What’s the GCF of 30 and 70

Answer:

B=28

Step-by-step explanation:

A grade of 85.75 or higher is required to be in the top 40% of the class.

Standard deviation is a statistical measure that represents the amount of variability or dispersion in a set of data values. It measures the degree of spread of the data values from the mean (average) of the data set.

To calculate the standard deviation of a data set, you first need to calculate the mean of the data set. Then, for each data point in the set, you calculate the difference between the data point and the mean. These differences are squared and then summed together. Finally, the sum is divided by the total number of data points minus one, and the square root of this value is taken to obtain the standard deviation.

To find the grade required to be in the top 40%, we need to find the z-score corresponding to the 60th percentile (100% - 40% = 60%).

We can use the standard normal distribution, where the mean (μ) is 0 and the standard deviation (σ) is 1, to find the z-score.

The formula for the z-score is:

z = (x - μ) / σ

where x is the value we want to find the z-score for.

To find x, we can rearrange the formula as:

x = μ + z * σ

where μ = 83 and σ = 11 (given in the problem statement).

To find the z-score for the 60th percentile, we can use a standard normal distribution table or a calculator that has a normal distribution function. Using a standard normal distribution table, we find that the z-score corresponding to the 60th percentile is approximately 0.25.

Plugging in the values, we get:

x = 83 + 0.25 * 11

x = 85.75

Therefore, a grade of 85.75 or higher is required to be in the top 40% of the class.

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Answer:

33 miles

Step-by-step explanation: I think it is correct

Monday: 3 miles

Tuesday: 10 miles

Wednesday: 20 miles because 10 x 2 = 20

3 miles + 10 miles + 20 miles = 33 miles

Hope this helps!

Answer:

P=RS1000

R=10%

T=?

COMPOUND AMOUNT=RS 1200

I=1200-1000=RS200

IF IT IS SIMPLE INTEREST

T={I×100}/(P×R)=(200×100)/(1000×10)=20000/10000=2YEARS=2×12=24MONTHS

Answer: (-3)^8

Step-by-step explanation:

Answer:

(-3)^8

Step-by-step explanation:

2 x 4 = 8

Hence,( -3)^8

[RevyBreeze]

Rainbow punch, made by Frutayuda, Inc., was sold in 12-ounce cans to benefit victims of Hurricane Zero. The mean number of ounces placed in a can by an automatic fill pump is 11.7 ounces with a standard deviation of 0.18 ounce. Assuming a normal distribution, the probability that more than 12 ounces will be released by the pump and overflow the can is 0.02275.

This can be calculated by finding the probability that the filling pump will cause a can to have an amount less than 12 ounces. This probability can be calculated by finding the area under the normal distribution curve from 11.7 to 12. To do this, the z-score of 11.7 must be found. This z-score is -1.05.

The area under the curve from -1.05 to 0 is 0.1587. Subtracting this from 1 gives 0.8413, which is the probability that the filling pump will cause a can to have an amount less than 12 ounces. This means that the probability that the filling pump will cause an overflow in a can is 0.02275 (1-0.8413 = 0.02275).

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Answer:

Where's the grid? From what I gathered it is essential in this question.

Step-by-step explanation:

Ce clasă ești sa văd daca te pot ajuta

Answer:

Step-by-step explanation:

i believe it is c

Answer:

c

Step-by-step explanation:

Answer The picture shows you where to place your line

Step-by-step explanation:

In linear equation, 0.005 pints are pints of yellow paint should be mixed with 10 pints of red paint to make this shade of orange.

What is a linear equation example?

Given,  

         A painter mixes 2%, pints of yellow paint with 4 pints of red paint

So to make this shade of orange  ⇒

10 red pints × (2 % yellow pints/ 4 red pints) ≈  0.005 pints

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1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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at:5

ts:11

oa:5

hope this helps you!

Answer:

the second and 3rd one

Step-by-step explanation:

The angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\),\) which is approximately 1.107 radians or 63.43 degrees.

To determine the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\),\) we can follow these steps:

1. Express \(\(z_0\)\) in polar form: To find the polar form of \(\(z_0\)\), we need to calculate its magnitude \((\(r_0\))\) and argument \((\(\theta_0\))\). The magnitude can be obtained using the formula \(\(r_0 = |z_0| = \sqrt{\text{Re}(z_0)^2 + \text{Im}(z_0)^2}\)\):

\(\[r_0 = |2i + 1| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}\]\)

  The argument \(\(\theta_0\)\) can be found using the formula \(\(\theta_0 = \text{arg}(z_0) = \arctan\left(\frac{\text{Im}(z_0)}{\text{Re}(z_0)}\right)\)\):

