Is 9/12 bigger then 6/2

The volume of the pyramid  of height h with an equilateral triangle base with side a, by using the method of volumes by SLICES  is V = a²h/3.

We can use the method of volumes by slices to find the volume of the pyramid.

Consider a slice of the pyramid that is perpendicular to the base and at a distance x from the apex. This slice has a cross-sectional area of a square with side length (base of pyramid) s, We can use the Pythagorean theorem to find that the

Height of the slice is \(\sqrt{(a^2 - (a/2)^2 - x^2)} = \sqrt{(3a^2/4 - x^2).\)

Therefore, the volume of the slice is given by the product of its cross-sectional area and height:

dV = s^2 dh = (a^2 - 4x^2)/4 dh

To find the total volume of the pyramid,

we integrate dV from x=0 to x=h:

V = ∫₀ʰ (a²-4x²)/4 dx

Simplifying the integrand, we get:

V = (1/4) ∫₀ʰ (a² - 4x²) dx

V = (1/4) [a²x - (4x³)/3] from x=0 to x=h

V = (1/4) [a²h - (4h³)/3]

V = a²h/3

Therefore, the volume of the pyramid is V = a²h/3.

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By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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Answer:

A) 75

Step-by-step explanation:

All 3 angles of any triangle add up to 180° so we can subtract all known angles from 180° to get the missing angle.

40°+65°=105°

180°-105°

75°

Answer:

y=1/3x

When x of the line is -3, y of the line must be -1.When x of the line is 6, y of the line must be 2. y=1/3x+b. b is what we want, the 1/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the two points (-3,-1) and (6,2).(-3,-1). y=mx+b or -1=1/3 × -3+b, or solving for b: b=-1-(1/3)(-3). b=0.b came out to be zero, so there is no "+b" term.

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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The additional two roots of the polynomial are 1 - √11 and - 3 - √17.

In accordance with quadratic formula, quadratic functions of the form a · x² + b · x + c have two roots of the form α ± β: x₁ = α + β, x₂ = α - β, where α, β are real numbers. Therefore, the polynomial must be a quartic function, whose complete set of roots are: x₁ = 1 + √11, x₂ = 1 - √11, x₃ = - 3 + √17, x₄ = - 3 - √17.

The quartic function has two additional roots: 1 - √11, - 3 - √17.

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Answer:

x = 4√2

Step-by-step explanation:

Identifying the triangle in the diagram:

45-45-90 triangle rules:

Finding x:

Since the hypotenuse is 8 units long and, we can find x by setting 8 equal to x√2:

(8 =  x√2) / √2

8/√2 = x

Rationalize the denominator to simplify:

(8/√2) * (√2/√2)

8√2 / 2

4√2

Thus, x = 4√2

nose si entendí bien el problema pero espero poder ayudar

Step-by-step explanation:

8 es igual a 100%, por lo que podemos guardarlo como 8 = 100% El valor que buscamos puede llamarse x Ahora sabemos que xes 72 del valor de salida, por lo que podemos escribirlo como x = 72. Así que tenemos dos ecuaciones simples: 1) 8=100% 2) = 72%Cuando comparamos estas dos ecuaciones, obtenemos: 8 / x = (100%) / (72%)Ahora solo tenemos que resolver la ecuación simple. Nosotros calculamos 72 por ciento de 8: 8 / x = 100/72(8 / x) * x = (100/72) * x8 = 1,3888888888889 * X8 / 1.3888888888889 = X5.76 = xx = 5,76

The solutions to the questions are:

The function is an exponential function.

So, the parent function has the form

y = ab^x

Using the function in (a), the parent function is: y = -7/8 * 2^x and the form of the function is g(x) = -7/8(2^-5x) + 7

First, the function is horizontally stretched by -5

This gives

g(x) = -7/8(2^-5x)

First, the function is shifted up by 7 units

This gives

g(x) = -7/8(2^-5x) + 7

The equation of the function is given as:

g(x) = -28/[2^(5x + 5)] + 7

Rewrite the equation as follows:

g(x) = -28/[2^(5x) * 2^5] + 7

Evaluate the exponent

g(x) = -28/[2^(5x) * 32] + 7

Divide

g(x) = -7/[2^(5x) * 8] + 7

Rewrite as:

g(x) = -7/[8 * 2^(5x)] + 7

Further, rewrite as:

g(x) = -7/8 * 2^(-5x) + 7

Rewrite properly as:

We have:

g(x) = -7/8 * 2^(-5x) + 7

Set the radical to 0

g(x) = 0 + 7

Evaluate

g(x) = 7

This represents the horizontal asymptote (it has no vertical asymptote)

Hence, the horizontal asymptote is y = 7 and the function is an example of exponential decay

The function can take any input

So, the domain is -∝ < x < ∝

We have the horizontal asymptote to be

y = 7

The function cannot equal or exceed this value.

