What is the distance around a circle called?

Let price of adult ticket is $x

And price of child ticket is $y

So we can make two equations using the given data

[tex] 3x+4y = 122 [/tex]

[tex] 2x+3y = 87 [/tex]

Now we can use eliminator method to solve the two equations

Multiply first equation by 2 and second equation by -3

[tex] 2(3x+4y = 122) [/tex]

[tex] -3(2x+3y = 87) [/tex]

[tex] 6x+8y = 244 [/tex]

[tex] -6x-9y =-261 [/tex]

now add both the equations so we get

[tex] 6x-6x+8y-9y=244-261 [/tex]

combine the like terms

[tex] -y=-17 [/tex]

Divide both sides by -1

[tex] y=17 [/tex]

Plug y=17 in any one of the equations to solve for x

[tex] 3x+4(17) = 122 [/tex]

[tex] 3x+68 = 122 [/tex]

Subtract 68 from both sides

[tex] 3x = 54 [/tex]

Divide both sides by 3

[tex] x=18 [/tex]

So x=18 and y=17

So

Price of adult ticket= $18

Price of child ticket = $17

Answer:

[tex]2713cm^3[/tex]

Step-by-step explanation:

From the given figure, the radius of the cylinder is=8cm, height of cylinder is =18cm  and the radius of the sphere is= 6cm.

Thus, [tex]Volume of cylinder={\pi}r^2h[/tex]

[tex]V=3.14(8)^{2}(18)[/tex]

[tex]V=3.14(64)(18)[/tex]

[tex]V=3617.28cm^3[/tex]

And [tex]volume of sphere=\frac{4}{3}{\pi}r^3[/tex]

[tex]V=\frac{4}{3}(3.14)(6)^3[/tex]

[tex]V=\frac{4}{3}(3.14)(216)[/tex]

[tex]V=904.31cm^3[/tex]

Thus, the volume of the shaded part of the figure=Volume of cylinder-volume of sphere

⇒volume of the shaded part of the figure=[tex]3617.28-904.31[/tex]

=[tex]2712.97[/tex]

≈[tex]2713cm^3[/tex]

Thus,volume of the shaded part of the figure=[tex]2713cm^3[/tex]

Final answer:

The probability of grabbing a yellow ball from a box with 2 green and 2 yellow balls is 0.5, calculated by dividing the number of yellow balls by the total number of balls.

Explanation:

In probability, the chance of an event happening is expressed as a fraction of the number of successful outcomes over the number of total possible outcomes. Since there are 2 yellow balls and 4 balls in total, the probability (P) of drawing a yellow ball is calculated as follows:

Number of successful outcomes (yellow balls) = 2

Total number of possible outcomes (total balls) = 4

P(yellow ball) = Number of yellow balls / Total number of balls = 2/4 = 0.5

Therefore, the probability of grabbing a yellow ball is 0.5 when expressed as a decimal.

Answer:

volume of water cup could hold is, 14.13 square inches.

Step-by-step explanation:

Volume of a cone(V) is given by:

[tex]V = \frac{1}{3} \pi r^2 h[/tex]      .....[1]

where,

r is the radius of the cone

h is the height of the cone

As per the statement:

A  water cup is in the shape of the cone. The diameter of the cup is 3 inches and the height is 6 inches.

⇒height(h) = 6 inches and diameter(d) = 3 inches

We know that:

diameter(d) =2 (radius)

[tex]3 = 2r[/tex]

Divide both sides by 2 we get;

[tex]r = 1.5[/tex]

substitute these in [1] we have;

Use [tex]\pi = 3.14[/tex]

[tex]V = \frac{1}{3} \cdot 3.14 \cdot 1.5^2\cdot 6[/tex]

⇒[tex]V = \frac{1}{3} \cdot 3.14 \cdot 13.5[/tex]

Simplify:

[tex]V = 14.13 in^3[/tex]

Therefore, the volume of water the cup could hold is, 14.13 square inches.

Final answer:

The volume of water a cone-shaped cup can hold, with a diameter of 3 inches and height of 6 inches, using the formula for the volume of a cone, is 14.13 cubic inches.

Explanation:

The question asks us to calculate the volume of water a cone-shaped cup can hold given its dimensions. The diameter of the cup is 3 inches, and its height is 6 inches. To find the volume of a cone, we use the formula V = 1/3 πr²h, where V is the volume, r is the radius, h is the height, and π (pi) is approximately 3.14.

First, we find the radius of the cup. The diameter is 3 inches, so the radius (half the diameter) is 1.5 inches. Substituting the radius and the height into the formula, we get:

V =1/3 × 3.14 × (1.5²) × 6 = 1/3 × 3.14 × 2.25 × 6 = 1/3 × 3.14 × 13.5 = 14.13 cubic inches

Therefore, the volume of water the cup could hold is 14.13 cubic inches.

The speed of the car in sunny weather is calculated to be 60 mph, given that it travels the same distance in less time compared to its speed in a rainy weather, which is 20 mph slower.

Finding the Car's Speed in Sunny Weather:

Let's assume the speed of the car in sunny weather is s mph. Therefore, the speed of the car in a rain storm would be (s - 20) mph. Given that the car travels the same distance in both weathers, we can use the formula distance = speed * time to express the distance travelled in sunny weather and rainy weather.

In sunny weather, the car travels for 2 hours, hence the distance covered is 2s miles. In rainy weather, it travels for 3 hours, covering a distance of 3(s - 20) miles.

Since the distances are equal, we can equate them and solve for s:

2s = 3(s - 20)

2s = 3s - 60

s = 60 mph

Therefore, the speed of the car in sunny weather is 60 mph.

