Set up an equation and show all work to solve. Round final answers to the nearest hundredth.

Answer:

(7-2√6)/10

Step-by-step explanation:

I assumed the fraction in the question was:

(√6 - 1) / (2√6 + 2)

Working is attached below.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}[/tex]

[tex]1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P[/tex]

The exponential function graphed is defined as follows:

y = 4(3)^x - 1.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function in this problem has an horizontal asymptote at y = -1, hence it is defined as follows:

y = ab^x - 1.

When x increases by one, y is multiplied by 3, hence the parameter b is given as follows:

b = 3.

Hence:

y = a(3)^x - 1.

When x = 0, y = 3, hence the parameter a is given as follows:

a - 1 = 3

a = 4.

Thus the function is:

y = 4(3)^x - 1.

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The area of the regular polygon, or equilateral triangle, is determined as  27.71 mm².

The area of a regular polygon can be calculated using the formula:

Area = (perimeter * apothem) / 2

where;

Assuming the regular polygon is an equilateral triangle, the following formula will be used to find the area of the triangle.

A = a² × √3/4

where;

a is the side length of the  equilateral triangle = 8 mm

The area of the equilateral triangle is calculated as follows;

A = ( 8² ) x √ ( 3 ) / 4

A = 27.71 mm²

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Step-by-step explanation:

to find the percentage you have to take 5 as 100% so to find the percentage of 4 you have to divide 100 by 5 making 20%. then do 20 multiplied by 4 which is 80%. so the answer is 80^

Answer: 58.72 degrees Celsius.

Step-by-step explanation:

We can use the following formula to estimate the temperature of the coffee when t = 10:

T(t) = T(room) + [T(initial) - T(room)] * e^(-r(t) * t)

where T(t) is the temperature of the coffee at time t, T(room) is the temperature of the room, T(initial) is the initial temperature of the coffee, and r(t) is the rate of change of the coffee's temperature.

Substituting the given values, we get:

T(10) = 20 + [90 - 20] * e^(-(-7 e^(-0.1 * 10)) * 10)

T(10) = 20 + 70 * e^(0.7)

T(10) ≈ 58.72 degrees Celsius (rounded to two decimal places)

Therefore, the estimated temperature of the coffee when t = 10 is 58.72 degrees Celsius.

The 99.7% confidence interval for the mean of the population is (112.82, 125.18).

The degree of variance or dispersion in a collection of data is measured by standard deviation. It is a statistic that gauges how much values deviate from the dataset's mean (average).

To calculate the 99.7% confidence interval for the mean of the population, we need to use the formula:

Confidence Interval = X ± Z(α/2) * (σ/√n)

where:

X is the sample mean

Z(α/2) is the critical value of the standard normal distribution at α/2 level of significance (α is the level of significance)

σ is the population standard deviation (unknown)

n is the sample size

In this case, X = 119, σ = 16, n = 64, and α = 0.003 (because 99.7% corresponds to the area under the curve outside the range of ±3 standard deviations from the mean, and the standard normal distribution is symmetric around the mean, so we need to split the area of 0.003 equally between the two tails).

Using a standard normal distribution table or calculator, we find that Z(α/2) = Z(0.0015) = 3.090.

Plugging in the values, we get:

Confidence Interval = 119 ± 3.090 * (16/√64)

Confidence Interval = 119 ± 6.18

Therefore, the 99.7% confidence interval for the mean of the population is (112.82, 125.18).

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For the augmented matrix,

1. Row 1 multiplied by -5 is

[tex]\left[\begin{array}{cccc}20&-30&25&15\\-2&4&0&-3\\2&-6&1&-1\end{array}\right][/tex]

2. Row 1 interchanged with row 3

[tex]\left[\begin{array}{cccc}2&-6&1&-1\\-2&4&0&-3\\20&-30&25&15\end{array}\right][/tex]

3. Row 1 multiplied by -2 and added to row 3

[tex]\left[\begin{array}{cccc}2&-6&1&-1\\-2&4&0&-3\\16&42&23&17\end{array}\right][/tex]

An augmented matrix can be described as a rectangular shaped array of numbers that represents a system of linear equations. These numbers are arranged in rows and colums. They can differ  in sizes depending on the array of numbers in the matrix.

The above answer is in response to the questions below as seen in the picture.

Perform the indicated row operation on the given augmented matrix.

[-4 6 -5 -3, -2 4 0 -3, 2 -6  1  -1]

a. Multiply row 1 by -5

[_ _ _ _, _ _ _ _, _ _ _ _]

b. interchange row 1 and row 3

[_ _ _ _, _ _ _ _, _ _ _ _]

c. Multiply row 1 by -2 and add to row 3

[_ _ _ _, _ _ _ _, _ _ _ _]

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Answer:

degree is 4

Step-by-step explanation:

The degree is the largest exponent on the variable, which is 4.

Answer:

Diego will need 21 gallons of yellow paint to make the shade of green paint he desires.

Step-by-step explanation:

According to the given information, Diego wants to make a shade of green paint that requires 3 parts yellow and 7 parts blue.

This means that for every 7 gallons of blue paint, Diego needs 3 gallons of yellow paint.

As Diego is using 49 gallons of blue paint, we can set up the following proportion:

7/49 = 3/x

where x is the amount of yellow paint needed.

To solve for x, we can cross-multiply and simplify:

7x = 3 * 49

7x = 147

x = 21

Therefore, Diego will need 21 gallons of yellow paint to make the shade of green paint he desires.

Answer:

degree of -2x^4 is 4

degree of -3 is 0

degree of 4x^6 is 6

degree of -6x^7 is 7

degree of the polynomial 17

Step-by-step explanation:

the degree of a term is the exponent of the variable. so for the terms, just write down the exponent of X. since -3 does not have a variable, it has a degree of 0. the degree of a polynomial is the sum of the exponents on all variables so 4+6+7=17.

A painting contractor determined the average amount of time needed to paint a house.

- When 2 painters are used, it takes 15 hours to paint

- When 6 painters are used, it takes 5 hours to paint.

If p represents the number of painters and h represent the number of hours required to paint the house, which statement is true about this relationship?

F. The time required to paint a house varies directly with

the number of painters because h = 30p.

G. The time required to paint a house varies directly with

the number of painters because ph = 30.

H. The time required to paint a house varies inversely

with the number of painters because h = 30p.

J. The time required to paint a house varies inversely

with the number of painters because ph = 30.

Answer: 12 years

Step-by-step explanation:

     We will substitute the given amount after the investment period and then solve for t, the number of years the period was.

     Given:

A = 10,000(1 + 0.043t)

     Substitue:

15,160 = 10,000(1 + 0.043t)

     Distribute:

15,160 = 10,000 + 430t

     Subtract 10,000 from both sides of the equation:

5,160 = 430t

     Divide both sides of the equation by 430:

t = 12 years

Since the point (-4, a) is on the graph of y = x², the value of a is equal to 16.

In Mathematics and Geometry, a quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Where:

When x = -4, the value of y or a can be calculated as follows;

y = x²

y = a = (-4)²

y = a = 16.

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the coefficient of the squared term in the equation of this parabola is -1/9.

what is parabola ?

A parabola is a type of symmetrical curve that is defined by a set of points in a plane. It is a conic section, meaning it is formed by the intersection of a plane and a cone. A parabola has a U-shape and can be either upward-facing or downward-facing, depending on its equation.

In the given question,

If the vertex of a parabola is at (h,k), then the equation of the parabola can be written in vertex form as y = a(x - h)² + k, where "a" is the coefficient of the squared term.

We are given that the vertex of the parabola is at (1,-4), so we can write:

y = a(x - 1)² - 4

We are also given that when the y-value is -5, the x-value is 4. Substituting these values into the equation, we get:

-5 = a(4 - 1)² - 4

Simplifying this equation, we get:

-5 = 9a - 4

9a = -1

a = -1/9

Therefore, the coefficient of the squared term in the equation of this parabola is -1/9.

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Solve the trigonometric equation to find a particular solution: [tex]\theta=\text{arccos} \ (0.9659)[/tex] or [tex]\theta=2\pi -\text{arccos} \ (0.9659)[/tex]

Solve the trigonometric equation to find a general solution: [tex]\theta=\text{arccos} \ (0.9659)+2n\pi[/tex] or [tex]\theta=2\pi -\text{arccos} \ (0.9659)+2n\pi[/tex], [tex]n \ \in Z[/tex]

Approximate the inverse trigonometric value: [tex]\theta\thickapprox0.261899+2n\pi[/tex] or [tex]\theta\thickapprox2\pi +-0.261899+2n\pi[/tex], [tex]n \ \in Z[/tex]

Calculate: [tex]\theta\thickapprox6.021286+2n\pi[/tex], [tex]n \ \in Z[/tex]

Find the union of solution sets: [tex]\theta\thickapprox0.261899+2n\pi[/tex] or [tex]\theta\thickapprox6.021286+2n\pi[/tex], [tex]n \ \in Z,n \ \in Z[/tex]

Answer: [tex]\bold{\theta\thickapprox0.261899+2n\pi}[/tex] or [tex]\bold{\theta\thickapprox6.021286+2n\pi}[/tex]

The value of A is approximately 19.318 units.

We can now find the value of side A using the formula for a right-angled triangle:

Cos θ = A / H

where A is the length of the adjacent side, and H is the length of the hypotenuse.

Let's substitute the given values:

0.9659 = A / 20

To find the value of A, we can multiply both sides of the equation by 20:

A = 0.9659 * 20

A ≈ 19.318

So, the value of A is approximately 19.318 units.

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Since the y-intercept of f(x)=4(3)ˣ is (0,4) and the y-intercept for the  table whose function is g(x) = 3²⁻ˣ is (0,9). See the attached graph. Hence, the function with the larger y-intercept is g(x) = 3²⁻ˣ.

In analytic geometry, a point where the graph of a given function or relation intersects with the y-axis of its coordinate system is known as the vertical intercept.

It obeys one standard convention: That all horizontals correspond to values on x and all verticals correspond to those on y. At these points, metrics assessing intersection require that x must always equal zero.

Hence, on the basis of the points at which the curve meets the y axis in  both graphs, we can correctly state that: the function with larger y-intercept is g(x) = 3²⁻ˣ.

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The diameter of the circle is 4 inches.

The diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circumference of the circle.

The area of the circle is 12.6 inches square. Let's find the diameter of the circle as follows:

area of a circle = πr²

area of a circle = π(d / 2)²

where

Therefore,

12.6 = 3.14 × d² / 4

12.6 = 0.785d²

divide both sides by 0.785

d² = 12.6 / 0.785

d = √16.050955414

d = 4.00635744786

Therefore,

diameter = 4 inches

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The domain and range of y = Q(-t) are [-3,-1] and [-4,7], respectively.

The domain and range of y = -Q(t) are [1,3] and [-7,4], respectively.

The domain and range of y = -Q(-t) are [-3,-1] and [-4,7], respectively.

a) In the domain of Q(t), we must replace t with -t for the transformation y = Q(-t). The domain of y = Q(-t) will be [-3,-1] because the domain of Q(t) is [1,3]. The range of Q(t), which is [-4,7], will not change.

As a result, the domain and range of y = Q(-t) are [-3,-1] and [-4,7], respectively.

b) For the transformation y = -Q(t), we must take the negative of Q(t)'s range. Because Q(t) has a range of [-4,7], y = -Q(t) has a range of [-7,4]. The domain of Q(t), [1,3], will remain unchanged.

As a result, the domain and range of y = -Q(t) are [1,3] and [-7,4], respectively.

c) We must take the negative for the transformation y = -Q(-t). in the domain of Q(t) and replace t with -t in the range of Q(-t). Because Q(t) has the domain [1,3], Q(-t) has the domain [-3,-1]. Reflecting the range of Q(t) about the y-axis yields the range of Q(-t). As a result, the range of Q(-t) is [-7,4]. Taking the inverse of the range, we get [-4,7] for y = -Q(-t).

As a result, the domain and range of y = -Q(-t) are [-3,-1] and [-4,7], respectively.

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Answer: 3237 photos

Step-by-step explanation:

Let the number of photos of size 3R that the school ordered be 'x', and the number of photos of size 6R be 'y'.

We know that the school ordered 308 photos of size 3R, so:

x = 308

We also know that the total amount spent on photos was Rs 18500, so:

3x + 6y = 18500

Substituting the value of x from the first equation:

3(308) + 6y = 18500

924 + 6y = 18500

6y = 17576

y = 2929.33 (rounded off to the nearest whole number)

Since the number of photos must be a whole number, we can assume that the school ordered 2929 photos of size 6R.

Therefore, the total number of photos that the school ordered together is:

x + y = 308 + 2929 = 3237

Hence, the school ordered a total of 3237 photos.

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Answer:y = 9x - 1

Step-by-step explanation:

Calculate the slope (m) using the two points (x1, y1) = (2, 17) and (x2, y2) = (-7, -64):

m = (y2 - y1) / (x2 - x1)

m = (-64 - 17) / (-7 - 2)

m = (-81) / (-9)

m = 9

Now that we have the slope (m = 9), we can use one of the points (either (2, 17) or (-7, -64)) to find the y-intercept (b). Let's use (2, 17):

y = mx + b

17 = 9 * 2 + b

17 = 18 + b

b = -1

Now we have the slope (m = 9) and the y-intercept (b = -1), so we can write the equation of the line in the form y = mx + b:

y = 9x - 1

The speed of P when t = 3 seconds is  95.00 m/s

We can find the speed by finding the net force acting on the particle P. Let F_net be the net force acting on P, then we have:

F_net = F₁ + F₂

where:

F₁ = (-i + 2j)N

F₂ = the direction of the vector (i + j).

Let's find the magnitude and direction of F₂. We know that F_net is in the direction of the vector (i + 3j), so we can write:

F_net = F₂ + k(i + 3j)

where:

k = some constant. Since F₂ is in the direction of (i + j), we can write:

F₂ = a(i + j)

where:

a = constant.

Substituting the into the equation for F_net:

F_net = a(i + j) + k(i + 3j)

To find the values of a and k, we use the acceleration of P which is (31 + 9j) m/s². The net force on P is:

F_net = m*a

where m = the mass of P.

Equating the two expressions for F_net:

a(i + j) + k(i + 3j) = m(31 + 9j)

Expanding both sides:

(ai + aj) + (ki + 3kj) = 31m + 9mj

Equating the coefficients of i and j, we get two equations:

a + k = 31m (1)

a + 3k = 9m (2)

Solving these equations:

a = 9m

k = 22m

Substituting these values back into the expression for F_net, we have:

F_net = 9m(i + j) + 22m(i + 3j) = 31mi + 69mj

Now, we can use the equation for acceleration to find the mass of P:

F_net = m*a

31mi + 69mj = m(31 + 9j)

m = 31 / (31 + 9j) = 31 / (31 - 9i)

Next, we shall use the initial velocity and acceleration to find the velocity of P after 3 seconds.

Let v(t) be the velocity of P at time t, then:

v(t) = v(0) + a*t

where v(0) = 3i - 22j and

a = (31 + 9j) m/s²

Substituting t = 3 seconds:

v(3) = (3i - 22j) + (31 + 9j)(3)

= 96i - 1j

Therefore, the speed of P at t = 3 seconds is the magnitude of v(3):

v(3)| = ([tex]\sqrt{96^{2} }[/tex] + (-1)²) = [tex]\sqrt9217[/tex] = 95.00 m/s

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8 feet is the distance between the ground and the top of the ladder

Given the following sides

length of ladder = hyp = 10foot

Distance from ladder to the base = adjacent  = 6 feet

Substitute the given parameters into the formula to have:

10² = opp² + 6²

opp²=100 - 36

opp² = 64

Take square root on both sides

opp = 8 feet

Hence, 8 feet is the distance between the ground and the top of the ladder

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If the given integer is positive, then it is plotted to the right of zero on the number line. If the given integer negative, then it is plotted to the left of zero on the number line.

The series [tex]\lim_{n \to \infty} sin(n)[/tex] does not converge, because the function [tex]sin(n)[/tex] oscillates infinitely between -1 and 1 as n approaches infinity.

More formally, for any positive integer [tex]k[/tex], we can find an integer [tex]n[/tex] such that [tex]n\pi[/tex] is very close to [tex]\pi[/tex], which implies that [tex]sin(n)\approx(-1)^k[/tex]. Therefore, the sequence [tex]{sin(n)}[/tex] does not converge to any limit as [tex]n[/tex] approaches infinity.

Alternatively, we can also prove that [tex]\lim_{n \to \infty} sin(n)[/tex] does not exist using the epsilon-delta definition of a limit. Suppose there exists a limit [tex]L[/tex], then for any [tex]\epsilon > 0[/tex], there exists a positive integer [tex]N[/tex] such that for all [tex]n > N[/tex], we have [tex]|sin(n) - L| < \epsilon[/tex].

However, we can choose [tex]\epsilon = 1/2[/tex] and find two subsequences [tex]{a_n}[/tex] and [tex]{b_n}[/tex] such that [tex]|sin(a_n) - sin(b_n)| = 1[/tex]. Therefore, for any possible limit [tex]L[/tex], we can always find two subsequences that converge to different values, contradicting the assumption that the limit exists.

[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

♥️ [tex]{\underline{\underline{\textrm{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:}}}}}}\\[/tex]

Answer:

FD = 16 units

Step-by-step explanation:

The value of the percentage 64% of 35 is 22.4

To find 64% of 35, we can use the following formula:

percent × whole = part

where percent is the percentage we want to find, whole is the total value, and part is the result we are looking for.

In this case, we want to find 64% of 35, which means that percent = 64 and whole = 35.

Let's substitute these values into the formula:

64% × 35 = part

To calculate the product of 64% and 35, we can convert 64% to a decimal by dividing it by 100:

64% ÷ 100 = 0.64

Substituting this value into the formula, we get:

0.64 × 35 = part

Multiplying 0.64 by 35, we get:

22.4 = part

Therefore, 64% of 35 is 22.4.

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The possible solutions are (1,2), (1,5), (3,4). So correct options are B, C, and D.

In mathematics, an inequality is a statement that compares two values or expressions using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Inequalities are used to represent a range of values that satisfy a certain condition, rather than just a single value.

For example, the inequality x > 5 represents all the possible values of x that are greater than 5. This can include 6, 7, 8, and so on. Similarly, the inequality y ≤ 2x + 1 represents all the possible values of y that are less than or equal to 2 times x plus 1.

Inequalities can be graphed on a number line or in the coordinate plane to show the range of values that satisfy the inequality. They are commonly used in solving problems involving equations, functions, and systems of equations.

We can graph the two inequalities to find the solutions that satisfy both.

The graph of y > 4x - 3 is a blue dashed line with a slope of 4 and y-intercept of -3. We shade the region above the line since the inequality is "greater than".

The graph of y ≥ -2x + 3 is a green dashed line with a slope of -2 and y-intercept of 3. We shade the region above the line since the inequality includes "greater than or equal to".

The shaded regions overlap in the upper-right quadrant, so any point in that region satisfies both inequalities. Looking at the options given:

A. (1,1): Does not satisfy y > 4x - 3

B. (1,2): Satisfies both inequalities

C. (1,5): Satisfies both inequalities

D. (3,4): Satisfies both inequalities

E. (0,5): Satisfies y ≥ -2x + 3 but not y > 4x - 3

Therefore, the possible solutions are B, C, and D.

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