Solve the equation 3x = 9.5 Show and justify each step you take to solve the equation . 3x = 9 Write the equation 9 Divide each side by 3. x =​

we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

The xz-plane is the plane formed by the x-axis and the z-axis. To find a vector parametrization of a curve in this plane, we need to express the x and z coordinates of the curve as functions of a parameter t. In this case, we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

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Answer:

C. m^2+n^2=p^2

Step-by-step explanation:

The Pythagorean Theorem is a^2+b^2=c^2, so C is correct. This can be proven by using a triangle with the sides 3,4, and 5.

In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Answer:

5.63

Step-by-step explanation:

The value of x in the given triangle is 5.62 cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle

We have to find the value of x

We know that by cosine function is a ratio of adjacent side and hypotenuse

cos 62 = x/ 12

0.469 = x/12

Apply cross multiplication

x=12×0.469

x=5.63

Hence, the value of x in the given triangle is 5.62 cm.

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Answer:

f(-3) = |(-3)-2| = |-5| = 5

Answer:

(i) The value of m when t = 30 is 13.2

(ii) The value of t when the mass is half of its value at t=0 is 34.7

(iii) The rate of the mass when t=50 is -0.18            

Step-by-step explanation:

(i) The m value when t = 30 is:

\( m = 24e^{-0.02t} = 24e^{-0.02*30} = 13.2 \)

Then, the value of m when t = 30 is 13.2

(ii) The value of the mass when t=0 is:

\( m_{0} = 24e^{-0.02t} = 24e^{-0.02*0} = 24 \)    

Now, the value of t is:

\( ln(\frac{m_{0}/2}{24}) = -0.02t \)

\( t = -\frac{ln(\frac{24}{2*24})}{0.02} = 34.7 \)

Hence, the value of t when the mass is half of its value at t=0 is 34.7

(iii) Finally, the rate at which the mass is decreasing when t=50 is:

\( \frac{dm}{dt} = \frac{d}{dt}(24e^{-0.02t}) = 24(e^{-0.02t})*(-0.02) = -0.48*                            (e^{-0.02*50}) = -0.18 \)

Therefore, the rate of the mass when t=50 is -0.18.

I hope it helps you!                  

Answer:

The answer is $14.6 for the plain paper and $14.12

Step-by-step explanation:

I think i'm probably wrong but 6+9= 15 so 219 divided by 15 is 14.6 so thats answer 1 and 12+13=25 and 353 divided by 25 is 14.12

:p sorry if im incorrect

Answer: The first answer for 6 of wrapping paper and 9 wrapping paper is $7.30. The second answer for 12 wrapping paper and 13 rolls of SHINY wrapping paper is $4.38.

Step-by-step explanation:

The domain of the function can be written in the form of interval as  (-∞, ∞).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The function is given as y = aˣ.

Its domain can be found as follows,

For x = 0, y is a⁰ = 1.

For x = n, where n > 0, y is given as,

y = aⁿ, which is greater than zero.

For x = n, where n < 0, y is given as,

y = a⁻ⁿ

⇒ y = 1/aⁿ

Thus, the given function is valid for all real numbers.

Which implies its domain is (-∞, ∞).

Hence, the domain of the given function is obtained as (-∞, ∞).

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Answer:

D

Step-by-step explanation:

It's been a while since i've done these, but I think I know.

Process of ellimination:

A.Nope. 500 is waaaaay to far from 132 to be used here.

B.The use of the number 25 is not needed nor is it correct.

C. This one uses both incorrect numbers, 8500 and 25.

D.Its D. Again, I'm not positive, but it makes the most sense. 8000 is the closest to 8132, and 8000 and 20 are very easy to do mentally and are divisable easily. it should be D.

If, we invested $2,800 at a 6% annual interest rate. We will have $2972.70 in 1 year and $3063 in 1.5 year of time.

In the fields of finance and economics, interest is defined as the payment of a sum over and above the principal amount (the amount borrowed) at a set rate by a borrower or deposit-taking financial institution to a lender or depositor. It is different from a fee that the borrower may pay to the lender or another entity. It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve, but not at a set rate predetermined beforehand, but rather on a pro rata basis as a portion of the rewards received by risk-taking businesspeople when revenue is earned that exceeds all costs.

