calculate the number in the middle of 15 and 24

70 adults and 100 children attended the carnival.

Step-by-step explanation:

Given,

Cost of each adult ticket = $10

Cost of each child ticket = $5

Total tickets sold = 170

Total revenue generated = $1200

Let,

Number of adults = x

Number of children = y

According to given statement;

x+y=170      Eqn 1

10x+5y=1200    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=170)\\10x+10y=1700\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](10x+10y)-(10x+5y)=1700-1200\\10x+10y-10x-5y=500\\5y=500[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{500}{5}\\y=100[/tex]

Putting y=100 in Eqn 1

[tex]x+100=170\\x=170-100\\x=70[/tex]

70 adults and 100 children attended the carnival.

Keywords: linear equation, elimination method

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Answer:

  (x -4)^2 +(y +5)^2 = 2

Step-by-step explanation:

The equation of a circle centered at (h, k) through point (p, q) is ...

  (x -h)^2 +(y -k)^2 = (p -h)^2 +(q -k)^2

Filling in your given numbers gives ...

  (x -4)^2 +(y +5)^2 = (5-4)^2 +(-4+5)^2

  (x -4)^2 +(y -5)^2 = 2

The equation of the circle is (x - 4)² + (y + 5)² = 2.

The center of the circle is (4, -5). The circle passes through the point (5, -4).

The general formula for the equation of a circle is: (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.

The radius is the distance between the center (4, -5) and the point (5, -4).

Use the distance formula: Distance = √ [(x2 - x1)² + (y2 - y1)²]

Distance = √ [(5 - 4)² + (-4 - (-5))²]

Distance = √ [(1)² + (1)²]

Distance = √ [1 + 1]

Distance = √ [2]

So, the radius r = √ [2].

Substitute the center (4, -5) and radius √ [2] into the circle equation: (x - 4)² + (y + 5)² = (√ [2])² (x - 4)² + (y + 5)² = 2

Answer:

-23/2h+3/2

Step-by-step explanation:

7/2h-3(5h-1/2)

7/2h-15h+3/2

7/2h-30/2h+3/2

-23/2h+3/2

Answer:

(-23h+3)/2

Step-by-step explanation:

7/2h-3(5h-1/2)=

7/2h-3*5h+3*1/2=

7/2h-15h+3/2=

7/2h-30/2h+3/2=

-23/2h+3/2 or

(-23h+3)/2

Answer:

Step-by-step explanation:

each is divided into 8 sections.

So1 1/2 =1  1*4/2*4 =1 4/8 . plot in the 4 th point after 1

2 3/4

3*2/4*2 = 6/8

2 3/4 = 2 6/8. so plot in the 6th point after 2

The volume of scaled object is 0.039375 cubic inches

Solution:

Given that,

Volume of box = 39.375 cubic inches

Scaled down by a factor  = [tex]\frac{1}{10}[/tex]

The volume of a scaled object will be equal to the volume of object times scale factor cubed

Therefore,

Volume of scaled object = Volume of box x scale factor cubed

[tex]Volume\ of\ scaled\ object = 39.375 \times (\frac{1}{10})^3\\\\Volume\ of\ scaled\ object = 39.375 \times \frac{1}{1000}\\\\Volume\ of\ scaled\ object = 0.039375[/tex]

Thus volume of scaled object is 0.039375 cubic inches

The distance that the train travels is 18.84 feet

Solution:

Given that,

A play train travels around a Christmas  tree in a circle

The train track measures 6  feet in diameter

To find: distance that the train travels

The distance the train travels is equal to the circumference of circle

The circumference of circle is given as:

[tex]C = \pi d[/tex]

Where, "d" is the diameter of circle

From given,

d = 6 feet

[tex]C = 3.14 \times 6\\\\C = 18.84[/tex]

Thus the train travels 18.84 feet

Answer: 8 tacos

Step-by-step explanation: 2 hotdogs are $10 as they are $5 each. Tacos are $2.50 each. $2.50 x 8 equals $20. $20 + 10 = $30. Eva can buy 8 tacos.

After buying 2 hotdogs with $10, Eva will have $20 left. With the remaining $20, she can buy a maximum of 8 tacos at $2.50 each.

Since Eva is determined to buy 2 hotdogs at $5 each, she will spend $10 on hotdogs. She has a total of $30 to spend, meaning she will have $20 left after purchasing the hotdogs. Tacos cost $2.50 each. Therefore, with the remaining $20, Eva can afford to buy a maximum of 8 tacos (since $20 divided by $2.50 equals 8). This will also meet the condition of purchasing at least 7 hotdogs and tacos in total.

