six positive integers are written on the faces of a cube. each vertex is labeled with the product of the three numbers on the faces adjacent to the vertex. if the sum of the numbers on the vertices is equal to $1001$, then what is the sum of the numbers written on the faces?

the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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The solution of the inequality for the number of people (p) who can go to the amusement park will be;

⇒ p < 8

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

They have no more than $235 to spend on parking and admission.

And, Parking is $7, and tickets cost $28.50 per person, including tax.

Now,

Let the number of people who can go to the amusement park = p

So, We can formulate;

⇒ 28.50p + 7 < 235

Solve for p as;

⇒ 28.50p < 235 - 7

⇒ 28.50p < 228

⇒ p < 228/28.50

⇒ p < 8

Thus, The solution of the inequality for the number of people (p) who can go to the amusement park is;

⇒ p < 8

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Answer:

A) Length = 94 m

B) Width = 79 m

Step-by-step explanation:

A)

The area of a parking lot is 7802 m²

Area = length x width

7802 = length x 83

length = 7802 ÷ 83

length = 94 m

b)

The perimeter of a pool is 353 m

Perimeter = 2(length + width)

352 = 2(97 + width)

352 = 194 + 2width

2width = 352 - 194

2width = 158

width = 158/2

width = 79 m

-Chetan K

The average of the set of values is 11.70.

The term "average" typically refers to the arithmetic mean of a set of values. It is a measure of central tendency that represents the typical or typical value in a dataset. To calculate the arithmetic mean or average, you add up all the values in the dataset and divide the sum by the total number of values.

To calculate the average of the set of values 18, 4, 12.99, 13.772 and 9.704 we need to add all the numbers in the set and then divide the sum by the number of values in the set.

We can then simplify the answer to the nearest hundredth (two decimal places).

Here's the calculation:

18 + 4 + 12.99 + 13.772 + 9.704

= 58.48658.486 ÷ 5

= 11.6972 ≈ 11.70

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The equation of the circle, obtained by applying the completing the square method to the specified equation indicates that the center and radius of the circle are;

Center (0, 6) and radius 7.5

The general form of the equation of a circle is; (x - h)² + (y - k)² = r², where;

(h, k) = The coordinates of the center of the circle

r = The measure of the length of the radius

The possible equation obtained from a similar question on the internet can be presented as follows;

x² + y² - 12·y - 20.25 = 0

The above equation can be evaluated using the completing the square method and excluding the x² term as follows;

y² - 12·y - 20.25 = 0

y² - 12·y = 20.25

y² - 12·y + (-12/2)² = 20.25 + (-12/2)²

y² - 12·y + (-6)² = 20.25 + (-6)² = 56.25

(y - 6)² = 56.25

Therefore;

y - 6 = √(56.25) = ±7.5

The possible equation of the circle obtained by plugging in the x² term therefore is; (x - 0)² + (y - 6)² = 7.5²

The center of the circle is therefore;

(h, k) = (0, 6)

The radius of the circle, r = 7.5

The possible correction is therefore, option (a), where the 5 is a typing error

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Answer:

So basically if there's 6 numbers on each dice, that means that there's a 5/6 chance of not getting a 3. So multiply that and you get 5/6*5/6. That is equal to 25/36 change.

Answer: The product of the two numbers is 2400.

Step-by-step explanation: You multiply the numbers on the ratio with the difference first you multiply 2 with 20 then you multiply 3 with 20.

The given force field is F(r,θ,z) = −kr3r^. To check whether the given force is conservative or not, it is required to confirm whether the given force is a central force or not.

Given force is F(r,θ,z) = −kr3r^.

So, F = -kr3r^ where r^ is a unit vector in the radial direction.

In the radial direction, F = F r r^

For the given force, F r = -kr³ is only dependent on the magnitude of the radius vector r, and not on its direction.

In other words, F r is a function of r only and hence the given force is a central force. Thus, the given force is conservative

The potential energy of the particle moving around in F(r,θ,z) = −kr3r^ is given as follows:

V(r) = -W(r) where, W(r) is the work done by the force F(r,θ,z) in moving a particle from infinity to the point P(r,θ,z).

To find W(r), consider a particle starting from infinity moving along a path r→0.

The work done by the force F along this path is given by the integral of F over this path.

W(r→0) = ∫r→0 F(r) · dr = -∫r→0 kr³ · dr = -k/4 r⁴ → infinity

Thus, the potential energy of the particle is V(r) = k/4 r⁴ + C, where C is the integration constant.

As the force is conservative, the total energy of the particle E = K + V is constant where K is the kinetic energy of the particle.

Substituting v = d/dt r in the equation of energy, we get

E = 1/2 m (dr/dt)² + k/4 r⁴ + C.

Rearranging the terms, we get

E = 1/2 m (dr/dt)² + 1/2 k r² + C.

