The admission fee at an amusement park is $20 for children and $35 for adults. On a certain day, 390 people entered the park, and the admission fees collected totaled $10650. How many children and how many adults were admitted? NUMBER OF CHILDREN= ? NUMBER OF ADULTS= ?

Answer:

0.0471

Step-by-step explanation:

Here, we want to find the area of the shaded region.

The area of the shade region = 1- area of the unshaded region

The area of the unshaded region is as follows;

P(b) - P(a)

and that is;

P(-1.88<x<2.12) = 0.95294 from z table

So the area of the shaded region = 1-0.95294 =

0.04706 = 0.0471 to 4 d.p

Answer:

49/90 is simplified

Step-by-step explanation:

Answer:

Step-by-step explanation:

49/90

Answer:

(1,-1)

Step-by-step explanation:

If you try plugging in the numbers for x in the equation y > Ix + 1I - 1, you'll find the answer.

Answer:

The perimeter of the actual playground is 22000 units

Step-by-step explanation:

By measurement, the width of the scale drawing = 16 units

The breadth of the scale drawing = 6 units

Therefore, given that the scale is 1:500, we have that the actual dimensions of the playground are;

Actual width of the playground = 500×16 = 8,000 units

Actual breadth of the playground = 500×6 = 3,000 units

Therefore;

The perimeter of the actual playground = 2 × 8000 + 2 ×3000 =  22000 units.

Answer:

The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle

Use rule ; SOHCAHTOA .Where sin x = opp/hyp

cos x = adj/hyp

tan x= opp/adj

Substitute the given values for the three sides

into any of the above rules

[tex]example = Hyp = 2\\opp = 1\\sin- x = 1/2\\x = sin^{-1} 1/2\\x = 30[/tex]

Step-by-step explanation:

I Hope It Helps :)

Answer:

3

Step-by-step explanation:

Adjacent angles have a common side and no common interior points.

Answer:

t = 4

Step-by-step explanation:

you have -8 and twelve you equation is x -12 = -8 so we just have to flip the equation around to make it x = 12 -8 which is easy . You just have to make sure you don't get mixed up while flipping the signs.

The value of t is 4.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

The temperature in January = 12 °F

And the low temperature is = -8 °F

The equation of temperature t can be given as

t= high temperature + low temperature

t= 12 - 8

t=4

The value of t is 4.

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Answer:

Median=3, Mean=2.333

Step-by-step explanation:

Answer:

34%

Step-by-step explanation:

According to the empirical rule, 68% of all of the data in a normal distribution falls within one standard deviation of the mean.

Applying to this particular case, 68% of the requests fall within (50 - 7) and (50+ 7). The percentage of requests from 43 to 50 is equal to the percentage of requests from 50 to 57.

Therefore, the percentage of light bulb replacement requests numbering between 50 and 57 is 68/2 =  34%.

Answer:

6.04 km

Step-by-step explanation:

From the image attached, both triangles form are similar to each other because their corresponding angles are equal, therefore they are equiangular triangles. equiangular triangles have the same shape but different sizes and the ratio of their corresponding sides are equal.

Therefore since their corresponding sides are equal we can calculate the distance from the main gate to Manatee Springs. It is given by:

[tex]\frac{3500\ yards}{2000\ yards} = \frac{4200\ yards}{x}\\ x= \frac{4200\ yard*2000\ yards}{3500\ yards}=2400\ yards[/tex]

x = 2400 yards.

The distance from the main gate to Manatee Springs = x + 4200 yards = 2400 + 4200 = 6600 yards

The distance from the main gate to Manatee Springs = 6600 yards = (6600 * 0.0009144) km = 6.04 km

The distance from the main gate to Manatee Springs = 6.04 km

Answer:

48

Step-by-step explanation:

Answer:

Solution,

Let the length of tunnel be 'l'

Area=25 m^2

Volume of tunnel= cross sectional area* length

[tex] or \: 575 = 25 \times l \\ or \: l = \frac{575}{25} \\ l = 23 \: m[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

Option B.

Step-by-step explanation:

From the given graph it is clear that it is a V-shaped graph. It means, it is the graph of absolute function.

The vertex form of an absolute function is

[tex]y=a|x-h|+k[/tex]

where, a is a constant and (h,k) is the vertex.

From the given graph it is clear that the vertex is at (7,-3). It means h=7 and k=-3.

[tex]y=a|x-(7)|+(-3)[/tex]

[tex]y=a|x-7|-3[/tex]    ...(1)

It passes through (4,0).