Isabella needs a minimum of 9216 tiles to cover her 2ft by 2ft tabletop. This is calculated by converting all measurements to inches, finding the area of both the tabletop and a single tile, and dividing the total area of the tabletop by the area of a single tile.

To answer Isabella's question let's first convert everything into the same units to make it easier. The tabletop in inches would be 2ft * 12in/ft = 24in by 24in. The area of the tabletop is then 24in * 24in = 576in^2. Each tile is 1/4in by 1/4in in size, so the area of a single tile is 1/4in * 1/4in = 0.0625in^2. To find the minimum number of tiles needed to cover the tabletop, divide the total area of the tabletop by the area of a single tile: 576in^2 / 0.0625in^2 = 9216 tiles. Therefore, Isabella needs a minimum of 9216 tiles to cover the square tabletop.

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Mathematics defines function as an expression that points a relationship between two variables.

Sequence is a list of numbers in certain order.

The function that defines the sequence -6,-10,-14,-18 is [tex]\rm f(x)= -4x-2[/tex]

Given:

[tex]\rm f(1)=-6\\f(2)=-10\\f(3)=-14\\f(4)=-18\\f(6)=-26[/tex]

Substituting x=1 in function [tex]\rm f(x)= -4x-2[/tex]

[tex]\begin{aligned}\rm f(1)&= -4(1)-2\\&=-6\end[/tex]

x=2

[tex]\begin{aligned} \rm f(2)&= -4(2)-2\\&=-10\end[/tex]

x=6

[tex]\begin{aligned}\rm f(6)&= -4(6)-2\\&=26\end[/tex]

Therefore the function [tex]\rm f(x)= -4x-2[/tex] defines the sequence.

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Final answer:

To convert the 3-ton weight of Mr. Johansson's truck to ounces, we multiply 3 tons by 2,000 to get pounds and then multiply that figure by 16 to get 96,000 ounces.

Explanation:

Mr. Johansson's truck weighs 3 tons. To convert this weight to ounces, we need to know that one ton is equal to 2,000 pounds and one pound is equal to 16 ounces.

First, we convert tons to pounds:
3 tons x 2,000 pounds/ton = 6,000 pounds

Next, we convert pounds to ounces:
6,000 pounds x 16 ounces/pound = 96,000 ounces

Therefore, the weight of Mr. Johansson's truck is 96,000 ounces. This conversion showcases the application of the conversion factors between tons, pounds, and ounces, providing a precise measure of the truck's weight in a more universally comprehensible unit.

Final answer:

The truck weighs 96,000 ounces.

Explanation:

To convert tons to ounces, we can use the conversion factor that 1 ton is equal to 32,000 ounces.

So, to find how many ounces the truck weighs, we can multiply the weight of the truck in tons by the conversion factor.

Weight of the truck in ounces = Weight of the truck in tons x Conversion factor

Weight of the truck in ounces = 3 tons x 32,000 ounces/ton

Weight of the truck in ounces = 96,000 ounces.

Circumference of the circle is 25.136 cm with radius 4 cm.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The radius of circle = 4 cm

We know that;

The circumference of circle = 2πr

Where, 'r' is radius of circle.

So, We get;

The circumference of circle = 2πr

                                           = 2 × 3.142 × 4

                                           = 25.136 cm

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Answer:

(3,6)

Step-by-step explanation:

Believe me this is correct I just did the test

There is no hole in the graph of the function f(x) = x^2 - 9x - 3.

To find the coordinates of the hole in the graph of the function f(x) = x^2 - 9x - 3, we need to determine the x-value at which the function is undefined. This occurs when the denominator of the function is equal to zero. In this case, the function has no denominator, so there is no hole in the graph.

The residuals of any data set should get added to zero. If there are three residuals (say A, B, and C) in any data set, then it could be written as A + B + C = 0.

Given are the two residuals -10 and -20 out of three point in a particular data set.

Let's assume A = -10 and B = -20, so that we could find third value C of the given data set.

We know A + B + C = 0

(-10) + (-20) + C = 0

(-30) + C = 0

C = 30

It means that third residual must be 30.

Hence, the final answer is 30.

Answer:

30

Step-by-step explanation:

Solution:

Question 1:

we are given that

A football player who runs 5yds/sec and starts on the 25 yard line.

So here rate is 5yds/sec

and 25 yards is the y- intercept.

Hence it can be written as

[tex]y=5x+25[/tex]

Question 2:

Based on the given equations, which one represents the greatest rate?

As we know in the standard form of equation of starlight line

[tex]y=mx+b[/tex]

m represents the rate or gradient.

As we can observe from the given options [tex]y = 7x + 5[/tex] has the greatest gradient.

Hence the correct option is [tex]y = 7x + 5[/tex]

Answer:

The correct option is C.

Step-by-step explanation:

∵ The given graph is of increasing nature.

∴The base of the exponential will be greater than 1.

∴ option A is incorrect.

Also, at x=0 the value of y=3, but in option B at x=0 ⇒y= 3^0 =1

∴ option B is also incorrect.

At x=0, y=3 for option 3 which satisfies the graph.

∴ the option C is correct.

option D is incorrect because the base of an exponential can never be negative.

area/width

=length

=1176÷21

=56m

Answer:

Length = 56 meters

Step-by-step explanation:

We can find the length of the rectangle which has an area of 1,176 square meters and width of 21 meters with this formula:

[tex]\boxed{Area(A)=length(l)\times width(w)}[/tex]

Given:

Then:

[tex]\begin{aligned}A&=l\times w\\1,176&=l\times21\\l&=1,176\div21\\l&=56\ m\end{aligned}[/tex]

Answer:

i have ttm also

Step-by-step explanation: