Which type of graph is typically not used for quantitative data?

Answer:

A

Step-by-step explanation:

Using the properties of logarithms, we can simplify the expression:

4 log3x + 6 log3y - 7 log3z = log3x^4 + log3y^6 - log3z^7

Now, we can use another property of logarithms, which states that:

loga (mn) = loga m + loga n

Using this property, we can combine the logarithms with addition or subtraction:

log3x^4 + log3y^6 - log3z^7 = log3(x^4 * y^6 / z^7)

Therefore, the simplified form of 4 log3x + 6 log3y - 7 log3z is log3(x^4 * y^6 / z^7).

Answer:

it would be in the 100eds place

Step-by-step explanation:

Answer:

AC=18.1cm

Step-by-step explanation:

I assume the given expression is

\(\sqrt x \sqrt[4]{x}\)

We can write each root as a rational power of x, then add the exponents:

\(\sqrt x \sqrt[4]{x} = x^{\frac12} x^{\frac14} = x^{\frac12 + \frac14} = x^{\frac34}\)

Then putting it back into radical form, we have

\(\sqrt x \sqrt[4]{x} = \sqrt[4]{x^3}\)

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Answer:

Subtraction property of inequality

Step-by-step explanation:

Step 1: Definition of Subtraction property

Subtraction property of equality refers to balancing an equation by using the same mathematical operation (minus) on both sides.

Step 2: Relate the definition above with the given question.

It can be seen from the statements in the question that 3 was subtracted from both sides of the initial equation to get:

\(x + 3 = 17 \\ x + 3 - 3 = 17 - 3 \\ x = 14\)

Answer:

The answer is 20-6x

La maxima velocidad lineal de la masa con la que se puede girar la masa es igual a 40 newtons.

En este problema tenemos el caso de una masa (m), en kilogramos, conectada a una cuerda y que experimenta un movimiento circular uniforme, en donde la partícula describe un movimiento a velocidad lineal constante (v), en metros por segundo, debido a una aceleración radial que está en la forma de tensión (T), en newtons, a través de la cuerda. En consecuencia, la velocidad máxima permitida es determinada a partir de las leyes de Newton:

T = m · (v² / R)

Donde:

Si sabemos que m = 2 kg, R = 5 m y T = 40 N, entonces la maxima velocidad lineal permitida es:

40 N = (2 kg) · v² / (5 m)

v = 10 m / s

La maxima velocidad lineal permitida es igual a 10 metros por segundo.

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Answer:

(x + 2) (x +4) (x^2 + 25)

Step-by-step explanation:

Just did this problem

(  +  2 )  ( ^3  +  4 ^2  +  2 5  +  1 0 0 )

(  +  2 )  (  +  4 )  ( ^2  +  2 5 )

A factor is a number that completely divides another number. The factored form of the polynomial is (x² + 25 )(x + 2 )(x + 4 ).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

The given expression can be factorized using the steps as shown below. Therefore, we can write the steps as,

Rewrite for factoring : (\(x^{2}\) + 33\(x^{2}\) + 200) + 6\(x^{3}\) + 150\(x^{}\)

Rewrite the term: x⁴ + 8x² + 25x² + 200 + 6x³+ 150x

Regroup terms into two proportional parts: (x⁴ + 8x²) + (25x² + 200) + 6x³ 150x

Factor Greatest Common Factors out: x²(x² + 8 ) + 25(x² + 8) + 6x³ +150x

Factor Greatest Common Factors out:

(x² + 8 )(x² +25 ) + (6x³ + 150 )

Rewrite the term: (x² +25 )(x² + 2x + 4x + 8)

Regroup terms into two proportional parts: (x² + 25 ){(x + 2x ) + (4x +8)}

Factor Greatest Common Factors out: ( x² + 25 ){(x(x + 2)  + 4(x + 2)}

Factor Greatest Common Factors out: (x² + 25 )(x + 2)(x + 4)

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The parabola \(y = √(x - 4)\) opens upward.

The parabola y = √(x - 4) represents the square root function of x minus 4. To determine the direction in which the parabola opens, we examine the behavior of the square root function.

The square root function (√x) returns non-negative values for non-negative inputs. Since the expression inside the square root, (x - 4), must be non-negative for real solutions, we have x - 4 ≥ 0. Solving this inequality, we find x ≥ 4.

