Find the value of x

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The vector parametrization for the equation of line passing through points (2,5,3) and (6,9,6) is: r(t)= (2i + 5j + 3k) + μ(6i + 9j + 6K).

WE know that parameterization of the a curve is provided by each vector-valued function.

Since the pair of equations x = x (t) and y = y (t) that express the coordinates of a point along a curve in terms of such a parameter is known as a parameterization of a curve.

Given passing points:

(2,5,3) and (6,9,6)

In vector form;

Let vector a = 2i + 5j + 3k

Let vector b = 6i + 9j + 6K

Let μ be any constant.

Then, using the vector parametrization:

The equation of line in vector form for the given points is;

r(t)= a + μb

r(t)= (2i + 5j + 3k) + μ(6i + 9j + 6K)

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Correct question:

Find the vector parametrization for equation of the line that passes through the points (2,5,3) and (6,9,6). (Give your answer in the form 〈∗,∗,∗〉. Express numbers in exact form. Use symbolic notation and fractions where needed.)

r(t)=?

The freezing point is normally distributed with mean of 0 degrees celsius and a standard deviation of 1 degree celsius. The probability of getting a score between -1.5 and 2.5 is 0.9332.

To find the probability of getting a score between -1.5 and 2.5, we need to find the area under the normal distribution curve for this range using a z-score table.

First, we need to convert the range into standard units, which is done by subtracting the mean and dividing by the standard deviation:

z1 = ( -1.5 - 0 ) / 1 = -1.5

z2 = ( 2.5 - 0 ) / 1 = 2.5

Next, we look up the z-scores in a z-score table to find the area under the normal curve:

P(-1.5 < Z < 2.5) = 0.9332

This means that the probability of getting a score between -1.5 and 2.5 is 0.9332 or 93.32%.

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Therefore , the solution of the given problem of unitary method comes out to be Amy creates the sand masterpiece by using 8 cups of sand.

To complete the assignment, use the tried-and-true straightforward methodology, the real variables, and any pertinent details from the preliminary and specialised questions. In response, customers might be given another opportunity to range sample the products. In the absence of such changes, major advances in our knowledge of programmes will be lost.

Here,

If Amy fills 16 bottles with 1/2 cup of each colour of sand, the total amount of sand she uses may be calculated by multiplying the total number of bottles by the amount of sand in each container.

The total quantity of sand utilised is thus:

=> 16 x 1/2 = 8 cups

Amy creates the sand masterpiece by using 8 cups of sand.

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The point in the feasible region maximizes the objective function is (5, 0)

The given parameters are

Objective function: C = 7x - 3y

Subject to (i.e. the constraints)

    x ≥  0, y ≥ 0

    y ≤ 1/5x + 2, 5 ≥ y + x

Next, we plot the graph of the constraints (see attachment)

This is done by entering the inequalities in a graphing calculator

From the graphing calculator, we have the feasible regions to be

(5, 0), (2.5, 2.5) and (0, 5)

Substitute (5, 0), (2.5, 2.5) and (0, 5) in the objective function: C = 7x - 3y

So, we have

(5, 0): C = 7(5) - 3(0)

C = 35

(2.5, 2.5): C = 7(2.5) - 3(2.5)

C = 10

(0, 5): C = 7(0) - 3(5)

C = -15

The value 35 is greater than 10 and -15

The coordinates at this value are (5, 0)

Hence, the coordinates is (5, 0)

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The L1 norm of vector A is greater than or equal to the L1 norm of vector B.

Basically, if the L2 norm of vector A is greater than the L2 norm of vector B, it is indeed always true that the L1 norm of vector A is greater than or equal to the L1 norm of vector B. The Lp norm is defined as follows:

\(||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p)^(1/p),\)

where x = [x₁, x₂, ..., xₙ] is a vector.

For the L2 norm (p = 2), the formula is:

\(||x||_2 = \sqrt(|x_1|^2 + |x_2|^2 + ... + |x_n|^2).\)

For the L1 norm (p = 1), the formula is:

\(||x||₁ = |x_1| + |x_2| + ... + |x_n|.\)

If ||A||₂ > ||B||₂, it implies that:

\(\sqrt(|A_1|^2 + |A_2|^2 + ... + |A_n|^2) > \sqrt(|B_1|^2 + |B_2|^2 + ... + |B_n|^2).\)

Squaring both sides of the inequality, we get:

\(|A_1|^2 + |A_2|^2 + ... + |A_n|^2 > |B_1|^2 + |B_2|^2 + ... + |B_n|^2.\)

Since the squares of the magnitudes are positive, we can conclude that:

\(|A_1| + |A_2| + ... + |A_n| > |B_1| + |B_2| + ... + |B_n|.\)

Therefore, the L1 norm of vector A is greater than or equal to the L1 norm of vector B.

