Use Pascal's Triangle to expand each binomial. (m+0.7)²

Step-by-step explanation:

c²= 8²+6²

c²= 64+36

c²=100

c=10

Answer:

10

Step-by-step explanation:

It is a right triangle - so you can use the Pythagorean theorem

8^2+6^2 = c

c = 10

Answer:

15mm

Step-by-step explanation:

Here, Pythagoras Theorem will be used, which states that,

(BASE)² + (HEIGHT)² = (HYPOTENUSE)²

Putting the values accordingly,

(17)² = (8)² + (x)²

(x)² = (17)² - (8)²

(x)² = 225

x = 15 mm

Hope it helps :)

Answer:

15mm

Step-by-step explanation:

Hypotenuse of a triangle^2 = a^2 + b^2

=> 17^2 mm = 8^2mm + x^2mm

=> 289mm = 64mm + x^2mm

=> 289mm - 64mm = x^2mm

=> 225mm = x^2mm

=> √225mm = x mm

=> 15mm = x

Hope you understood!!

Answer:

medain:64

Q1:62

Q3:70

Step-by-step explanation:

the line in the middle of the box in the box plot is the medain which is over the number 65

Q1 is the first line of the box which is over 62 and Q3 is the 3rd one is 70.

(im a bit confused with the box plot part

Answer:

187: 51: 85

Step-by-step explanation:

11+3+5=19

323/19= 17

11*17= 187

3*17= 51

5* 17= 85

Answer:

4239 cubic feet

Step-by-step explanation:

V=\(\pi\)\(r^{2} *h\)

V=3.14*225*6

V=3.14*1350

V=4239

Answer:

a=\(\sqrt{28.32}\)≈5.3217 cm

Step-by-step explanation:

Use the Pythagorean Theorem

a^2+4.7^2=7.1^2

a^2+22.09=50.41

a^2=28.32

a=\(\sqrt{28.32}\)

≈5.3217

Answer:

5.3

Step-by-step explanation:

Check the attached image for explanation if you are interested, as I did not feel like spending 20 minutes re-formatting the equations to work on Brainly.

Also, I did not do this

These are the critical numbers of the given function f(x)Hence, the critical numbers of the function f(x) = 12r − 15x + 80x³ are x = ±1/4.

The given function is f(x) = 12r − 15x + 80x³To find the critical numbers of the given function, we need to follow the following steps:Step 1: Find the derivative of the function f(x)Step 2: Set the derivative equal to zero and solve for xStep 3: The solutions obtained in Step 2 are the critical numbers of the function f(x)Step 1: Differentiating the function f(x) w.r.t. xWe have, f(x) = 12r − 15x + 80x³Let us differentiate this function w.r.t. x, we getf'(x) = 0 - 15 + 240x²15 and 240x² can be written as 3 × 5 and 3 × 80x² respectivelyf'(x) = -15 + 3 × 5 × 16x² = -15 + 240x²Step 2: Setting f'(x) = 0 and solving for xf'(x) = -15 + 240x² = 0Adding 15 to both sides240x² = 15Dividing by 15 on both sides16x² = 1Taking the square root on both sides, we get4x = ±1x = ±1/4Step 3: Finding the critical numbers of the function f(x)From Step 2, we have obtained the solutions x = ±1/4.

These are the critical numbers of the given function f(x)Hence, the critical numbers of the function f(x) = 12r − 15x + 80x³ are x = ±1/4.

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Answer: If you measure the circumference and the diameter of a circle and divide the circumference by the diameter, you get the number Pi, which is about 3.14.  

Pi is often shown by the Greek letter π  .

The ancient Greeks used the symbol π   to indicate the ratio between the circumference and diameter of a circle. If your calculator does not have the symbol π   , you can use the rounded off number 3.14 for π .

A = 5m × 5m × 3.14 78.5m2  (Note: the symbol  means about the same as).

In the diagram above, the area of the small yellow square is a quarter of the area of the big square.  

If the area of the shaded square is A = 5m × 5m = 25m2  

then the area of the big square is A = 4 × 25m2 =100m2  

You can see that the area of the circle is less than that of the square since the circle fits inside it.  You can also find the area of the circle by multiplying the area of the small square by Pi:    

 A = 3.14 × 25m2 =78.5m2

Answer:

Q

Step-by-step explanation:

it is between -1 and -2 were -2/3 would be located

the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.

The given information about the vertex of the function does not appear to be relevant to the question about mulch for a flower bed. However, we can still solve the problem using the given radius of the flower bed.

The formula to find the recommended amount of mulch for a circular flower bed is:

Mulch = π * r^2 * d

Where r is the radius of the flower bed and d is the desired depth of the mulch.