Calculations:

The Future value= fv= Pv x \((1+r/m)^{mt}\)

R= Rate per period

mt= years x compounding

The Future value in 1 year= 2800x\((1+0.06/12)^{1x12}\)

                                   = $2972.70

The Future value in 1.5 years=2800x\((1+0.06/12)^{1.5x12}\)

                                       = $3063.00

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Answer:  We can use the Pythagorean theorem to find the length of the hypotenuse (c) of a right triangle, which is given by:

c^2 = a^2 + b^2

where a and b are the lengths of the legs.

In this case, a = 4 and b = 6. Substituting these values into the formula, we get:

c^2 = 4^2 + 6^2

c^2 = 16 + 36

c^2 = 52

Taking the square root of both sides, we get:

c = sqrt(52)

Simplifying, we can factor out a 4 from under the radical:

c = sqrt(4 * 13)

c = 2 sqrt(13)

Therefore, the exact length of the hypotenuse is 2 sqrt(13) units.

Step-by-step explanation:

The maximum volume of the box in terms of A will be √3A/4 -3√3/4 cu cm.

It is given that the box has an open top and a square base.

This implies length = breadth.

Let them be x cm

Now, the area of the box is A sq cm

This means

lb + 2bh + 2lh = A

or, x² + 2xh + 2xh = A

or, 4xh + x² = A

or, h = A/4x - x/4

Now volume (V) = lbh

= x²(A/4x - x/4)

= Ax/4 - x³/4

Now to maximize volume we will first differentiate with respect to x and equate it to zero. Hence we get

V' =0

or, A/4 - 3x²/4 = 0

or 3x²/4 = A/4

or, x² = 3

or, x = √3

Now t check whether this gives us the maximum volume we will calculate V"(√3)

V" = -3x/2

V"(√3) = -3√3/2

Since V"(√3) is negative we will get maximum value for x = √3

Now the volume is

A√3/4 - (√3)³/4

= √3A/4 -3√3/4 cu cm

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To answer this question, solve the given expression for calculating velocity for a, this way:

The correct answer is B.

Answer:

y = -\(\frac{2}{5}\)x + 9

Step-by-step explanation:

slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

an equation with the SLOPE (m) of -\(\frac{2}{5}\) and Y-INTERCEPT (b) of 9 would be

y = -\(\frac{2}{5}\)x + 9

The association suggested by the two-way table is Those who like football tend to like baseball.

The relative frequency for each category can be calculated by dividing the count in each cell by the total count in the table.

For the "Likes Football" category:

Relative frequency of "Likes Football"

= 72 / 100 = 0.72

For the "Does Not Like Football" category:

Relative frequency of "Does Not Like Football"

= 28 / 100 = 0.28

For the "Likes Baseball" category:

Relative frequency of "Likes Baseball"

= 54 / 100 = 0.54

For the "Does Not Like Baseball" category:

Relative frequency of "Does Not Like Baseball"

= 46 / 100 = 0.46

Therefore, the correct association suggested by the two-way table is Those who like football tend to like baseball.

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The trigonometric function simplified as a single expression is cosec² t .

The given trigonometric function is  : \(\frac{sin^2t+cos^2t}{sin^2t}\)

We know from trigonometric identity : that sin²t +cos²t = 1

hence the given expression simplifies to 1 / sin²t

Again trigonometric ratios states that :

1 / sin t =  cosec t

∴ 1 / sin²t = cosec² t

Hence the trigonometric function is of the form cosec² t .

The right-angled triangle's angle and the ratios of its two side lengths are connected by the trigonometric functions, which are actual functions. They are also referred to as goniometric functions, circular functions, and angle functions .

The three trigonometric functions that are used in modern mathematics the most commonly are sine, cosine, and tangent. The less frequent cotangent, cosecant, and secant are their reciprocals.

Disclaimer: The complete question is :

simplify sin² ( t ) + cos ² ( t ) / sin ² ( t ) to an expression involving a single trig function with no fractions.

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Answer:

2.5

Step-by-step explanation:

just trust me it 2.5

True, to calculate the average of numeric values in the list, the first step is to get the total of values in the list.

Steps to calculate the Average:

Let’s assume there are 4 numbers having values of 2,8,22,48 respectively.

To find the average we first have to take the total of all values.

2+8+22+48=80.

Our next step will be to divide this total by the number we have in our question i.e., 4.

so, our average will be 80/4= 20.

So, 20 will be our average.

