Identify the type of function represented by f(x) = 3(1:5)*.
A. Quadratic
B. Linear
C. Exponential decay
D. Exponential growth

Answer:

∠ B ≈ 53°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan B = \(\frac{opposite}{adjacent}\) = \(\frac{AC}{BC}\) = \(\frac{4}{3}\) , then

∠ B = \(tan^{-1}\) (\(\frac{4}{3}\) ) ≈ 53° ( to the nearest degree )

Answer:

A.true

Step-by-step explanation:

:)

Answer:

False

Step-by-step explanation:

the Triangle Sum Inequality states that the sum of any two sides is greater than the third

since 9+4 is not greater than 15, the answer to the question is no, these segments could not form a triangle

Using the sine function:

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$40\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases} \\\\\\ 40 = (500)(\frac{r}{100})(4) \implies 40=20r\implies \cfrac{40}{20}=r\implies \stackrel{\%}{2}=r\)

Ava method of simplifying the expression was wrong

Ava's mistake is (−(2x−3y))^2 = −1⋅(2x−3y)^2 this was wrong. the square of a negative is positive. (−(2x−3y))^2 = (2x−3y)^2 this is correct

(2x - 3y)^2 / (3x - 2y)^2

Simplifying the numerator

= (2x - 3y)^2

= (2x - 3y) * (2x - 3y)

= 4x^2 - 6xy - 6xy + 9y^2

Simplifying the denominator

= (3y - 2x)^2

= (3y - 2x) * (3y - 2x)

= 9y^2  - 6xy - 6xy + 4x^2

rearranging gives

= 4x^2 - 6xy - 6xy + 9y^2

putting together

= (4x^2 - 6xy - 6xy + 9y^2) / (4x^2 - 6xy - 6xy + 9y^2)

= 1

In Ava's method, at this stage (−(2x−3y))^2

(−(2x−3y))^2 = (2x−3y)^2

(−(2x−3y))^2 ≠ −1⋅(2x−3y)^2 -  this was wrong

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Given,Gross Income of Alex and Tory = $150,000 The standard deduction for Aiden = $6,847.50 Gross Income of Aiden = $63,000

a) Taxable Income To calculate the taxable income, we first need to deduct the standard deduction from the gross income.Taxable income = Gross Income - Standard Deduction For Aiden, Taxable Income = Gross Income - Standard Deduction= $63,000 - $6,847.50= $56,152.50 For Alex and Tory, they can either take the standard deduction or itemized deductions. We do not have the details about their itemized deductions. Hence, for the sake of the solution, we will assume that they take the standard deduction. The standard deduction for married couples filing jointly for 2021 is $25,100.

Taxable Income for Alex and Tory = Gross Income - Standard Deduction= $150,000 - $25,100= $124,900b) Marginal Tax Rate To calculate the marginal tax rate, we need to know the tax brackets. For the year 2021, the tax brackets for married couples filing jointly are as follows:Taxable Income Tax Rate Up to $19,900 10% $19,901 to $81,050 12% $81,051 to $172,750 22% $172,751 to $329,850 24% $329,851 to $418,850 32% $418,851 to $628,300 35% Over $628,300 37%Since the taxable income of Alex and Tory is $124,900, their marginal tax rate would be 24%.c) Effective Tax Rate To calculate the effective tax rate, we need to divide the total tax amount by the taxable income.

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The required value of the given expression at z = 6 is 51.

Given that,
The value of the expression z² + 3z - 3 is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= z² + 3z - 3
Put z = 6 and simplify the expression,
= 6² + 3(6) - 3
= 36 + 18 - 3
= 54 - 3
= 51

Thus, the required value of the given expression at z = 6 is 51.

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The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral \(\( \int_{1}^{2} x \ln x \, dx \)\) is approximated using \(\( n = 4 \)\)subintervals. In part (b), the integral\(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) is given with incorrect limits, so it cannot be evaluated.

To approximate \(\( \int_{1}^{2} x \ln x \, dx \)\) using the Composite Trapezoidal rule, we divide the interval \(\([1, 2]\) into \( n = 4 \)\) subintervals. The step size, \(\( h \)\), is calculated as\(\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)\). Then, we evaluate the function \(\( x \ln x \)\)at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: \(\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\]\)

Using this formula, we can calculate the approximation for the given integral. The limits of the integral \(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) are given as \(\( 2 \)\) to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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The value of x in the figure is 18

The angle with the measure 9x -12 and the angle with the measure 30 degrees are internal angles of a transversal

This means that

9x -12 + 30 = 180

Evaluate the like terms

9x = 162

Divide by 9

x = 18

Hence, the value of x in the figure is 18

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Block Y has the smallest acceleration

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{3 +5}{4 +2} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }\)

Answer:

this is one of the property

Step-by-step explanation:

(-2)×2=(-4)

hope it helps

Answer:

your answer is 256

Step-by-step explanation:

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.