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Step-by-step explanation:

\( \bf➤ \underline{Given-} \\ \)

\(\sf{x^{2013} + \frac{1}{x^{2013}} = 2}\\\)

\( \bf➤ \underline{To\: find-} \\ \)

\(\sf {the\: value \: of \: x^{2022} + \frac{1}{x^{2022}}= ?}\\\)

\( \bf ➤\underline{Solution-} \\ \)

Let us assume that:

\( \rm: \longmapsto u = {x}^{2013} \)

Therefore, the equation becomes:

\( \rm: \longmapsto u + \dfrac{1}{u} = 2\)

\( \rm: \longmapsto \dfrac{ {u}^{2} + 1}{u} = 2\)

\( \rm: \longmapsto{u}^{2} + 1 = 2u\)

\( \rm: \longmapsto{u}^{2} - 2u + 1 =0\)

\( \rm: \longmapsto {(u - 1)}^{2} =0\)

\( \rm: \longmapsto u = 1\)

Now substitute the value of u. We get:

\( \rm: \longmapsto {x}^{2013} = 1\)

\( \rm: \longmapsto x = 1\)

Therefore:

\( \rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 1 + 1\)

\( \rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 2\)

★ Which is our required answer.

\(\textsf{\large{\underline{More To Know}:}}\)

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(x + a)(x + b) = x² + (a + b)x + ab

(x + a)(x - b) = x² + (a - b)x - ab

(x - a)(x + b) = x² - (a - b)x - ab

(x - a)(x - b) = x² - (a + b)x + ab

Answer:

D. 2/10, 3/10, 4/10

Step-by-step explanation:

D. is the correct answer because the fractions have a common denominator of 10, whereas the other answer choices do no.

D. has similar fractions

Good luck to you!

Answer:

x=0,x=1/4

Step-by-step explanation:

2x=8(x^2)

Subtract 8(x^2) from both sides

2x-8x^2=8x^2-8x^2

Simplify

2x-8x^2=0

Factor 2x-8x^2;

2x-8x^2

=-8xx+2x

Rewrite 8 as 2*4

=-2*4xx+2x

Factor out common term -2x

=-2x(4x-1)

-2x(4x-1)=0

x=0 or 4x-1=0

Solve 4x-1=0;x=1/4

4x-1=0

Add 1 to both sides

4x-1+1=0+1

Simplify

4x=1

Divide both sides by 4

4x/4=1/4

Simplify

x=1/4

The solutions to the quadratic equation are;

x=0,x=1/4

Hope this helped!!!!

Answer:

If all other factors are controlled, and the only variable being changed is the new medication, then Byron can conclude that the new medication is effective at reducing coughing. This can be further tested by repeated experiments by peers. 

Step-by-step explanation:

The Byron can conclude from the experiment, that the new medication is effective in reducing coughing.

The experiment is the type of statistical study, in which the observer or the researcher see the change in the variable of a study with change in other variable experimentally by providing the necessary conditions.

Byron is conducting an experiment to determine whether a new medication is effective in reducing coughing.

He finds 1,200 volunteers with coughing issues and divides them into two groups such as,

The patients in the treatment group show reduced signs of coughing.  This indicates that the medication is effective on reducing the coghing if he controll other factors.

Thus, the Byron can conclude from the experiment, that the new medication is effective in reducing coughing.

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Answer:

a,c,c,b

Step-by-step explanation:

Id give a explanation but u need asap

Answer:

1st photo is B  2nd photo is B as well

Step-by-step explanation:

1st photo explanation= negatives are the least and -8 1/3 is -8.3 repeating so its the least then is -8.1 then -8

2nd photo explanation= 7/10 is 70% and 2/3 is 66.67% so you plug those in then you can get your answer

Answer:

1•4

Step-by-step explanation:

1•54÷1•1

1•54

1•1

divide by 10 both side with can move decimal

15•4

11

=my answer is 1•4.

Answer:

The correct answer for algebraic expression 1.54÷1.1 is = 1.4.

Step-by-step explanation:

this is question based on simple algebra -

Simple Algebraic equations -  An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.

these equations are two algebraic expressions that are joined together using an equal to ( = ) sign. An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials

so in the question algebraic operation used to solve is simple division.

therefore here in question we have to divide 1.54 with 1.1,

using the concept written above,

let the value of division be 'x'

we can write 1.54/1.1 = x

by dividing and multiplying the equation by 100 to remove the decimals.

