Solve the equation.

9( x− 2)²-4=14

To eliminate factors not discussed, the answer would be 3/7 shed each, assuming everyone builds at the same rate and effort.

The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to achieve the required value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. For example, if a car travels 44 kilometers on two litres of gasoline, we may use the unitary technique to calculate how far it will go on one litre of gasoline.

Here,

3 sheds built by 7 workers,

let x = amount of shed each built

7x = 3

x = 3/7

Assuming everyone built at equal speeds and effort, to remove variables not addressed, the answer would be 3/7 shed each.

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Answer:

145°

Step-by-step explanation:

Angle x and the 35-deg angle are a liner pair, so they are supplementary.

The sum of the measures of two supplementary angles is 180°.

x + 35° = 180°

x = 145°

Answer:

y=1/2x+1

Step-by-step explanation:

I think so I'm not an expert

Answer:

y = - [tex]\frac{1}{2}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 2 ) and (x₂, y₂ ) = (- 4, 1 )

m = [tex]\frac{1-(-2)}{-4-2}[/tex] = [tex]\frac{1+2}{-6}[/tex] = [tex]\frac{3}{-6}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 2 ) , then

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{2}[/tex] x - 1 ← equation of line

(i) Yes, it is even and divisible by 3 as 1 + 0 + 2 = 3

(ii) No, it does not end in 5 or 0

What are Divisibility Rules?

Divisibility criteria can be used to determine whether or not to diminish a fraction. The rules are based on patterns seen while listing the multiples of any integer.

Solution:

(i) 102 is divisible by 6 - TRUE

It is because 102 is even number thus, it is divisible by 2 and since the sum of digits 1 + 0 + 2 is 3 therefore, it is divisible by 3

- Yes, it is even and divisible by 3 as 1 + 0 + 2 = 3

(ii) 102 is divisible by 5 - FALSE

It is because any number to be divisible by 5 it should always end with 5 or 0 at ones place.

- No, it does not end in 5 or 0

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The area of the region bounded by the given curves. y = 6x2 ln(x), y = 24 ln(x) is 2.85 sq.units.

In this question we need to find the area of the region bounded by the given curves. y = 6x^2 ln(x), y = 24 ln(x)

Equating both the equations of the curve,

6x^2 ln(x) = 24 ln(x)

24 ln(x) - 6x^2 ln(x) = 0

x = 1, 2

This means,  the curves intersect at x = 1 and x = 2.

So, the required area would be,

A = ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx

First we find the indefinite integral ∫[24 ln(x) - 6x^2 ln(x)] dx

= -6  ∫[-4 ln(x) + x^2 ln(x)] dx

= -6 ∫ln(x) (x^2 - 4) dx

= -6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x

So,  ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx

= [-6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x] _(x = 1 to x = 2)

= 32 ln(2) - 58/3

= 22.18 - 19.33

= 2.85 sq.units.

Therefore, the area of the region is 2.85 sq.units.

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Answer:

ok so I am also a high school student so my answer may not be correct but here are the answers.

1. 18500

2. 16000

3. 68.3%

4. 47.7%

5. 2.3%

Step-by-step explanation:

To find the answers to questions 1, 2, just add 500 to mean for above and substract 500 for below. I just used a graphic calculator for 3, 4 and 5.

For a casio calculator, here are the steps

menu, 2, dist, norm, ncd,

data: variable

lower: 3. 16500, 4. 17000, 5. 0

upper: 3. 17500, 4. 18000, 5. 16000

deviation: 500

Mean: 17000

Hope this helps.

Answer:

  16.65 ft

Step-by-step explanation:

You want the length of the shortest ladder that will reach from the ground to a building over an 8 ft fence at a distance of 4 ft from the building.

We recall that the trig relations in a right triangle are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

In the model attached, the ladder (GH) makes angle α with the ground. The above relations tell us the ladder length is ...

  GH = GC +CH

  GH = 8/sin(α) +4/cos(α)

Using the reciprocal trig relations, this becomes ...

  GH = 8·csc(α) +4·sec(α)

The minimum length of the ladder corresponds to the value of α that makes the derivative of GH with respect to α be zero.

  GH' = -8·cos(α)csc(α)² +4·sin(α)sec(α)² = 0

Dividing by 4·cos(α)csc(α)², we get

  tan(α)³ -2 = 0

  α = arctan(∛2) ≈ 51.56095°

The length of the shortest ladder is then ...

  GH = 8·csc(51.56095°) +4·sec(51.56095°) ≈ 16.65 . . . . feet

The shortest ladder that will reach is 16.65 feet long.

__

Additional comments

In the second attachment, the horizontal axis is degrees of angle α, and the vertical axis is feet of length GH. The calculator is set to degrees mode.

The derivatives of the trig functions can be found from a suitable table, or by using the power rule with the derivatives of the primary sin and cos functions.

We can divide by cos(α)csc(α)² because we know it is not zero for the angle of interest. The value 2 in the tangent formula is h/d, where the fence is h units high and d units from the building. You will notice the length expression is h·csc(α)+d·sec(α). This is a generic solution for this sort of problem.

The problem can be worked using similar triangles and the Pythagorean theorem. This seems easier. The solution in most cases will be irrational, involving cube roots at some point.

An expression to represent the total penalty fees after 3 days late is given by T = 25d.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total penalty fees after 3 days late;

T = md + b

Where:

Therefore, the required linear function that represents the total penalty fees after 3 days late is given by this mathematical expression;

T = 25d

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Answer:

6

Step-by-step explanation:

        6 is a factor of X , Y and Z.

    So, 6 will be a common factor of X + Y + Z.

The variance of the number of heads which come up when a fair coin is flipped 9 times is 2.25.

In this case, number of trials n = 9

Note that X = X₁ + X₂ + X₃ + X₄ +X₅ + X₆ + X₇ + X₈ + X₉

Xₐ = 0 if the flip #i is tails, and

Xₐ = 1 if the flip #i is heads.

Since the Xi are independent, then we have:

Var (X) = Var (X₁ + … + X₉)

= Var (X₁) + Var (X₂) + … + Var (X₉)

Then,

Var (Xₐ) = E(Xₐ^2) – E(Xₐ)^2

= 1/2 – 1/4

= 1/4

So, the variance is:

Var (X) = Var (X₁) + Var (X₂) + … + Var (X₉)

= 9 * (1/4)

= 9/4

= 2.25

Hence, the variance of the number of heads which come up when a fair coin is flipped 9 times is 2.25.

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Answer:

Day 7

Step-by-step explanation:

Given information:

Therefore, each day Celeste has three times as much as she had the previous day.

This can be expressed by the recursive rule:

[tex]\begin{cases}a_n=3a_{n-1}\\a_1=3\end{cases}[/tex]

Therefore:

[tex]\textsf{Day 2}: \quad a_2=3 \cdot a_{1}=3 \cdot 3=9[/tex]

[tex]\textsf{Day 3}: \quad a_3=3 \cdot a_{2}=3 \cdot9=27[/tex]

[tex]\textsf{Day 4}: \quad a_4=3 \cdot a_{3}=3 \cdot 27=81[/tex]

[tex]\textsf{Day 5}: \quad a_5=3 \cdot a_{4}=3 \cdot 81=243[/tex]

[tex]\textsf{Day 6}: \quad a_6=3 \cdot a_{5}=3 \cdot 243=729[/tex]

[tex]\textsf{Day 7}: \quad a_7=3 \cdot a_{6}=3 \cdot 729=2187[/tex]

So the day on which Celeste will have 2,187¢ is day 7.

The empirical probability of rolling a 3 is 467% more than its theoretical probability

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A six-sided pass-on from obscure predisposition is moved multiple times, and the number 3 comes up multiple times. In the following three adjustments (the bite of the dust is moved multiple times in each round), the number 3 comes up 6 times, 5 times, and 7 times.

Then empirical probability is given as,

P = (6/20) x (5/20) x (7/20)

P = 21/800

P = 0.02625

The theoretical probability is given as,

P = (1/6) x (1/6) x (1/6)

P = 1 / 216

P = 0.004629

Then the percentage is given as,

Percentage = [(0.02625 - 0.004629) / 0.004629] x 100

Percentage = 467%

The empirical probability of rolling a 3 is 467% more than its theoretical probability

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The smaller number is 25 and the larger number is 30.

Given that, the sum of two numbers is 55.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the smaller number be x.

The larger number is 5 more than the smaller number.

Then, the larger number be x+5

The sum of two numbers is 55.

x+x+5=55

⇒ 2x+5=55

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 2x+5=55

⇒ 2x=50

⇒ x=25

So, x+5=30

Therefore, the smaller number is 25 and the larger number is 30.

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b. The correlation coefficient for this data-set is given as follows: r = -0.9877.

c. The correlation between the variables x and y is strong negative.

The correlation coefficient is an index between -1 and 1 that measures the relationship between two variables, as follows:

A data-set is composed by a set of points, and these points are inserted into a correlation coefficient calculator to obtain the coefficient.

From the table described in this problem, the points are given as follows:

(1, 9), (2, 7), (3,6), (4, 1), (7, -2), (8, -5) and (10, -8).

Inserting these points into a calculator, the coefficient is given as follows:

r = -0.9877.

Hence it is a negative and strong relationship, as the absolute value of r is of 0.9877 > 0.6.

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g(x) intercepts the x-axis at x = 3, then the correct option is (3, 0)

For a function y = f(x), we define the x-intercept as the value of x for which:

f(x)=  0

The x-intercepts are also called zeros or roots of the function, and are the points where the graph of the function intercepts the x-axis.

In this case, the function is g(x) = -3x + 9, so here we need write and solve the equation:

g(x) = 0

-3x + 9 = 0

9 = 3x

9/3 = x

3 = x

This means that the x-intercept is x = 3, or (3, 0) written in point form, when we evaluate g(x) in x = 3 we get:

g(3) = -3*3 + 9

g(3) = -9 + 9

g(3) = 0

As expected.

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A level curve of the function f(x, y) is a curve that satisfies the equation f(x, y) = c, where c is a constant.

The diagram is attached at the end of the solution.

A contour map, which is also called a topographic map, is a representation of a three-dimensional feature using contour lines on a plane surface.

The map shows a bird's-eye view and allows people to visualize the hills, valleys, and slopes that are being mapped.

People can see the hills, valleys, and slopes that are being mapped thanks to the map's bird's-eye perspective.

The title, scale, contour interval, legend, and whether latitude and longitude or Universal Transverse Mercator (UTM) coordinates are used are typically included.

Numerous activities, such as camping, urban planning, meteorology, and geologic investigations, can benefit from using this kind of map.

Consider the surface [tex]$f(x, y)=\ln \left(x^2+4 y^2\right)$[/tex].

The level curves for the surface are given by the equation, [tex]$k=\ln \left(x^2+4 y^2\right)$[/tex], where [tex]$k \in \mathbb{R}$[/tex]

Take k = . . . , -3, -2, -1, 0, 1, 2, 3, . . .

Then, draw the different level curves of the surface.

The diagram is attached at the end of the solution.

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The area of the region enclosed by one loop of the curve r = sin(12θ) is π/48.

We have to find the area of the region enclosed by one loop of the curve.

The given curve is:

r = sin(12θ)

Consider the region r = sin(12θ)

The area of region bounded by the curve r = f(θ) in the sector a ≤ θ ≤ b is

A =

Now to find the area of the region enclosed by one loop of the curve, we have to find the limit by setting r=0.

sin(12θ) = 0

sin(12θ) = sin0   or    sin(12θ) = sinπ

So θ = 0             or      θ = π/12

Hence, the limit of θ is 0 ≤ θ ≤ π/12.

Now the area of the required region is

A = [tex]\int ^{\pi/12}_{0} \frac{1}{2}(\sin12\theta)^2d\theta[/tex]

A = [tex]\frac{1}{2}\int ^{\pi/12}_{0}\sin^212\thetad\theta[/tex]

A = [tex]\frac{1}{2}\int ^{\pi/12}_{0}\frac{1-\cos24\theta}{2}d\theta[/tex]

A = [tex]\frac{1}{4}\int ^{\pi/12}_{0}(1-\cos24\theta)d\theta[/tex]

A = [tex]\frac{1}{4}\left[(\theta-\frac{1}{24}\sin24\theta)\right]^{\pi/12}_{0}[/tex]

A = [tex]\frac{1}{4}\left[(\frac{\pi}{12}-\frac{1}{24}\sin24\frac{\pi}{12})-(0-\frac{1}{24}\sin24\cdot 0)\right][/tex]

A = [tex]\frac{1}{4}\left[(\frac{\pi}{12}-\frac{1}{24}\sin2\pi)-(0-\frac{1}{24}\sin0)\right][/tex]

A = 1/4[(π/12-0)-(0-0)]

A = 1/4(π/12)

A = π/48

Hence, the area of the region enclosed by one loop of the curve r = sin(12θ) is π/48.

