Use the associative property to simplify the expression.

43 +30+70

OA. 43+30+70 = 73 +70 = 143

OB. 43+ (30+70) = 43+ 100 = 143

OC. 43+ 10(3 + 7) = 43 + 10(10) = 143

OD. 43 +70+ 30 = 113 +30 = 143

SUBMIT

Answer:

  61

Step-by-step explanation:

You want the number of positive integers less than 2021 that can be written as the difference of two powers of 2.

2^12 = 4096 and higher powers cannot produce integers less than 2021 when other powers of 2 are subtracted. Hence we're looking for pairs of powers that are 2^11 and smaller.

2^11 = 2048, which is 27 more than 2021. This means a number in range can be generated only by subtracting a power of 2 from 2^11 that is 2^5 = 32 or greater.

There are 66 pairs (combinations) of numbers in the range 0 to 11. Except for the 5 pairs (11, 0), (11, 1), (11, 2), (11, 3), (11, 4), they all represent pairs of powers of 2 that will have a unique difference less than 2021.

There are 61 positive integers less than 2021 that can be written as the difference of powers of 2.

Answer:

Step-by-step explanation:

trfhvugfhgr6uf475ugf7t,f6ydrb 7857 f5r  dtd67e7 r6ft7 v 7t  fvt t7 6r r6 7ry  t7 fu7 r6 7tgfv7t ug fy f c  y uygfg  gdv cbj c v  fv

The actual distance between the basketball court and the pool is 37.5 feet

Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.

The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.

We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:

3 inches / 5 feet = 22.5 inches / x

We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:

3 inches x x = 5 feet x 22.5 inches

3x = 112.5

x = 37.5 feet

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Complete Question:

The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?

The horizontal and vertical translations applied to ΔABC:

A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.

Given that,

[tex]\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right][/tex]   = ?

After using matrix operation it can be further solved as,

[tex]\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right][/tex]

Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

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Answer:

Step-by-step explanation:

o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.

For the first inequality: 8r - 3 ≥ 7r - 7

Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r

Combining like terms: 15r - 3 ≥ 14r

Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0

Combining like terms: r - 3 ≥ 0

Adding 3 to both sides: r ≥ 3

For the second inequality: 2r + 4 ≤ r - 3

Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r

Combining like terms: 4 ≤ -r - 3

Adding r and 3 to both sides: 4 + r + 3 ≤ -r

Combining like terms: 7 ≤ -r

Multiplying both sides by -1: r ≤ -7

The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.

To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7:

The solution to the given differential equation is y = e⁽ˣ³⁾⁽²⁸ˣ ⁺ ᶜ⁾, where C is a constant.

To solve the first-order linear differential equation of the form y' + p(x)y = q(x), where p(x) and q(x) are functions of x:

Find the integrating factor (IF) = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾

Multiply both sides of the equation by the IF.

Apply the product rule to the left side and simplify the right side.

Integrate both sides with respect to x.

Solve for y.

Using this method, for the given equation:

y' - 3x²y = 28e⁽ˣ³⁾

Find the integrating factor (IF):

IF = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾ = e⁽⁻³/¹ * ∫ˣ²ᵈˣ⁾ = e⁽⁻ˣ³⁾

Multiply both sides by the IF:

e⁽⁻ˣ³⁾y' - 3x²e⁽⁻ˣ³⁾y = 28

Apply the product rule to the left side and simplify the right side:

d/dx (e⁽⁻ˣ³⁾y) = 28

Integrate both sides with respect to x:

e⁽⁻ˣ³⁾)y = 28x + C, where C is the constant of integration.

Solve for y:

y = e⁽ˣ³⁾(28x + C)

Therefore, the solution to the given differential equation is y = e⁽ˣ³⁾(28x + C), where C is a constant.

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Complete question:

How to solve the first order linear differential equation

Y'- 3x²y=28eˣ³

Answer: eat grass whor

Step-by-step explanation:

The coordinates of the fourth vertex of the parallelogram are (1, -3).

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Three vertices are located at these coordinates: (-1, 2), (1, 2), and (-1,-3).

we have three points in the coordinate plane, we can use the concept of vector addition to find the fourth point.

The vectors connecting the first and second points, and the first and third points can be determined as follows:

v₁ = (1,2) - (-1,2) = (2,0)

v₂ = (-1,-3) - (-1,2) = (0,-5)

The fourth point will be located at the vector sum of the first point and the vector formed by adding v₁ and v₂.

v₃ = v₁ + v₂ = (2,0) + (0,-5) = (2,-5)

So, the fourth point will be located at:

(-1,2) + (2,-5) = (1,-3)

Thus, the coordinates are (1, -3).

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The volume of the rectangular prism will be (4x - 3)(x + 1)( x+2) cubic feet.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

Given that the length, width, and height of the rectangular prism are,

The volume of the rectangular prism will be calculated as,

Volume = Length x width x Height

Volume = (4x - 3)(x + 1)( x+2) cubic feet

Therefore, the polynomial for the volume will be (4x - 3)(x + 1)( x+2) cubic feet.

