What is the intersection of plane HGY and plane GEF?

The smaller container holds 17 gallons, and the larger container holds 27 gallons.

Let's represent the smaller container's capacity as x gallons. According to the problem, the larger container can hold 7 gallons less than twice the capacity of the smaller container, which can be expressed as 2x - 7.

The total capacity of both containers is given as 44 gallons, so we can set up the equation:

x + (2x - 7) = 44

Simplifying the equation:

3x - 7 = 44

3x = 51

x = 17

Therefore, the smaller container holds 17 gallons.

To find the capacity of the larger container, we substitute the value of x back into the expression 2x - 7:

2(17) - 7 = 34 - 7 = 27

Hence, the larger container holds 27 gallons.

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Answer:

-2

Step-by-step explanation:

hope it helps

Answer:

Jamie read 0.75 pages a minute

Step-by-step explanation:

1 hour is 60 minutes. 2 hours is 120 minutes. Now, you divided 90 by 120. so 0.75

Answer:

0.75

Step-by-step explanation:

[tex]90 \div 120 = \frac{3}{4} [/tex]

The exercise involves calculations with matrices A, B, and C. We need to determine if matrix products AB, BA, BC, and CB are defined. Additionally, we need to calculate the specific matrix products and determine if BC is equal to CB.

Let's perform the calculations step by step:

(a) To determine if AB is defined, we need to check if the number of columns in matrix A is equal to the number of rows in matrix B. If they are equal, the matrix product AB is defined. If not, the product is not defined.

Matrix A has 2 columns and matrix B has 2 rows, so the product AB is defined.

Calculating AB:

AB = [23 + 83 20 + 88]

[23 + 03 20 + 08]

= [30 64]

[6 0]

To calculate BA, we need to check if the number of columns in matrix B is equal to the number of rows in matrix A. In this case, matrix B has 2 columns and matrix A has 2 rows, so the product BA is also defined.

Calculating BA:

BA = [32 + 02 38 + 02]

[32 + 02 38 + 02]

= [6 24]

[6 24]

(b) To determine if BC is defined, we need to check if the number of columns in matrix B is equal to the number of rows in matrix C. In this case, both matrices have 2 columns and 2 rows, so the product BC is defined.

Calculating BC:

BC = [26 + 85 23 + 81]

[06 + 05 03 + 01]

= [52 22]

[0 0]

To calculate CB, we need to check if the number of columns in matrix C is equal to the number of rows in matrix B. In this case, matrix C has 2 columns and matrix B has 2 rows, so the product CB is also defined.

Calculating CB:

CB = [62 + 30 68 + 30]

[52 + 10 58 + 10]

= [12 48]

[10 40]

Is it true that BC = CB?

BC = [52 22]

[0 0]

CB = [12 48]

[10 40]

BC and CB are not equal. The matrix product is not commutative, so BC and CB may yield different results.

In summary:

(a) AB is defined and the result is:

AB = [30 64]

[6 0]

BA is also defined and the result is:

BA = [6 24]

[6 24]

(b) BC is defined and the result is:

BC = [52 22]

[0 0]

CB is also defined and the result is:

CB = [12 48]

[10 40]

BC and CB are not equal, indicating that matrix multiplication is not commutative.

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Answer:

(-7.5, 3.5)

Step-by-step explanation:

[tex]midpoint \: = ( \frac{x1 + x2}{2} \: , \: \frac{y1 + y2}{2} )[/tex]

[tex] = ( \frac{ ( - 5) + ( - 10)}{2} , \frac{(5) + (2)}{2} )[/tex]

[tex] = ( \frac{ - 15}{2} , \frac{7}{2} )[/tex]

[tex] = ( - 7.5,3.5)[/tex]

Answer:

Step-by-step explanation:

one hour  you travel 45 miles

there are 60 minutes in one hour

the 60/45= 1 1/3 minutes

it takes 1 1/3 minutes to travel one mile

divide 60 minutes by 45 miles:

60 min              45 miles

 ??                      1 mile

cross multiply

60*1/45=60/45=1 1/3 minutes

Answer:

12 bouquets, each having 6 red roses, 5 pink roses, and 4 yellow roses.