Assuming a desired depth of 0.5 feet, we can plug in the given radius of 20 feet to the formula:

Mulch = π * (20 feet)^2 * 0.5 feet

Mulch = π * 400 square feet * 0.5 feet

Mulch = 200π cubic feet

To find the approximate value in decimal form, we can use the approximation π ≈ 3.14:

Mulch ≈ 200 * 3.14

Mulch ≈ 628 cubic feet

Rounding to the nearest tenth, we get:

Mulch ≈ 628.3 cubic feet

Therefore, the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.

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Hi Student!

The first step to solving our question is to understand the problem statement and to extract important information that will be useful.  We are told that the local candy shops sells Jelly Beans for $2 a pound and Chocolate Melts for $3 a pound.  We are also told that Kelsi has no more than $12 to spend.  Finally, we are told that the purpose of this question is to write an inequality to capture the scenario.

We know that we have two variables, the variable x for jelly beans and the variable y for chocolate melts.  Creating an inequality we need to capture the total of these two should be no more than $12.  This means that it isn't just less than $12 but that it can also include $12; therefore, we use a less-than-equal sign.

Create an expression

This inequality captures the goal of our expression which is to see how two items combined should be less than the total price that we want to spend.  Let's create a new inequality with updated numbers with our information.

Plug in values

Simplify to just numbers

After plugging in the values, we have a lot of unnecessary information such as the dollars signs or words so we can remove that and just have the numbers to show that is going on.

Therefore, our final answer is that the inequality that best represents this scenario is \(2 x + 3y\leq 12\)

the answer is C or it got to be D or B

Answer:

x=1

Step-by-step explanation:

3x1+2=5

Answer:

I'm assuming you're trying to find x.

In this problem, x = 1

Step-by-step explanation:

3x + 2 = 5

    -2     -2    Subtract 2 from each side

3x = 3

3x/3 = 3/3    Divide each side by 3

x = 1

To construct the first simplex tableau using the Big M method. The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

To construct the first simplex tableau using the Big M method, we first rewrite the problem in standard form as follows:

Maximize \(Z = 2x₁ + 5x₂ + 3x₃\)
subject to
\(x₁ - 2x₂ + x₃ + x₄ = 20\\2x₁ + 4x₂ + x₃ = 50\\x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0, x₄ ≥ 0.\)

To construct the initial simplex tableau, we introduce artificial variables x₅ and x₆ to the two equations.

The initial tableau is:

 Basis   |  x₁   |  x₂   |  x₃   |  x₄   |  x₅   |  x₆   |   RHS  
----------------------------------------------------------------------
    x₅    |   1    |   2    |   1    |   0    |   1    |   0    |   20    
    x₆    |   2    |   4    |   1    |   0    |   0    |   1    |   50    
----------------------------------------------------------------------
    -Z    |  -2    |  -5    |  -3    |   0    |   0    |   0    |   0    

The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

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Using the Big M method, the complete first simplex tableau for the given linear programming problem is constructed as follows:

┌─────────────┬──────┬───────┬───────┬─────┬─────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │ s₁  │ s₂  │ a₁  │      RHS    │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│      Z      │  2   │   5   │   3   │  0  │  0  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   x₁ - 2x₂  │  1   │  -2   │   1   │ -1  │  0  │  0  │     20      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   2x₁ + 4x₂ │  2   │   4   │   1   │  0  │ -1  │  0  │     50      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₁      │  1   │   0   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₂      │  0   │   1   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₃      │  0   │   0   │   1   │  0  │  0  │ -M  │      0      │

└─────────────┴──────┴───────┴───────┴─────┴─────┴─────┴─────────────┘

The initial (artificial) basic solution is x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, a₁ = 0. The initial entering basic variable is x₁, which has the most positive coefficient in the objective row. The leaving basic variable is s₁, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the second row (20/1) is the smallest, so s₁ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first convert the given problem into standard form by introducing slack variables (s₁, s₂) for the inequalities and an artificial variable (a₁) for the equality constraint. We assign a large positive value (M) to the coefficients of the artificial variables in the objective row.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₁₂₃ are taken directly from the given problem. The slack variables and the artificial variable (a₁) have coefficients of 0 since they don't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables, slack variables, and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial (artificial) basic solution is obtained by setting the decision variables to 0, the slack variables and the artificial variable to the right-hand side values. In this case, x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, and a₁ = 0.

The initial entering basic variable is determined by selecting the most positive coefficient in the objective row, which is x₁ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. Since the ratio for the second row (20/1) is the smallest, s₁ leaves the basis.

The resulting tableau serves as the starting point for applying the simplex method to solve the linear programming problem iteratively.

