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The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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The best estimate of how much she will spend on movies and eating out is given as follows:

$162.

The best estimate of how much she will spend on movies and eating out is obtained applying the proportions in the context of the problem.

The percentages associated with movies and eating out are given as follows:

The amount that she has left is given as follows:

$300.

Hence the best estimate of how much she will spend on movies and eating out is obtained as follows:

(0.3 + 0.24) x 300 = 0.54 x 300 = $162.

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Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Answer:

5x=4

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer: Two numbers are said to be relatively prime if they share no common factors other than 1. To find a number that is relatively prime to 63, we need to find a number that has no factors in common with 63 other than 1.

The prime factorization of 63 is 3 * 3 * 7. Therefore, any number that is divisible by 3 or 7 is not relatively prime to 63.

For example, 21 is not relatively prime to 63 because both 21 and 63 are divisible by 3. Similarly, 35 is not relatively prime to 63 because both 35 and 63 are divisible by 7.

One number that is relatively prime to 63 is 25. 25 is not divisible by 3 or 7, and therefore has no common factors with 63 other than 1.

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

\(\implies {\blue {\boxed {\boxed {\purple {\sf { \: 28 {x}^{3} + 48 {x}^{2} + 62x + 30}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\((4 {x}^{2} + 4x + 6)(7x + 5)\)

\( = \: 7x(4 {x}^{2} + 4x + 6) + 5(4 {x}^{2} + 4x + 6)\)

\( = \: 28 {x}^{3} + 28 {x}^{2} + 42x + 20 {x}^{2} + 20x + 30\)

Combining like terms, we have

\( = \: 28 {x}^{3} + (28 {x}^{2} + 20 {x}^{2} ) + (42x + 20x) + 30\)

\( = \: 28 {x}^{3} + 48 {x}^{2} + 62x + 30\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}\)

infinitely many solutuinsAnswer:

Step-by-step explanation:

If radius of a circle is 15 m then the area of circle is \(\sf 225\pi\) square units.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.

Given that radius of a circle is 15m.

We have to find the area of the circle.

The formula for area of the circle is \(\sf A=\pi r^2\)

Given r is 15

Substitute r = 15 in the area formula.

\(\sf A=\pi (15)^2\)

\(\sf =\pi \times15\times15\)

\(\sf =225\pi\)

Hence, if the radius of a circle is 15 m then the area of circle is \(\sf 225\pi\) square units.

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An expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes is (0.55 + (n - 5) x 0.07) dollars.

Given:

Long Distance Rates Time (minutes) Cost5 $0.556 $0.627 $0.698 $0.769 $0.8310 $0.90We need to find an expression that can be used to find the cost of an n-minute long-distance call, where n is at least 5 minutes.

The cost of making a long-distance call is given for 5 minutes, 6 minutes, 7 minutes, 8 minutes, 9 minutes, and 10 minutes.

We can observe from the above table that for every increase of 1 minute, the cost increases by $0.07.

We can conclude that the cost of n minutes long-distance call is given by: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes.

Therefore, the required expression is: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes. The above expression is based on the pattern in the table provided for long-distance call rates. We can use this expression for values of n greater than or equal to 5.

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Answer: 306

Step-by-step explanation:

Formula to find sample size:

\(n=(\dfrac{\sigma\times z^*}{E})^2\) , where \(\sigma\) = standard deviation, E = margin of error, z* = critrical z-value.

As per given,

\(\sigma=9.5 , E=1.4\)

Critical z-value for 99% confidence = 2.576

Now , the minimum sampl size :\(n=(\dfrac{9.5\times2.576}{1.4})^2\)

\(\Rightarrow\ n=305.5504\approx306\)

Hence, the required sample size = 306

Answer:

D

Step-by-step explanation:

C is the first quadrant (where both x and y are positive).

A is the y-axis.

B is the origin.

D is the x-axis

Answer: D

Step-by-step explanation: it wouldn't be B because that's the origin point and A is the y-axis and C is in the open, the Answer is D

Answers :

you will nees to use pythagorean theorem a^2 + b^2 = c^2

the a and b values will be 12 and 5 feet. So just plug them in and solve for c

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2 square root both sides

13 = c

so the ladder has a length of 13 feet.

Answer:

10.3

Step-by-step explanation:

(7 + 8 + 10 + 10 + 12 + 15) / 6 = 10.333

Answer:

20 times

Step-by-step explanation:

2/6

she rolls it 60 times so it turns into

2/6 = x/60

60*2 = 120

60/120 = 20

so

2/6 = 20/60

Answer:

B

Step-by-step explanation:

Given: x = 5 ; x - 5=0

x = -1; x+ 1= 0

x = -1/4; 4x + 1 = 0

Then; (x - 5)(x + 1)(4x + 1)

Answer:

\((f + g)(x) = 4x + 1\)

Step-by-step explanation:

\((f + g)(x) = f(x) + g(x) \\ = (3x - 1) + (x + 2) \\ \\ = 4x + 1\)

I hope I helped you^_^

The following matches a quadrilateral with the listed characteristics below is square. Option C is the correct answer.

A square is a quadrilateral with the following characteristics:

A rectangle also has the first two characteristics, but it does not necessarily have the third characteristic. A trapezoid does not have any of the three characteristics. A parallelogram has the third characteristic, but it does not necessarily have the first two characteristics.

Therefore, the only quadrilateral that matches all three characteristics is a square.

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It will take 4. 09 weeks for the tires to be rotated at the current rate.

When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.

25, 200 rotations / day x 7 days / week = 176, 400 rotations per week

To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:

C = 2πr

Rotation per mile is:

1 mile / 87.96 inches / rotation = 72.26 rotations / mile

Number of weeks:

10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations

722, 600 rotations / 176, 400 rotations/week = 4.09 weeks

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Answer:

x + y = 8 + (-14) = 8 - 14 = -6

x/y = -20/4 = -5

x/y = 45/-9 = -5

Step-by-step explanation:

Replace the given values of x and y in the expressions

Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

Im not sure, but i thinks its 240

Answer:

\(\pi\)

Step-by-step explanation:

Area = \(\pi x^{2}\)  For a full circle.  This is 1/4 of a circle

A= \(\frac{\pi 2^{2} }{4}\) = \(\frac{\pi 4}{4}\) = \(\pi\)

Answer : The area of the shape is, 111.02 units 2

Answer:

x=-8

Step-by-step explanation:

(-4-2x)/3=4

-4-2x=4*3

-4-2x=12

-2x=12+4

-2x=16

x=16/-2

x=-8

Answer:

X= -8 I believe sorry if it's wrong

Answer:

One proportion is 15 songs / 2.5 hours = 18 songs / h hours.

ok I'll try to answer

first the given 15/2.5=18/h

so the second hour is missing so we have to multiply cross then the result will be

15h=45

divide 15 for 15 and we got h

again divide 45 for 15

[h=3]

The ways to elect the candidates from the total is 462

From the question, we have

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 11 and r = 6

Substitute the known values in the above equation

Total = ¹¹C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 11!/5!6!

Evaluate

Total = 462

Hence, the number of ways is 462

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