Step-by-step explanation:

The Greatest Common Multiple is 12

72/12 = 6

60/12 = 5

48/12 = 4

Answer:

C. 9

Step-by-step explanation:

When dividing exponents with the same base, always subtract the top from the bottom, which in this case would be 9-5=4

The equation is an exponential equation, and the value of n in the equation is 9

The equation is given as:

[tex]\frac{12^n}{12^5} = 12^4[/tex]

Apply the law of indices, to the equation

[tex]12^{n-5} = 12^4[/tex]

Cancel out the common base in the equation

n - 5 = 4

Add 5 to both sides

n = 9

Hence, the value of n in the equation is 9

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Answer: C. 13/24 i hope it help you out

Answer:

it was just a joke chilll

Answer:

3 and 5

Step-by-step explanation:

You have to realize that Integers is another word for numbers

Answer:

0

Step-by-step explanation:

7x - 4 = -4

add 4 to both sides

7x = 0

x = 0

Answer:

x = 0

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 4 to both sides of the equation:

7x - 4 (+4) = -4 (+4)

7x = -4 + 4

7x = 0

Next, divide 7 from both sides of the equation:

(7x)/7 = (0)/7

x = 0/7

x = 0

0 is your answer.

~

If the price of rough rice increases from 12,000 to 20,000 rupees per ton, the supply curve of milled rice in India will decrease by 96 million tons per year.

To determine how the supply curve changes when the price of rough rice increases from 12,000 to 20,000 rupees per ton, we need to analyze the given supply function:

Q = 8 + 9p - 12p,

In the supply function, "p" represents the price of milled rice in thousands of rupees per ton. However, there is a typo in the equation provided for the supply function. It appears that the equation contains two terms with the variable "p," which should be corrected.

Assuming the corrected supply function is:

Q = 8 + 9p - 12p',

Where p' represents the price of rough rice in thousands of rupees per ton.

Now, let's calculate the initial supply quantity and then compare it with the new supply quantity after the increase in the price of rough rice.

For the initial price of rough rice (p') at 12,000 rupees per ton:

Q1 = 8 + 9p - 12(12)

Q1 = 8 + 9p - 144

For the new price of rough rice (p') at 20,000 rupees per ton:

Q2 = 8 + 9p - 12(20)

Q2 = 8 + 9p - 240

The change in supply can be calculated as the difference between Q2 and Q1:

Change in supply (ΔQ) = Q2 - Q1

= (8 + 9p - 240) - (8 + 9p - 144)

= -240 + 144

= -96

The change in supply (ΔQ) is -96 millions of tons of rice per year.

Therefore, if the price of rough rice increases from 12,000 to 20,000 rupees per ton, the supply curve of milled rice in India will decrease by 96 million tons per year.

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Answer: Q= 6x+1

R= -7x+1

Step-by-step explanation:

The quotient is (6x + 1) and the remainder is (-7x + 1).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given A cubic polynomial 24x³ - 14x² + 20x + 6 divided by 4x² - 3x + 5.

So, (24x³ - 14x² + 20x + 6)/(4x² - 3x + 5).

= (4x² - 3x + 5)(6x + 1) + (-7x + 1)/(4x² - 3x + 5) in rhe form N = DQ + R.

The same applies to the division of polynomials.

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Answer:

the circumference divided by diameter

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given data

speed v= 13 miles per hour

time taken t= 20min to hour 0.3 hours

the distance D

We know that the relationship between speed, time, and distance

speed=distance/time

13=D/0.3

(the expression above describes the relationship between  distance, speed, and time)

making D subject of formula we have

D= 0.3*13

D= 3.9 miles

hence the distance is 3.9miles

Answer:

If your looking for the equation it will be

D = 13 · 1/3

And the answer to this equation is 3.9 miles

Hope this helps

To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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Answer:

13) 12000

14) 0.000096000

Step-by-step explanation:

The market price per ordinary share is $ 266.67 given that the profit is $ 2,000,000 and there are 150,000 ordinary shares while the price earnings ratio is 1.2.

Below is the solution:
Formula used: Market price per share = (Profit/Number of ordinary shares) * Price earnings ratio
Calculation: Market price per share = (2,000,000/150,000) * 1.2
Market price per share = 13.33 * 1.2
Market price per share = $ 16
Given that the profit is $ 2,000,000 and there are 150,000 ordinary shares while the price earnings ratio is 1.2, this question is asking about the market price per ordinary share. To find this, we need to use the formula of market price per share, which is (Profit/Number of ordinary shares) * Price earnings ratio. Applying the given values, the answer would be:
Market price per share = (2,000,000/150,000) * 1.2
Market price per share = 13.33 * 1.2
Market price per share = $ 16
Therefore, the market price per ordinary share is $ 266.67 ($ 16 * 16.67). Hence, option D is the correct answer.

The market price per share is calculated as (Profit/Number of ordinary shares) * Price earnings ratio. Given the values, the answer would be $ 16. Therefore, the market price per ordinary share would be $ 266.67.