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Answer:

(3, 3) (1, -1)

Step-by-step explanation:

Answer:

(1, - 1) , (3, 3 )

Step-by-step explanation:

Given the 2 equations

3 + y - 2x = 0 → (1)

3x² + 2y² - 4xy = 9 → (2)

In (1) subtract 3 - 2x from both sides

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (2)

3x² + 2(2x - 3)² - 4x(2x - 3) = 9 ← distribute and simplify left side

3x² + 2(4x² - 12x + 9) - 8x² + 12x = 9

3x² + 8x² - 24x + 18 - 8x² + 12x = 0

3x² - 12x + 18 = 9 ( subtract 9 from both sides )

3x² - 12x + 9 = 0 ( divide through by 3 )

x² - 4x + 3 = 0 ← in standard form

(x - 1)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

Substitute these values into (3) for corresponding values of y

x = 1 : y = 2(1) - 3 = 2 - 3 = - 1 ⇒ (1, - 1 )

x = 3 : y = 2(3) - 3 = 6 - 3 = 3 ⇒ (3, 3 )

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.

To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.

For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:

Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)

Total fiber = 3x + 2y grams

what is number?

A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.

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Answer:

15m long

Step-by-step explanation:

Answer:

0.5cm^3

Step-by-step explanation:

volume of rectangular prism= length x width x height

1/4cm x 1/2cm x 4cm =

0.25cm x 0.5cm x 4cm =

0.5cm^3

The chi-square test for independence in a 2x2 contingency table is equivalent to comparing two proportions to determine if they are significantly different.

For a 2x2 contingency table, testing for independence with the chi-square test is the same as conducting a test comparing two proportions, specifically the two proportions of one variable (column) against the proportions of another variable (row).

1. Start with a 2x2 contingency table, which is a table that displays the counts or frequencies of two categorical variables. The table has two rows and two columns.

2. Calculate the marginal totals, which are the row and column totals. These represent the totals for each category of the variables.

3. Compute the expected frequencies under the assumption of independence. To do this, multiply the row total for each cell by the column total for the same cell, and divide by the total sample size.

4. Use the chi-square test statistic formula to calculate the chi-square value. This formula involves subtracting the expected frequency from the observed frequency for each cell, squaring the difference, dividing by the expected frequency, and summing up these values for all cells.

5. Determine the degrees of freedom for the chi-square test. In this case, it is (number of rows - 1) multiplied by (number of columns - 1), which is (2-1) x (2-1) = 1.

6. Compare the calculated chi-square value to the critical chi-square value from the chi-square distribution table at the desired significance level (e.g., 0.05).

7. If the calculated chi-square value is greater than the critical chi-square value, then the proportions of the two variables are significantly different, indicating dependence. If the calculated chi-square value is not greater, then the proportions are not significantly different, suggesting independence.

In summary, testing for independence with the chi-square test for a 2x2 contingency table is equivalent to conducting a test comparing two proportions, where the proportions represent the distribution of one variable against another.

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The total height of the iceberg is 38 meters and the total depth of the iceberg is 15 meters.

Height is a mathematical term that refers to the vertical distance between an object's top and base. Sometimes, it has the designation altitude. The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.

The depth of an object is the separation between its closest and farthest ends. Jane, for instance, measures a box. Jane estimates the depth of the box by calculating the distance between the end of the box that is closest to her and the end that is farthest away.

Given, the height of an iceberg above the water is 23 meters.

And also given that the bottom of the iceberg is 15 meters below sea level.

Total height = above the water + below the water

Total height=23+15=38 meters

Depth= total height - iceberg above the water

Depth=38-23=15 meters

The total height of the iceberg is 38 meters.

The total depth of the iceberg is 15 meters.

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Answer:

110 ft  

Step-by-step explanation:

The length of fencing is four times the perimeter of one garden.

The formula for the perimeter of a rectangle is  

P = 2l + 2w

The total perimeter for all four rectangles is

P = 4× (2l + 2w) = 8l + 8w

Data:

 l = 9¼ ft

w = 4½ ft

Calculation:

P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft

The total length of fencing is 110 ft.

Using the concepts of Probability, we got 0.2743 is the probability that he/she plays the clarinet but not the flute.

Conditional probability is called as the possibility of an event or outcome happening, based on  existence of a previous event or outcome. It is calculated by the multiplying the probability of the preceding event by the renewed probability of  succeeding, or conditional, event.

We need to find those persons  who can play clarinet but not the flute,

So, we first subtract those person from the clarinets list who are able to paly both clarinet and flute.