So, the range is y < 7

Set x = 0

g(0) = -7/8 * 2^(-5 * 0) + 7

This gives

g(0) = -7/8 * 2^(0) + 7

Evaluate the exponent

g(0) = -7/8 + 7

Evaluate the sum

g(0) = 49/8

So, the y-intercept is 49/8

Set g(x) = 0

0 = -7/8 * 2^(-5x) + 7

This gives

-7 = -7/8 * 2^(-5x)

Divide by -7

1 = 1/8 * 2^(-5x)

Multiply by 8

8 = 2^(-5x)

Solve for x

x = -0.6

So, the x-intercept is -0.6

See attachment for the sketch

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The distance between the points P and Q is 25 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by,

\(D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1_)^2\).

Given, Point P has coordinates (1, 3) and point Q has coordinates (25,10).

Therefore, The 25 units.of the line segment, PQ is,

\(|PQ| = \sqrt{(25 - 1)^2 + (10 - 3)^2\).

\(|PQ| = \sqrt{(24)^2 + (7)^2\).

\(|PQ| = \sqrt{576 + 49\).

\(|PQ| = \sqrt{625}\).

PQ = 25 units.

So, The length of the line segment PQ is 25 units.

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The surface area of the right rectangular prism is given as follows:

358 m².

The surface area of a prism is obtained with the sum of the areas of each part of the prism.

The parts that compose the prism are given as follows:

The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.

Hence the surface area of the prism is calculated as follows:

S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².

(multiplication by two due to the two rectangles with each of the dimensions).

The prism is given by the image shown at the end of the answer.

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The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.

Time series data refers to a collection of data points that are measured over time at regular intervals. The time series data could refer to various metrics such as sales, revenue, foot traffic, website traffic, inventory levels, and other relevant business metrics that change over time.

By analyzing time series data, businesses can gain insights into trends, patterns, and other factors that can affect their operations.  

Time series can be used for forecasting. By analyzing past trends and patterns, businesses can make predictions about future performance and take proactive measures to achieve their goals.  

Since the time series will follow the trend, have multiple choices, and will be cyclical and it will analyze the patterns over time periods seasonally.

Therefore,

The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.

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Where F_pivot is the magnitude of the force exerted on the pivot point.

What are perpendicular lines?

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, if you draw a line perpendicular to another line, the two lines will form four right angles at the point where they intersect.

(a) The torque applied by the adult rider (on the left) can be calculated as the product of the force applied by the rider and the perpendicular distance from the pivot to the force. Let F_a be the force applied by the adult rider and let r_a be the perpendicular distance from the pivot to the force. Then, the torque applied by the adult rider is:

τ_a = F_a * r_a

The perpendicular distance r_a can be calculated using the Pythagorean theorem:

r_a = sqrt((L/2 - d)^2 + Xoffset^2)

Therefore, the torque applied by the adult rider is:

τ_a = F_a * sqrt((L/2 - d)^2 + Xoffset^2)

(b) Similarly, the torque applied by the child rider (on the right) can be calculated as:

τ_c = F_c * sqrt((L/2 + d)^2 + Xoffset^2)

where F_c is the force applied by the child rider and r_c is the perpendicular distance from the pivot to the force, which can be calculated using the Pythagorean theorem.

(c) The torque applied by the board can be calculated as the sum of the torques applied by the two riders:

τ_b = τ_a + τ_c

Substituting the expressions for τ_a and τ_c, we get:

τ_b = F_a * sqrt((L/2 - d)^2 + Xoffset^2) + F_c * sqrt((L/2 + d)^2 + Xoffset^2)

(d) To determine the distance d in terms of given quantities and variables, we can use the condition for static equilibrium, which requires that the sum of the torques about the pivot point is zero:

τ_a + τ_c = 0

Substituting the expressions for τ_a and τ_c and simplifying, we get:

F_a * (L/2 - d) = F_c * (L/2 + d)

Solving for d, we get:

d = (F_a/F_c - 1) * L/4

Substituting F_a = Mg and F_c = mg, where M is the mass of the adult rider, m is the mass of the child rider, and g is the acceleration due to gravity, we get:

d = (M/m - 1) * L/4

(e) The magnitude of the force exerted on the pivot point by the see-saw while in use can be calculated using the condition for static equilibrium, which requires that the sum of the forces in the vertical direction is zero:

F_a + F_c = Mg + mg

Substituting F_a = Mg and F_c = mg, we get:

F_pivot = Mg + mg

Therefore, where F_pivot is the magnitude of the force exerted on the pivot point.

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Roland's percent error is approximately 3.889%.

This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.

The positive sign indicates that Roland's measured value is slightly lower than the actual value.

To calculate Roland's percent error, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100

Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:

Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100

Simplifying the expression within the absolute value:

Percent Error = (|-0.007| / 0.180) \(\times\) 100

Since the absolute value of -0.007 is 0.007, we have:

Percent Error = (0.007 / 0.180) \(\times\) 100

Calculating the division:

Percent Error = 0.03889 \(\times\) 100

Percent Error = 3.889%.