\(\[\theta_0 = \text{arg}(2i + 1) = \arctan\left(\frac{2}{1}\right) = \arctan(2)\]\)

2. Find the polar form of \(\(w\)\): The polar form of \(w\) can be expressed as \(\(w = |w|e^{i\theta}\)\), where \(\(|w|\)\) is the magnitude of \(\(|w|\)\) and \(\(\theta\)\) is its argument. Since \((w = z^2\)\), we can substitute z with \(\(z_0\)\) and calculate the polar form of \(\(w_0\)\)using the values we obtained earlier for \(\(z_0\)\):

 \(\[w_0 = |z_0|^2e^{2i\theta_0} = \sqrt{5}^2e^{2i\arctan(2)} = 5e^{2i\arctan(2)}\]\)

3. Determine the argument of \(\(w_0\):\) To find the argument \(\(\theta_w\)\) of \(\(w_0\)\), we can simply multiply the exponent of \(e\) by 2:

  \(\[\theta_w = 2\theta_0 = 2\arctan(2)\]\)= 1.107 radians

Therefore, the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\).\)

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The complete question is:

"Determine the angle of rotation, in radians and degrees, at the point z0 = 2i + 1 when w = z^2."

The purpose of a variable is to hold and represent a value Option C.

The purpose of a variable in programming or mathematics is to hold and represent a value that can be assigned, changed, and used in various operations or calculations. Variables are fundamental components of programming languages and mathematical equations, enabling flexibility and dynamic behavior in computational tasks.

Option (c) "to hold a value" is the most accurate answer, as variables are used to store data or information in memory locations. This value can be of different types, such as integers, floating-point numbers, characters, or even more complex data structures like arrays or objects.

Variables allow programmers to work with and manipulate data efficiently. By assigning values to variables, we can reference and modify them throughout the program, making it easier to manage and organize information.

Variables also play a crucial role in performing calculations, as mentioned in option (b). We can use variables in mathematical expressions and algorithms to perform arithmetic operations, comparisons, and other computations. By storing values in variables, we can reuse them in multiple calculations and update them as needed.

While option (a) "to assign values" is a specific use case of variables, it is not the sole purpose. Variables not only store values but also facilitate data manipulation, control flow, and the implementation of algorithms and logic.

Option (d) "to hold a constant value" is incorrect because variables, by definition, can hold varying values. Constants, on the other hand, are fixed values that do not change during the execution of a program. Option C is correct.

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Answer:

£7

Step-by-step explanation:

Since the sale is 10% the original price, every item is being sold for 90% of its original price. Now the problem is: £6.30 is 90% of what number?

Let x = original price before sale

6.30 = 0.9x

0.9x = 6.3

Divide both sides by 0.9

x = 6.3/0.9

x = 7

Answer: £7

The main 3 methods to solve system of equations are Graphing method, Substitution method, and Elimination method.

In Graphing method, the equations are graphed on a coordinate plane, and the solution is found by identifying the point of intersection of the two graphs. This method is relatively simple and intuitive, but it can be difficult to find an accurate solution if the equations are complex or if the intersection point is not clearly defined.

In Substitution method, one of the equations is solved for one of the variables in terms of the other variable, and then that expression is substituted into the other equation. This creates an equation in one variable, which can be solved to find the value of that variable. The solution is then back-substituted into one of the original equations to find the value of the other variable.

In Elimination method, one or both of the equations are multiplied by a constant factor so that one of the variables will cancel out when the equations are added or subtracted. This creates an equation in one variable, which can be solved to find the value of that variable. The solution is then back-substituted into one of the original equations to find the value of the other variable.

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Answer:

x = 6

Step-by-step explanation:

Given equation,

→ 3x - (2/3)x = 14

Now the value of x will be,

→ 3x - (2/3)x = 14

→ (9/3)x - (2/3)x = 14

→ ((9 - 2)/3)x = 14

→ (7/3)x = 14

→ 7x = 14 × 3

→ x = 42/7

→ [ x = 6 ]

Hence, the value of x is 6.

(i) Euler's method: At x = 0.05, y ≈ 1.05, At x = 0.1, y ≈ 1.107, At x = 0.15, y ≈ 1.174

(ii) Fourth-order Runge-Kutta method: At x = 0.05, y ≈ 1.05 , At x = 0.1, y ≈ 1.107, At x = 0.15, y ≈ 1.174

(i) Euler's Method:

Euler's method is a simple numerical method for approximating solutions to differential equations. It uses the formula:

yᵢ₊₁ = yᵢ + h * f(xᵢ, yᵢ),

where yᵢ is the approximate value of y at xᵢ and f(x, y) is the given differential equation.

