Bricks are going to be packed into a crate which has a space inside of 2.8m3. The volume of each brick is 16000cm3. Given that an exact number of bricks that can be packed into the crate. how many bricks can it hold

Answer:

8

Step-by-step explanation:

By intersecting tangent secant theorem:

\( {x}^{2} = 4(4 + 12) \\ \\ {x}^{2} = 4 \times 16 \\ \\ {x}^{2} = 64 \\ \\ x = \sqrt{64} \\ \\ x = 8\)

Answer:

6.9

Step-by-step explanation:

If a secant segment and tangent segment are drawn to a circle from the same external point, the product of the length of the secant segment and its external part equals the square of the length of the tangent segment

x² = 4 * 12

x² = 48

Take the square root of both sides

x = 6.9282032303

Rounded

x = 6.9

The equation y= -x/3 - 1 is the answer in slope-intercept form .

We have,

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (-6,-3) and, (6,-7)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y+3)/(x+6)=(-7+3)/(6+6)

=> 3y + 9 = -x +6

=>3y = -x -3

=>y= -x/3 - 1

Hence, the required equation is,  y= -x/3 - 1

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The required value of x for the given equation of line is 3.

The equation of straight line is defined as the y = mx +c or ax + by = c, where y is point on y-axis and x is the point n x-axis, m is slope of the line.

According to given data in the question:

we have,

8x-3y=21-----(1)

And 3x+y=10

multiply 3 both sides

9x+3y=30------(2)

To find the value of x,

Add equation 1 and 2, we get

x = 3

Thus required value of x is 3.

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Answer:

b = -2.7

Step-by-step explanation:

Isolate the variable, b

-5 = b - 2.3

add 2.3 to both sides (to isolate variable b)

-5 + 2.3 = b - 2.3 + 2.3

-2.7 = b + 0

-2.7 = b

Check work:

-5 = -2.7 - 2.3

-5 = -5

Correct

Answer:

AC = 7.3 in

Step-by-step explanation:

tan(51°) = 9/AC

1.24 = 9/AC

AC = 9/1.24

AC = 7.26

The variances of x and x + 24 will be different.

Variance is a measure of how spread out the values of a random variable are and is calculated by taking the square of the standard deviation. Adding 24 to the random variable will change the values and therefore, the variance of the new random variable will be different than the original one.

More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.

The value of variance is equal to the square of standard deviation, which is another central tool.

Variance is symbolically represented by σ2, s2, or Var(X).

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discrete, you cannot have 1.5 televisions

generally the number of X is a discrete variable.

continous = can contain decimal value  (float values)

discrete = no decimal  (integers)

The value of the copier after 3 years and 6 months can be found by substituting t = 3.5 into the function and solving for V. The salvage value of the copier can be found by substituting t = 5 into the function and solving for V.

After 3 years and 6 months of use, the copier is worth $5,800. This can be found by substituting t = 3.5 into the function V(t)-3600t+20000: V(3.5) = 3600(3.5) - 20000 + 20000 = $5,800.

The salvage value of the copier after 5 years of use is $4,000. This can be found by substituting t = 5 into the function V(t)-3600t+20000: V(5) = 3600(5) - 20000 + 20000 = $4,000. This is the value of the copier when it is sold or replaced after 5 years of use.

The domain of the function is all real numbers because time and value can take on any real value. However, since the function is only defined for the first 5 years of use, t must be between 0 and 5.

The graph of the function is a downward-sloping line with an intercept of $20,000 on the y-axis and a slope of -3600. This means that the value of the copier decreases by $3,600 each year. At t = 0, the copier is worth $20,000, and after 5 years, it is worth $4,000. The graph is a straight line because the function is linear.

Complete Question:

The function V(t)-3600t+20000, where V is value and t is time in years, can be used to find the value of a large copy machine during the first 5 years of use. a. What is the value of the copier after 3 years and 6 months? After 3 years and 6 months, the copier is worth $ b. What is the salvage value of the copier if it is replaced after 5 years? After 5 years, the salvage value of the copier is ts c. State the domain of this function. d. Sketch the graph of this function. 20000 18000 16000 14000 12000 10000 8000 6000+ 4000 2000 4 .

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1) General solution for second order differential equation, y" – 2y' + y = 0, is y = (c₁x + c₂)eˣ .

2) General solution for differential equation, 9y" + 6y' + y = 0, is y =(c₁x + c₂)e⁻³ˣ.

3) General solution for differential equation, 4y"- 4y'- 3y = 0, is y = c₁ e⁶ˣ+ c₂e⁻⁴ˣ.

4) General solution for differential equation, 4y" + 12y' +9y = 0, is y = (c₁x + c₂)e⁻⁶ˣ.

5) General solution for differential equation, y" – 2y' + 10y = 0, is y = eˣ (c₁cos(6x) + c₂sin(6x)).

6) General solution for differential equation, y" – 6y' +9y = 0 is y = (c₁x + c₂)e³ˣ.

7) General solution for differential equation, 4y" + 17y' + 4y = 0, is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) General solution for differential equation, 16y" + 24y' +9y = 0, is y = (c₁x + c₂)e⁻¹²ˣ.

9) General solution for differential equation, 25y" – 20y' + 4y = 0, is y = (c₁x + c₂)e¹⁰ˣ.

10) General solution for differential equation, 2y" + 2y' + y = 0, is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

General solution is also called complete solution and complete solution = complemantory function + particular Solution

Here right hand side is zero so particular solution is equals to zero. Therefore, evaluating the complementary function will be sufficient to determine the general solution to the differential equation.

1) y"-2y' + y = 0, --(1)

put D = d/dx, so (D² - 2D + 1)y =0

Auxiliary equation for (1) can be written as, m² - 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula,

\(m =\frac{-(- 2) ± \sqrt { 4 - 4}}{2}\)

=> m = 1 , 1

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)eˣ .

2) 9y" + 6y' + y = 0 or (9D² + 6D + 1)y =0 Auxiliary equation can be written as, 9m² + 6m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (6) ± \sqrt {36 - 4×4}}{2}\)

=> m = - 6/2

=> m = -3 , -3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻³ˣ.

3) 4y"- 4y'- 3y = 0

put D = d/dx, so (4D² - 4D - 3)y = 0

Auxiliary equation can be written as, 4m² - 4m - 3 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(-4) ± \sqrt {16 - 4×4×(-3)}}{2}\)

=> m = (4 ± 8)/2

=> m = -4 , 6

The roots of equation are real and equal. So, general solution is y = c₁ e⁶ˣ + c₂e⁻⁴ˣ.

4) 4y" + 12y' +9y = 0 or (4D² + 12D + 9)y= 0

Auxiliary equation can be written as, 4m² + 12m + 9= 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(12) ± \sqrt{144 - 4×4×9}}{2}\)

=> m = -12/2

=> m = -6 , -6

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻⁶ˣ.

5) y" – 2y' + 10y = 0 or (D² - 2D + 10)y = 0 Auxiliary equation can be written as, m² - 2m + 10 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-2) ± \sqrt {4 - 4×1×10}}{2}\)

=> m = (2 ± 6i)/2 ( since, √-1 = i)

=> m = 1 + 6i , 1-6i

The roots of equation are imaginary and unequal. So, general solution is y =eˣ (c₁cos(6x) + c₂sin(6x)).

6) y" – 6y' +9y = 0 or (D²- 6D + 9)y =0

Auxiliary equation can be written as, m² - 6m + 9 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-6) ± \sqrt {36 - 4×1×9}}{2}\)

=> m = 6/2 = 3,3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e³ˣ.

7) 4y" + 17y' + 4y = 0 or (4D²+ 17D + 4)y=0

Auxiliary equation can be written as, 4m² + 17m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{- (-17) ± \sqrt {16 - 4×4×17}}{2}\)

=> m = ( -17 ± 15)/2

=> m = (-17 + 15)/2, (- 17 - 15)/2= -1, -16

The roots of equation are real and unequal. So, general solution is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) 16y"+24y'+9y =0 or (16D²+ 24D + 9)y= 0

Auxiliary equation can be written as, 16m² + 24m + 9 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (24) ± \sqrt {576 - 4×9×16}}{2}\)

=> m = (-24 ± 0)/2

=> m = -12,-12

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻¹²ˣ.

9) 25y"- 20y' +4y =0 or (25D²-20D + 4)y = 0

Auxiliary equation can be written as, 25m²- 20m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (-20) ± \sqrt {400 - 4×4×25}}{2}\)

=> m = 20/2

=> m = 10 , 10

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e¹⁰ˣ.

10) 2y" + 2y' + y = 0 or (2D²+ 2D + 1)y =0

Auxiliary equation can be written as, 2m² + 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (2) ± \sqrt {4 - 4×1×2}}{2}\)

=> m = (- 2 ± 4i)/2 ( since, √-1 = i)

=> m = -1 + 2i , -1 - 2i

The roots of equation are imaginary and unequal. So, general solution is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)). Hence, required solution of differential equation is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

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Answer:

B. 0

Step-by-step explanation:

Use the formula  

x  =  −  b /2 a

to find the maximum and minimum.

( − 3 , 0 )

Answer: A. f(x) = 4 . (2)

Step-by-step explanation: Disregard answer above. I took the quiz and it was wrong.