This means that the parabola is defined for x values greater than or equal to 4. As we increase x from 4, the value of √(x - 4) will also increase. Therefore, the graph of the parabola opens upward.

The parabola \(y = √(x - 4)\) opens upward.

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Answer:

x=1

Explanation:

When x=-1, the value of y=3.

The other domain value whose range is y=3 from the graph is x=1.

Step-by-step explanation:

Greater than 4 means  it lands 5 or 6  or  1/3 of the possible rolls

  1/3 * 45 = 15 times

Answer:

The 2nd answer

Step-by-step explanation:

because the light figure had more mature in the materials

Answer:

1. -4 - 1.5 = -5.5

2. -4 + 5 = 1

3. 5 + (-4) - 1.5 = -0.5

Step-by-step explanation:

The true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

The expression is given as:

\(x^{2} -7x + 6\)

Expand;

\(x^{2} -6x - x +6\)

Factorize;

x(x-1) - 6 (x- 1)

Factor out x - 6

(x - 6) (x- 1)

This means that the factors of \(x^{2} -7x + 6\) are x - 1 and x - 6

Hence, the true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

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Answer: Answer is C

Step-by-step explanation:

Answer:

no it does not

Step-by-step explanation:

Answer: no it doesn't

Step-by-step explanation:

The reason for this is that even when the process does shift, the sample means from the shifted process may still fall within these wide UCL and LCL limits.

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;

$78,000

An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.

The annual salary of Winston as an accountant = $60,000

The amount Winston's financial asset generates = $4,000 per year

The cost of running the business = $8,000

The amount Winston earns as revenue = $150,000

Therefore;

Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000

The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business

The cost of running the business = $8,000

The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost

The total cost = $60,000 + $4,000 + $8,000 = $72,000

The economic profit = The total revenue - The total cost

Therefore;

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The numbers replacing A, B and C in the polynomial equation  are -2, -2 and 2 respectively.

In the equation y = x² + 3x - 2,

When x = -3 ,

y = 9- 9- 2

 = -2 = A

So, A = -2

When x = 0 ,

y = 0+ 0- 2

 = -2 = B

So, B = -2

When x = 1 ,

y = 1 + 3 - 2

  =4 -2

  =2 = C

So, C = 2

The numbers replacing A, B and C in the polynomial equation  are -2, -2 and 2 respectively.

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Answer:

(a) A(0)= 0 (kg)

(b) \(R_{in}=0.28\dfrac{kg}{min}\)

(c) \(C(t)=\dfrac{A(t)}{2840}\)

(d) \(R_{out}=\dfrac{A(t)}{710}\)

(e) \(\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}\)

Step-by-step explanation:

A tank contains 2840L of pure water.

A solution that contains 0.07 kg of sugar per liter enters a tank at the rate 4 L/min. The solution is mixed and drains from the tank at the same rate.

(a) Amount of sugar initially in the tank.

Since the tank initially contains pure water, the amount of sugar in the tank

A(0)= 0 (kg)

(b) Rate at which the sugar is entering the tank. (kg/min)

\(R_{in}\)=(concentration of sugar in inflow)(input rate of the solution)

\(=(0.07\dfrac{kg}{liter}) (4\dfrac{liter}{min})\\R_{in}=0.28\dfrac{kg}{min}\)

(c) Concentration of sugar in the tank at time t

Volume of the tank =2840 Liter

Concentration c(t) of the sugar in the tank at time t

Concentration, C(t)= \(\dfrac{Amount}{Volume}\)

\(C(t)=\dfrac{A(t)}{2840}\)

(d) Rate at which the sugar is leaving the tank

\(R_{out}\)=(concentration of sugar in outflow)(output rate of solution)

\(=\dfrac{A(t)}{2840})( 4\dfrac{Liter}{min})=\dfrac{A}{710}\\R_{out}=\dfrac{A(t)}{710}\)

(e) Differential equation representing the rate at which the amount of sugar in the tank is changing at time t.

\(\dfrac{dA}{dt}=R_{in}-R_{out}\\\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}\)

Answer:

-41 is the ANS.

Step-by-step explanation:

9-25*2

9-50

-41

Answer:

[-4, 2]

Step-by-step explanation:

the domain is between -4 and 2, but it also includes those numbers, so you get:

[-4, 2]

The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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