Let's start by calculating the approximate solution using Euler's method.

Step size, h = 0.05

At x = 0.05:

x₀ = 0

y₀ = 1

Using the given differential equation: dy/dx = 2x + eˣʸ

We have: f(x, y) = 2x + eˣʸ

Using Euler's method:

x₁ = x₀ + h = 0 + 0.05 = 0.05

y₁ = y₀ + h * f(x₀, y₀)

   = 1 + 0.05 * (2(0) + e^(0*1))

   = 1 + 0.05 * (0 + e^0)

   = 1 + 0.05 * (0 + 1)

   = 1 + 0.05

   = 1.05

At x = 0.1:

x₂ = x₁ + h = 0.05 + 0.05 = 0.1

y₂ = y₁ + h * f(x₁, y₁)

 \(= 1.05 + 0.05 * (2(0.05) + e^(0.05*1.05)) = 1.05 + 0.05 * (0.1 + e^(0.0525))\)

   = 1.05 + 0.05 * (0.1 + 1.05383959925)

   = 1.05 + 0.05 * (1.15383959925)

   = 1.107691979963

At x = 0.15:

x₃ = x₂ + h = 0.1 + 0.05 = 0.15

y₃ = y₂ + h * f(x₂, y₂)

  \(= 1.107691979963 + 0.05 * (2(0.1) + e^(0.1*1.107691979963)) = 1.107691979963 + 0.05 * (0.2 + e^(0.1107691979963))\)

   = 1.107691979963 + 0.05 * (0.2 + 1.12281597877)

   = 1.107691979963 + 0.0661407989385

   = 1.173832778901

Approximate solution using Euler's method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

(ii) Fourth-order Runge-Kutta Method:

The fourth-order Runge-Kutta method is a more accurate numerical method

for approximating solutions to differential equations. It uses the formula:

k₁ = h * f(xᵢ, yᵢ)

k₂ = h * f(xᵢ + h/2, yᵢ + k₁/2)

k₃ = h * f(xᵢ + h/2, yᵢ + k₂/2)

k₄ = h * f(xᵢ + h, yᵢ + k₃)

yᵢ₊₁ = yᵢ + (k₁ + 2k₂ + 2k₃ + k₄)/6

Let's calculate the approximate solution using the fourth-order Runge-Kutta method.

Step size, h = 0.05

At x = 0.05:

x₀ = 0

y₀ = 1

k₁ = 0.05 * f(x₀, y₀)

   = 0.05 * (2(0) + e^(0*1))

   = 0.05 * (0 + e^0)

   = 0.05 * (0 + 1)

   = 0.05

k₂ = 0.05 * f(x₀ + 0.05/2, y₀ + k₁/2)

   = 0.05 * f(0 + 0.025, 1 + 0.025/2)

   = 0.054123529771

k₃ = 0.05 * f(x₀ + 0.05/2, y₀ + k₂/2)

   = 0.05 * f(0 + 0.025, 1 + 0.054123529771/2)

   = 0.05 * (1.08260731316)

   = 0.054130365658

k₄ = 0.05 * f(x₀ + 0.05, y₀ + k₃)

   = 0.05 * f(0 + 0.05, 1 + 0.054130365658)

   = 0.05 * (1.15381700056)

   = 0.057690850028

y₁ = y₀ + (k₁ + 2

k₂ + 2k₃ + k₄)/6

   = 1 + (0.05 + 2(0.054123529771) + 2(0.054130365658) + 0.057690850028)/6

   = 1 + (0.05 + 2(0.054123529771) + 2(0.054130365658) + 0.057690850028)/6

   = 1.04999993086

At x = 0.1:

x₁ = x₀ + h = 0 + 0.05 = 0.05

k₁ = 0.05 * f(x₀, y₁)

   = 0.05 * (2(0.05) + e^(0.05*1.04999993086))

   = 0.05 * (1.15382091332)

   = 0.057691045666

k₂ = 0.05 * f(x₀ + 0.05/2, y₁ + k₁/2)

   = 0.05 * f(0 + 0.025, 1.04999993086 + 0.057691045666/2)

   = 0.05 * f(0.025, 1.076845501196)

   = 0.05 * (1.08293606756)

   = 0.054146803378

k₃ = 0.05 * f(x₀ + 0.05/2, y₁ + k₂/2)

   = 0.05 * f(0 + 0.025, 1.04999993086 + 0.054146803378/2)

   = 0.05 * (0.05 + 1.03297648754)

   = 0.05 * (1.08297648754)

   = 0.054148824377

k₄ = 0.05 * f(x₀ + 0.05, y₁ + k₃)

   = 0.05 * f(0 + 0.05, 1.04999993086 + 0.054148824377)

   = 0.05 * f(0.05, 1.104148755237)

   = 0.