But, we know that, k/4 r⁴= 1/2 k r².

Therefore, E = 1/2 m (dr/dt)² + 1/2 k r² + C.

Thus, the total energy of the particle E is given by

E = 1/2 m (dr/dt)² + 1/2 k r² + C.

The given force F(r,θ,z) = −kr3r^ is a conservative force, as it is a central force. The potential energy of the particle moving around in this force field is given by V(r) = k/4 r⁴ + C, where C is the integration constant. The total energy of the particle E is given by E = 1/2 m (dr/dt)² + 1/2 k r² + C.

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(fg)(x)= x³ - 7x² - 9x + 8

domain is (-∞,∞)

Given: f(x)= x-8, g(x)= x² +1x - 1

To find (fg)(x) we multiply f(x) and g(x)

(fg)(x) = f(x) * g(x)

(fg)(x)= (x-8) (x²+x-1)

(fg)(x)= x³ + x² - x - 8x² - 8x +8

(fg)(x)= x³  - 7x²  - 9x + 8

we know, domain for all cubic function is set of all real numbers

domain is (-∞,∞)

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Answer:

c

Step-by-step explanation:

\(25\pi + (8*10\pi)+[(35*12)-25\pi]+(35*12)+ 2(15*12)+2(35*15)=\\25\pi +80\pi + (420-25\pi) + 420 + 360 + 1050=\\105\pi-25\pi + 840 +1410=\\80\pi+2250=\\2501.32741229\)

The expression is rewritten as 3(12 - 5)

Factorization is simply defined as a method of writing a number or another mathematical object as a product of several factors.

The different types of factorization are;

From the information given, we have that the expression is;

36- 15

Factor the expression

3(12 - 5)

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Answer:

B

There is no friction

Step-by-step explanation:

if the object is stationary , it's not moving, no forces acting on it how can it produces friction ?

The equation for the line t is:

f(x) = -3x + 3

Let's say that line t can be written as:

f(x) = a*x + b

Remember that two lines are perpendicular if the product between the slopes is -1, then if our line is perpendicular to:

y = 1/3x - 5

Then we will have:

a*(1/3) = -1

a = -3

The line is:

f(x) = -3*x + b

And this line must pass through (-2, 9), then:

9 = -3*-2 + b

9 = 6 + b

9 - 6 = b

3 = b

The line t is:

f(x) = -3x + 3

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Based on the vacation days that Lisa got when she first started her current job, the equation that models the relationship between the number of years worked and paid vacation days is y = 3x + 2

The number of paid vacation days to Lisa increases by 3 days every year. This is in addition to the 2 days that Lisa got when she first started the job.

The relationship between the vacation days and the number of years worked is therefore:

Number of paid vacation days = Number of years x Increase in paid vacation days annually + Number of paid vacation days when job started

y = 3x + 2

Full question is:

When Lisa started at her current job, her employer gave her two days of paid vacation time with a promise of three additional paid vacation days for each year she remains with the company to a maximum of four work weeks of paid vacation time.

Let x represent the number of years she has worked for this employer and y represent the number of paid vacation days she has earned. Write an equation that models the relationship between these two variables.

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Answer:

58

Step-by-step explanation:

Hello, let's note the two digits a and b. the first number 'ab' can be written as 10a +b. For instance if this is 24 it can be written 20 + 4.

If the digits are interchanged the number become 'ba' so 10b + a

We can say that 10a + b + 10b + a = 143

11(a+b)=143

We divide by 13 both sides and we take

a+b = 143/11 = 13

and we know that the digits differ by 3 so b = a + 3

then a + b = a + 3 + a = 2a + 3 = 13

so 2a = 10 and then a = 5

Finally, b = 5+3=8 so the number is 58.

And we can verify that 58 + 85 = 143.

Thanks

Answer:

❍ According to Question now,

➥ 10(x + 3) + x + 10x + x + 3 = 143

➥ 10x + 30 + 12x + 3 = 143

➥ 22x + 33 = 143

➥ 22x = 143 - 33

➥ 22x = 110

➥ x = 110/22

➥ x = 5

Therefore,

The unit digit number = x = 5

The tens digit number = x + 3 = 5 + 3 = 8

The original number = 10(x + 3) + x

The original number = 10(5 + 3) + 5

The original number = 50 + 30 + 5

The original number = 85

Hence,the original number is 85.

The probability of selecting ko and vz but excluding pfe and ge from a set of 8 stocks is 0.0625 or 6.25%.

To see why, we can use the formula for the probability of an event occurring, which is:

P(event) = (number of ways the event can occur) / (total number of possible outcomes)

The total number of possible outcomes when selecting 4 stocks from a set of 8 is:

C(8,4) = 8! / (4! * 4!) = 70

where C(n,r) is the number of combinations of r objects chosen from a set of n objects.

