The sum of the digits of a two-digit number is 16. if the digits are reversed, the new number is 18 less than the original number. find the original number.

Answer:

6.86

Step-by-step explanation:

\Omega=\{1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9;\ 10\}\\\\|\Omega|=10\\\\A=\{1;\ 3;\ 6;\ 7\};\ B=\{2;\ 3\}\\\\A\ \cup\ B=\{1;\ 2;\ 3;\ 6;\ 7\}\\\\|A\ \cup\ B|=5\\\\P(A\ \cup\ B)=\dfrac{|A\ \cup\ B|}{|\Omega|}\to P(A\ \cup\ B)=\dfrac{5}{10}=\dfrac{1}{2}=0.5=0.50

The answer is 210 miles.

Two parallel lines intersected by a transversal create angles that are congruent or supplementary. The given 88° angle determines the measures of all other angles, which can either be 88° or supplementary to it, totaling 180°.

When two parallel lines are intersected by a transversal, several angles are formed. These angles have special relationships with each other. Since one of the angles is given as 88°, we can determine the measures of all other angles formed by using the properties of parallel lines and a transversal.

There are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles (also known as same-side interior angles). Corresponding angles and alternate angles are equal, while consecutive interior angles are supplementary, meaning they add up to 180°.

Given that one of the angles measures 88°, its corresponding angle also measures 88°. The alternate exterior and alternate interior angles relative to the 88° angle would also measure 88°. The consecutive interior angles to the given angle would measure 92° (180° - 88° = 92°).

In a situation where mirrors are placed at an angle relative to each other, the same principle of angle measurement applies. For example, if two mirrors are inclined at an angle of 60°, the reflections would follow geometry consistent with angle relationships.

Final answer:

To find the percent increase from $6 to $10, subtract the initial cost from the final cost, divide by the initial cost, and multiply by 100. The percent increase is 66.67%.

Explanation:

To find the percent increase, you need to calculate the difference between the final cost and the initial cost, and then divide that difference by the initial cost. Finally, multiply by 100 to get the percentage.

Given that the initial cost is $6 and the final cost is $10, the difference is $10 - $6 = $4.

To find the percent increase, divide $4 by $6: $4/$6 = 0.6667 (rounded to four decimal places).

Multiply by 100 to get the percentage: 0.6667 * 100 = 66.67% (rounded to two decimal places).

If each text message costs $.15, and you have $10, you can send a maximum of 66 text messages after rounding down.

To figure out how many text messages you can send with $10, given that each text message costs $.15, we need to divide the total amount of money ($10.00) by the cost of each text message ($.15).

It's a simple division problem: $10.00 ÷ $.15 = 66.67.

However, you can't send a fraction of a message, so we need to round down to the nearest whole number. So, you can send a total of 66 text messages for $10.

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Therefore, the height of the ground floor is 9.2 meters above the ground.

The pattern observed in the data is that the difference in height between consecutive floors remains constant. To find this constant difference, we can subtract the height of one floor from the height of the next floor.

For example:

Height of floor 1 (15th floor) - Height of ground floor (8th floor) = 54 m - 31.6 m = 22.4 m

Height of floor 2 (22nd floor) - Height of floor 1 (15th floor) = 76.4 m - 54 m = 22.4 m

The constant difference is 22.4 meters. This represents the height between each residential floor. To find the height of the ground floor (floor 0), we can subtract this constant difference from the height of the first residential floor.

Ground floor height = Height of floor 1 - Constant difference

Ground floor height = 31.6 m - 22.4 m = 9.2 meters.

The sum of the given geometric series (5 + 25 + 125 + 625 + 3,125 + 15,625) is -78120.

The question is asking for the sum of a geometric series. In a geometric series, each term is multiplied by a common ratio to get the next term. In this case, the first term (a) is 5 and the common ratio (r) is 5 (since we get each term by multiplying the previous one by 5).

The sum (S) of the first n terms of a geometric series can be calculated using the formula S = a * (1 - r^n) / (1 - r). In this case, there are n=6 terms in the series, so we will plug these values into the formula.

Therefore, S = 5 * (1 - 5^6) / (1 - 5). So, the sum of this geometric series is -78120.