05 * (2(0.05) + e^(0.05*1.104148755237))

   = 0.05 * (1.15636272702)

   = 0.057818136351

y₂ = y₁ + (k₁ + 2k₂ + 2k₃ + k₄)/6

   = 1.04999993086 + (0.057691045666 + 2(0.054146803378) + 2(0.054148824377) + 0.057818136351)/6

   = 1.04999993086 + (0.057691045666 + 2(0.054146803378) + 2(0.054148824377) + 0.057818136351)/6

   = 1.10730401829

At x = 0.15:

x₂ = x₁ + h = 0.1 + 0.05 = 0.15

k₁ = 0.05 * f(x₁, y₂)

   = 0.05 * (2(0.1) + e^(0.1*1.10730401829))

   = 0.066134153561

k₂ = 0.05 * f(x₁ + 0.05/2, y₂ + k₁/2)

   = 0.05 * f(0.1 + 0.025, 1.10730401829 + 0.066134153561/2)

   = 0.05 * (1.40252551209)

   = 0.070126275604

k₃ = 0.05 * f(x₁ + 0.05/2, y₂ + k₂/2)

   = 0.05 * f(0.1 + 0.025, 1.10730401829 + 0.070126275604/2)

   = 0.05 * f(0.125, 1.13726868037)

   = 0.05 * (1.40260973286)

   = 0

.070130486643

k₄ = 0.05 * f(x₁ + 0.05, y₂ + k₃)

   = 0.05 * f(0.1 + 0.05, 1.10730401829 + 0.070130486643)

   = 0.05 * (1.49307437508)

   = 0.074653718754

y₃ = y₂ + (k₁ + 2k₂ + 2k₃ + k₄)/6

   = 1.10730401829 + (0.066134153561 + 2(0.070126275604) + 2(0.070130486643) + 0.074653718754)/6

   = 1.17379707103

Approximate solution using the fourth-order Runge-Kutta method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

Therefore, the approximate solutions using Euler's method and the fourth-order Runge-Kutta method at x = 0.05, 0.1, and 0.15 are as follows:

Euler's method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

Fourth-order Runge-Kutta method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

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Answer:

4/3

Step-by-step explanation:

Answer:

12L/3L

4: 1

four litre of sparkling water for 1 liter juice

The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

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The weighted average cost of capital WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

To calculate the cost of capital for Brozierz Ltd, we need to calculate the cost of each component of their capital structure and weight them according to their proportion in the overall capital structure.

First, let's calculate the cost of equity using the Capital Asset Pricing Model (CAPM):

Cost of equity = risk-free rate + beta x (return on market - risk-free rate)

= 0.06 + 1.4 x (0.15 - 0.06)

= 0.165 or 16.5%

Next, let's calculate the cost of preference shares:

Cost of preference shares = (fixed dividend rate / market price of preference shares) + flotation costs

= (0.1 x 3 / 2.5) + 0

= 0.12 or 12%

The cost of debt is simply the interest rate on the bank loan, which is 12% per annum.

Now, we can calculate the weighted average cost of capital (WACC) using the formula:

WACC = (proportion of equity x cost of equity) + (proportion of preference shares x cost of preference shares) + (proportion of debt x cost of debt) x (1 - tax rate)

Let's calculate the proportion of each component:

Proportion of equity = 300,000 x 2.40 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.375

Proportion of preference shares = 100,000 x 2.50 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.125

Proportion of debt = 500,000 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.5

Therefore, the WACC is:

WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

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|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000

Answer:

9 4/6

Step-by-step explanation:

5 + 4 = 9

1/6 + 3/6 = 4/6

9 4/6

Hope this helps! :)

Step-by-step explanation:

a thing or situation that is annoying because it is complicated or involves a lot of effort

Answer:

\( y = 2 \frac{1}{2} \)

Step-by-step explanation:

\(y + 6 \frac{1}{2} = 9 \\ \\ y + \frac{6 \times 2 + 1}{2} = 9 \\ \\ y + \frac{12 + 1}{2} = 9 \\ \\ y + \frac{13}{2} = 9 \\ \\ y = 9 - \frac{13}{2} \\ \\ y = \frac{9 \times 2 - 13}{2} \\ \\ y = \frac{18 - 13}{2} \\ \\ y = \frac{5}{2} \\ \\ y = 2 \frac{1}{2} \)

Answer:

13.47

Step-by-step explanation:

When put into a calculator it comes up to 13.47125. In this case though, I'm assuming we round to the hundredths place.

Answer:

Should be 13.47125 I could be completely wrong though..

Step-by-step explanation:

I used a calculator