Tickets for a carnival cost $8 for children 12 and under and $12 for anyone over the age of 12. The carnival sold 233 tickets and collected $2,156. How many children's tickets were sold?

Answer:

area = 12.6 m²

Step-by-step explanation:

r = 4/2 = 2

area = πr² = (3.14)(2²) = 12.56 m²

Answer:

yeah same for me but with ice cream

Answer:

A. -25

Step-by-step explanation:

sana nakatulong :-)

ig hanganaahajssislaalalla

Answer:

452.16 cm³

Step-by-step explanation:

I assume the shape of the volcano is a cone.

V = (1/3)πr²h

r = d/2 = 12 in./2 = 6 in.

V = (1/3)(3.14)(6 in.)²(12 in.)

V = 452.16 in.²

Answer:

Step-by-step explanation:

Radius r = 6 inches

Height h = 12 inches

volume of cone = πr²h/3 ≈ 3.14∙6²∙12 = 1,356.48 in³

Answer:

he can buy 6 gift cards, 7 theatre cards with a remainder of $10.

Step-by-step explanation:

Answer:

. Statement. 1. AD ≅ CE & DB ≅ EB Side. 2. ∠B ≅ ∠B Angle. 3. AD + DB ≅ CE + EB or AB ≅ BC Side. 4. ΔABE ≅ ΔBCD. 5. ∠1 ≅ ∠2. 6. ∠1 & ∠3

Step-by-step explanation:

Answer:

Total interest to be paid: $210

Total amount to be repaid: $3,710

Step-by-step explanation:

You can ignore the monthly payment for this problem.

For simple interest, the formula is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.

I = (3,500)(0.06)(1)

I = 210

Then add that to the amount borrowed ($3,500) and you're done.

3,500 + 210 = $3,710

Please let me know if you have questions.

Answer:

the answer for this question is option c

Answer:

276

Step-by-step explanation:

Circumference = 2πr

= 276

Answer:

30 ft

Step-by-step explanation:

[tex]C=\frac{n^2}{5} +175\\\\355=\frac{n^2}{5} +175\\\\180=\frac{n^2}{5}\\\\n^2=900\\\sqrt{n^2} =\sqrt{900} \\n=30[/tex]

Answer:

96

Step-by-step explanation:

12.50 + 18.50 + 20 + 20 + 13 + 12 = 96

Answer:

16 hats

Step-by-step explanation:

8h+12s=272

h+s=28

isolate s to get s=28-h

substitute that in for s and solve for h

you will get h=16 meaning 16 hats were sold

Answer:

D.

Step-by-step explanation:

The situation that can be modeled by the expression -3/4 x 2/5  is:

Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes.

The expression -3/4 x 2/5 gives us the fraction of a dollar that Kim receives from Abdi, which is -3/10 of a dollar.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The expression -3/4 x 2/5 means that we multiply -3/4 by 2/5.

Multiplying two fractions involves multiplying their numerators together and their denominators together. So,

-3/4 x 2/5 = (-3 x 2) / (4 x 5) = -6/20 = -3/10

Therefore,

The situation that can be modeled by the expression -3/4 x 2/5  is:

Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes.

The expression -3/4 x 2/5 gives us the fraction of a dollar that Kim receives from Abdi, which is -3/10 of a dollar.

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Answer:

b. (6, 4)

Step-by-step explanation:

i hope this helps :)

Answer:

B. (6,4)

Step-by-step explanation:

The point is inside the triangle.

Answer:

It's the third option

Step-by-step explanation:

One sides needs to have Lunches and the other needs to have how many is sold

It also needs to be clear and option 2 Is not as clear as 1 and 3

the only options that leaves us is 1 and 3

option 1 has the wrong labels

so.it is OPTION 3

Answer:

hmmmm

Step-by-step explanation:

Answer:

Here, I graphed this especially for you.

Check attachment.

Answer:

Step-by-step explanation:

The voloum is 8 cubic cm.

if the surface area is 24 the volume is 8.

Answer:

17,160

Step-by-step explanation:

250. Milliliters = 12 minutes

1 liter= 250/12

= 20.83

Therefore the time required to reach 825 ministers

= 825×20.8

= 17,160

Hence the time needed is 17, 160

Answer:

5.6 miles per gallon

Step-by-step explanation:

Equation for Mrs Sanchez: y = 36x

The rate of change = miles/gallon for Mrs Sanchez = 36 miles/gallon

Let's find the rate of change for Mr White:

Rate of change = change in y/change in x

Using two pairs of values form the table given, (2.5, 76) and (5, 152),

Rate of change = (152 - 76)/(5 - 2.5) = 76/2.5

Rate of change = miles/gallon = 30.4 miles/gallon

The difference between the miles per gallon of Mrs Sanchez and Mr White = 36 - 30.4 = 5.6 miles per gallon.