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Answer:

The options are: A, C and D

Step-by-step explanation:

The sine wave has a general form : y = A sin (BX)

Where A is the amplitude and B = 2π/period

So, we will check which of the options will be a harmonic on a string that is 10 cm long.

A.) y=2sin(pi/5 x)

B = π/5 ⇒ period = 2π/B = 2π ÷ π/5 =  2π * 5/π = 10

So, one cycle of y=2sin(pi/5 x) will be a harmonic on a string that is 10 cm long.

B.) y=2sin(2pi/7 x)

B = 2π/7 ⇒ period = 2π/B = 2π ÷ 2π/7 =  7  

C.) y=2sin(pi/10 x)

B = π/10 ⇒ period = 2π/B = 2π ÷ π/10 = 20 = 2 * 10

So, half a cycle of y=2sin(pi/10 x) will be a harmonic on a string that is 10 cm long.

D.) y=2sin(10pi x)

B = 10π ⇒ period = 2π/B = 2π ÷ 10π = 1/5 = 10/50

So, 50 cycles of y=2sin(10pi x) will be a harmonic on a string that is 10 cm long.

E.) y=2sin (5/2pi x)

B = 5/2π ⇒ period = 2π/B = 2π ÷ (5/2π) = 4π²/5

So, options A, C and D can be a harmonic on a string that is 10 cm long.

Answer:

A. y=2sin(pi/5x)

C. y=2sin(pi/10x)

D. y=2sin(10pix)

Step-by-step explanation:

When speed and time are known, distance can be calculated using the formula 'distance = speed x time'. Given Bert's speed of 50 mph and travel time of 0.5 hours each way, the distance from his home to the office is calculated to be 25 miles.

The subject of this problem is fundamentally about understanding the relationship between speed, time, and distance. In this particular case, Bert is spending a total of an hour commuting to and from office. However, this total time includes both the journey to work and the journey back home so each journey takes half an hour or 0.5 hours. Given that his average speed is 50 mph, we can calculate the distance he travels one way using the formula "Distance = Speed x Time."

So, for Bert:
Distance = 50 mph x 0.5 hours = 25 miles

Therefore, "Bert lives 25 miles from his office."

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Answer:

Step-by-step explanation:

8(6-k)+2k ≥-15-(-3k)

Opening bracket

48 - 8k + 2k ≥ -15 + 3k

-8k - 3k + 2k ≥ -15 - 48

-9k ≥ -63

k ≤ -63/-9

k ≤ 7

Answer:

k ≤ 7

Step-by-step explanation:

8 (6 - k) + 2k ≥ - 15 -(-3k)

Let's simplify this by solving each side.

First side:

8 (6 - k) + 2k ≥ - 15 -(-3k)

48 - 8k + 2k ≥ - 15 -(-3k)

48 - 6k ≥ - 15 -(-3k)

Second side:

48 - 6k ≥ - 15 -(-3k)

48 - 6k ≥ -15 + 3k

DONE SIMPLIFYING!

Now solve for "k" algebraically (transitions are in bold):

48 - 6k ≥ -15 + 3k

-6k ≥ -15 - 48 + 3k

-6k ≥ -63 + 3k

-6k - 3k ≥ -63

-9k ≥ -63

-k ≥ -63 ÷ 9

-k ≥ -7

k ≤ 7

Option C: [tex]$148 \mathrm{in}^{2}$[/tex] is the area of the trapezoid.

Explanation:

The image of the trapezoid having these descriptions is attached below:

Now, we shall determine the area of the trapezoid using the formula,

[tex]$A=\frac{a+b}{2} h$[/tex] where a and b are the base of the trapezoid and h is the height of the trapezoid.

Thus, we shall find the value of a and b from the diagram given below.

[tex]a= AB=14in[/tex]

[tex]b=DC\\b=DF+FE+EC\\b=3+14+6\\b=23in[/tex]

It is given that the height of the trapezoid [tex]h=8in[/tex]

Thus, substituting the values of a,b and h in the formula [tex]$A=\frac{a+b}{2} h$[/tex], we get,

[tex]A=\frac{14+23}{2}(8)\\ A=\frac{37}{2} (8)\\A=148in^2[/tex]

Thus, the area of the trapezoid is [tex]$148 \mathrm{in}^{2}$[/tex]

Hence, Option C is the correct answer.

Answer:

35+65+80=180

Step-by-step explanation:

the total interior angle of a triangle is 180

Answer:

its the third answer

[tex]35 \: \: 65 \: \: 80[/tex]

Step-by-step explanation:

because the addition of a interior angles has to be 180.'

Answer:

I'd don't now

Step-by-step explanation:

ok am sorry

conducting the survey as visitors leave the park

The park manager wants to figure out how people like the park so she will conduct the survey as people leave the park.

