Charlie drove for 5 hours to get from his house to grandma’s house. He averaged 47 miles per hour on the trip. Write
and solve an expression that represents the approximate distance from Charlie’s house to grandma’s house.

The rope would be about 4,285,082.98 feet high above the ground.

Answer: The circumference of the earth is 24,902 miles. We have to add 3 ft of rope and keep its circular shape. We must determine how high the rope would be from the ground.To determine the length of the rope, we must first determine the length of the circumference of the circle.Circumference of the circle = πd = π * 8000 miles = 25132 miles (taking radius of earth as 4000 miles).1 mile is 5280 feet, which implies that the distance around the circle is 25132 * 5280 = 132712960 feet.

The length of the rope will be equal to the distance around the circle, plus 3 feet.Length of the rope = 132712963 feet.Now, to determine how high the rope would be from the ground, we need to use the Pythagorean theorem.Height of the rope = √(length of the rope² - radius of earth²) = √(132712963² - 4000²) = √17602394294769 = 4,285,082.98 feet (approx.)The rope would be about 4,285,082.98 feet high above the ground.

Read more about areas related to circle at

https://brainly.com/question/27120842

#SPJ11

Answer:

.25

Step-by-step explanation:

distance between 0,4 is 1. The distance between _2 and _3 is minus 5. X equals.

.25

Answer:

The area of Polygon

W

WW is

49

4949 square units.

Step-by-step explanation: dk

Scale factors are used to enlarge or reduce the size of a shape

The area of polygon w is 49 square units

The area of polygon v is given as:

\(v =1\)

The scale factor of the sides of polygon v, that forms polygon w is given as:

\(k=7\)

The area of polygon w is then calculated as:

\(w =v\times k^2\)

So, we have:

\(w =1\times 7^2\)

Evaluate the exponents

\(w =1\times 49\)

Multiply 1 and 49

\(w =49\)

Hence, the area of polygon w is 49 square units

Read more about scale factors at:

https://brainly.com/question/10253650

Answer:

x = 27°

Step-by-step explanation:

Because of the two parallel lines, we can conclude that

corner DAB = corner FDE = 2x

In ∆DAB

Corner DAB = 2x

Corner BDA = 2x (given)

Corner ABD = 72 (given)

The sum of three corners in any trianle, adds up to 180°.

So if one corner is 72° and the other two corners are the same, then the two corners together, must be 180-72 = 108°.

For each corner that is 108/2= 54

so corner BDA = 54° and also corner DAB = 54°.

Given was BDA = 2x and BDA = 54°

so 2x = 54°

then x = 27°

Answer: Subtraction Property of Equality

Step-by-step explanation: The Subtraction Property of Equality tells us that

we can subtract the same quantity, or equal quantities,

from both sides of an equation.

To get from the statement 7x + 11 = 39 to 7x = 28,

we subtract 11 from both sides to get 7x = 28.

The sum of the multiplicities of the roots in a polynomial equation is equal to the degree of the polynomial (the highest power of the variable in the equation).

This is known as the Fundamental Theorem of Algebra. The multiplicity of a root is the number of times a root appears in a polynomial equation, and it can be a whole number, a fraction, or even an irrational number.

For example, if the polynomial equation is x³ + 2x² + 4x - 8 = 0, then the degree of the polynomial is 3 and the multiplicities of the roots are 1, 2, and 1, respectively.

Therefore, the sum of the multiplicities of the roots in this equation is 3. This is true for any polynomial equation: the sum of the multiplicities of the roots will always be equal to the degree of the polynomial.

Learn more about polynomial equation:

https://brainly.com/question/29513223

#SPJ4

The Nitrogen is commonly considered as a Trigonal Pyramidal molecule .

In a Trigonal Pyramidal arrangement, there are three atoms attached to the central atom at the corners of a triangular plane, with the fourth atom attached above or below the plane.

This molecular geometry is commonly observed in compounds where the central atom has five valence electrons, such as nitrogen in its most common oxidation state of +3.

The Nitrogen in this oxidation state forms compounds like nitrogen triiodide (NI₃) and nitrogen trioxide (NO₃), which have a trigonal pyramidal geometry.

Therefore , Yes , Nitrogen is trigonal pyramidal .

Learn more about Trigonal Pyramidal here

https://brainly.com/question/28358543

#SPJ4

Answer:

All your answers are right. A and d are functions but b and c are not.

Step-by-step explanation:

The net profit for the year ending December 31, 2021, is £1,000. Therefore, the correct answer is d) £1,000.