Therefore, Mrs Sanchez gets 5.6 miles per gallon than Me White

Answer:

I think it's 25

Step-by-step explanation:

I used a protractor

Kevin knit 9 scarves, and each scarf was 49.2 inches long.

Converting this length to feet, we find that each scarf is 4.1 feet long.

Let's use the variable "L" to represent the length of each scarf in inches. Since Kevin knit 9 scarves, we can write the equation for the total length of all scarves as:

[tex]\(L_{\text{total}} = L \times 9\)[/tex]

We are given that the total length of all scarves is 442.8 inches. So, we can write:

[tex]\(442.8 \text{ inches} = L \times 9\)[/tex]

To find the length of each scarf, we need to isolate "L" on one side of the equation. To do that, we can perform the following steps:

Divide both sides of the equation by 9 to get:

[tex]\(\frac{{442.8 \text{ inches}}}{{9}} = \frac{{L \times 9}}{{9}}\)[/tex]

Simplifying, we get:

[tex]\(49.2 \text{ inches} = L\)[/tex]

Now, we have found the length of each scarf in inches (49.2 inches). To convert this length to feet, we know that 1 foot is equal to 12 inches. So, to find the length in feet, we divide the length in inches by 12:

[tex]\(L_{\text{feet}} = \frac{{L_{\text{inches}}}}{{12}}\)[/tex]

Substituting the value of [tex]\(L_{\text{inches}}\)[/tex] with 49.2 inches:

[tex]\(L_{\text{feet}} = \frac{{49.2 \text{ inches}}}{{12}}\)[/tex]

Now, let's perform the division:

[tex]\(L_{\text{feet}} = 4.1 \text{ feet}\)[/tex]

So, each scarf is 4.1 feet long.

Kevin knit 9 scarves, and each scarf was 49.2 inches long.

Converting this length to feet, we find that each scarf is 4.1 feet long.

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Answer:

I think its A

Step-by-step explanation:

because it's a tighter angle than 29,46,and 134 degrees i might not be right but i hope it is :)

Answer:

Height of building = 86.9 ft

Step-by-step explanation:

I've drawn a triangle image to depict this question and I have attached it.

From the attached image, we can see that ABC is the height of the building.

We can see the distance from your eye to the ground indicated and also the distance from the horizontal distance from the building to you indicated.

We can use pythagoras theorem to find AB.

AB/57 = tan 55°

AB = 57 × 1.4281

AB = 81.4 ft

Now, total height of the building is AB + BC.

BC = 5.5 ft since B is parallel to your eye and height from there to the ground is 5.5 ft.

Thus;. Height of building = 81.4 + 5.5 = 86.9 ft

Answer:

The answer is A

Step-by-step explanation:

edge21

The statement which is true of the right triangles ABC and DEF is Area of ABC is greater than area of DEF.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given two right angled triangles, ABC and DEF.

Area of a triangle = 1/2 × base × height

Area of ΔABC = 1/2 × 14 × 6

                        = 42 square units

Base of ΔDEF = √(7² + 4²) = √65

Height of ΔDEF = √(5² + 8²) = √89

Area of ΔDEF = 1/2 × √65 × √89

                       = 38.03 square units

Hence the correct option is Area of ABC is greater than area of DEF.

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Answer:

a. The distance the train travelled in the first hour is approximately 28.3 miles

b. The location of the train at 5:00 p.m. is 53 miles east, and 46 miles west

c. The location of the train at any given time by the function, f(t) = (-8 + 24·t, -10 + 15·t)

d. The train does not collide with the cyclist when the bike goes over the train tracks

Step-by-step explanation:

a. The given information on the train's motion are;

The location south the train is spotted = 10 miles south and 8 miles west

The time the observer spotted the train = 2:00 pm

The location the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east

Therefore, the difference between the two times the train was spotted, t = 3:00 p.m. - 2:00 p.m. = 1 hour

Making use of the coordinate plane for the two locations the train was spotted, we have;

The initial location of the train = (-10, -8)

The final location of the train = (5, 16)

Therefore the distance the train travelled in the first hour is given by the formula for finding the distance, 'd', between two points, (x₁, y₁) and (x₂, y₂) as follows;

[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]

Therefore;

[tex]d = \sqrt{\left (5-(-10) \right )^{2}+\left (16-(-8) \right )^{2}} = 3 \cdot\sqrt{89}[/tex]

The distance the train travelled in the first hour, d = 3·√89 ≈ 28.3 miles

b. The speed of the train, v = (Distance travelled by the train)/Time

∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour

The speed of the train in the first hour, v ≈ 28.3 mph

The direction of the train, θ, is given by the arctangent of the slope, 'm', of the path of the train;