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The range of the function is the distance from the maximum of the function to the minimum of the function. The minimum amount of pairs of plates that you can add to the bar (x) is 0, meaning you add no plates. The maximum amount of plates that you can add to the bar is 6, because this is how many plates come in one weight set. The range of the function is y values, and 0 and 6 are x values, so we must plug these values into the function to find the range values.

f(x) = 20x + 4 = 20(0) + 4 = 0 + 4 = 4

f(x) = 20x + 4 = 20(6) + 4 = 120 + 4 = 124

Therefore, the range of the function is 120 pounds, or from [4, 124].

Hope this helps!

The range of a function is the possible output values of the function. The range of [tex]f(x) =20x + 4[/tex] is [4,124]

Given that:

[tex]f(x) =20x + 4[/tex]

To determine the range of the function, we simply determine the value of f(x) using the input values

When no pair is added (this means x = 0).

So, we have:

[tex]f(0) =20 \times 0 + 4[/tex]

[tex]f(0) = 0 + 4[/tex]

[tex]f(0) = 4[/tex]

When 4 pairs are added (this means x = 4).

So, we have:

[tex]f(4) = 20 \times 4 + 4[/tex]

[tex]f(4) = 84[/tex]

When 6 pairs are added (this means x = 6).

So, we have:

[tex]f(6) = 20 \times 6 + 4[/tex]

[tex]f(6) = 124[/tex]

f(6) is greater than f(4).

i.e. [tex]124 > 84[/tex]

So, the range of the function is: [0,124] or [tex]4 \le x \le 124[/tex]

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Station P is approximately 15.0 km away from the fire.

Given that:

A right triangle with sides PQ: 20.0 km

And QF: 15.0 km

Where F is the location of the fire.

To find how far station P is from the fire, use trigonometry.

Let's call the distance from station P to the fire x km.

The angle between PQ and PF is given.

Using the trigonometric tangent function:

tan(angle) = opposite/adjacent

In this case, the opposite side is QF , and the adjacent side is PQ.

tan(angle) = 15.0 km / 20.0 km

Now, let's find the value of the angle:

angle = arctan(15.0 km / 20.0 km)

Using a calculator to get,

angle ≈ 36.87 degrees

Now, use trigonometry again to find x:

tan(36.87 degrees) = x / 20.0 km

x ≈ 20.0 km * tan(36.87 degrees)

x ≈ 20.0 km * 0.75

x ≈ 15.0 km

So, station P is approximately 15.0 km away from the fire.

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The distance from station P to the fire is approximately 21.23 km.

To find the distance from station P to the fire, we can use trigonometry. Since the ranger at station Q sees the fire at an angle between the line PQ and the line from P to the fire, we can consider the triangle created by station P, station Q, and the fire.

Using the tangent function, we can determine this distance:

tan(angle) = opposite / adjacent

Let x be the distance from station P to the fire:

tan(angle) = x / 15

Solving for x, we get:

x = 15 * tan(angle)

Now, we need to find the angle between the lines PQ and the line from P to the fire. Since the triangle created by station P, station Q, and the fire is a right triangle, we can use the inverse tangent function to find the angle:

angle = arctan(opposite / adjacent) = arctan(20 / 15)

Using a calculator, we find that the angle is approximately 53.13 degrees.

Substituting this angle into the equation for x, we have:

x = 15 * tan(53.13)

Solving for x, we get:

x ≈ 21.23 km

Answer:

D) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake and Mike have the same amount of money?

Step-by-step explanation:

The answer is D, because it make them equal

The surface area of a cone is b. 240 cm^2.

The surface area of a cone is equal to the curved surface area plus the area of the base: π r^2 + π L r .

where r denotes the radius of the base of the cone, and L denotes the slant height of the cone.

Here, we have,

from the given figure,

we get,

L= 12.5 cm

r=9/2

 =4.5cm

by using the formula, we get,

the surface area of a cone is = 240.33 cm^2

Hence, the surface area of a cone is b. 240 cm^2.

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Answer:

B. 24

Step-by-step explanation:

We have been given a data set that represents the math scores of five of Max's classmates. We are asked to find the range of the given data set.

Math score: 98, 76, 100, 88, 82.

Since we know range is the difference between the largest and smallest values of the data set.

[tex]\text{Range}=\text{The largest value of data set - The smallest value of data set}[/tex]

We can see that largest score is 100 and smallest score is 76.

[tex]\text{Range}=100-76[/tex]

[tex]\text{Range}=24[/tex]

Therefore, the range of the given test scores is 24 and option B is the correct choice.