To count the number of ways to select ko and vz while excluding pfe and ge, we need to choose 2 stocks out of the remaining 4, which can be done in:

C(4,2) = 4! / (2! * 2!) = 6

ways.

Therefore, the probability of selecting ko and vz but excluding pfe and ge is:

P(ko and vz but not pfe or ge) = 6 / 70 = 0.0625 or 6.25%.

In summary, the probability of selecting ko and vz but excluding pfe and ge from a set of 8 stocks is 0.0625 or 6.25%, which can be calculated using the formula for probability and the number of possible outcomes that satisfy the given conditions.

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complete question:

If you selected four of these stocks at random, what is the probability that your selection included KO and VZ but excluded PFE and GE?

Answer:

x=3!

Step-by-step explanation:

To do this, you would have to divide by 2 on both sides.

2x/2=x

6/2=3

x=3

Answer:

1. First choice, 1/2

2. First choice, 1/2

Step-by-step explanation:

3 odd numbers on a dice, so 3/6 = 1/2

12 numbers, 1- 12, the even numbers are 2, 4, 6, 8, 1-, and 12. 6 out of 12 = 6/12 = 1/2

Answer:

Step-by-step explanation:

area of garden = 38 m²

width = 4 m

find Length

area = L x W

38 = L (4)

L = 38 / 4

L = 9.5 m

The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5

(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.

(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.

Given: Function f(x) is (x - 5)3(x + 2)2

If a curve touches the x-axis then f(x) = 0

⇒ (x - 5)3(x + 2)2 = 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ (x - 5)3 = 0 and (x + 2)2 = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

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For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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Answer:

9s+11

Step-by-step explanation:

Combine like terms → (7s+2s and 2+9 = 9s and 11) and boom

Answer:

\(9s + 11\)

Step-by-step explanation:

First:

\(7s - 2s \\ = 9s\)

second:

\(9 + 2 \\ = 11\)

the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

The minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is as follows:

95% confidence, within 5 percentage points, and a previous estimate of 0.25.

The formula to calculate the sample size required for the study to determine the proportion is given by:

`n = Z²pq / E²`

Where n = sample size

Z = z-value (1.96 at 95% confidence interval)

E = margin of error

p = estimated proportion of the population

q = 1 - pp

q = estimated proportion of population without the condition (1 - 0.25 = 0.75)

Given,

Z = 1.96E = 0.05p = 0.25q = 0.75

Substituting these values in the above formula, we get;

`n = (1.96)²(0.25)(0.75) / (0.05)²``n = 384.16`

Therefore, the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

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Answer:

9. 5y

10. 6x^2 + 4x^2 + 4 * (-1) = 10x^2 - 4

11. 2a^5 + 4b + b = 2a^5 + 5b

12. 14- 12= 2

8m + 2 + 4n = 8m + 4n +2

Step-by-step explanation:

Answer:  b.) 1 hour at 35 mph when the car spends 3 hours at 55mph

c.) The trip will take 3.64 hours which is about about  3 hours and 38 minutes if the car travels at 55mph the entire time.

(But it could take longer if the police stop the car to issue a ticket for going 55 mph in a 35mph zone!)

Step-by-step explanation:

b.) 55(3) + 35y = 200  Multiply 55(3) = 165

165 + 35y = 200.    Subtract 165 from both sides 200- 165 = 35

35y = 35 divide both sides by 35

y = 1, So the time traveling at 35mph is 1 hour

c.) 55x + 35y = 200

55x + 35(0) = 200  35×0 = 0

55x = 200 . Divide 200 miles by 55mph to find the time, x

200/55 = 3.63636 hours

To convert to minutes, multiply 60 × .63636 ≈ 38.18 minutes

A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Answer:

10,000

Step-by-step explanation:

1 * 10,000 = 10,000

Answer:

10000 = 1 *10^4

Step-by-step explanation:

1* 10000

10000

In scientific notation

There are 4 zeros

1 * 10 ^4

The probability that a student passed the course depends on various factors, such as the grading criteria, the weightage of homework in the overall assessment, and the performance of the students.

To determine the probability that a student passed the course given that they did not complete their homework, we need to consider the grading criteria and the weightage of homework in the overall assessment. If the completion of homework carries a significant weight in the final grade, students who did not complete their homework would have a lower chance of passing the course. However, if homework is not a major factor in the grading scheme, other factors such as class participation, performance on exams, and projects might have a greater impact on the final grade.

Additionally, the overall performance of the students in the class would affect the probability. If the majority of students perform well in the course, irrespective of completing their homework, the probability of passing the course without completing homework could be higher. On the other hand, if the majority of students who pass the course have consistently completed their homework, the probability would be lower.

Without specific information about the grading criteria, weightage of homework, and the performance distribution of the students, it is challenging to provide an exact probability. Therefore, the probability that a student passed the course given that they did not complete their homework can vary based on these factors and would need more specific information to be determined accurately.

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