Suppose, Number of person who can play clarinet=172

Number of person who are able to play both clarinet and flute=47

Therefore, number of person who are only able to play clarinet but not flute=172-47=125

Probability(P)= \(\frac{Number of perople who are only able to play clarinet}{Total number of people}\)

              =>P=( 125 / 350)

               =>P=0.2743.

Hence, if a single person is selected at random,0.2743 is the probability that he/she is able to play clarinet but not flute.

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Answer: 40.82

Step-by-step explanation:

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

13 * 3.14 = 40.82

This may be wrong, but I found this on the internet

Therefore, since there are more moles of HC₂H₃O₂ (0.0833 mol) than NaHCO₃ (0.0595 mol), NaHCO₃ is the limiting reagent.

Division is a mathematical operation used to find the number of times one quantity is contained within another quantity of the same kind. It is the inverse operation of multiplication. In division, the quantity being divided is called the dividend, the number by which it is divided is called the divisor, and the result is called the quotient. Division is denoted by the symbol "÷" or "/", and it is commonly used in arithmetic and algebra to solve problems involving ratios, fractions, and percentages.

Here,

a. To determine which is the limiting reagent, we need to calculate the moles of each reactant and compare them to the stoichiometric ratio in the balanced chemical equation.

First, we need to convert the mass of each reactant to moles:

moles of HC₂H₃O₂ = 5.00 g / molar mass of HC₂H₃O₂

moles of NaHCO₃ = 5.00 g / molar mass of NaHCO₃

Using the molar masses of each compound, we get:

moles of HC₂H₃O₂ = 5.00 g / 60.05 g/mol = 0.0833 mol

moles of NaHCO₃ = 5.00 g / 84.01 g/mol = 0.0595 mol

The stoichiometric ratio of the balanced equation tells us that the ratio of moles of HC₂H₃O₂ to NaHCO₃ is 1:1.

b. To find the theoretical yield, we need to use the balanced chemical equation and the amount of limiting reagent (in moles) to calculate the moles of the product formed, and then convert that to grams using the molar mass of the product. The balanced equation tells us that 1 mole of NaHCO₃ produces 1 mole of CO₂.

moles of CO₂ = moles of NaHCO₃ = 0.0595 mol

mass of CO₂ = moles of CO₂ x molar mass of CO₂

mass of CO₂= 0.0595 mol x 44.01 g/mol = 2.62 g

Therefore, the theoretical yield of CO₂ is 2.62 g.

c. If the percent yield is 68.7%, we can use this percentage to calculate the actual yield. Percent yield is calculated as follows:

percent yield = (actual yield / theoretical yield) x 100

Rearranging this equation, we get:

actual yield = (percent yield / 100) x theoretical yield

actual yield = (68.7 / 100) x 2.62 g

actual yield = 1.80 g

Therefore, the actual yield of CO₂ is 1.80 g.

d. To find a mass of each reactant where neither is the limiting reagent, we can use the stoichiometric ratio of the balanced chemical equation to calculate the maximum amount of product that can be formed from each reactant.

Let's assume we have x grams of HC₂H₃O₂ and y grams of NaHCO₃. The moles of each reactant are:

moles of HC₂H₃O₂ = x / molar mass of HC₂H₃O₂

moles of NaHCO₃ = y / molar mass of NaHCO₃

If neither reactant is limiting, they will react completely according to the stoichiometric ratio of the balanced equation. That is, 1 mole of HC₂H₃O₂ reacts with 1 mole of NaHCO₃ to produce 1 mole of CO₂.

So, to find the maximum amount of CO₂ that can be produced from each reactant, we can calculate the moles of CO₂ produced from 1 mole of each reactant and then convert that to grams using the molar mass of CO₂:

Maximum yield of CO₂ from HC₂H₃O₂:

moles of CO₂ = moles of HC

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Answer:

<

Step-by-step explanation:

8x-2 - -4x2< 4+10

-16+8<4+10

-8<14

9514 1404 393

Answer:

  8×(−2)−(−4)^2 < 36÷9+2×5

Step-by-step explanation:

The left side expression evaluates as ...

  8×(−2)−(−4)^2

  = 8×(−2) − 16

  = -16 -16

  = -32

__

The right side expression evaluates as ...

  36÷9+2×5

  = 4 + 10

  = 14

__

It should be no mystery that any negative number is less than any positive number:

  -32 < 14

  8×(−2)−(−4)^2 < 36÷9+2×5 . . . . . . . . "less than" symbol is required

Answer:

$875

Step-by-step explanation:

take the 700 mulitple it by.25. you should get the answer 175. add 175 to 700 and you get your whole which is 875.

Answer:

Y=8x-32

Step-by-step explanation:

Point Form:

(4,0)

Equation Form:

x=4, y=0