Final answer:

The most representative sample for a survey on park facilities satisfaction would be obtained by conducting the survey as visitors leave the park, ensuring a broad and unbiased cross-section of park users are included.

Explanation:

The question asks which method would provide the most representative sample for a survey about how people like the park facilities. The most representative sample would be achieved by conducting the survey as visitors leave the park. This method ensures a wide cross-section of park users are surveyed, capturing various interests and usage patterns of the park facilities, from those who come for leisure activities at the softball diamond or playground to those seeking quiet contemplation or exercise.

Conducting the survey in other locations like a shopping mall or specific areas within the park, such as the softball diamond or playground, would likely bias the results. Surveying at a shopping mall doesn't guarantee participants have visited or are familiar with the park, and focusing solely on one area within the park would not capture the diverse usage and opinions of all park visitors. Therefore, surveying as visitors leave the park is the most inclusive and unbiased approach to understanding how the facilities meet the needs of the community.

Answer:

636

Step-by-step explanation:

the area of the footpath=

(50m+3m+3m)^2-50^2

Answer:

Debt

Step-by-step explanation:

Let's say someone uses debit instead of credit and they don't have any money in their account. If used multiple times you could potentially end up owing the bank (be in debt) .

Negative numbers are used in real-world contexts to describe temperatures below zero, financial debts, or elevations below sea level, helping to clearly indicate quantities that are less than a referenced zero point.

You would use a negative number to describe a real-world amount when talking about temperatures below zero, debts, or elevations below sea level, among other scenarios. For example, if the temperature is 5 degrees below zero, it could be represented as -5°C. This indicates that it is 5 degrees colder than the point at which water freezes (0°C). Another example is financial: if you owe $100, you could represent your account balance as -$100, indicating a debt. Similarly, a town located 100 meters below sea level could have its elevation represented as -100 meters.

These examples show how negative numbers can effectively convey quantities less than zero in various real-world contexts, providing a clear understanding of situations where values are lacking or in deficit compared to a reference point.

Answer:

10%

Step-by-step explanation:

Let the third number is X.

then first number = (100-30)% of X

= 70% of X = 7X/10

Second number is (63X/100)

Difference = 7X/10 - 63X/100 = 7X/10

So required percentage is, difference is what percent of first number

=> (7X/100 * 10/7X * 100 )% = 10%

Answer:

W=41

Step-by-step explanation:

You have to isolate the W, so you have to carry the -4 to the other side. You do the opposite, so for a -4, you have to +4 to cancel it out. Whatever you do to one side, you have to do to the other and 37+4=41

Answer:

41

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Expression 5*10 is also known as 5 x 10 which is indeed 50.

Or if 5 is to the power of 10 (5^10) the answer would be 9765625

Hope this helped!

Step-by-step explanation:

Perhaps you want to simplify the given expression: Let's do it.

[tex](3x + 4) - (x + 2) \\ \\ = 3x + 4 - x - 2 \\ \\ = 3x - x + 4 - 2 \\ \\ = 2x + 2 \\ this \: is \: the \: simplest \: form \: of \: the \: \\ given \: expression.[/tex]

Answer:

2(x + 1)

Step-by-step explanation:

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

3x + 4 - x - 2

3x - x + 4 - 2

2x + 2

2(x + 1)

(1) 10(e + 0.5)g

Using distributive property, a × (b + c) = a × b + a × c

10(e + 0.5)g = 10 eg + 10 × 0.5g

Therefore, 10(e + 0.5g) and 10e + 5g are not equivalent.

(2) 6(p + q)

Using distributive property,

6(p + q) = 6p + 6q

Therefore, 6(p + q) and 6p + q are not equivalent.

(3) 7y – 15 + 2y

Using commutative property, a + b = b + a

7y – 15 + 2y = 7y + 2y – 15

                    = 9y – 15

Therefore 7y – 15 + 2y and 9y – 15 are equivalent.

(4) 1 + (8r + 9)

Using associative property, a + (b + c) = (a + b) + c

1 + (8r + 9) = (1 + 9) + 8r

                 = 10 + 8r

                 = (2 + 8) + 8r

Therefore 1 + (8r + 9) and (2 + 8) + 8r are equivalent.

(5) 0 × 11 + 5n

Using multiplicative identity property: a × 0 = 0

0 × 11 + 5n = 0 + 5n

                 = 5n

Therefore, 0 × 11 + 5n and 5n are equivalent.

(6) 16s – 4 + s

Using associative property, a + (b + c) = (a + b) + c

16s – 4 + s = 16s + s – 4

                  = 17s – 4

Therefore,  16s – 4 + s and 12s not equivalent.

(7) 11d × 2 = 22d

Therefore, 11d × 2 and 22d are equivalent.