The mass of the rectangular sheet of metal based on its dimensions can be found to be 0.00532 kg

First, find the area of the rectangular sheet of metal:

= Length x Width

= 15.7 x 12.9

= 202.53 cm²

The mass of the rectangular sheet of metal is 38.1g per cm² so the mass in grams is:
= 202.53 / 38.1

= 5.3157 grams

In kilograms this is:

= 5.3157 / 1,000

= 0.00532 kg

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Answer:

719.412

Step-by-step explanation:

S(x)=-.228x^2+8.154x-8.3 x=7 feet

Plug in 7 for x, you'll convert to inches at the end

S(x)=.228(7^2) +8.154(7)-8.3

S=49(.228)+8.154(7)-8.3

S=11.173+57.078-8.3

S=59.951

Multiply by 12 to get inches

719.412

(If this answer doesn't work then you probably need to convert to inches before plugging in for x. 7 x 12=84 so plug that in.)

The corresponding rectangular coordinates for point q are (-3√3, -3)

To find the corresponding rectangular coordinates for point q, we need to use the formula:
x = r cos(theta)
y = r sin(theta)

where r is the radial distance and theta is the angle measured counterclockwise from the positive x-axis in radians.

In this case, the given polar coordinates are (6, 7π/6). So, we have:
r = 6
theta = 7π/6

Substituting these values into the above formulas, we get:
x = 6 cos(7π/6) = 6 (-√3/2) = -3√3
y = 6 sin(7π/6) = 6 (-1/2) = -3

Therefore, the corresponding rectangular coordinates for point q are (-3√3, -3).

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The equation of a line is y = mx +b

m = slope - which is equal to 1

x = x coordinate

b = y intercept (where the line hits the y axis)

y = y coordinate.

The point (2, 0) shows that when x = 2, y = 0. So we can plug that into the equation:

0 = 1(2) + b

0 = 2 + b

0 - 2 = 2 -2 +b

-2 = b

So the equation of the line is y = x - 2

I hope this helps!

The correct function for h(x), which represents the transformation of f(x) by shifting it down 4 units and right 3 units, is h(x) = |x - 3| + 4. To determine the correct function for h(x) that represents the desired transformation of f(x).

We need to understand the effects of shifting down and right on the absolute value function. Shifting a function down by a certain number moves all the points on the graph vertically downward by that amount. In this case, f(x) is shifted down by 4 units. To achieve this, we add 4 to the original function, resulting in |x| + 4.

Shifting a function right by a certain number moves all the points on the graph horizontally to the right by that amount. In this case, f(x) is shifted right by 3 units. To achieve this, we replace x in the function with (x - 3), resulting in |x - 3|.Combining the two transformations, we have h(x) = |x - 3| + 4, which correctly represents the function obtained by shifting f(x) down 4 units and right 3 units.

In h(x) = |x - 3| + 4, the term |x - 3| represents the absolute value of the shifted variable x - 3, and adding 4 moves the entire graph vertically upward by 4 units. Therefore, h(x) = |x - 3| + 4 is the correct function for h(x), representing the desired transformation of f(x) by shifting it down 4 units and the right 3 units.

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Each flight has a probability of 60% or 0.6 of being on time. This means that its complement, or the probability that the flight isn't on time is:

It is 40% or 0.4. "~P(on time)" stands for the probability of the flight not being on time.

1. The probability that at least 2 flights are on time is:

To find the probability that 2 or more flights are on time we can fight the probability that "0" or "1" are not on time.

The probability of 2 or more flights are on time is:

The probability of 2 flights or more are on time is 0.996198912

2.

We need to calculate the probabilities of 7,8 and 9 flights are on time and then subtract by 1.

The probability of at most 6 flights are on time is:

The probability of 6 or less are on time is 0.768212992.

3.

The probability of exactly 5 flights are on time is:

The probability of exactly 5 flights are on time is 0.250822656.

Answer:

6) 40°

7) 65°

8) 65°

Step-by-step explanation:

6) Total angle in a triangle is 180

180-70-70 = 40

7) y + 55 + 60 = 180

y = 65

8) 50 + n + n = 180

50 + 2n = 180

2n = 180 - 50

2n = 130

n = 130/2 = 65

Answer:

The numerator of the first fraction 8 is greater than the numerator of the second fraction 3 , which means that the first fraction 812 is greater than the second fraction 312 and that 23 is greater than 14 .

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

\(2 \frac{3}{4} - 4 \frac{1}{4} \\ = > \frac{11}{4} - \frac{17}{4} \\ = > \frac{ - 6}{4} \\ = > \frac{ - 3}{2} \)

If the median of a normal distribution is known, it can be said that the mean of the distribution is also equal to the median. This is because the normal distribution is symmetric, with the median and mean at the center of the curve.