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Answer:

0

Step-by-step explanation:

7 + (-8) + 2 + (-1)

is the same as:

7 - 8 + 2 - 1

Simplify these:

-1 + 1

Solve:

0

The data correlation in the scatter plot above include the following: B. positive.

In Mathematics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.

By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation between the x-values and y-values because they both increase simultaneously.

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Answer:

17

Step-by-step explanation:

STUDY HARD GUYS I NEED HW HELP

Answer:

1

Step-by-step explanation:

65.751 = 6 x 10 + 5 x 1 + 7 x 1/10 + 5 x 1/100 + 1 x 1/1,000

6 x 10 = 60

5 x 1 = 5

7 x 1/10 = 0.7

5 x 1/100 = 0.05

1 x 1/1000 = 0.001

60 + 5 + 0.7 + 0.05 + 0.001 = 65.751

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the quantity (in mL) of pure alcohol needed for the mix. Then the amount of 75% needed is (250-x). The amount of alcohol in the mixture is ...

  1.00x +0.75(250 -x) = 0.90(250)

  0.25x +187.5 = 225 . . simplify

  0.25x = 37.5 . . . . . . . . subtract 187.5

  x = 150 . . . . . . . . . . . . . divide by 0.25

  (250 -x) = 100 . . . . mL of 75% solution

You need 100 mL of the 75% solution and 150 mL of pure alcohol to obtain the desired mixture.

Answer:

.aabc=amn0#1211

Step-by-step explanation:

nosascoOsasco n=12.8

Answer:

21

Step-by-step explanation:

(-4)(-2)+2(6+5)

(8)+2(11)

10+11

21

Hope this helps! :)

Answer:32

Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32

It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.

As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.

The right axis indicates the global consumption rate of oil in millions of barrels per day.

To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.

The bottom axis is time in years.

The graph attached at the end of the solution.

Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.

Let the number of years of transition from using 100 million to 200 million barrels per day be b.

From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.

But it takes 50 years to go from 100 million to 200 million.

This is known as exponential growth.

Therefore, the value of a is 120 and the value of b is 50.

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Step-by-step explanation:

Given:

h=7in

w=9in

l=6in

Required:

v=?

Formula:

v=l*w*h

Solution:

v=l*w*h

v=6in*9in*7in

v=54in^2*7in

v=378in^3

Hope this helps ;) ❤❤❤

Answer:

43.6 has 3 significant figures.

Answer:

Step-by-step explanation:

y = mx + b

y = -x/3 + b

1 = -2/3 + b

b = 5/3

y = -x/3 + 5/3

Answer:

D

Step-by-step explanation:

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

The distance between the two points is 19 units.

The formula for measuring distance between two lines, the total length of all a polygon's sides, the perimeter of a polygon on a coordinate plane, the area of a polygon, and many other things are all found in analytical geometry. For instance, we can use the distance formula to find the lengths of a triangle's sides and determine whether it is scalene, isosceles, or equilateral.

Distance formula: \(d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

The distance between two points in a coordinate plane is given by the distance formula:

\(d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

Using the given coordinates:

\(d = \sqrt{((-3 - (-3))^2 + ((-9) - 10)^2)}\)

Simplifying:

\(d = \sqrt{(0^2 + (-19)^2)}\\\\d =\sqrt{(361)}\\\\d = 19\)

Therefore, the distance between the two points is 19 units.

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The rocket will splash down in t = 17.054 seconds and the rocket peaks at 423.694 meters.

Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given function is a quadratic function.

Height of the rocket, as a function of time, is given by,

h(t) = -4.9t² + 76t + 129

When the rocket splash down into the ocean, the height of the rocket above sea level will be 0.

-4.9t² + 76t + 129 = 0

Solving the quadratic equation will get the required t.

Discriminant = \(\sqrt{(76)^2-(4*-4.9*129)}\) = 91.1285

t = (-76 ± 91.1285) / (2 × -4.9)

t = 17.054 or t = -1.5437

Negative time is not possible.

So t = 17.054 seconds

Graph of a quadratic function is a parabola.

Since the leading coefficient of the given function is -4.9, which is negative, parabola opens downward.

Peak point will be the vertex of the parabola.

Vertex of the parabola f(x) = ax² + b x + c = (-b/2a, f(-b/2a))

Vertex of h(t) = -4.9t² + 76t + 129 :

t = -76 / (2 × -4.9) = 7.755 seconds

h(7.755) = -4.9(7.755)² + (76 × 7.755) + 129

             = 423.694 meters

Hence rocket will splash down into the ocean in t = 17.054 seconds and the maximum height of the rocket will be 423.694 meters.

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x=62 bec 180-118=62.

Step-by-step explanation:

180=118-x

180-118=x

x=62