12
14
(hyp)2 = (leg)2 + (leg)
1) Which side is the hypotenuse?
2) Fill-in the Pyth. Thm. Equation:
1
1)2 = (14) ²+ (
) 2
3) Solve for c. Round to the nearest tenth.
C =

The value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.

To evaluate the definite integral 2t sin(-9t)dt using integration by parts, we first need to choose u and dv.

Let u = 2t and dv = sin(-9t)dt. Then du/dt = 2 and v = (-1/9)cos(-9t).

Using the integration by parts formula ∫udv = uv - ∫vdu, we can evaluate the definite integral as follows: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - ∫(-2/9)cos(-9t)dt

Next, we need to evaluate the integral on the right-hand side.

Let u = -2/9 and dv = cos(-9t)dt. Then du/dt = 0 and v = (1/9)sin(-9t).

Using integration by parts again, we get: ∫cos(-9t)dt = (1/9)sin(-9t) + ∫(1/81)sin(-9t)dt = (1/9)sin(-9t) - (1/729)cos(-9t)

Substituting this result back into the original equation, we get: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - [(-2/9)(1/9)sin(-9t) + (2/9)(1/729)cos(-9t)]

Now, we can evaluate the definite integral by plugging in the limits of integration (0 and π) and simplifying:

∫π0 2t sin(-9t)dt

= [-2π/9 cos(-9π)] - [(-2/9)(1/9)sin(-9π) + (2/9)(1/729)cos(-9π)] - [(-2/9)cos(0)]

= [-2π/9 cos(9π)] - [(-2/9)(1/9)sin(9π) + (2/9)(1/729)cos(9π)] - [(-2/9)cos(0)]

= [-2π/9 (-1)] - [(-2/9)(1/9)(0) + (2/9)(1/729)(-1)] - [(-2/9)(1)]

= (2π/9) + (2/6561) + (2/9) = 5.25π

Therefore, the value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.

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Answer:

this is beautiful ty for blessing my eyes it does NOT SUCK

Work Shown:

d = diameter = 12 ft

r = radius = d/2 = 12/2 = 6 ft

circumference = 2*pi*r = 2*pi*6 = 12pi feet

area = pi*r^2 = pi*6^2 = 36pi square feet

Answer:

$10:$30:$50

Step-by-step explanation:

1:3:5

1+3+5 = 9

90 / 9 = 10

1 x 10 = 10

3 x 10 = 30

5 x 10 = 50

$10:$30:$50

Hope this helps.

Therefore , the solution to the given equation problem can be represented as  t= 1+h.

A mathematical expression of the form A=B that is used to arrive at values or solutions is known as an equation. Equations frequently include variables (unknowns). The equation x + 4 = 14, where x is a variable, serves as an example. Finding the value of x that results in the equal (=) sign being true is the goal. In this situation, the solution is x = 10.

Here,

To write a polynomial in terms of h for the average velocity from t=1 to the time h

We thus write it as,

t = 1 +  h

Where t is the time and h not equal to zero.

Thus , we can write the expression as

=> t= 1+h

Therefore , the solution to the given equation problem can be represented as  t= 1+h.

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there are no values of x that make the equation true.

There are 26 automobiles and 13 vans available for the field excursion.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. A mathematical statement that expresses the connection between two values is simply characterized as an equation. In an equation, the two values are usually equated by an equal sign. Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). A linear equation can include several variables.

Here,

If c represents the number of cars and v represents the number of vans,

5c+8v=234

c=2v

10v+8v=234

v=234/18

v=13 vans

c=26 cars

The number of cars for field trip is 26 and number of vans is 13.

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Answer:20

Step-by-step explanation:

i wrote 10 for some reason

Answer:

give me brainlist please

Step-by-step explanation:

We can use the formula for conditional probability and the formula for the probability of the union of events to find P(C).

Using the formula for conditional probability, we can find P(A|B) = P(A n B) / P(B) = 0.05 / 0.26 = 0.192

Using the formula for conditional probability again, we can find P(A|C) = P(A n C) / P(C) = 0.05 / P(C)

Since A and C are independent events, we know that P(A|C) = P(A), so we can write:

0.05 / P(C) = 0.24

Solving for P(C) we get P(C) = 0.05/0.24 = 0.208

Alternatively, we can use the formula for the probability of the union of events:

P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)

We know that P(A u B u C) = 1 - P((A u B u C)^/) = 1 - 0.33 = 0.67

and we know the values of P(A), P(B), P(A n B), P(A n C), P(B n C), P(A n B n C)

We can substitute these values into the above equation to find P(C)

P(C) = 0.67 - 0.24 - 0.26 + 0.05 + 0.05 + 0.05 - 0.02 = 0.208

So P(C) = 0.208

The coefficient of determination in this scenario is 0.747, which means that approximately 74.7% of the variation in the dependent variable is explained by the independent variable(s). The remaining 25.3% is unexplained and may be due to other factors or errors in the model.

The coefficient of determination, also known as R-squared, is a statistical measure that represents the proportion of the variation in the dependent variable that is explained by the independent variable(s).

It is calculated as 1 - (SSE/SST).

Given that the SST is 225 and SSE is 57, we can calculate the coefficient of determination as follows:

R-squared = 1 - (SSE/SST)
R-squared = 1 - (57/225)
R-squared = 0.747

Therefore, the coefficient of determination in this scenario is 0.747, which means that approximately 74.7% of the variation in the dependent variable is explained by the independent variable(s).

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The equation of the amount to be paid by anyone using the ride in slope intercept form is; y = 0.5x + 10

The general form of the equation of a Line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Now, we are told that;

Amount charge by Winter Wonderland per child = $0.50

We are told that there is a separate entrance fee.

Amount of times todd sled down the hill = 16 times

Amount paid by todd = $18

Thus, using the slope intercept form, we have;

18 = 0.5(16) + b

18 = 8 + b

b = 10

Thus, the equation of this amount to be paid in slope intercept form is;

y = 0.5x + 10

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Explanation

We are given a right-angled triangle with the following:

We are required to determine the missing side (i.e. the value of x).

We can achieve this by using the Pythagorean theorem as follows:

Hence, the answer is:

Both approaches to geometry have their strengths and weaknesses and can be useful depending on the context and problem at hand.

What is Euclidean geometry?

Euclidean geometry is a branch of mathematics that deals with the study of points, lines, angles, planes, and solid figures in two- and three-dimensional space.

In Euclidean geometry, the focus is on the properties and relationships of geometric figures without the use of numerical measurements. It is a deductive system of mathematics that starts with a set of axioms, definitions, and postulates, and uses logical reasoning to deduce new results. This approach to geometry is useful for developing logical thinking and problem-solving skills and has been used for centuries to develop our understanding of geometric concepts and their applications.

On the other hand, in analytical geometry, the focus is on the relationship between algebra and geometry, using positions of points in a Cartesian coordinate system. It is a more algebraic approach to geometry that involves representing geometric objects as equations or functions. This approach to geometry is useful for applications that involve quantitative analysis, such as physics, engineering, and computer graphics.

Therefore, both approaches to geometry have their strengths and weaknesses and can be useful depending on the context and problem at hand.

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Answer: ion know help ur self

Step-by-step explanation:

The missing number refers to the sum of all the given numbers

The probability would be P = 3/40.

option B is correct. To give a margin of error within in estimating a population proportion with 99% confidence, the formula for calculating sample size is:n = (z² * p * q) / E²

Where:n = Sample sizeZ = Confidence intervalP = Estimated proportionQ = (1 - P)E = Margin of errorAs we have to calculate the sample size, we rearrange the above formula and get:n = (z² * p * q) / E²Given: E = 0.01, Z = 2.576 (for 99% confidence interval)

Now, we need to estimate the proportion of the population (p). If we don't have any estimates or data, we can assume 0.5 for p, which gives the maximum sample size. Therefore:p = 0.5q = 1 - p = 1 - 0.5 = 0.5n = (z² * p * q) / E²n = (2.576² * 0.5 * 0.5) / 0.01²n = 663.85Rounding the value up to the nearest integer, the sample size needed to give a margin of error within in estimating a population proportion with 99% confidence is 664.Hence, option B is correct.

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A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

Answer:

The value of 3⁴ is:

3⁴ = 3 × 3 × 3 × 3 = 81

Therefore, 3⁴ is equal to 81.

b. The distribution is roughly symmetric.

This is because the shape of the boxplot resembles a bell-shaped curve, which is symmetric. The boxplot has a box that extends from 12 to 18, with a vertical line segment through the box at 16. This indicates that the median of the distribution is 16.

There are also two horizontal line segments extending from the left and right sides of the box to 0 and 20, respectively. This indicates that the distribution is roughly symmetric, with the majority of the data concentrated around the median. The symmetric shape of the distribution suggests that the data is not skewed to either side.