(8) 8m + (9m – 1)

Using associative property, a + (b + c) = (a + b) + c

8m + (9m – 1) = (8m + 9m) – 1

                      = 17m – 1

Therefore, 8m + (9m – 1) and 8m – 8 not equivalent.

Answer:

yes

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

9 tenths is 90. 5 fifths is 25.

Answer:

16

Step-by-step explanation:

(3x - 1) + 2

(3(5) - 1) + 2

(15 - 1) + 2

14 + 2

16

Answer:

16

Step-by-step explanation:

Start by plugging in 5 for x in the equation.

(3 x 5 - 1) + 2

Next do the multiplication.

15 - 1 + 2

Add and subtract.

16

You have your answer.

Hope this helped.

Answer:

  25.2 in

Step-by-step explanation:

The short piece will have a length that is 2/(2+3) = 2/5 of the entire usable length. The usable length is 60-2 = 58 inches long, so the cut will be ...

  (2/5)(58 in) = 23 1/5 in

from the beginning of the usable part. Since the usable part of the ribbon starts 2 inches in, the cut will be 23 1/5 + 2 = 25 1/5 inches from the frayed end of the ribbon.

Answer:

25.2

Step-by-step explanation:

Correct on Edge 2020

Answer:

the anwser is a

Step-by-step explanation:

The expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].

Given that

Lauryn grew p tomato plants.

The Padma grew 5 fewer than 3 times the number Lauryn grew.

Kent grew 6 more than 4 times the number Lauryn grew.

We have to determine

Choose an expression and a simplified expression to represent the total number of tomato plants that Lauryn, Padma, and Kent grew.

According to the question

Let the number of tomato plants be p.

Lauryn grew p tomato plants.

[tex]\rm = p[/tex]

The Padma grew 5 fewer than 3 times the number Lauryn grew.

[tex]\rm= 3p-5[/tex]

Kent grew 6 more than 4 times the number Lauryn grew.

[tex]\rm = 4p+6[/tex]

Therefore,

An expression to represent the total number of tomato plants =  Lauryn + Padma + and Kent grew.

[tex]\rm p + (5 - 3p) + (6 + 4p)[/tex]

Hence, the expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].

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Answer: = [tex]\frac{25+\sqrt{949} }{6}[/tex] and y = \frac{25+\sqrt{949} }{6} - 3.

Step-by-step explanation:

Take x as the larger number and y as the smaller number.

x + 3 = y

[tex]\frac{16}{y}[/tex]+ [tex]\frac{9}{x}[/tex] = 1

Substitute x + 3 for y in the second equation.

[tex]\frac{16}{x+3}[/tex]+ [tex]\frac{9}{x}[/tex] = 1

Make a common denominator.

[tex]\frac{16(x) + 9(x+3)}{(x+3)(x)} =1[/tex]

Simplify and get rid of that fraction.

[tex]16x + 9x + 27 = x^{2} + 3x[/tex]

[tex]x^{2} + 3x - 25x - 27 = 0[/tex]

[tex]x^{2} -22x - 27 = 0[/tex]

By quadratic formula (and because they must be positive), x = [tex]\frac{25+\sqrt{949} }{6}[/tex] and then y = \frac{25+\sqrt{949} }{6} - 3.

To solve for the two positive numbers, we can set up an equation and solve for x.

Let's call the smaller number x and the larger number x + 3.

From the given information, we can write the following equation:

16(1/x) + 9(1/(x + 3)) = 1

To solve this equation, we can find a common denominator and then simplify:

16(x + 3)/(x(x + 3)) + 9x/(x(x + 3)) = 1

After simplifying and solving for x, we find that the smaller number is 4 and the larger number is 7.

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Answer:

 the answer is 240

Answer:

240

Step-by-step explanation:

i used a calculator

Step-by-step explanation:

In the question figure,

∠ 1 = 115 °, ∠ 2 = 115 °, ∠ 3 = 120 °, ∠ 4 = 14x °, ∠ 5 = 133 °, ∠ 6 = 167 °, ∠ 7 = 138° and ∠ 8 = 18x °

To find, the value of x = ?

We know that,

The sum of all angles of heptagon = 1080°

∴ ∠ 1 + ∠ 2 + ∠ 3 + ∠ 4 + ∠ 5 + ∠ 6 + ∠ 7 + ∠ 8 = 1080°    

⇒ 115 ° + 115 ° + 120 ° + 14x ° + 133 ° + 167 ° + 138° + 18x ° = 1080°  

⇒ 32x ° + 788° = 1080°  

⇒ 32x ° = 1080°  - 788° = 292°

⇒ x ° = 9.125°

∴ x ° = 9.125°