given two sides of a triangle, find a range of possible lengths for the third side. a) 24 ft, 52 ft answer < x < answer b) 16 km, 17 km answer < x < answer

The given function f(x) = 16^x is an exponential function.

An exponential function is a mathematical function in which an independent variable appears in the exponent. In this case, the base of the function is 16, and the variable x is the exponent.

In the given function f(x) = 16^x, the variable x represents the exponent to which 16 is raised. As x increases, the function value grows rapidly, indicating exponential growth. The base of 16 signifies that the function is being multiplied by 16 for each unit increase in the exponent.

In contrast, a linear function has a constant rate of change, and a quadratic function has a squared term. The given function does not involve a linear relationship or a squared term, which confirms that it is not a linear or quadratic function.

Therefore, based on the given form f(x) = 16^x and the exponential growth nature of the function, we can classify it as an exponential function.

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Answer:

840cm³is a required answer.

Answer:

x : 4y

Step-by-step explanation:

For every one chocolate he buys, he gains 4 free game tokens

The points 1 and 2 are both on lines {1, 2, 5, 6} and {2, 3, 4, 6}. Thus, these two lines share the two points 1 and 2 and do not satisfy the third axiom of incidence geometry.

Q1) Assume the four axioms of incidence geometry. Prove the following claims: (a) Given a line L and a point A that lies on L, there exists a point B that lies on L and is distinct from A. (b) Given any line, there exists a point that does not lie on it.(a)  Proof: Assume that A is a point on line L. Since we have a line L, the first three axioms imply that there are at least two points on this line. Let the two points on line L be A and B. Therefore, B is a point on L and is distinct from A. (b) Proof: Let L be a line. By the first axiom of incidence geometry, there are at least two points on this line. Let these two points be A and B. Since there are at least three points in the plane, then there exists a point C which is not collinear with A and B. By the second axiom, line AC exists, and C is not on L. Therefore, there exists a point C that does not lie on line L. Q2) Define the Three-Ring Geometry as follows: a point is any one of the numbers 1, 2, 3, 4, 5, 6; a line is any one of the sets {1, 2, 5, 6}, {2, 3, 4, 6}, or {1, 3, 4, 5}; and lies on means is an element of. Provide a sketch of the geometry and determine if it is a model of incidence geometry. Explain why? The figure below is a sketch of the Three-Ring Geometry.The Three-Ring Geometry is not a model of incidence geometry because the third axiom is not satisfied. The third axiom states that given any two distinct points, there exists a unique line that passes through both of them. However, this is not true for the Three-Ring Geometry. For example, the points 1 and 2 are not collinear, yet they do not determine a unique line. The points 1 and 2 are both on lines {1, 2, 5, 6} and {2, 3, 4, 6}. Thus, these two lines share the two points 1 and 2 and do not satisfy the third axiom of incidence geometry.

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Only (d) 1 equation can you write to represent a single line using a point-slope equations

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

Equation = Linear equation

A linear equation can only be represented with one equation

When it is represented with multiple equations, the equations are equivalent equations

This means that the equations can be converted to one another

Hence, the solution is (d) 1 equation

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Answer:

the right answer is 50,40,30

Step-by-step explanation:

where Hypotenuse=50, Opposite=30, Adjacent=40

Answer:

a) Range = 7.7

b) Standard deviation = 2.78

Step-by-step explanation:

Find (a) the range and (b) the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4,5.6, 7.0,3.3 Round to the nearest hundredth if necessary

We are rearrange the given data:

2.4, 2.6, 3.3, 4.8, 5.6, 7.0, 8.2, 10.1

a) Range

This is calculated as: Highest value - Lowest value

Highest value = 10.1

Lowest value = 2.4

Range = 10.1 - 2.4

= 7.7

b) Standard deviation

Step 1

We find the mean

= Sum of values/ Number of value

= 2.4 + 2.6+ 3.3+ 4.8+ 5.6+7.0+8.2+10.1/8

= 44/8

= 5.5

The formula for standard deviation

= √(x - mean)²/n - 1

= √((2.4 - 5.5)² +( 2.6 - 5.5)²+ (3.3 - 5.5)²+ (4.8-5.5)²+ (5.6 - 5.5)²+(7.0-5.5)² +(8.2 - 5.5)² +(10.1-5.5)2)/8 - 1

= √54.06/7

= √7.722857143

= 2.779002904

approximately = 2.78

Answer:

a=8

Step-by-step explanation:

The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.

In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:

Each term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.

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The full question is:

How many terms are in the following expression 6 + 2 x - 4 y + 5 z

Answer:

10) \(10v^2-19v+6\)

11) \(15x^3-7x^2-29x+20\)

Step-by-step explanation:

Well first let's make the box.

