someone took the elevator down 2 floors to the basement. would it be positive/negative?

The interval shown on the number line is (-infinity,5].

What is the number line?

A number line is a visual depiction of numbers on a straight line drawn either horizontally or vertically. When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them.

One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero. In other words, as we move to the right on a number line, the value of the numbers increases. This shows that the numbers on the right are more numerous than those on the left.

From the given number line, we can see that the green ray is increasing towards the left from point 5.

Therefore, the interval shown on the number line is (-infinity,5].

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Answer:

2^1010 x 5^1011

Step-by-step explanation:

This expression can be simplified by combining the exponents of the similar bases.

2^2010 x 5^2011 / 10^1000 = (2^2010 x 5^2011) / (2^1000 x 5^1000)

= (2^1010 x 5^1011) / 10^1000

The final answer is 2^1010 x 5^1011.

The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.

The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

An expression of two terms having a degree n can be represented as,

(a - b)ⁿ = \(^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n\).

Given, (y - 3)⁴ = \(^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4\).

(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.

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To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2√3/4 dx

Simplifying, we get:

V = √3∫[0,π] sin x dx

Using the substitution u = cos x, we get:

V = √3∫[-1,1] √(1 - u^2) du

Using the formula for the integral of the half-circle, we get:

V = (√3/2)π

Therefore, the volume of the solid is (√3/2)π.

To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.

Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2 dx

Simplifying, we get:

V = 4∫[0,π] sin x dx

Using the identity ∫sin x dx = -cos x + C, we get:

V = -4cos x ∣[0,π]

Since cos π = -1 and cos 0 = 1, we get:

V = -4(-1 - 1) = 8

Therefore, the volume of the solid is 8.

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(L3) The orthocenter will lie in the exterior of a(n)  obtuse triangle. Contrary to an acute triangle, the orthocenter of an obtuse triangle will lie in the exterior of the triangle.

The orthocenter is the point of intersection of the altitudes of the triangle, which are perpendicular lines drawn from each vertex to the opposite side. In an obtuse triangle, one of the angles measures more than 90 degrees, so when an altitude is drawn from this vertex to the opposite side, it will lie outside of the triangle. Therefore, the three altitudes will intersect outside of the triangle, forming the orthocenter in the exterior. This is in contrast to an acute triangle, where all three altitudes intersect inside the triangle.

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Answer:

y + 6 = 4 times ( x - 1 )

Step-by-step explanation:

hope this helps

Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

What is Distance?

Distance is defined as the space between two points in space.

To find out how far Jake will have traveled after 3 hours, we can use the formula:

distance = speed x time

where speed is the rate at which Jake is traveling and time is the duration of the travel. In this case, the speed is 12 mph and the time is 3 hours.

So, the distance traveled after 3 hours is:

distance = 12 mph x 3 hours = 36 miles

Therefore, Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

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Answer:

x - 80

Step-by-step explanation:

Ravi had x dollars in all.

x - 80

The divisor in the long division bracket for converting the volume of Solution A from a fraction to a decimal number would be the denominator of the fraction.

To convert the volume of Solution A from a fraction to a decimal number, you need to set up a long division problem. In a fraction, the denominator represents the total number of equal parts, which in this case is the volume of Solution A. Therefore, the denominator should be placed in the divisor position in the long division bracket. The dividend, on the other hand, represents the number of parts being considered, so it should be placed in the dividend position. By performing the long division, you can find the decimal representation of the fraction.

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The years when the spending be more than $66 billion is in 4 years time.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation is given as y=12.7x+15.2 and the amount is $66 billion. Therefore, the value of x will be:

y=12.7x+15.2

66 = 12.7x + 15.2

Collect like terms

12.7x = 66 - 15.2

12.7x = 50.8

Divide

x = 50.8 / 12.7

x = 4

The number of years is 4.

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Answer:

look at attached image for the step-by-step proof. thanks for reposting this lol

The series ∑n=2 1/n(ln n)^a converges for values of 'a' greater than 1.  To determine the convergence of the given series, we can use the integral test, which compares the series to the integral of its terms.

Let's consider the integral of 1/x(ln x)^a with respect to x. Integrating this function yields ln(ln x) / (a-1). Now, we can examine the convergence of the integral for different values of 'a'.

When 'a' is less than or equal to 1, the integral ln(ln x) / (a-1) diverges as ln(ln x) grows slower than 1/(a-1) for large values of x. Since the integral diverges, the series also diverges for these values of 'a'.

On the other hand, when 'a' is greater than 1, the integral converges. This can be observed by considering the limit as x approaches infinity, where ln(ln x) / (a-1) approaches zero. Since the integral converges, the series also converges for 'a' greater than 1.

