Step-by-step explanation:

5 and 3/10 - 3 and 4/5 -

\(\frac{53}{10}\)  - \(\frac{19}{5}\)

=\(\frac{15}{10}\)

1 and 5/10 or 1 and 1/2

Answer:

Step-by-step explanation:

36

The polling agency must survey at least 3075 college students to estimate the proportion of students who voted in the last election within a 0.025 margin of error with a 95% confidence level.

In order to determine the sample size needed for a public opinion polling agency to estimate the proportion of college students who voted in the last election within a 0.025 margin of error, you can follow these steps:

1. Determine the desired level of confidence, usually expressed as a percentage (e.g., 95% confidence level).

2. Calculate the z-score corresponding to the desired level of confidence. For a 95% confidence level, the z-score is 1.96.

3. Use the formula for estimating sample size:
  n = (z^2 * p * (1-p)) / E^2

  Here, n is the sample size, z is the z-score, p is the estimated proportion of students who voted, E is the desired margin of error (0.025 in this case).

4. Since we don't know the actual proportion (p) of students who voted, we can use the conservative assumption of p = 0.5 (50%), as this will result in the largest required sample size.

5. Plug the values into the formula:
  n = (1.96^2 * 0.5 * (1-0.5)) / 0.025^2
  n = (3.8416 * 0.5 * 0.5) / 0.000625
  n = 1.9208 / 0.000625
  n ≈ 3074.08

6. Since the sample size must be a whole number, round up to the nearest whole number: n = 3075.

Therefore, the polling agency must survey at least 3075 college students to estimate the proportion of students who voted in the last election within a 0.025 margin of error with a 95% confidence level.

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Answer:

Step-by-step explanation:

\(13x + 14y - 12 = 14x + 15y + 13\)

Collect like terms

\(14y-15y=14x-13x+13+12\)

Simplify

\(-y =x +25\)

Multiply through by -1(to reverse the inequality)

\(-1(-y=x+25)\\\\y =-x-25\)

Answer:

y= -x - 25

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Hope this helps

To determine the number of yards Ben will walk in one hour, we need to convert his speed from feet per second to yards per hour.

First, let's convert Ben's speed from feet per second to feet per hour: Speed in feet per hour = Speed in feet per second * 60 seconds * 60 minutes. Speed in feet per hour = 6 ft/s * 60 s * 60 min = 21,600 ft/hour. Next, we need to convert the speed from feet per hour to yards per hour. Since there are 3 feet in a yard: Speed in yards per hour = Speed in feet per hour / 3. Speed in yards per hour = 21,600 ft/hour / 3 = 7,200 yards/hour.

Therefore, Ben will walk 7,200 yards in one hour if he maintains a steady pace of 6 ft per second.

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Answer:

X=75 Bottom is 75, right is 105, up is 70, left is 110.

Step-by-step explanation:

4.4x+30=360

4.4x=330

x=75