10)

Look at the image below ↓

\(10v^2-19v+6\)

11)

Look at the image below ↓

\(15x^3-7x^2-29x+20\)

Thus,

number 10 is \(10v^2-19v+6\) and number 11 is \(15x^3-7x^2-29x+20\).

Hope this helps :)

The area between the curves y = 2x and y = \(x^2 - 3,\) within the interval x = -5 to x = 3, is 8/3 or approximately 2.67 square units.

To find the area between the curves, we need to determine the region bounded by the curves y = 2x and y = \(x^2 - 3\), within the given interval x = -5 to x = 3.First, let's find the points of intersection between the two curves.

Setting the equations equal to each other, we have:\(2x = x^2\) - 3.Rearranging the equation, we get: \(x^2 - 2x - 3\) = 0Factoring the quadratic equation, we have:(x - 3)(x + 1) = 0

So, the solutions are x = 3 and x = -1. Next, we integrate the difference between the upper curve (\(y = x^2 - 3\)) and the lower curve (y = 2x) within the interval [-1, 3] to find the area. The integral is given by: A = ∫[-1,3] [\((x^2\)- 3) - (2x)] dx.

Simplifying the equation, we have:\([-1,3] (x^2 - 2x - 3) dx\) To integrate, we split the integral into two parts: A = ∫[-1,3] \(x^2 dx\)  - ∫[-1,3] 2x dx - ∫[-1,3] 3 dx Integrating each term, we obtain: A = [1/3 * \(x^3\)] [-1,3] - [\(x^2\)] [-1,3] - [3x] [-1,3] Evaluating the integral at the upper and lower limits, we get:

A = (1/3 * \(3^3\) - 1/3 * \((-1)^3) - (3^2 - (-1)^2\)) - (3 * 3 - 3 * (-1)) Simplifying the expression further, we have: A = (27/3 + 1/3) - (9 - 1) - (9 + 3) A = 28/3 - 8 - 12 A = 28/3 - 20/3 A = 8/3

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The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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Answer:

Equally likely

Step-by-step explanation:

Hope this is right!

Answer:

see below

Step-by-step explanation:

x² = 30

x = ±√30 (take the square root of both sides)

The value of X in the equation is:

√30 or 5.48

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.

If X to the second power equals 30 can be written as:

X² = 30

To find the value of X, take the square root of both sides of the equation. That is:

√X² = √30

X = √30

X = 5.48

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The true statements about the result of simplifying the given polynomial expression are: 1. The resulting expression will be a polynomial. 2. The degree of the resulting polynomial will be less than or equal to 3.

To simplify the given polynomial expression, we need to apply the distributive property and combine like terms. Let's break down the given expression step by step:

t^3(8+9t)-(t^2+4)(t^2-3t)

Expanding the terms within the parentheses:

= 8t^3 + 9t^4 - (t^4 - 3t^3 + 4t^2 - 12t)

Combining like terms:

= 8t^3 + 9t^4 - t^4 + 3t^3 - 4t^2 + 12t

Simplifying further:

= (9t^4 - t^4) + (8t^3 + 3t^3) - 4t^2 + 12t

= 8t^4 + 12t^3 - 4t^2 + 12t

The resulting expression is a polynomial with terms of varying degrees (4, 3, 2, and 1). The highest degree term is 8t^4, which means the degree of the resulting polynomial is 4.

Therefore, statement 1 is true. Additionally, since the highest degree is 4, which is less than or equal to 3, statement 2 is also true.

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Answer:

width is 2√33 cm

Step-by-step explanation:

you will make a right triangle with hypothenuse 14 , one side 8 and the other side x is the width.

use Pythagorean Th.

14² = 8² + x²

x² = 14² -8²

x² = 132

x = √132 = 2√33

Answer:

b = -10

c = 25

Step-by-step explanation:

Since the only solution to x is 5 that mean answer will look something like this:

(x-5) (x-5) = 0

x(x-5) -5(x-5)

x^2 -5x -5x + 25

x^2 -10x + 25

This is same as x^2 + bx + c = 0

where b is -10 and c is 25

Using the t-distribution, as we have the standard deviation for the sample, it is found that it cannot be concluded that the diet has a long-term effect.