Answer:

2 , -4 , (2,0)

Step-by-step explanation:

The slope of the linear function is 2.

The y-intercept of the linear function is -4.

The solutions of the linear function are (0, -4), (1, -2), (2, 0), etc..

The graph is given below.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The linear function is y = mx + c

The linear function passes through (-2, -8) and (1, -2)

Now,

m = (-2 + 8) / (1 + 2)

m = 6/3

m = 2

The slope of the linear function is 2.

Now,

(-2, -8) = (x, y)

-8 = 2 x (-2) + c

-8 = - 4 + c

c = -8 + 4

c = -4

The y-intercept is -4.

The equation of the linear function.

y = 2x - 4

The solution of the line are (0, -4), (1, -2), (2, 0), etc..

When x = 0,

y = -4

When x = 1,

y = -2

When x = 2,

y = 0

Now,

The graph of the line is given below.

Thus,

The slope is 2.

The y-intercept is -4.

The solutions are (0, -4), (1, -2), (2, 0), etc..

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The given series with partial sums sn = (n² - 1) / (3n²) has a sum of 1/3. The convergence of the partial sums to 1/3 as n approaches infinity confirms this result.

To calculate the sum of the series where the partial sums are given as

sn = (n² - 1) / (3n²), we can analyze the expression and determine its behavior as n approaches infinity.

Looking at the expression, we can simplify it as sn = (1 - 1/n²) / 3. As n approaches infinity, the term 1/n² becomes negligible, and we are left with sn = 1 / 3. This means that the partial sums converge to a fixed value of 1/3 as n becomes larger.

Since the partial sums converge to 1/3, we can conclude that the sum of the series is also equal to 1/3. This is because the sum of an infinite series is defined as the limit of its partial sums as n approaches infinity. In this case, the partial sums approach 1/3, indicating that the series converges to 1/3.

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The probability of Bo, Colleen, Jeff, and Rohini winning the first, second, third, and fourth prizes, respectively, is 1 in 6,497,400.

The probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in the contest with 52 entrants and no one winning more than one prize can be calculated as follows:
1. Probability of Bo winning the first prize: 1/52 (since there are 52 people, and Bo is one of them)
2. Probability of Colleen winning the second prize after Bo has won the first prize: 1/51 (since there are now 51 people left)
3. Probability of Jeff winning the third prize after Bo and Colleen have won: 1/50 (50 people remaining)
4. Probability of Rohini winning the fourth prize after Bo, Colleen, and Jeff have won: 1/49 (49 people left)
To find the overall probability, multiply all individual probabilities together:
(1/52) x (1/51) x (1/50) x (1/49) = 1/6,497,400

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The probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in the drawing is approximately 1.0625 × 10^-9.

To find the probability of Bo, Colleen, Jeff, and Rohini winning the first, second, third, and fourth prizes, respectively, follow these steps:
Calculate the total number of ways to choose 4 winners from 52 people (order matters, since the prizes are distinct). This is a permutation, so use the formula nPr = n! / (n - r)!,

where n = 52 (total number of people) and r = 4 (total number of prizes). In this case, 52P4 = 52! / (52 - 4)! = 52! / 48!.
Calculate the probability of Bo winning the first prize:

There is 1 favorable outcome (Bo winning) out of 52 possible outcomes, so the probability is 1/52.
Calculate the probability of Colleen winning the second prize, given that Bo has already won:

There is 1 favorable outcome (Colleen winning) out of the remaining 51 possible outcomes, so the probability is 1/51.
Calculate the probability of Jeff winning the third prize, given that Bo and Colleen have already won:

There is 1 favorable outcome (Jeff winning) out of the remaining 50 possible outcomes, so the probability is 1/50.
Calculate the probability of Rohini winning the fourth prize, given that Bo, Colleen, and Jeff have already won: There is 1 favorable outcome (Rohini winning) out of the remaining 49 possible outcomes, so the probability is 1/49.
To find the overall probability of this specific order of winners (Bo, Colleen, Jeff, Rohini), multiply the individual probabilities: \((1/52) × (1/51) × (1/50) × (1/49) ≈ 1.0625 × 10^-9.\).

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Answer:

10

Step-by-step explanation:

3/5 simpilfied is 0.6

So 6/0.6 = 10

Answer: 225°

Step-by-step explanation:

To convert radians to degrees, multiply by 180/π (1 rad = 180° )

(5π/4) * (180/π/) = 225°

Answer:

Option (iv) is correct.

Step-by-step explanation:

The linear equation is the equation in which the degree of the equation is 1.

(i) x/3 = 12

As the degree of equation is 1, so, it is a linear equation.

(ii) x + 1 = 6

As the degree of equation is 1, so, it is a linear equation.

(iii) x + y + z = 17

As the degree of equation is 1, so, it is a linear equation.

(iv) x y + x / y = 3

x y^2 + x = 3 y

The degree of equation is 3, so the equation is non linear.

If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

The energy an item has as a result of motion is known as kinetic energy in mechanics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its propulsion until its speed changes.

The kinetic energy is given as,

KE = (mv²)/2

Where m is the mass and v is the velocity.

Shawn and his bike have a total mass of 48.1 kg. Shawn rides his bike 1.5 km in 12.5 min at a constant velocity.

The velocity is given as,

v = 1.5/12.5

v = 0.12 km/min

v = 0.12 x 1000 / 60

v = 2 m/s

Then the kinetic energy of Shawn will be given as,

KE = (48.1 x 2²) / 2

KE = 48.1 x 2

KE = 96.2 J

If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

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The solution to the homogeneous system of equations is:

\(x_1 = 5x_3\\x_2 = -2x_3\\x_3 = x_3\)

To solve the homogeneous system of equations using Gaussian elimination, we can write the system in augmented matrix form:

\(\left[\begin{array}{ccc|c}1&3&3&0\\-4&-9&2&0\\0&-3&-6&0\end{array}\right]\)

Performing row operations to reduce the matrix to row-echelon form:

Add a second row four times the first row,

\(\left[\begin{array}{ccc|c}1&3&1&0\\0&3&6&0\\0&-3&-6&0\end{array}\right]\)

Divide the second row with 3 and solve further,

\(\left[\begin{array}{ccc|c}1&0&-5&0\\0&1&2&0\\0&0&0&0\end{array}\right]\)

From the last equation, we can see that we have a free variable. Let's solve for the dependent variables in terms of this free variable:

The row-echelon form has been achieved, and we can now read the solution directly from the matrix:

\(x_1 = 5x_3\\x_2 = -2x_3\\x_3 = x_3\)

The solution to the homogeneous system of equations is:

\(x_1 = 5x_3\\x_2 = -2x_3\\x_3 = x_3\)

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2.28% probability that a person selected at random will have an IQ of 110 or greater.

The normal distribution is one of the most commonly used probability distributions. This is because it can closely replicate many situations and also because it can be easily converted into other distributions.

In a set with mean  and standard deviation , the z score of a measure X is given by:

Z = x - μ /σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p value, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

μ = 100 , σ =5

Z = 110 - 100 / 5

Z = 10/5

Z = 2 has a p value of 0.9772

1 - 0.9772 = 0.0228

Hence, 2.28% probability that a person selected at random will have an IQ of 110 or greater.

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The distance from the center of dilation, P, to.the image vertice S' is; 6 units.

It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.

Hence, since the dilation factor as given in the task content is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6units.

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Answer:7$ per hour

Step-by-step explanation:

Answer:

About 7 dollars

Step-by-step explanation:

Answer:

Step-by-step explanation:

The required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system. which is the correct answer would be an option (A).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The video game system will cost at least $450.

He earns $6 per hour babysitting and $10 per hour tutoring.

Let x be the number of hours babysitting and y be the number of hours of tutoring.

According to the given situation, we can write the inequality would be as:

⇒ 6x + 10y ≥ 450

Rearrange the terms of variables in the above inequality,

⇒ 10y ≥ 450 - 6x

Divided by 10 into both sides of the above inequality,

⇒ 10y/10 ≥ 450/10 - 6x/10

⇒ y ≥ 45 - 0.6x or

⇒ y ≥ - 0.6x + 45

Thus, the required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system.

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Answer:

ans = $105 per hour

Step-by-step explanation:

first: you subtract the charge for parts from the total and this gives you $446.25.

second: because the technician worked for 4.25 hours = $446.25,if the technician worked for an hour what would be the cost?

4.25hr = $446.25

1 hr      = x . then cross multiply.

4.25x = 446.25 then divide by 4.25 both sides to find th value of x, which is the cost of labour per hour

The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

In the question ,

it is given that ,

the initial point of the vector = (1 , -1)

the terminal point of the vector = (4,2)

we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

V = (x₂ - x₁)i + (y₂ - y₁)j

Substituting the values from the point ,

we get the vector as

V = (4 - 1)i + (2 -(-1))j

V = 3i + (2 + 1)j

V = 3i + 3j

Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

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The value of a/b is  \(\sqrt{6}\) / 2

The area of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.

According to the question:-

Side of an equilateral triangle equals a/3.

Therefore, the equilateral triangle's area is equal to (1/2)(a/3)2 sqrt (3) / 2 = a2 [sqrt (3)/ 36].

Hexagonal side equals b / 6.

The area is thus 6 (1/2) (b/6)^2 sqrt (3) / 2 

= b^2 [ 3 sqrt (3) / 72] = b^2 [sqrt (3) / 24]

So

sqrt (3) / 36 a2 = sqrt (3) / 24 b2

So

A2 / B2 = [Sqrt(3)/24] / [Sqrt(3)/36]

a^2 / b^2 = [ 36 / 24 ]

a^2/ b^2 = 3/2

A/ B = Sqrt(3) / Sqrt(2)

=Sqrt(6) / 2

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