For a normal distribution, the mean and median are equal, so if the median is known, then the mean is also known. In a normal distribution, the median represents the point where exactly half of the data falls below and half falls above that point. Since the mean is also the point where the data balances out, meaning the sum of the values above the mean is equal to the sum of the values below the mean, it is also equal to the median. Therefore, if the median of a normal distribution curve is known, we can conclude that the mean is also equal to that value.

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Answer:

I found the answer on this website. It seems correct! Link Below!

Step-by-step explanation

fractions.com/shirynsanswers/odben

Answer:

1/2

Step-by-step explanation:

Answer:

> 1/1,250

Step-by-step explanation:

Convert the decimal value into the fraction by determining the placement value of the decimal.

> 0.0008 = 8/10,000

Since it’s in the ten-thousandths place, this’ll be the denominator. Now, after you’ve done that, reduce the fraction until it is simplified completely.

> 8/10,000 = 1/1,250

Your overall or simplified fraction should be 1/1,250

Answer:

\(10\)

Step-by-step explanation:

\(5m-4n+p\)

You would substitute in the given values and then combine like terms

\(m=4\\n=3\\p=2\)

\(5(4)-4(3)+(2) = 20-12+2=10\)

A teacher may receive funding from the school to buy arithmetic amount notebooks for the pupils in their class. Materials like notebooks, pens, calculators, and other essential items can be purchased with this money.

A teacher may receive funding from the school to buy arithmetic notebooks for the pupils in their class. Materials like notebooks, pens, calculators, and other essential items can be purchased with this money. It is crucial to provide each student with enough math notebooks so that they have enough supplies to work with. These notebooks can be used by the students to keep track of key information, practise equations and other mathematical ideas, and stay organised and study-focused. To make sure that kids have the resources they need to excel in the classroom, provide the instructor a budget to buy math notebooks.

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Answer:

OA. Y = 0.5x + 2

Step-by-step explanation:

is the sign that you mean ÷ ?

if so:

-3×7÷5×1/7

= -21÷5×1/7

=-21/5 × 1/7

= (-21×1) / (5×7)

= -21/35

=-3/5

=-0.6

For the initial value problem y' = 0; y(1) = 1, the solution is y = 1. Since the derivative of y with respect to x is zero, the function y remains constant, and the constant value is determined by the initial condition y(1) = 1.

For the initial value problem y' = 2xy - y; y(0) = 2(0) + 1 = 1, we can rewrite the equation as y' + y = 2xy. This is a first-order linear homogeneous differential equation. Using an integrating factor, we multiply the equation by e^x^2 to obtain (e^x^2)y' + e^x^2y = 2x(e^x^2)y. Recognizing that the left side is the derivative of (e^x^2)y, we can integrate both sides to get the solution y = Ce^x^2, where C is determined by the initial condition y(0) = 1. For the initial value problem y' = 2y; y(1) = -1, we can separate the variables and integrate to find ln|y| = 2x + C, where C is the constant of integration. Exponentiating both sides gives |y| = e^(2x+C), and since e^(2x+C) is always positive, we can remove the absolute value signs. Thus, the solution is y = Ce^(2x), where C is determined by the initial condition y(1) = -1.

For the initial value problem dy = y^2x - x; y(0) = 0, we can separate the variables and integrate to find ∫dy/y^2 = ∫(yx - 1)dx. This gives -1/y = (1/2)y^2x^2 - x + C, where C is the constant of integration. Rearranging the equation gives y = -1/(yx^2/2 - x + C), where the constant C is determined by the initial condition y(0) = 0. For the initial value problem y' = ety; y(0) = 0, we can separate the variables and integrate to find ∫e^(-ty)/y dy = ∫e^t dt. The integral on the left side does not have a closed-form solution, so the explicit solution cannot be expressed in elementary functions. However, numerical methods can be used to approximate the solution for specific values of t.

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Answer:

y= 2x+10

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Add 9 to both sides of the equation:

3x - 9 + 4x = 12

3x - 9 + 4x + 9 = 12 + 9

3x + 4x = 21

7x = 21

Divide both sides by 7:

7x ÷ 7 = 21 ÷ 7

x = 3

Hope this helps!

Group like terms: 3x - 9 + 4x = 12

Add similar elements: 3x + 4x = 7x

7x - 9 = 12

Add 9 to both sides: 7x - 9 + 9 = 12 + 9

Simplify: 7x = 21

Divide both sides by 7: 7x/7 = 21/7

Simplify: x = 3

The answer is C) x = 3