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The number of different outfits that Aldo can create from the shirts and the pairs of pants are 6 outfits.

In this case, Aldo has 2 options for his shirt and 3 options for his pants. To find the total number of outfits, we can multiply these numbers together:

= Number of shirts x Number of pairs of pants

= 2 x 3

= 6 outfits

Therefore, Aldo can create 6 different outfits by choosing a shirt and a pair of pants from the available options.

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The two lines have the same slope and different y-intercepts, thus, the lines are parallel.

Here we want to find the relation between the two lines:

8x = 3y + 3

-24x + 9y = 3

First, we need to write these two as lines in the slope-intercept form. We will get:

3y = 8x - 3

y = (8/3)*x - 3/3

y = (8/3)*x - 1

And the other one:

9y = 3 + 24x

y = (3/9) + (24/9)*x

y = (1/3) + (8/3)*x

So, we can see that both lines have the same slope (and different y-intercept), thus, the lines are parallel lines.

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The number of Canadian dollars the bank exchange for $160 US dollars is 100.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.

A current medium of exchange in the form of coins and banknotes.

Given that, the bank would exchange 1.6 Canadian dollars for one US dollar.

Here, there are $160 US dollars.

So, number of Canadian dollars

= 160/1.6

= 100

Therefore, the number of Canadian dollars the bank exchange for $160 US dollars is 100.

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Answer:

**DUE TOMORROW, NEED ANSWER ASAP**

NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).

a.) An ultraviolet telescope in space

b.) An optical telescope in a remote location in Michigan's upper peninsula

c.) A radio telescope in the Mojave desert in Arizona

d.) An x-ray telescope in the Andes mountains in Chile

e.) An optical telescope in space

Step-by-step explanation:

Answer:

12 red marbles.

Step-by-step explanation:

No step by step explanation.

Answer: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]

Step-by-step explanation:

cosθ = 4/9

tan < 0

This means our reference angle is either in Quadrants II or IV, (where tangent is negative). Since cosine is positive, it must be Quadrant IV.

Therefore we know that sinθ will be negative.

we also know that [tex]cos^2(\theta) + sin^2(\theta) = 1[/tex], from the Pythagorean identities

.: 16/81 + sin^2(θ) = 1,

.: sinθ = [tex]\sqrt{\frac{65}{81} }[/tex]= [tex]\frac{\sqrt{65}}{9}[/tex]

But since this angle is in Quadrant IV, sinθ will be negative.

.: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]

The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.

The density and mass are related to each other with the formula -

Density = mass/volume

So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.

Volume of hemisphere = 2/3πr³, where r represents radius.

Volume = 2/3×π×5³

Performing multiplication, division and taking cube

Volume = 261.8 feet³

Now, mass = density × volume

Mass = 62.7 × 261.8

Performing multiplication

Mass = 16,414.86 pounds

Rounding off

Mass = 16,415 pounds

Thus, the mass of liquid will be 16,415 pounds.

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The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

1/8

The probability of getting a head or a tail when flipping a coin is 1/2.  

Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.

The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.

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The graph showing the line of best fit for the function y = 3x + 1 is attached below

The line of best fit is a line that is used to represent the relationship between two variables in a scatterplot. It is a line that passes through the center of the data points in the scatterplot in such a way that the total distance between the line and the data points is minimized. The line of best fit can be used to make predictions about the value of one variable based on the value of another variable. There are several methods to obtain the line of best fit, including the method of least squares, which finds the line that minimizes the sum of the squares of the differences between the observed values and the values predicted by the line.

In the problem given, the line of best fit the line of best fit can be plotted on a graph using a graphing calculator.

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The amount of lent out at 15% and 16% will be ₹1,200 and ₹550, respectively.

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

Divide ₹1750 into 2 parts such that if one part is lent out at 15% per annum for 2 years and the other part at 16% per annum for 3 years, the total interest is 624.

Let 'x' be the amount of lent out at 15%. Then the amount of lent out at 16% is (₹1750 - x). Then the equation is given as,

(x · 0.15 · 2) + [(1750 - x) · 0.16 · 3] = 624

Simplify the equation, then we have

(x · 0.15 · 2) + [(1750 - x) · 0.16 · 3] = 624

0.30x + 840 - 0.48x = 624

0.18x = 216

x = ₹1,200

Then the value of (₹1750 - x) is given as,

₹1750 - x = (₹1750 - ₹1,200)

₹1750 - x = ₹550

The amount of lent out at 15% and 16% will be ₹1,200 and ₹550, respectively.

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The temperature at midnight would be -4°C - 8°C since the temperature at noon was -4°C and at midnight it dropped 8°C.

The temperature at midnight would be -4°C minus 8°C, which can be expressed as:

-4°C - 8°C = -12°C

Therefore, the temperature at midnight would be -12°C.