Therefore, the series ∑n=2 1/n(ln n)^a converges for values of 'a' greater than 1, while it diverges for 'a' less than or equal to 1.

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Answer: M= -3

Solve for m by simplifying both sides of the equation, then isolating the variable.

The answer of this question is c) 0.828, which means that 82.8% of the variation of y is explained by the LSRL of y on x.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It can range from -1 to +1, with 0 indicating no linear relationship and values closer to -1 or +1 indicating stronger relationships.

The coefficient of determination (r^2) is the square of the correlation coefficient and represents the proportion of the variation in the dependent variable (y) that is explained by the independent variable (x) in a linear regression model. Therefore, if the correlation coefficient is 0.828, the coefficient of determination is 0.686, meaning that 68.6% of the variation in y is explained by the LSRL of y on x.

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\(4\div\cfrac{5}{7}\implies \cfrac{4}{1}\div\cfrac{5}{7}\implies \cfrac{4}{1}\cdot \cfrac{7}{5}\implies \cfrac{28}{5}\implies 5\frac{3}{5}\)

Answer:

e

Step-by-step explanation:

The number -2² can be written as 4 without using exponents.

The number -2² can be written without using exponents by expanding it using multiplication:

-2² is equal to (-2)*(-2).

When we multiply a negative number by another negative number, the result is positive.

Therefore, (-2) times (-2) equals 4.

So, -2² can be written as 4 without using exponents.

In more detail, the exponent 2 indicates that the base -2 should be multiplied by itself. Since the base is (-2), multiplying it by itself means multiplying (-2) with (-2). The result of this multiplication is \(4\).

Hence, -2² is equal to 4 without using exponents.

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Answer:

Isosceles triangle

Step-by-step explanation:

Length of side AB = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

                              = \(\sqrt{(-11+3)^2+(2-6)^2}\)

                              = \(\sqrt{64+16}\)

                              = \(\sqrt{80}\)

                              = 4\(\sqrt{5}\)

Length of BC = \(\sqrt{(-4+11)^2+(-2-2)^2}\)

                      = \(\sqrt{49+16}\)

                      = \(\sqrt{65}\)

Length of AC = \(\sqrt{(-3+4)^2+(6+2)^2}\)

                      = \(\sqrt{1+64}\)

                      = \(\sqrt{65}\)

Since, AC = BC, ΔABC will be an isosceles triangle.

Answer:

its D

Step-by-step explanation:

got it correct on a test :)

The correct option is Option D: Adding 1.3 to both sides of the equation, subtracting 4x from both sides of the equation, then dividing both sides by the coefficient of x.

The linear equation is an equation where the highest degree of the variables used in the equation is 1.

For example 9x+5=23

Given the equation is -1.3 +4.6x= 0.3+ 4x

In order to the linear equation first, try to keep the constant and the variable part to one side by adding or subtracting the constant term.

Then divide the coefficient of the variable (if the coefficient is not equal to 1) on both sides.

Here the given equation is -1.3 +4.6x= 0.3+ 4x

Step-1: Adding 1.3 to both sides of the equation

⇒-1.3 +4.6x +1.3 = 0.3+ 4x +1.3

⇒4.6x = 4x+1.6

Step-2: subtracting 4x from both sides of the equation

⇒4.6x -4x = 4x+1.6-4x

⇒ 0.6x=1.6

Step-3:  dividing both sides by the coefficient of x i.e. 0.6.

⇒0.6x/0.6 = 1.6/0.6

⇒x= 2.67

Therefore the correct option is Option D: Adding 1.3 to both sides of the equation, subtracting 4x from both sides of the equation, then dividing both sides by the coefficient of x.

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The work done in propelling the lunar module from the surface of the moon to a height of 40 miles is 3,571,607,996 Joules.

This can be calculated as follows:

Weight of the lunar module on the surface of the Earth = 12 tons
converting weight to mass = weight/acceleration due to gravity
mass = 12 x 1000 / 9.81
mass = 1,224.6 kg

The force required to lift the module off the surface of the moon is equal to its weight, which is given by the formula:
force = mass x acceleration due to gravity
force = 1,224.6 x 1.62
force = 1,982.8 N

Calculating the total distance traveled:
distance = 1,737.1 + 64.37
distance = 1,801.47 km

Calculating the work done:
work = force x distance
work = 1,982.8 x 1,801,470
work = 3,571,607,996 J

Therefore, the work done in propelling the lunar module from the surface of the moon to a height of 40 miles is 3,571,607,996 Joules.

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The parametric equations for the tangent line to the helix at the point (0, 1, 2π) are x = 0, y = 1 + t, and z = 2π + t, where t is a parameter that determines the position along the tangent line.

To find the parametric equations for the tangent line to the helix at the given point (0, 1, 2π), we can use the following steps:

Step 1: Calculate the derivatives of the helix equations.

Given the helix parametric equations:

x = 2cos(t)

y = sin(t)

z = t

We need to find the derivatives dx/dt, dy/dt, and dz/dt with respect to t.

dx/dt = -2sin(t)

dy/dt = cos(t)

dz/dt = 1

Step 2: Substitute t = 2π into the derivatives.

We are interested in finding the tangent line at the point (0, 1, 2π). Substitute t = 2π into the derivatives calculated in Step 1.

dx/dt = -2sin(2π) = 0

dy/dt = cos(2π) = 1

dz/dt = 1

Step 3: Determine the direction vector of the tangent line.

The direction vector of the tangent line is given by the coefficients of dx/dt, dy/dt, and dz/dt. In this case, it is (0, 1, 1).

Step 4:

The parametric equations for the tangent line.

To write the parametric equations for the tangent line, we need the coordinates of a point on the line.

Since we are interested in the point (0, 1, 2π), the parametric equations for the tangent line are:

x = 0 + 0t

y = 1 + t

z = 2π + t

t is a parameter that determines the position along the tangent line.

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The area of each parallelogram or triangle is 24 cm²,22.5 cm², 98 ft²,48 cm², 90 m², and  30 in² respectively.

In this skills practice problem, we are asked to find the perimeter and area of each parallelogram or triangle, based on their given dimensions. Let's start by defining the formulas for calculating the perimeter and area of each shape:

Perimeter of a parallelogram = 2 x (length + width)

Area of a parallelogram = base x height

Perimeter of a triangle = sum of the lengths of its sides

Area of a triangle = 1/2 x base x height

Now, let's apply these formulas to each shape:

Parallelogram with length 6 cm and width 4 cm:

Perimeter = 2 x (6 + 4) = 20 cm

Area = 6 x 4 = 24 cm²

Triangle with base 9 cm and height 5 cm:

Perimeter = 9 + 8 + 7 = 24 cm

Area = 1/2 x 9 x 5 = 22.5 cm²

Parallelogram with length 14 ft and width 7 ft:

Perimeter = 2 x (14 + 7) = 42 ft

Area = 14 x 7 = 98 ft²

Triangle with base 12 cm and height 8 cm:

Perimeter = 12 + 8 + 10 = 30 cm

Area = 1/2 x 12 x 8 = 48 cm²

Parallelogram with length 18 m and width 5 m:

Perimeter = 2 x (18 + 5) = 46 m

Area = 18 x 5 = 90 m²

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#SPJ11Triangle with base 6 in and height 10 in:

Perimeter = 6 + 8 + 10 = 24 in

Area = 1/2 x 6 x 10 = 30 in²

Therefore, we have calculated the perimeter and area of each given parallelogram or triangle.

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Answer:

the fisrst cup has a volume of 100.53

Step-by-step explanation:

Correct Answer:

y = -1/3x

Step-by-step explanation:

I see what you were tying to do and you did a good job at trying but the slope is negative 1/3, not negative 1. To find the slope, you have to divide the y by the x for example point (3, -1)

-1 ÷ 3 = -1/3

Remember the phrase Rise over Run where the Rise is y and Run is x

Hope you have a good day and luck in finding good memes!

Answer:

0.91

30.4

850

Step-by-step explanation:

The simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

As given in the question,

Given fraction :\(\frac{4^{11} }{4^{-8} }\)

Simplify the given fraction using the formula of exponents

\(\frac{x^{a} }{x^{b} } =x^{a-b}\)

The simplified form of the given fraction is given by :

\(\frac{4^{11} }{4^{-8} }\)

Substitute the value in the formula of exponent we get:

Here the value of x= 4 ,value of a=11 and value of b= -8

=(4¹¹ ⁻ ⁽⁻⁸⁾)

=(4¹¹ ⁺ ⁸)

=4¹⁹

Therefore, the simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

The complete question is:

Simplify the given fraction in simplified form: \(\frac{4^{11} }{4^{-8} }\).

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The mean for boxplot #3 should be less than its median. In a negatively skewed distribution, the mean is less than the median.

This is because the few small values in the data pull the mean down, while the median is still at the middle value. A boxplot can give us an idea of the shape of the distribution, and if it is negatively skewed, it suggests that the mean will be less than the median.

It's important to note that without actually seeing the boxplot, this conclusion may not be accurate. There could be other factors that affect the mean and median, such as outliers or the size of the sample. However, based on the information given that the boxplot is negatively skewed, it is likely that the mean will be less than the median.

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Answer:

f ( x )  = \(x^{3}\) −  2 \(x^{2}\)  +  x  +  C