At the null hypotheses, it is tested if there is no difference in the weights, that is:

\(H_0: \mu_A - \mu_B = 0\)

At the alternative hypotheses, it is tested if the weights decrease, that is:

\(H_1: \mu_A - \mu_B < 0\)

Using a calculator, for each sample, we have that:

\(\mu_B = 210.8, s_B = 33.85, sE_B = \frac{33.85}{\sqrt{15}} = 8.74\)

\(\mu_A = 207.2, s_A = 33.47, sE_A = \frac{33.47}{\sqrt{15}} = 8.64\)

Hence, for the distribution of differences, we have that:

\(\overline{x} = \mu_A - \mu_B = 207.2 - 210.8 = -3.6\)

\(s = \sqrt{sE_B^2 + sE_A^2} = \sqrt{8.74^2 + 8.64^2} = 12.3\)

It is given by:

\(t = \frac{\overline{x} - \mu}{s}\)

In which \(\mu = 0\) is the value tested at the null hypothesis.

Then:

\(t = \frac{\overline{x} - \mu}{s}\)

\(t = \frac{-3.6 - 0}{12.3}\)

\(t = -0.29\)

Considering a left-tailed test, as we are testing if the mean is less than a value, with a standard significance level of 0.05 and 15 + 15 - 2 = 28 df, the critical value is of \(t^{\ast} = -1.7\).

Since the test statistic is greater than the critical value for the left tailed test, it cannot be concluded that the diet has a long-term effect, as the null hypothesis is not rejected.

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Answer:

4. \(4x^{2} +2x-2\)

Step-by-step explanation:

To add these two equations together, you have to combine like terms.  

1. \(x^{2} +3x^{2} = 4x^{2}\)

2. \((-3x)+5x = 2x\)

3. 7 - 9 = -2

Then you just combine all of these terms together into one equation and you have your answer.

Hope this helped!

The diameter of a hemisphere with a volume of 863 in^3 is 40.596 in.

In the given question we have to find the diameter of a hemisphere with a volume of 863 in^3.

As we know that the volume of hemisphere is (2/3)πr^3 cubic unit.

The given volume of hemisphere is 863 in^3.

Now we firstly finding the radius of hemisphere then we find the diameter of hemisphere

The volume of hemisphere = 863 in^3

(2/3)πr^3 = 863

We know that; π = 22/7

(2/3) * (22/7) *r^3 = 863

44/21 * r^3 = 863

Multiply by 21/44 on both side, we get

r^3 = 863*21/44

r^3 = 411.89

r^3 = 412 (approx)

Taking cube root on both side, we get

r = 20.298

Now finding the diameter,

Diameter = 2*radius

Diameter = 2*20.298

Diameter = 40.596 in

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

The area of this shape is \(50cm^2\).

Step-by-step explanation:

To find the area of this figure, you only need to know the area of the rectangle and the area of the triangle. The area of the rectangle would be 5 * 6 = \(30cm^2\). Since the length of the rectangle plus the base of the triangle is equivalent to 14, that means the base of the triangle is equal to 14 - 6 = 8 cm. The formula for the area of a triangle is \(\frac{1}{2} bh\), the base you now know is 8 cm, and the height is 5 cm, which means the area of the triangle would be \(\frac{1}{2} *5*8\) = \(\frac{1}{2} * 40\) = \(20cm^2\). Add the area of the rectangle to the area of the triangle and you'll get the area of the entire shape, which is 30 + 20 = \(50cm^2\).

13% of 11900 films are action films =1547 films.

Answer:

\({ \tt{ = \frac{13}{100} \times 11900 }} \\ = 1547 \: action \: films\)

The equation that best represents Area covered by the mold and the number of days is A(t) = e^2t

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Exponential growth happens when an initial population increases by the same percentage or factor over equal time increments or generations.

Exponential growth is represented by ;

P(t) = p(o) e^kt

p(t) = population at time t

p(o) is the initial population

for the area,

A(t) = A(o) e^kt

where A(t) = Area at time t

A(o) = initial area

A(o) = 1

k = 2

Therefore A(t) = e^2t

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The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.

It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.

The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.

The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.

A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.

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The probability of a human character being chosen when the selection is done randomly is 1/3.

To find the probability of a human character being chosen when the selection is done randomly, we need to determine the total number of possible character choices and the number of choices that correspond to a human character.

There are 8 animals and 4 humans, making a total of 8 + 4 = 12 possible character choices.

Since the selection is done randomly, each character has an equal chance of being chosen. Therefore, the probability of selecting a human character is the number of human characters divided by the total number of character choices.

The probability of selecting a human character is:

Number of human characters / Total number of character choices

Substituting the values:

4 / 12

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:

4 / 12 = 1 / 3

Therefore, the probability of a human character being chosen when the selection is done randomly is 1/3.

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Answer:

1,3 is the answer... if you look down here↓:

Step-by-step explanation: