A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph. What is the speed of the flying carpet in still air?

The solution is, the expression is => 4*(5-x)

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

let, the number is x.

now, when,

4 is multiplied by the difference of 5 and a number.

so, we get,

the expression is => 4*(5-x)

Hence, The solution is, the expression is => 4*(5-x)

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Answer:

It is x = 7 1/3

Step-by-step explanation:

2 feet is being used in the scale factor and 2 x 3 2/3 is 7 1/3.

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Answer:

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

we have:

\(scale \: factor = \frac{smaller \: length}{larger \: length} \)

let the length be x.

we have

\(2 = \frac{x}{3 \frac{2}{3} } \)

\(x = 2 \times \frac{11}{3} \)

\(x = 7 \frac{1}{3} \)

so.

C .\(x = 7 \frac{1}{3} \) is your answer

Anne's number is a

Brenda's number is b

_________________________________

Anne multiplies her number by Brand's :

\(a \times b\)

_________________________________

Then squares the answer :

\( ({a \times b})^{2} \)

_________________________________

The expression which represents her answer is :

\( {a}^{2} \times {b}^{2} \)

The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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The surface area of the given triangular prism having an isosceles triangle   base with sides 40,41 and 43 cm, is 2274 cm².

Area is a measure of the size of a two-dimensional shape or surface, such as a rectangle, triangle, circle, or any other shape that has length and width. It is usually expressed in square units, such as square meters, square centimeters, square feet, or square inches.

To find the surface area of a triangular prism, we need to find the area of each face of the prism and add them up.

The triangular base of the prism is an isosceles triangle with sides of 40 cm, 41 cm, and 43 cm.We may use Heron's formula to determine the area of this triangle:

s = (40 + 41 + 43) / 2 = 62

A = √(s(s-40)(s-41)(s-43)) = √(622221*19) = 798

Therefore, the area of the triangular base is 798 cm².

The height of the prism is given as 18 cm, which is also the length of the rectangular side of the prism.

The two other faces of the prism are rectangles with lengths equal to the base of the triangle (41 cm), and widths equal to the height of the prism (18 cm). The area of each rectangle is:

A = lw = 4118 = 738

Therefore, the area of both rectangles is 2*738 = 1476 cm².

The total surface area of the prism is the sum of the area of the base and the area of both rectangular sides:

Total surface area = Area of base + 2*(Area of rectangle)

Total surface area = 798 + 2*738

Total surface area = 2274 cm².

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Answer:

121

Step-by-step explanation:

firstly you arrange the numbers in ascending order the number in the middle is considered to be the median

Answer:

60 tiles

Step-by-step explanation:

Make equations equal,

.99x + 24 = 1.39x

Move all terms containing  x  to the left side of the equation & subtact 24

-.4x = -24

Divide

x = 60

Double check:

.99(60) + 24 = 83.4

1.39(60) = 83.4

i hope this helps :)

Answer:

A)  2x3 + 11x2 + 8x - 16.

Step-by-step explanation:

s(x).t(x) = (x + 4)( 2x2 + 3x - 4)

= x(2x2 + 3x - 4) + 4( 2x2 + 3x - 4)

= 2x3 + 3x2 - 4x + 8x2 + 12x - 16

= 2x3 + 11x2 + 8x - 16

The rate at which the surface area of the sphere is increasing is 16π cm^2/s.(option-c)

To find the rate at which the area of a sphere increases when its radius is increasing at a given rate, we can use the formula for the surface area of a sphere, which is A =\(4πr^2\), where r is the radius of the sphere and A is its surface area. We can then differentiate this with respect to time t to find the rate of change of area with respect to time, which is given as dA/dt.

Given that the radius of the sphere increases at the rate of 0.4 cm/s, we can find the rate of change of area as follows:

- Differentiate the surface area formula with respect to time t:

dA/dt = d/dt \((4πr^2)\)

- Use the chain rule to differentiate\(r^2\)with respect to time t:

d/dt (r^2) = 2r (dr/dt)

- Substitute the value of dr/dt given as 0.4 cm/s, and the radius value as 5 cm:

dA/dt = 4π(5)^2 (2 × 0.4)

- Simplify the expression to get the rate of change of area with respect to time:

dA/dt = 16π \(cm^2/s\)

(option-c)

Here is the final matching of multiplication expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173

81.4 x 32.1 ≈ 2,618

32.9 x 4.81 ≈ 158

46.7 x 31.7 ≈ 1,479

59.3 x 3.57 ≈ 212

Match each multiplication expression on the left with the best estimate of its product on the right:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9

81.4 x 32.1

32.9 x 4.81

46.7 x 31.7

59.3 x 3.57

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

Estimates for the remaining expressions:

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

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∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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jw

Step-by-step explanation:

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Answer:

84.37 %.

Step-by-step explanation:

The question is shown in the attached figure.

We have,

\(f(t)=2t^3+10,\ t=3\)

We can find the value of f(t) at t = 3,

\(f(3)=2(3)^3+10\\\\f(3)=64\)

Finding f'(t).

\(f'(t)=6t^2\)

Finding f'(t) at t = 3

\(f'(3)=6(3)^2\\\\=54\)

The relative change is calculated as :

\(\dfrac{f'(t)}{f(t)}=\dfrac{54}{64}\\\\=0.8437\)

In percentage rate of change,

\(\dfrac{f'(t)}{f(t)}=0.8437\times 100\\\\=84.37\%\)

Hence, the required percent change is 84.37 %.

Answer:

That would be 40%.