            (1•54/ 1•1)×100/100    = x

                    154/110    =  x

now by simple division,

                      1.4   =  x  answer

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The algebraic expression that models each word phrase, "The sum of the product of a number k and 4, and a number m" is k × 4 + m.

The given word phrase is, "The sum of the product of a number k and 4, and a number m".

We need to write an algebraic expression for this word phrase.

We know that the word "sum" means addition, "product" means multiplication and "a number" means a variable, for example, k, x, y, etc.

Hence, the algebraic expression that models each word phrase, "The sum of the product of a number k and 4, and a number m" is:

k × 4 + m

Answer: k × 4 + m

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The values of x and y using the concept of similar figures are:

y = 166 and x = 3.33 units

Two triangles are said to be similar if their corresponding side proportions are the same and their corresponding pairs of angles are the same. When two or more figures have the same shape but different sizes, such objects are called similar figures.  

We are told that Polygon ABCD is similar to Polygon EFGH and as such applying the similar figure definition above, we can say that:

∠B = ∠F

Thus:

∠B = 360 - (61 + 116 + 90)

∠B = 360 - 267

∠B = 93°

Thus:

y - 73 = 93

y = 166

Using the concept of similar figures, then:

6/4 = 5/x

x = 20/6

x = 3.33 units

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The percentage of runners who took 21.67 minutes or less to complete the race is 0.606%

It is also known as Gaussian distribution. It shows the data near the more. This appears as a bell curve in graphical form. It is a continuous random variable's frequency distribution curve in the shape of a bell. It is employed to describe real-valued random variables with an unknowable distribution. It is important in statistics and is also applied in the natural and social sciences. The data has a bell shape when plotted on a graph.

μ=24.7 min

σ=2.02 min

z=((x-μ)/σ)

p(x<21.67)=p((x-24.7)/2.02) ≤ ((21.67-24.7)/2.02)

p(z≤-1.5)

p(z <21.67)=0.606

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(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

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Answer:

$13.90

Step-by-step explanation:

1. Get rid of the tax by subtracting 2.70 from the total.  

2. Next, divide the total by 3 to find the price of each CD.

Answer:

200 ml

Step-by-step explanation:

Orange squash is mixed with water in the ratio 1 : 3. If you use 600 ml of water, how much squash do you need?

1 is to 3 as x is to 600

1 is 1/3 of 3 so x should be 1/3 of 600

1/3 of 600 = 200

use 200 ml squash to keep the ratio the same.

Answer:

(C)    $18.00

Step-by-step explanation:

10% = 0.1

180 * 0.1 = 18

(C) $18.00

A hypothesis test is the significance test we will do.

Given;

Our goal is to find out whether students' self-reported grade point averages and their transcript-reported GPAs differ from one another. What kind of significant test will you administer to your class of 50 SRS students?

hypothesis test:

To decide or judge the value of a parameter, such as the population mean, hypothesis tests are utilized. A hypothesis test can be conducted using either the critical value approach or the P-value approach. There are two sorts of errors made when doing a hypothesis test: Type I Error and Type II Error. Because a sample statistic is being used to make conclusions or judgments about the value of a parameter, the decision obtained may be incorrect.

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The exponential growth function will be:  y = 4000(1 + 0.04)⁴

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.

We are given;,

Initial population = 4000

Rate of increase = 4%

Let current population be p.

Let number of years passed be t.

Thus, the exponential growth function will be:

y = 4000(1 + 0.04)⁴

Complete question is;

A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals make up 3 percent of the town's population.

Part A

Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.

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Answer:

number of emergency response professionals = 3% of population

e = 0.03p

e is a function of p

e(p) = 0.03p

Step-by-step explanation:

edumentum

(a) To determine dy/dx at the point (x, y) = (1, 0), we can use implicit differentiation.

Differentiating both sides of the equation x^2 + y + 2xy = 1 with respect to x:

2x + dy/dx + 2y + 2xdy/dx = 0

Simplifying the equation:

2x + 2y + dy/dx(1 + 2x) = 0

Now we substitute the values (x, y) = (1, 0) into the equation:

2(1) + 2(0) + dy/dx(1 + 2(1)) = 0

2 + dy/dx(1 + 2) = 0

2 + 3dy/dx = 0

Solving for dy/dx:

3dy/dx = -2

dy/dx = -2/3

Therefore, dy/dx at the point (x, y) = (1, 0) is -2/3.