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To calculate how much Kaitlyn will have after four years with continuous compounding, we can use the following formula:

A = P * e^(r*t)

where A is the final amount, P is the initial principal (in this case, $3,000), r is the annual interest rate (4.08%), and t is the number of years (4). Plugging these values into the formula, we get:

A = $3,000 * e^(0.0408*4)

= $3,000 * e^0.1632

= $3,000 * 1.1759

= $3,527.77

Therefore, Kaitlyn will have $3,527.77 after four years with continuous compounding, which is close to [A] $3,532.18.

Answer:

The answer C) 5 * 106

Step by step explanation:

Answer:

4 ( 2q + 5 )

Step-by-step explanation:

8q + 20

HCF is 4

= 4 ( 2q + 5 )

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Answer:

Below

Step-by-step explanation:

Slope = rise/run = 2/3

Point (3,5)      y-5 = 2/3 (x-3)

                         y = 2/3x +3

Answer:

The area of the rectangular lawn is 100m long and 45m wide, so it has an area of 100 * 45 = <<10045=4500>>4500m².

The three circular ponds have diameters of 20m, 10m, and 5m, so their areas are 314.16, 78.54, and 19.63 square meters respectively.

The total area of the ponds is 314.16 + 78.54 + 19.63 = <<314.16+78.54+19.63=412.33>>412.33 square meters.

The total area of the lawn that needs to be covered with grass seed is 4500 - 412.33 = <<4500-412.33=4087.67>>4087.67 square meters.

Each packet of grass seed covers 50 square meters, so Mrs Jones will need 4087.67 / 50 = <<4087.67/50=81.75>>81.75 packets of grass seed.

Each packet costs £1.49, so the total cost to Mrs Jones will be 81.75 * 1.49 = £<<81.751.49=121.78>>121.78. Answer: {121.78}.

Step-by-step explanation:

The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.

We have been given parametric equations x = t^2 − 3t, y = √t

We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

NWe know that the formula to find the area under the curve.

A = ∫[a to b] g(t)f'(t) dt

here, a = 0 and b = 3

so, A = ∫[0 to 3] √t (2t - 3) dt

A = ∫[0 to 3] (2t√t - 3√t) dt

A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt

A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]

A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0

A = 4/5 3^(5/2) - 2 3^(3/2)

A = 6√3 /5

A = 2.08

Therefore,  the area of the curve is 2.08 square units.

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Answer:

-6, 7

Step-by-step explanation:

Answer: B(-6,7)

Step-by-step explanation:

M(-5, 1)      A(-4,-5)       B(x,y)=?

[tex]\displaystyle\\M_x=\frac{x_A+x_B}{2} \\\\-5=\frac{-4+x_B}{2}\\\\[/tex]

Multiply both parts of the equation by 2:

[tex]-5(2)=-4+x_B\\\\-10=-4+x_B\\\\-10+4=-4+x_B+4\\\\-6=x_B\\\\Thus,\ x_B=-6[/tex]

[tex]\displaystyle\\\\\\1=\frac{-5+y_B}{2} \\\\[/tex]

Multiply both parts of the equation by 2:

[tex]1(2)=-5+y_B\\\\2=-5+y_B\\\\2+5=-5+y_B+5\\\\7=y_B\\\\Thus,\ y_B=7[/tex]

Answer: 1. 108.     2. 1         mark brainlist if helpful

Step-by-step explanation: hope it helps

98 plus 10.   108 plus one 109.  

Answer:

C. y=4/3x-1

Step-by-step explanation:

I plotted all equations on Desmos. A, B and D all had a solution with the equation of line a, they both had an interception so they were wrong. C. is the only that does not have an interception with line a. They didn't intercept and were parallel meaning that they will never touch or won't have a solution.

To determine the length of the picture, we can set up the following equation:

length = 4 * width

Substituting in the given value for the width, we get:

length = 4 * 24 inches

Solving this equation gives us a length of 96 inches. Therefore, the length of the picture is 96 inches.

Answer:

1080cm²

Step-by-step explanation:

Area of a quadrilateral = 1/2 x length of diagonal (length of perpendicular)

[tex] \frac{1}{2} \times 10(18 \times 12) \\ \frac{1}{2} \times 10(216) \\ \frac{1}{2} \times 2160 \\ {1080cm}^{2} [/tex]