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Answer:

x = -16

Step-by-step explanation:

given:

\(h(x) = -2x - 4\)

solve for x, when:

\(h(x) = 6\)

~~~~~~~~~~~~

➡️ \( x = -2(6) - 4 \)

➡️ \( x = -12 - 4\)

➡️ \( x = -16 \)

The solution of x when the function h ( x ) = 6 is x = -5

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as h ( x )

Now , the value of h ( x ) is given by

h ( x ) = -2x - 4   be equation (1)

On simplifying the function rule , we get

when h ( x ) = 6

Substitute the value of h ( x ) = 6 , we get

6 = -2x - 4

Adding 4 on both sides , we get

-2x = 10

Divide by -2 on both sides , we get

x = 10 / -2

x = -5

Therefore , the value of x is -5

Hence , the equation is x = -5

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Answer:

1 over 36

Step-by-step explanation:

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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Answer:

To perform a 180° rotation about the origin, we simply switch the signs of the coordinates and flip them across the x-axis. So, the new coordinates of the vertices will be:

(2, 1) -> (-2, -1)

(4, 2) -> (-4, -2)

(2, 4) -> (-2, -4)

Plotting these points and connecting them, we get the triangle:

      (2, 4)

        *

       / \

      /   \

(-2, -4)---(-4, -2)

    (2, 1)

After the 180° rotation, the triangle is flipped upside down and its position is mirrored across the origin.

Step-by-step explanation:

The angle pair that is a pair of vertical angles from the given option is:

B. ∠TRS and ∠VRW.

What does the phrase "vertical angles simple" mean?

An intersection of two lines produces a vertical angle, which is a pair of opposed angles. Vertical angles in the illustration are 1 and 3 respectively. Likewise, 2 and 4 are. Congruent vertical angles are universal.

The lines shown are attached below (see attachment).

Vertical angles are two set of angles that are formed lying opposite each other when two straight lines intersect.

From the diagram given:

<WRS is directly opposite <VRT, therefore, they are a pair of vertical angles that are formed.

<TSR is directly opposite <VRW, therefore, they are also a pair of vertical angles.

Thus, the angle pair that is a pair of vertical angles from the given option is: B. ∠TRS and ∠VRW.

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Answer: C: 10/3

Step-by-step explanation:

An improper fraction is a fraction that's top number (numerator) is bigger than the bottom number (denominator)

Answer:

10/3

Step-by-step explanation:

Improper fractions are fractions where there is a larger number in the numerator than there is in the denominator. The numerator is the number on the top of the fraction, and the denominator is on the bottom. 10 is on top and it is greater than 3, so it is an improper fraction. Improper fractions can also be simplified. 10/3 can be simplified to 3 1/3.

Hope this helps!

Answer:

its irrational

7.07106781187

look at how the decimals are all over the place

if it was rational it would've been something like this

7.070707070707 or 7.071071071071

hope that answers your question

Step-by-step explanation:

Non-linear relationships are those depicted by curved graphs. A curve denotes a variation in the rate (or speed) of a response over time.

Graphs representing reaction rates frequently have curves. A curve denotes a variation in the rate (or speed) of a response over time, while a straight line would represent a constant rate of reaction.

If a curve or straight line becomes horizontal, it means the reaction's rate has reached its maximum level and cannot vary any further.

Lines of best fit can also be used to spot outliers and anomalous data that won't fall along the line of greatest fit. Additionally, lines of best fit may be extrapolated (extended). This enables us to forecast values that are outside the range of the given data using a graph.

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Answer:

a = 2

b = 4

Step-by-step explanation:

Δy   = 2x + a.................for turning point, Δy/Δx = 0.

Δx

0 = 2x + a

x = -a/2.........from ( -1, 3), x = -1...............so,

-1 = -a/2.................a = 2.

y = x^2 + ax + b.

y = 3  ,    a = 2.................substitute.

3 = (-1)^2 + 2(-1) + b

3 = 1 -2 + b

b = 4

Answer:

The turning point of a parabola is the vertex

Vertex form of a quadratic equation: \(\sf y=a(x-h)^2+k\)

(where (h, k) is the vertex and a is the coefficient of the variable x²)

Given:

Therefore, a = 1

Substituting a = 1 and the given vertex into the equation:

\(\sf \implies y=1(x-(-1))^2+3\)

\(\sf \implies y=(x+1)^2+3\)

\(\sf \implies y=x^2+2x+1+3\)

\(\sf \implies y=x^2+2x+4\)

Therefore, a = 2 and b = 4

Answer:

1,044

Step-by-step explanation:

14 x 46 = 644

16 x 25 = 400

644 + 400 = 1,044