[tex]0=a|4-7|-3[/tex]

[tex]3=3a[/tex]

[tex]1=a[/tex]

Put this in (1).

[tex]y=1|x-7|-3[/tex]

[tex]y=|x-7|-3[/tex]

Therefore, the correct option is B.

Answer:

A: i

Step-by-step explanation:

i^57=i use the calculator

Answer:

7 red marbles

Step-by-step explanation:

P( red) = red marbles / total marbles = 1/8

We know there are 56 marbles

red marbles/56 = 1/8

Multiply by 56

red marbles = 1/8 *56 = 7

There are 7 red marbles

Answer:

$35.2

Step-by-step explanation:

Marked price of hat = $40

Sale discount = 20%

discount in $ = 20% of $40 = 20/100 * 40 = $8

Thus, sale price = marked price - sale discount = $40 - $8 = $32

Now it is given that there is sales tax of 10%

This sales tax will be applied on sale price

thus,

sales tax in dollars = 10% of sale price of hat = 10/100 * $32 = $3.2

Total price paid for hat = Sale price+ sales tax = $32 +$3.2 = $35.2

Thus, Bob ended up paying $35.2 for the hat.

Answer:

A ; -4

Step-by-step explanation:

3a = 12b then a = 4b (dividing by 3)

we put 4b in the equation instead of a:

(-4b / b) = -4

.. ..

Answer:

A. -4

Step-by-step explanation:

3a/b = 12

Let b = 2

3a/2 = 12

3a = 24

a = 8

( - a/b)

( - 8/2)

( - 4)

Answer:

y= -4x                                                                                                                                                                                      

Step-by-step explanation:

hope this helps and lmk if you need anything!

Answer:

Not a function

Step-by-step explanation:

For an equation to be a function, there should be only one y-coordinate per x-coordinate. Since this relation has both (-1,9) and (-1,4), this is not a function.

Answer:not a function

Step-by-step explanation:

because when you put the points on the coordinate plane your shape will come out as a v shaped object. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers

Answer: A

Step-by-step explanation:

So we know that to find the area of a triangle you have to multiply the base times the height and divide it by two or multiply it by 1/2.Looking the information given it say that theta is equal to 26 degrees  and the length of a or the hypotenuse is 25 and b which in this case is the base is 32. So the information gives us the base but now we need to find the height.

To find  H we need to apply trigonometry solve for h the height.

As we could see theta which is 26 degrees is opposite the height and we know the hypotenuse length. So using soh cah toh we have to know that the length of h is  going to be using the sin formula opposite over hypotenuse.

[tex]sin(26)=\frac{h}{25}[/tex]    solve for h by multiplying both sides by 25.

h= 25 sin(26)

h= 10.96   is being rounded to the nearest hundredth because that is essential

Now we know H is equal to 10.96  which is the Height so now we have all the information we need the height and the base.

Multiply 10.96 by 32 and divide it by 2.

10.96 * 32 =  350.72

350.72 /2 = 176.36  

The best answer is A  because that is the only best approximation to 175.35.

Answer:

Option (D)

Step-by-step explanation:

Function in red is,

f(x) = x²

When a function f(x) is translated h units to the left, rule to be followed,

f(x) → f(x + h)

If the function is translated 2 units left,

Translated function (in blue) will be,

g(x) = (x + 2)²

Option (D) will be the answer.

Answer:

I think the answer should be 112

I'm guessing the supports in the water are equally distanced. Therefore, I'd divide 168 by four to get a singular distance between two supports. I got 42 yards.

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

I guess that we want to create 4 digit numbers that are divisible by 5, only using the odd numbers in the image.

We know that a number is divisible by 5 only if the last digit (the units digit) is a zero or a five, in the image we only have a five, so our 4-digit numbers need to end with a five, so we have a digit fixed in five and the other 3 digits can be other numbers.

We have two different approaches to this:

First, if each odd number can be used only once, we already used the five, so we can use the other 4 numbers.

Then, for the first digit, we have 4 options.

for the second digit, we have 3 options (because we already used one)

for the third digit, we have 2 options (because we already used 2)

then the number of combinations is equal to the product of the number of options for each selection:

C = 4*3*2 = 24 combinations.

The second approach is If the numbers in the image can be repeated (for example, 5555 or 3435 are allowed)

we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third, we also have 5 options, then, with the same reasoning as above, we have:

C = 5*5*5 = 25*5 = 125 combinations.