To determine the net profit for the year ending December 31, 2021, we need to calculate the total revenue and subtract the total expenses. Let's analyze the transactions provided:

The owners invested £550,000 of their own funds into the business bank account. This does not affect the net profit as it represents an owner's contribution of capital.

The business used £16,000 from the bank account to purchase short features and fashion. This expense reduces the net profit.

The business used £10,000 from the bank account to buy new inventory. This expense also reduces the net profit.

The business bought additional inventory worth £9,000 on credit. This is not an expense for the current year as it represents an increase in assets.

The shop sold £28,000 worth of inventory to customers for cash. This revenue increases the net profit.

The business sold goods costing £6,000 to another business on credit for £8,000. This revenue also increases the net profit.

The business paid £9,000 in rent from the bank account. This expense reduces the net profit.

Depreciation and estimated electricity expenses are not mentioned in the given transactions and cannot be calculated.

The owners withdrew £10,000 in cash for personal use. This is not an expense for the business and does not affect the net profit.

Based on the provided information, we can calculate the net profit as follows:

Total Revenue = £28,000 (from sales to customers) + £8,000 (from sales to another business) = £36,000

Total Expenses = £16,000 (short features and fashion) + £10,000 (new inventory) + £9,000 (rent) = £35,000

Net Profit = Total Revenue - Total Expenses = £36,000 - £35,000 = £1,000

Therefore, the net profit obtained is £1,000.

To know more about net profit refer here:

https://brainly.com/question/32239002#

#SPJ11

Answer:

the gcf is 4

Step-by-step explanation:

First you have to solve the multiplication problems. then you have to figure out the factors of each one, write them down, and then circle the ones all of them have in common, and the greatest number they have in common is 4

The Polynomial of least degree with roots 7 and -9 is x^2 + 2x - 63.

To polynomial with roots at 7 and -9, we can use the fact that if a number r is a root of a polynomial, then the corresponding factor is (x - r).

Let's begin by setting up the factors for the given roots:

Factor 1: (x - 7)

Factor 2: (x - (-9)) = (x + 9)

To find the polynomial of least degree, we multiply these factors together:

Polynomial = (x - 7)(x + 9)

To simplify further, we can use the distributive property:

Polynomial = x(x + 9) - 7(x + 9)

Expanding the terms:

Polynomial = x^2 + 9x - 7x - 63

Combining like terms:

Polynomial = x^2 + 2x - 63

Therefore, the polynomial of least degree with roots 7 and -9 is x^2 + 2x - 63. This polynomial is in standard form with a leading coefficient of 1, which is the desired format.

To know more about Polynomial .

https://brainly.com/question/2833285

#SPJ11

Each element of the resulting vector represents the difference between the corresponding elements of vector b and vector a. Therefore, the result of b - a is {2, 3, 6}.

To calculate b - a, we perform component-wise subtraction between vector b and vector a. This means we subtract the corresponding elements of vector a from vector b.

Given:

a = {1, 2, 3}

b = {3, 5, 9}

To calculate b - a, we subtract the first element of vector a from the first element of vector b, the second element of vector a from the second element of vector b, and the third element of vector a from the third element of vector b.

Subtracting the corresponding elements:

b - a = {3 - 1, 5 - 2, 9 - 3}

= {2, 3, 6}

To know more about vector,

https://brainly.com/question/31900604

#SPJ11

Answer: (3.5,-2)

Step-by-step explanation:

To solve this problem, all we have to do is plug in y=-2 into either equations from step one to find the coordinate. To make sure we have the right x-coordinate, let's plug in y for both equations.

4x-7y=28        [plug in y=-2]

4x-7(-2)=28    [multiply]

4x+14=28       [subtract both sides by 14]

4x=14              [divide both sides by 4]

x=3.5

------------------------------------------------------------------------------------------------------------

6x-5y=31        [plug in y=-2]

6x-5(-2)=31    [multiply]

6x+10=31       [subtract both sides by 10]

6x=21             [divide both sides by 6]

x=3.5

Now, we know the solution to the system is (3.5,-2).

Answer:

(3.5, -2)

Step-by-step explanation:

Hi there!

We are given a system of equations, and the value for y is already solved (y=-2)

We want to find the value of x

To do that, substitute -2 as y into either one of the equations in the system (the system has the equations 4x-7y=28 and 6x-5y=31) and solve for x

Let's use 4x-7y=28, although picking 6x-5y=31 is completely fine

Substitute -2 as y into the equation

4x-7(-2)=28

Multiply

4x+14=28

Subtract 14 from both sides

4x=14

Divide both sides by 4 and simplify

x=7/2, or 3.5

We found the value of x in the system

Substitute the values of x and y into a point form (x, y)

The solution is (3.5, -2)

Hope this helps!

Answer:

See below

Step-by-step explanation:

Given numbers:

Standard notation:

Scientific Notation​:

Answer:

The guy above me is right

Step-by-step explanation:

Given numbers:

5.91E10

0.0000734

2.66 x 10^-3

641,000,000,000

Standard notation:

0.0000734

641,000,000,000

Scientific Notation​:

5.91E10

2.66 x 10^-3

(a) The ratio of the number of Ali's muffins to the number of Bala's muffins to the number of Charles' muffins is A:B:C is 576:0.8:1.

(b) Charles baked 1500 number of muffins.

To find the ratio of the number of muffins baked by each baker, we can use the given information:

1/5 of Ali's muffins = 3/10 of Bala's muffins.

(1/5)A = (3/10)B

Bala's muffins were 80% of Charles' muffins.

B = 0.8C

If Bala baked another 300 muffins, he would have the same number of muffins as Charles.

B + 300 = C

To solve this system of equations, we can substitute the second equation into the first equation and solve for A:

(1/5)A = (3/10)(0.8C)

A = (3/2)(0.8C)

A = (12/10)C

A = (6/5)C

Substituting the value of A into the third equation:

(6/5)C + 300 = C

6C + 1500 = 5C

C = 1500

So, Charles baked 1500 muffins.

Now we can find the ratios:

A/B = (6/5)C/B = (6/5)(0.8C) = (6/5)(0.8)(1500) = 576

B/C = 0.8

C/C = 1

Therefore, the ratio of the number of Ali's muffins to the number of Bala's muffins to the number of Charles' muffins is A:B:C = 576:0.8:1

To learn more on Ratios click:

https://brainly.com/question/1504221

#SPJ1

Answer:

Charles baked 1500 Muffins.

Step-by-step explanation:

Let's assume the number of muffins baked by Ali, Bala, and Charles to be A, B, and C respectively.

From the given information:

1/5 of Ali's muffins = 3/10 of Bala's muffins

This can be written as:

(1/5)A = (3/10)B

To find the ratio of the number of Ali's muffins to the number of Bala's muffins to the number of Charles' muffins, we can use the information that Bala's muffins were 80% of Charles' muffins.

Bala's muffins = 0.8 * Charles' muffins

We can also use the information that if Bala baked another 300 muffins, he would have the same number of muffins as Charles.

B + 300 = C

Now we can solve these equations to find the values.

From (1/5)A = (3/10)B, we can simplify it by multiplying both sides by 10 to get:

2A = 3B

From Bala's muffins = 0.8 * Charles' muffins, we can substitute B with 0.8C:

2A = 3(0.8C)

2A = 2.4C

We can equate the two expressions for 2A and simplify:

2A = 2.4C

2A = 3B

3B = 2.4C

Now we have two equations:

2A = 3B

3B = 2.4C

To find the ratio, we need to find the least common multiple (LCM) of the coefficients of A, B, and C. The LCM of 2 and 3 is 6.

Multiply the first equation by 2 and the second equation by 3 to make the coefficients equal:

4A = 6B

9B = 7.2C

Now we have the following ratios:

A : B = 6 : 4 = 3 : 2

B : C = 9 : 7.2 = 10 : 8

Simplifying the ratios, we have:

A : B : C = 3 : 2 : 4

Therefore, the ratio of the number of Ali's muffins to the number of Bala's muffins to the number of Charles' muffins is 3 : 2 : 4.

To find the number of muffins Charles baked, we can substitute B with 0.8C in the equation B + 300 = C:

0.8C + 300 = C

300 = 0.2C

C = 300 / 0.2

C = 1500

Therefore, Charles baked 1500 muffins.

Answer: It would be about 10 cents an ounce.

Step-by-step explanation:

1.25/12 = ~.10

The given equation 3x^2 - y^2 + z^2 = 0 represents a surface known as an elliptic paraboloid. To sketch this surface using traces, we can fix one variable (either x, y, or z) and vary the other two to observe the resulting curve.

Let's fix x at a constant value of 0. Substituting x = 0 into the equation, we get -y^2 + z^2 = 0. This equation represents a pair of intersecting lines, forming a trace. By varying x and fixing y or z, we can obtain additional traces, which are also pairs of intersecting lines.

Thus, by considering multiple traces, we can sketch the elliptic paraboloid surface, which resembles a bowl or a saddle. The traces consist of intersecting lines that form a grid-like pattern on the surface.

Now, moving on to the second question, we are given two skew lines with parametric equations. To find the distance between these lines, we can use the closest distance formula.

First, we need to find a point on each line. By setting t = 0 in the first line's equations, we find a point (2, 3, 0). Similarly, setting s = 0 in the second line's equations gives us a point (1, 6, -2).

Next, we find the direction vectors for both lines. The direction vector for the first line is <1, 6, 2>, and for the second line is <2, 14, 5>.

Using the closest distance formula, we can calculate the distance between the two lines as follows:

distance = |(2-1, 3-6, 0+2) · (1, 6, 2) x (2, 14, 5)| / |(1, 6, 2) x (2, 14, 5)|

Simplifying this expression will give us the distance between the skew lines.

Please note that the exact calculations are omitted here, but following the steps outlined above will provide the desired distance.

To learn more about elliptic paraboloid, here

brainly.com/question/10992563

#SPJ11

The total number of white tiles that Paul used is 54

From the question, we have the following parameters that can be used in our computation:

Length of the entire floor = 9 feet

Width of the entire floor = 12 feet

The total number of white tiles used is calculated as

Total number of white tiles used = Length of the entire floor * Width of the entire floor/2ft²

Substitute the known values in the above equation, so, we have the following representation

Total number of white tiles used = 9ft * 12ft/2ft²

Evaluate

Total number of white tiles used = 54

Hence, the white tiles are 54

Read more about areas at

https://brainly.com/question/25292087

#SPJ1

Answer:

7 cm

Step-by-step explanation:

An equilateral triangle has all sides equal.

To find the measure of the side, simply divide the perimeter by 3. This is because a triangle has 3 sides.

21 ÷ 3 = 7

The equation of the red graph is,

⇒ y = x² + 4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The equation of blue graph is,

⇒ y = x²

Since, We have;

The red graph is 4 unit up from the blue graph.

Hence, The equation of the red graph is,

⇒ y - 4 = x²

⇒ y = x² + 4

Therefore, The equation of the red graph is,

⇒ y = x² + 4

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

It can be obtained from the circumference angle of 360 degree

2x + 6x + 60 + 4 x is = 360

12 x + 60 = 360

12x = 300

x = 25

An angle at the circumference of a circle is half the angle at the centre standing on the same arc. Two angles at the circumference standing on the same arc are equal.

To know more about circumference:

brainly.com/question/28757341

#SPJ1

The values of x in figure 1 and figure 2 simultaneously are 25 and 17.

What is the circumference angle?

An angle at the circumference of a circle is half the angle at the center standing on the same arc. Two angles at the circumference standing on the same arc are equal.

We have given,

In the first figure:

2x,

3x + 30

4x

In the second figure:

3x,

7x+10

It can be obtained from the circumference angle of 360 degree

For figure 1:

2x + 6x + 60 + 4x  = 360

12 x + 60 = 360

12x = 300

x = 25

For Figure 2:

2(3x + 7x + 10)  = 360

10x + 10 = 180

x = 17

Hence, the value of x in figure 1 and figure 2 simultaneously are 25 and 17.

To learn more about the circumference visit:

brainly.com/question/28757341

#SPJ1

The integral |cos(inx)| dx can be expressed as:

|cos(inx)| = -(1/in) sin(inx)  for π/(2n) ≤ x ≤ π/n

The summing of discrete data is indicated by the integration. To determine the functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To evaluate the integral ∫|cos(inx)| dx, we can break it down into two parts based on the periodicity of the absolute value function:

∫|cos(inx)| dx = ∫cos(inx) dx    for 0 ≤ x ≤ π/(2n)

             = -∫cos(inx) dx   for π/(2n) ≤ x ≤ π/n

Now, let's focus on the first part of the integral:

∫cos(inx) dx    for 0 ≤ x ≤ π/(2n)

We can use the substitution u = inx, which implies du = in dx. Rearranging, we have dx = du/(in). Substituting these values, we get:

∫cos(u) (1/in) du = (1/in) ∫cos(u) du

Integrating cos(u) with respect to u gives us sin(u):

(1/in) ∫cos(u) du = (1/in) sin(u) + C

Now, let's evaluate the second part of the integral:

-∫cos(inx) dx   for π/(2n) ≤ x ≤ π/n

Using the same substitution u = inx, we can rewrite the integral as:

-∫cos(u) (1/in) du = -(1/in) ∫cos(u) du

Again, integrating cos(u) with respect to u gives us sin(u):

-(1/in) ∫cos(u) du = -(1/in) sin(u) + C

Now we have evaluated both parts of the integral. Combining the results, we get:

∫|cos(inx)| dx = (1/in) sin(inx)   for 0 ≤ x ≤ π/(2n)

             = -(1/in) sin(inx)  for π/(2n) ≤ x ≤ π/n

Therefore, the integral |cos(inx)| dx can be expressed as:

|cos(inx)| = (1/in) sin(inx)   for 0 ≤ x ≤ π/(2n)

          = -(1/in) sin(inx)  for π/(2n) ≤ x ≤ π/n

Note: The second part of the integral could also be written as (1/in) sin(inx) with a negative constant of integration, but for simplicity, we have used the negative sign inside the integral.

Learn more about integration on:

https://brainly.com/question/12231722

#SPJ4

The probability of selecting a user who chooses cinnamon and is under 13 years old is: 0.18 or 18% (rounded to two decimal places).

In the problem, we are given the number of users who choose bacon and are under 13 years old, which is 8. We are also given the number of users who choose plain and are under 13 years old, which is 5. Therefore, the total number of users under 13 years old is 8 + 5 = 13.

Next, we are asked to find the probability of selecting a user who chooses cinnamon and is under 13 years old. We know that the number of users who choose cinnamon and are under 13 years old is 3. Therefore, out of the total 13 users under 13 years old, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

The total number of users under 13 years old is 8 (choose bacon) + 5 (choose plain) = 13.

The number of users who choose cinnamon and are under 13 years old is 3.

Therefore, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

3 / 13 ≈ 0.23 or 23% (rounded to two decimal places)

To know more about probability,

https://brainly.com/question/30034780

#SPJ11

Answer:

7mph and he stayed the same

Step-by-step explanation:

Larry's average speed from hour 2 to hour 4 and from hour 4 to hour 7 is the same, 7 mi/hr, he maintained a constant speed throughout this period.

Given that Larry recorded his time as he ran

Time elapsed(hr)         Distance run(mi)

     2                                       13.5

     4                                       27.5

     7                                       48.5

We need to calculate his average speed,

To calculate Larry's average speed, we need to divide the total distance he ran by the time elapsed.

Let's calculate his average speed from hour 2 to hour 4 and from hour 4 to hour 7:

Average speed from hour 2 to hour 4:

Distance covered = 27.5 mi - 13.5 mi = 14 mi

Time elapsed = 4 hr - 2 hr = 2 hr

Average speed = Distance covered / Time elapsed = 14 mi / 2 hr = 7 mi/hr

Therefore, Larry's average speed from hour 2 to hour 4 was 7 miles per hour.

Average speed from hour 4 to hour 7:

Distance covered = 48.5 mi - 27.5 mi = 21 mi

Time elapsed = 7 hr - 4 hr = 3 hr

Average speed = Distance covered / Time elapsed = 21 mi / 3 hr = 7 mi/hr

Therefore, Larry's average speed from hour 4 to hour 7 was also 7 miles per hour.

Since Larry's average speed from hour 2 to hour 4 and from hour 4 to hour 7 is the same (7 mi/hr), he maintained a constant speed throughout this period. He neither sped up nor slowed down.

Learn more about Average speed click;

https://brainly.com/question/13318003

#SPJ2

Complete question =

Larry recorded his time as he ran. What was his average speed from hour 2 to hour 4?

What was his average speed from hour 4 to hour 7?

Did he speed up or slow down?

time elapsed(hr)         distance run(mi)

2                                       13.5

4                                       27.5

7                                       48.5

It takes the second marathoner 4 hours and 40 minutes to complete the marathon.

Let's assume the distance of the marathon is "d" miles.

The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:

speed = distance / time = d / 4

The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:

speed = 4(d / 4) = d

For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:

d / 2 = (3/4)(d / 4)(t)

Simplifying this equation, we get:

t = (2/3) hours

So the total time it takes the second marathoner to finish the race is:

4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.

To learn more about speed click on,

https://brainly.com/question/31191256

#SPJ4

Answer:

This looks a lot like my work.

Step-by-step explanation:

I will take a look at it.

Answer:

8 divided by 864 = 108

6 divided by 3810 = 635

9 divided by 5319 = 591

Step-by-step explanation:

Hope this helped have an amazing day!