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The total surface area of the right trapezoidal prism is 536 square feet. Therefore, the approximate surface area of sphere is 1,256.6 square inches. The surface area of  right trapezoidal prism is 1,485 square feet.

Surface area of the sphere:

The formula for the surface area of a sphere is given by A = 4πr², where r is the radius of the sphere. Substituting the given radius of 10 inches, we have A = 4π(10)² = 400π square inches. The exact value is 400π square inches. To approximate it to the nearest tenth we can use the value of π as approximately 3.14159. Therefore, the approximate surface area is 400π ≈ 400(3.14159) = 1,256.6 square inches.

Surface area of the right trapezoidal prism:

The total surface area of a right trapezoidal prism can be calculated by adding the areas of all its faces. The formula is A = 2h(b₁ + b₂) + (b₁ + b₂)(x + y), where h is the height of the prism, b₁ and b₂ are the lengths of the parallel bases, and x and y are the lengths of the non-parallel sides.

Substituting the given dimensions, we have A = 2(16)(16 + 11) + (16 + 11)(12 + 11) = 2(27)(16) + (27)(23) = 864 + 621 = 1,485 square feet.

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The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral [tex]\( \int_{1}^{2} x \ln x \, dx \)[/tex] is approximated using [tex]\( n = 4 \)[/tex]subintervals. In part (b), the integral[tex]\( \int_{2}^{2} x^{3} e^{x} \, dx \)[/tex] is given with incorrect limits, so it cannot be evaluated.

To approximate [tex]\( \int_{1}^{2} x \ln x \, dx \)[/tex] using the Composite Trapezoidal rule, we divide the interval [tex]\([1, 2]\) into \( n = 4 \)[/tex] subintervals. The step size, [tex]\( h \)[/tex], is calculated as[tex]\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)[/tex]. Then, we evaluate the function [tex]\( x \ln x \)[/tex]at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: [tex]\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\][/tex]

Using this formula, we can calculate the approximation for the given integral. The limits of the integral [tex]\( \int_{2}^{2} x^{3} e^{x} \, dx \)[/tex] are given as [tex]\( 2 \)[/tex] to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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Answer:

Step-by-step explanation:

Use the midpoint formula: [tex]\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}[/tex]

So, the Change In X is 2-8 = -6

And the Change in Y is 7-4 = 3

Once you divide both of the changes by 2, you get

X: -3

Y:  [tex]\frac{3}{2}[/tex]

So the midpoint is: [tex](-3,\frac{3}{2})[/tex]

Answer:

Difference: c - d

Variable: a

Coefficient: 9

Step-by-step explanation:

Oh, I see what it is now. (Ngl, you should be able to know this)

A variable is something of a placeholder where you can plug in values into an equation.

Difference is when you subtract something.

Coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

The graph of the function is a parabola opening upwards. As x approaches negative or positive infinity, the function approaches positive infinity.

The given function is f(x) = 2x^2 + 10x + 12. Let's analyze the graph of the function and test its limits.

To graph the function, we can start by finding the vertex and the y-intercept. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b/2a. In this case, a = 2 and b = 10.

x = -10 / (2 * 2) = -10 / 4 = -2.5

Substituting the x-coordinate of the vertex back into the function, we can find the y-coordinate:

f(-2.5) = 2(-2.5)^2 + 10(-2.5) + 12

        = 2(6.25) - 25 + 12

        = 12.5 - 25 + 12

        = -0.5

So, the vertex of the parabolic graph is (-2.5, -0.5).

Next, let's find the y-intercept by setting x = 0:

f(0) = 2(0)^2 + 10(0) + 12

     = 12

So, the y-intercept is (0, 12).

Now, we can plot these points and sketch the graph of the function. The graph will be a parabola opening upwards since the coefficient of x^2 is positive.

To test the limits of the function, we'll consider the behavior of the function as x approaches positive or negative infinity.

As x goes to negative infinity, the quadratic term dominates, and the function approaches positive infinity. So, the limit as x approaches negative infinity is positive infinity.

As x goes to positive infinity, the quadratic term again dominates, and the function approaches positive infinity. So, the limit as x approaches positive infinity is positive infinity as well.

In summary, the graph of the function is a parabola opening upwards. As x approaches negative or positive infinity, the function approaches positive infinity.

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Answer:

x = 1/64

Step-by-step explanation:

2x = 1/32

Divide both sides by 2.

Simplify, and you will get 1/64.

Answer:

Its -5

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

5x12 is 60.