Answer:

1+1=2

Step-by-step explanation:

  1

+1

2

Answer:

see explanation

Step-by-step explanation:

The reciprocal of a number n is \(\frac{1}{n}\)

- 1 \(\frac{1}{17}\) ( change to improper fraction )

= - \(\frac{18}{17}\)

The reciprocal is then  \(\frac{1}{-\frac{18}{17} }\) = - \(\frac{17}{18}\)

B

The reciprocal of - \(\frac{17}{18}\) is - \(\frac{18}{17}\)

The product of a number and its multiplicative inverse equal one , so

- \(\frac{17}{18}\) × - \(\frac{18}{17}\) = 1

Then (a) is the multiplicative inverse of (b)

The reciprocal of the fraction 1 will be -  \($\frac{17}{18}\)  and the reciprocal of the fraction 2  will be - \($\frac{18}{17}\) . Answer for Part A to be the multiplicative inverse of the answer for Part B is also proved below.

We have two fractions -    \($1\frac{1}{17}\)     and      \($\frac{17}{18}\)

We have to find the reciprocal of both and explain why the answer of first fraction is the multiplicative inverse of the answer of second fraction.

For a fraction -  \($\frac{x}{y}\)  its reciprocal is given by -  \($\frac{y}{x}\)

According to the question, we have -

Converting it into normal fraction -  \($\frac{17\times 1 + 1}{17}\) =  \($\frac{18}{17}\)

Now, the reciprocal of the fraction above will be -  \($\frac{17}{18}\)

Now, the reciprocal of the fraction above will be - \($\frac{18}{17}\)

Multiplicative inverse of a number (x) is a number (y) such when multiplied by a given number yields 1.

Mathematically -

\(x\) x y = 1

Now -  for the answer for Part A to be the multiplicative inverse of the answer for Part B

reciprocal of fraction 2 x reciprocal of fraction 1  should be equal to 1. Therefore -

rec. fraction 2 x rec. fraction 1 =  \($\frac{18}{17} \times\)  \($\frac{17}{18}\) = 1

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A researcher wants to estimate the proportion of households with two cars. The researcher wants to be very sure of their estimation, so they choose a high level of confidence: 99%. This means that they want to capture the true proportion 99 times out of 100. The margin of error that they are willing to accept is 4% (0.04), which means that if the true proportion is, say, 21%, their estimate can range between 17% and 25%.

The formula to calculate the required sample size for estimating a proportion with a certain level of confidence and margin of error is:

n = (Z^2 * P * (1 - P)) / E^2

Here:

- n is the sample size.

- Z is the Z-score, which is a measure of how many standard deviations an element is from the mean. For a 99% confidence level, the Z-score is approximately 2.58.

- P is the estimated proportion of households with two cars. In this case, a previous study indicates it's 21%, or 0.21.

- E is the margin of error, which is 4% or 0.04 in this case.

Plugging in the values:

n = (2.58^2 * 0.21 * (1 - 0.21)) / 0.04^2

  ≈ (6.67 * 0.21 * 0.79) / 0.0016

  ≈ (1.10) / 0.0016

  ≈ 689.06

Since you can't have a fraction of a household, round up to the nearest whole number, which is 690.

This means that the researcher needs to randomly select a sample of at least 690 households in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 4%.

Keep in mind that this is a simplified explanation and in practice, researchers may take into account other factors, such as design effect, in determining sample size.

Answer: According to Newton s Second Law of Motion, also known as the Law of Force and Acceleration, a force upon an object causes it to accelerate according to the formula net force = mass x acceleration. So the acceleration of the object is directly proportional to the force and inversely proportional to the mass.

Step-by-step explanation:

If F = ma where m is the objects mass. if a 12-newton force causes the object to accelerate to 3 m/s2 , then the mass in kg of the objects is 4 kg

When a body tends to modify or change the state by an external cause, it is called Force.

Given:

F=ma

Where,

F = Force (N)

m = mass (kg)

a = acceleration (m/s²)

If

F = 12-Newton

m = 3 m/s²

a = ?

F = ma

12 = m × 3

12 = 3m

divide both sides by 3

m = 12/3

m = 4 kg

Therefore, the mass in kg of the objects is 4 kg

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Answer:

\(0.04 = 4 \div 100 \)

Answer:

If f(x) = +4, which of the following is the inverse of f(x)?

O A. ƒ˜¹(x) = 2(2+4)

B. ƒ˜¹(x) = 7(2-4)

C. ƒ˜¹(x) = 7(2+4)

D. f¯¹(x) = ²(2-4)

Step-by-step explanation:

Answer:

Recognize objects

Answer: i got 18

Step-by-step explanation:

Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

(657)

Step-by-step explanation:

Simplify the following:

3 (300 - 70/5 - (3×23 - (8 - 2×3)))

The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:

3 (300 + -14 - (3×23 - (8 - 2×3)))

-2×3 = -6:

3 (300 - 14 - (3×23 - (-6 + 8)))

8 - 6 = 2:

3 (300 - 14 - (3×23 - 2))

3×23 = 69:

3 (300 - 14 - (69 - 2))

| 6 | 9

- | | 2

| 6 | 7:

3 (300 - 14 - 67)

300 - 14 - 67 = 300 - (14 + 67):

3 ((300 - (14 + 67)))

| 1 |

| 6 | 7

+ | 1 | 4

| 8 | 1:

3 (300 - 81)

| | 9 |

| 2 | | 10

| | |

- | | 8 | 1

| 2 | 1 | 9:

3 (219)

3 (219) = (3×219):

(3×219)

3×219 = 657:

Answer: (657)