So yes, it is true that to calculate the average of numeric values in the list, the first step is to get the total of all values in the list.

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Answer:

24 79/200

Step-by-step explanation:

The Fundamental Theorem of Algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This theorem is important as it provides a way to prove the existence of solutions to polynomial equations and provides an analytical tool to find the exact location of the solutions.

This theorem is also known as the algebraic version of the Intermediate Value Theorem as it states that if a polynomial is continuous on a closed interval, then it must take on all values between its maximum and minimum.

The theorem can be easily proven by considering a single-variable polynomial of degree n and transforming it into a polynomial of degree n−1 with the same roots. By repeating this process, the polynomial can be reduced to a constant and hence, it must have at least one root.

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If your average test grade from earlier examinations and your most recent test grade is equal, your average test grade will remain constant.

Therefore, if your average test grade from earlier examinations and your most recent test grade is equal, your average test grade will remain constant.

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In Situation 1, we conducted a hypothesis test to determine if the mean amount of sleep for adults is less than 7 hours per night. Using a significance level of 0.05, we found that there is sufficient evidence to support this claim.

In Situation 2, we conducted a hypothesis test to determine if more than 38.3% of adults in the age range of 35-44 receive at least 7 hours of sleep per night. Using a significance level of 0.01, we found that there is not sufficient evidence to support this claim. In Situation 1, the possible errors that could have occurred are a Type I error or a Type II error. A Type I error occurs when we reject the null hypothesis when it is actually true, while a Type II error occurs when we fail to reject the null hypothesis when it is actually false. To prevent these errors from occurring in future hypothesis tests, we can increase the sample size, use a different significance level, or improve the accuracy of our measurement methods.

In Situation 2, the possible errors that could have occurred are also a Type I error or a Type II error. A Type I error occurs when we reject the null hypothesis when it is actually true, while a Type II error occurs when we fail to reject the null hypothesis when it is actually false. To prevent these errors from occurring in future hypothesis tests, we can increase the sample size, use a different significance level, or improve the accuracy of our measurement methods. Additionally, we can also use a different test statistic or adjust the sample selection criteria to reduce the likelihood of errors.

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If the inflation rate is 180%, the average prices will double in less than one year.

This is because inflation measures the increase in the prices of goods and services over a period of time. Therefore, the formula for calculating how many years it will take for average prices to double at a given inflation rate is:Years to double = 70/inflation rate

In this case, the inflation rate is 180%.

Therefore:Years to double = 70/180%

Years to double = 0.389 years

This means that average prices will double in approximately 4.67 months (0.389 years multiplied by 12 months per year).

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Since the average speed of the car is x miles per hour, then

We have to change the 90 minutes to hours

Since 1 hour = 60 minutes, then

Divide 90 by 60 to change from minutes to hours

90 minutes = 3/2 hours

By using the rule of the distance

s is the speed

t is the time

Since s = x and t = 3/2, then

The car can travel 3x/2 miles in 90 minutes

The answer is B

The matrices A = [-2 3] and B =[-4 0] then, A+B = [-6 3]

How does matrix addition work?

A = [-2 3] ; B =[-4 0]

A+B = [ -2+(-4)  3+0]

= [-6 3]

Hence, The matrices A = [-2 3] and B =[-4 0] then, A+B = [-6 3]

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The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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The area of each of the missing faces is 40 m².

The length of each of the missing faces is 10 m.

The missing dimension is 10 m by 4 m.

Area is the region bounded by a plane shape.

To calculate the area of each missing face, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

And the length of each of the missing edge can be calculated using the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute into equation 2

Hence, the length is 10 m.

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Answer:

Over 85 ft

Step-by-step explanation:

The maximum height of the ball is going to be located at the vertex of the parabola. First you need to find the x (or t in this case) coordinate for the axis of symmetry. Using the equation for the axis of symmetry of a parabola:

\(x=\frac{-b}{2*a}\)

\(t=\frac{-40}{2*(-4.9)}=\frac{-40}{-9.8}=4.0816\)

After finding the t-coordinate for the vertex, then plug this value into the original equation to find the corresponding h-coordinate:

Assuming the equation is \(h=-4.9t^{2}+40t+6\),

\(h=-4.9(4.0816)^{2}+40(4.0816)+6=-81.6313+163.264+6=87.6327\)

So the vertex can be represented as (4.016, 87.6327)

The maximum height is over 85 ft.