Answer:

Step-by-step explanation:

[tex] 3{x}^{4} - 48[/tex]

Factor out 3 from the expression:

[tex]3( {x}^{4} - 16)[/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex],factor the expression

[tex]3(( {x}^{2} ) ^{2} - {(4)}^{2} )[/tex]

[tex]3( {x}^{2} - 4)( {x}^{2} + 4)[/tex]

Again, factor using the formula of [tex] {a}^{2} - {b}^{2} [/tex]

[tex]3(x - 2)(x + 2)( {x}^{2} + 4)[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

3(x − 2)(x + 2)(x2 + 4)

Step-by-step explanation:

Took the quiz and got it right hope this helps :) , you can check out the other answer for explanation.

Answer:

7 formas

Step-by-step explanation:

En la pastelería, se han preparado 30 pasteles.

Cada bandeja contendrá la misma cantidad de pasteles.

Para encontrar de cuántas maneras puedes ponerlos, tenemos que encontrar los factores de 30. Ellos son:

1, 2, 3, 5, 6, 10, 15, 30

Esto significa que podemos tener:

30 bandejas que contienen 1 bandeja cada una

15 bandejas con 2 tortas cada una

10 bandejas con 3 tortas cada una

6 bandejas con 5 tortas cada una

5 pasteles que contienen 6 pasteles cada uno

3 bandejas con 10 pasteles cada una

2 bandejas con 15 tortas cada una

Esto significa que hay 7 formas de colocar los pasteles.

Answer:

B. regular octagon

I hope this will help you

The width for maximum area will be 40 metres.

Given,Simon has 160 metres of fencing to build a rectangular garden.

The garden's area (in square meters) as a function of the garden's width x(in meters) is modeled by,

[tex]A(x)=-x(x-80)[/tex].

We know that perimeter of rectangle will be,

[tex]P=2(L+B)\\[/tex]

Here p is 160,

So,[tex]160=2(L+B)[/tex]

[tex]\L+B= 80[/tex]

Now we have the sum of length and width off the rectangular garden is 80.

Since,

[tex]A(x)=-x(x-80)\\[/tex]

So, [tex]A(x)=x(80-x)[/tex]

We know that the area of rectangle will be the product of length and , here in question width is [tex]x[/tex] so the length will be[tex](80-x)[/tex].

Now we have to calculate the width for which the area will be maximum.

The area will be maximum when the first derivative of area function will becomes zero.

So,

[tex]\frac{\mathrm{d} }{\mathrm{d} x} A(x)=\frac{\mathrm{d} }{\mathrm{d} x}(-x)(x-80)[/tex]

[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=\frac{\mathrm{d} }{\mathrm{d} x}(-x^{2} +80x)[/tex]

[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=-2x+80\\[/tex]

For maximum area ,

[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=0[/tex]

Hence,

[tex]-2x+80=0\\x=40[/tex]

Hence the width for maximum area will be 40 metres.

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The maximum area is 1600 sq meters.

The garden's area is modeled by a quadratic function, whose graph is a parabola.

The maximum area is reached at the vertex.

So in order to find the maximum area, we need to find the vertex's y-coordinate.

We will start by finding the vertex's x-coordinate, and then plug that into A(x).

The vertex's x-coordinate is the average of the two zeros, so let's find those first.

A(x)=0    -x(x-80)=0

  ↓                  ↓

-x=0 or x-80=0

x=0 or x=80

Now let's take the zeros' average:

[tex]\frac{(0)+(80)}{2}=\frac{80}{2}=40[/tex]

The vertex's x-coordinate is 40. Now lets find A(40):

A(40)= -(40)(40-80)

        = -(40)(-40)

        = 1600

in conclusion, the maximum area is 1600 square meters.

Answer:

D. 10 feet

Step-by-step explanation:

40/8 = x/2 --> cross multiply

8x = 80

x = 10

Option D is correct, the person who casts a 2 feet shadow is 10 foot tall.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that At a certain time of day, a 40-foot building casts a 8 foot shadow.

We need to find how tall is a person who casts a 2 foot shadow.

Let x be the height of the person.

Let us form a proportional equation

40/8=x/2

Apply cross multiplication

80=8x

Divide both sides by 8

x=10

Hence, the person who casts a 2 foot shadow is 10 foot tall.

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Answer:

Step-by-step explanation:

Distribute 7 to the first number

7 * -3/4 = -21/4

-21/4 = 5  -1/4

Distribute 7 to the second number

7 * -3

= -21

Put the numbers together

They separated the parenthesis.

So it is still 7 * -3/4

and

7*-3.

Hope this helps,

Kavitha