[tex]\therefore The \ slope \ of \ the \ path \ of \ the \ train, \, m =tan(\theta) = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∴ m = tan(θ) = (5 - (-10))/(16 - (-8)) = 0.625

c. Distance = Velocity × Time

At 5:00 p.m., we have;

The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours

The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles

Using trigonometry, we have the horizonal distance travelled, 'Δx', in the 2 hours is given as follows;

Δx = d₁ × cos(θ)

∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48

The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles

The vertical distance increase in the two hours, Δy is given as follows;

Δy = 56.6 × sin(arctan(0.625)) ≈ 30

The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles

Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)

The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west

c. The function, 'f', that would give the train's position at time-t is given as follows;

The P = f(28.3·t, θ)

Where;

28.3·t = √(x² + y²)

θ = arctan(y/x)

Parametric equations

y - 5 = 0.625·(x - 16)

∴ y = 0.625·x - 10 + 5

The equation of the train's track is therefore, presented as follows;

y = 0.625·x - 5

d = 28.3·t

The y-component of the velocity, [tex]v_y[/tex] = 3*√89 mph × sin(arctan(0.625)) = 15 mph

Therefore, we have;

y = -10 + 15·t

The x-component of the velocity, vₓ = 3*√89 mph × cos(arctan(0.625)) = 24 mph

Therefore, we have;

x = -8 + 24·t

The location of the train at any given time, 't', f(t) = (-8 + 24·t, -10 + 15·t)

d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph

The distance of the cyclist from the track = The x-intercept = 5/0.625 = 8

The distance of the cyclist from the track = 8 miles

The time it would take the cyclist to react the track, t = 8 miles/10 mph = 0.8 hours

The location of the train in 0.8 hours, is f(0.8) = (-8 + 24×0.8, -10 + 15×0.8)

∴ f(0.8) = (11.2, 2)

At the time the cyclist is at the track along the east-west axis, at the point (8, 0), the train is at the point (11.2, 2) therefore, the train does not collide with the cyclist when the bike goes over the train tracks.

If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.

The location south the train is spotted = 10 miles south and 8 miles west

The time the observer spotted the train = 2:00 pm

The location of the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east

Thus, the difference between the two times the train was spotted,

t = 3:00 p.m. - 2:00 p.m. = 1 hour

The distance is the product of velocity and time.

Distance = Velocity × Time

The initial location of the train = (-10, -8)

The final location of the train = (5, 16)

Therefore the distance the train travelled in the first hour

[tex]d = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} } \\d = \sqrt{(5 -(-10) )^{2} +(16-(-8) )^{2} }[/tex]

d = 3√89

The distance the train travelled in the first hour, d = 28.3 miles

b. The speed of the train, v = (Distance travelled by train)/Time

∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour

The speed of the train in the first hour, v ≈ 28.3 mph

The direction of the train, θ, is given by the arc tangent of the slope, 'm', of the path of the train;

∴ m = tan(θ) = (5 - (-10))/(16 - (-8))

m = 0.625

c. Distance = Velocity × Time

At 5:00 p.m., we have;

The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours

The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles

Using trigonometry, we have the horizontal distance travelled, 'Δx', in the 2 hours is given as follows;

Δx = d₁ × cos(θ)

∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48

The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles

The vertical distance increase in the two hours, Δy is given as follows;

Δy = 56.6 × sin(arctan(0.625)) ≈ 30

The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles

Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)

The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west

c. The function, 'f', that would give the train's position at time-t is given as follows;

The P = f(28.3·t, θ)

28.3·t = √(x² + y²)

θ = arctan(y/x)

Parametric equations

y - 5 = 0.625·(x - 16)

∴ y = 0.625·x - 10 + 5

The equation of the train's track is, therefore, presented as follows;

y = 0.625·x - 5

d = 28.3·t

The y-component of the velocity,

= 3 × √89 mph × sin(arctan(0.625)) = 15 mph

Therefore, we have

y = -10 + 15·t

The x-component of the velocity,

vₓ = 3 × √89 mph × cos(arctan(0.625))

= 24 mph

Therefore, we have;

x = -8 + 24·t

The location of the train at any given time, 't',

f(t) = (-8 + 24·t, -10 + 15·t)

d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph

The distance of the cyclist from the track = The x-intercept

                                                                   = 5/0.625 = 8

The distance of the cyclist from the track = 8 miles

The time it would take the cyclist to reach the track, t = 8 miles/10 mph = 0.8 hours

The location of the train in 0.8 hours, is f(0.8)

= (-8 + 24×0.8, -10 + 15×0.8)

∴ f(0.8) = (11.2, 2)

therefore, If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.

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Answer:

AB   = 12

BC   = 9

Step-by-step explanation:

x= -4

AB   -4+16 = 12

BC  -4+13 = 9

  12+9 = 21