(b) To determine d^2y/dx^2 at the point (x, y) = (1, 0), we can differentiate the equation obtained in part (a) with respect to x:

d/dx(2x + 2y + dy/dx(1 + 2x)) = d/dx(0)

2 + 2dy/dx + dy/dx(2) + d^2y/dx^2(1 + 2x) + dy/dx(2x) = 0

Simplifying the equation:

2 + 2dy/dx + 2dy/dx + d^2y/dx^2(1 + 2x) = 0

4dy/dx + d^2y/dx^2(1 + 2x) = -2

Now substitute the values (x, y) = (1, 0) into the equation:

4(dy/dx) + d^2y/dx^2(1 + 2(1)) = -2

4(dy/dx) + 3d^2y/dx^2 = -2

Substituting dy/dx = -2/3 from part (a):

4(-2/3) + 3d^2y/dx^2 = -2

-8/3 + 3d^2y/dx^2 = -2

3d^2y/dx^2 = -2 + 8/3

3d^2y/dx^2 = -6/3 + 8/3

3d^2y/dx^2 = 2/3

d^2y/dx^2 = 2/9

Therefore, d^2y/dx^2 at the point (x, y) = (1, 0) is 2/9.

(c) To determine the degree 2 Taylor polynomial of y(x) at the point (x, y) = (1, 0), we need the values of y, dy/dx, and d^2y/dx^2 at that point.

At (x, y) = (1, 0):

y = 0 (given)

dy/dx = -2/3 (from part (a))

d^2y/dx^2 = 2/9 (from part (b))

Using the Taylor polynomial formula:

P2(x) = y + dy/dx(x - 1) + (d^2y/dx^2/2!)(x - 1)^2

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The given two-way Frequency table, there are 33 left-handed students who are not in the music program.

The number of left-handed students who are not in the music program, we need to examine the data presented in the two-way frequency table.

From the table, we can see that the number of left-handed students in the music program is 15, and the total number of left-handed students is 48.

the number of left-handed students not in the music program, we subtract the number of left-handed students in the music program from the total number of left-handed students.

Number of left-handed students not in the music program = Total number of left-handed students - Number of left-handed students in the music program

Number of left-handed students not in the music program = 48 - 15

Calculating this, we find that the number of left-handed students not in the music program is 33.

Therefore, there are 33 left-handed students who are not in the music program, based on the data provided in the two-way frequency table.

In conclusion, based on the given two-way frequency table, there are 33 left-handed students who are not in the music program.

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The answer will be option a .collinear

The gradient of a function points in the direction in which the function increases the fastest because it represents the direction of greatest increase of the function.

The gradient of a function is a vector that points in the direction of the steepest increase of the function at a particular point. This means that if we move in the direction of the gradient, the value of the function increases the fastest.

To understand why this is true, let's consider the definition of the gradient. The gradient of a function f(x) is defined as a vector of partial derivatives:

∇f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)

Each component of the gradient vector represents the rate of change of the function with respect to the corresponding variable. In other words, the gradient tells us how much the function changes as we move a small distance in each direction.

When we take the norm (or magnitude) of the gradient vector, we get the rate of change of the function in the direction of the gradient. This means that if we move in the direction of the gradient, the value of the function changes the fastest, because this is the direction in which the function is most sensitive to changes in the input variables.

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The constant ratio in each representation is 4 and it shows a constant ratio between consecutive output values of the function.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the constant ratio in each representation as follows;

Constant ratio, r = a₂/a₁ = a₃/a₂ = a₄/a₃ = a₅/₄

Constant ratio, r = 12/3 = 48/12 = 192/48 = 768/192

Constant ratio, r = 4.

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Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability.

The term "experiment" in the context of probability refers to a process or activity that involves observing or measuring an outcome that is subject to chance or uncertainty. The outcome of an experiment is not necessarily predictable with certainty, and it may depend on various factors such as the conditions under which the experiment is conducted and the randomness inherent in the process.

Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability. An experiment is essentially a process that leads to one of several possible outcomes, and the probability of each outcome can be calculated or estimated based on the underlying assumptions and factors involved. Examples of experiments in probability include rolling a die, tossing a coin, drawing a card from a deck, or conducting a clinical trial to test a new drug.

Option b) is not an appropriate definition of an experiment because it suggests that the outcome can be predicted with certainty based on mathematical analysis, which is not always the case in experiments involving chance or uncertainty.

Option c) is also not an appropriate definition of an experiment because it suggests that an experiment is conducted to confirm a hypothesis, which may or may not be true. While experiments can be used to test hypotheses and provide evidence to support or refute them, the primary goal of an experiment in the context of probability is to observe or measure the outcome and calculate the probability of each possible outcome.

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