Temperature is a measure of the degree of hotness or coldness of a body or an environment. It is a physical quantity that expresses the amount of thermal energy in a substance or a system, typically measured using a thermometer in units such as Celsius (°C) or Fahrenheit (°F). In general, the higher the temperature, the more thermal energy is present in the system, and the lower the temperature, the less thermal energy is present.

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Answer:

answer is A

Step-by-step explanation:

because area of a rectangle is L × B

or length × width

since the length is expanded by x

10.5 (12x)

Answer:

Option C

Step-by-step explanation:

The original length of the room = 12 feet

After expansion, the new length = [tex](12 + x)[/tex] feet

Width of the room = 10[tex]\frac{1}{2}[/tex] feet = 10.5 feet

Area of a rectangle = Length × Width

The shape of the living room is a rectangle.

∴Area of living room = [tex](12 + x)[/tex] feet × [tex](10.5)[/tex] feet  
                                     [tex]= 10.5(12 + x)[/tex] square feet

Expand the brackets or parenthesis by applying the Distributive Law:

                                  [tex]= (12)(10.5) + (10.5)(x)[/tex] square feet

                                  = [tex](125 + 10x)[/tex] square feet

∴Option C

Answer:

none of them do

Step-by-step explanation:

5/6=0.83

6/5=1.2

4/5=0.8

5/4=1.25

11/5=2.2

Step-by-step explanation:

the answer for -1/4(-8x+12y)

2x-3y

Answer:

2x-3y

Step-by-step explanation:

For this equation we are using distributive property

-1/4(-8x)           -1/4(12y)

     ↓                      ↓

    2x                   -3y

So, 2x-3y is the answer.

Casual relationship forecasting and Time series forecasting uses linear regression in forecasting.

Linear regression is a statistical tool used in forecasting to model the relationship between a dependent variable and one or more independent variables. Some of the common uses of linear regression in forecasting are:

Therefore, linear regression is a versatile tool in forecasting, with many useful applications for predicting future values, analyzing trends, evaluating accuracy, and identifying causal relationships.

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The complete question is :

In forecasting, there is more than one use for linear regression. What are the? Check all that apply.

1. Causal relationship forecasting

2. Time series forecasting

Answer:

34 miles per gallon

Step-by-step explanation:

850/25 = 34

Answer:

...here is the answer...

With her 5 3/5 gallons of paint, Latanya can paint up to 11 full bookcases.

Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is a solution to the problem. Solving an equation is locating its solution or solutions.

Let's first translate 5 3/5 gallons of paint into an incorrect fraction:

5 3/5 = (5 x 5 + 3)/5 = 28/5

Next, we can find the number of bookcases she can paint by dividing the total amount of paint by the amount needed for each bookcase:

28/5 ÷ 1/2

= 28/5 x 2/1

= 56/5

=11 1/5.

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The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).

In general, a system of linear equations can have one of three possible outcomes:

One unique solution (as in this case)

No solution (if the equations are inconsistent)

Infinitely many solutions (if the equations are dependent)

To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.

First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:

-10x - 4y = 14

5x + 2y = -7

-5x = 7

Now we can solve for x:

-5x = 7

x = -7/5

We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:

5x + 2y = -7

5(-7/5) + 2y = -7

-7 + 2y = -7

2y = 0

y = 0

Therefore, the solution to the system of equations is (x,y) = (-7/5,0).

This is called a unique solution, meaning there is only one possible solution for the system of equations.

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Complete Question:

Solve

5x + 2y = -7

10x + 4y = -14

And find the number of solutions for the equation

The price per can of a 12 pack of soda is 8.25.  the price per can of a 12 pack of soda is 0.6875.

To calculate this, we can use the following formula: Price per Can = Total Price of 12 Pack / 12 Price per Can = 8.25 / 12 Price per Can = 0.6875 Therefore, the price per can of a 12 pack of soda is 0.6875. To better understand the price per can of a 12 pack of soda, it is important to understand the concept of unit pricing. Unit pricing is the cost of a single item compared to a larger quantity. When shopping, it is beneficial to look at the unit pricing of items to ensure that you are getting the best deal. For example, if a 12 pack of soda is 8.25 and a 6 pack of soda is 4.00, then the unit price of the 12 pack is lower, which means it is a better deal. By understanding unit pricing, you can make the most cost-efficient decisions when shopping.

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The translation of the graph is represented by y = -6(x+2)² - 7.

A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.

Given that the graph of y= x² translated left 2 units and up 8 units. The translated equation is:-

Start with y = x².

Shift 2 units left to get y = (x+2)².

Vertically stretch to get y = 6(x+2)².

Reflect across x-axis to get y = -6(x+2)².

Shift 7 units down to get y = -6(x+2)² - 7.

Hence, the translation of the graph is represented by y = -6(x+2)² - 7.

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The question is incomplete so solved for,

Suppose the graph of y= x^2 translated left 2 units, and up 8 units