At the movie theater, child admission is $5.10 and adult admission is $9.10. On Monday, 151 tickets were sold for a total sales of $1030.10. How many adult tickets were sold that day?

Answer:30

Step-by-step explanation: its 30 because you divide 127 1/2 or 127.5 by 4.25 or 4 1/4.

Answer:

standard deviation will remain unchanged at 3.5

Step-by-step explanation:

Subtracting 2 from each of the values in the data set will only change the origin of the data set. The mean of the values will change but the variance and consequently the standard deviation will remain unchanged

Answer:

standard deviation of the resulting data will be 3.5

Step-by-step explanation:

When we add or subtract each values of the data set by some constant then the mean will change by the same amount whereas the there is no change in the standard deviation.

So, when we subtract 2 from each values of the data set, the standard deviation of the resulting data will be also 3.5.

Answer:

  see attached

Step-by-step explanation:

The chart shows you that w=2 when z=0. That's the point on the w-axis at lower left. Only one equation gives those results.

Answer:

  x = 7.5

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship between the angle and the sides of interest is ...

  Tan = Opposite/Adjacent

  tan(37°) = x/10 . . . . fill in given values

Multiplying by 10, we get ...

  x = 10·tan(37°) ≈ 7.5

Consider the attached figure. The height CD cuts the triangle exactly in half. This means that

[tex]\overline{AD}=\overline{BD}=\dfrac{1}{2}\overline{AB}=10[/tex]

Moreover, since CD is the height of the triangle, we know that ACD is a right triangle. We know the hypothenuse AC to be 20 feet because it is a side of the triangle, and we just found out that AD is 10. We can use the pythagorean theorem to deduce

[tex]\overline{CD}=\sqrt{\overline{AC}^2-\overline{AD}^2}=\sqrt{400-100}=\sqrt{300}[/tex]

So, the area is

[tex]A=\dfrac{bh}{2}=\dfrac{\overline{AB}\cdot\overline{CD}}{2} = \dfrac{20\cdot\sqrt{300}}{2}=10\sqrt{300}\approx 173[/tex]

Well to start off all sides are gonna be 20. To find area it’s lxw so 20•20=400

Dives 400 by 12 and you get 33.333333333 so you round that to the nearest whole foot and you get 33 feet

Answer:

  A.  216 cm³

Step-by-step explanation:

The volume of a cube is the cube of the side length:

  V = s³ = (6 cm)³ = 216 cm³

Answer:

  3.  P(R1|Q) = 3/19 ≈ 0.16

Step-by-step explanation:

The desired probability is the ratio of P(Q·R1) to P(Q). The probability P(Q) is not given, but there is sufficient information to find it.

  P(Q·R1) = P(Q|R1)·P(R1) = 0.40·0.15 = 0.06

  P(Q·R2) = P(Q|R2)·P(R2) = 0.20·0.55 = 0.11

  P(Q·R3) = P(Q|R3)·P(R3) = 0.70·0.30 = 0.21

Since R1 and R2 and R3 are mutually exclusive and have a joint probability of 1, this means ...

  P(Q) = P(Q·R1) +P(Q·R2) +P(Q·R3) = 0.06 +0.11 +0.21 = 0.38

Then the desired probability is ...

  P(R1|Q) = P(Q·R1)/P(Q) = 0.06/0.38

  P(R1|Q) = 3/19 ≈ 0.16

To determine the number of each type of question on the math test, set up a system of equations. Solve the system of equations using substitution or elimination method. The math test consists of 5 multiple-choice questions and 15 problem-solving questions.

To determine how many of each type of questions are used on the math test, we can set up a system of equations. Let's use x to represent the number of multiple-choice questions and y to represent the number of problem-solving questions. Since there are 20 questions in total, we have the equation x + y = 20. Each multiple-choice question is worth 5 points and each problem-solving question is worth 6 points, so we also have the equation 5x + 6y = 100.

We can solve this system of equations using substitution or elimination method. Let's solve it using elimination:

Therefore, the math test consists of 5 multiple-choice questions and 15 problem-solving questions.

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The dimensions should be 6ft by 9ft.

Final answer:

The dimensions of the floor with an area of 54 square feet, where the width is 2/3 of the length, are 9 feet in length and 6 feet in width.

Explanation:

Pascal wants to find the dimensions of a floor where the area is 54 square feet and the width is 2/3 the length. To find the dimensions, we set up an equation where the length is L and the width is W, with W = (2/3)L. Since area is calculated by the formula Area = length times width, we get 54 = L times (2/3)L. Solving this equation by multiplying the length terms and then dividing both sides by 2/3, we get L² = 54 times (3/2), which simplifies to L² = 81. Taking the square root of both sides gives us L = 9 feet. Consequently, the width would be W = (2/3) times 9 = 6 feet. Therefore, the dimensions of the floor are 9 feet by 6 feet.

Answer:

6

Step-by-step explanation:

(g o f)(3) = g(f(3))

We can find f(3) using its formula with x=3:

f(3) = -2·3 +8 = -6 +8 = 2

Now, we can find g(2) using its formula with x=2:

g(2) = 3·2 = 6

So, the composition value is ...

(g o f)(3) = 6

When writing rational expressions, you need to be aware that ...

  1/4x = (1/4)x ≠ 1/(4x)

Parentheses around the denominator are required, unless you're typesetting the expression and can use a fraction bar for grouping.

The derivative of the curve expression is ...

  y' = x - 1/(4x) . . . . . parentheses added to what you wrote

and the expression (1 -(y')^2) can be written ...

  1 -(y')^2 = x^2 +1/2 +1/(16x^2) . . . . . parentheses added to what you wrote

The first and last terms of this trinomial are both perfect squares, so you might suspect the whole trinomial is a perfect square. You recall that ...

  (a +b)^2 = a^2 + 2ab + b^2

This is a good "pattern" to remember. Using it is a matter of pattern recognition, as is the case with a lot of math.

Here, you have ...

  a = x

  b = 1/(4x)

In order for your trinomial to be a perfect square, the product 2ab must equal the middle term of your trinomial. (Spoiler: it does.)

  2ab = 2(x)(1/(4x)) = (2x)/(4x) = 1/2 . . . . . matches the middle term of 1 -(y')^2

Hence your trinomial can be written as the square ...

  1 -(y')^2 = (x +1/(4x))^2

_____

This is convenient because you want to integrate the square root of this. Your integral then becomes ...

[tex]\displaystyle\int\limits_{2}^{4}{\left(x+\frac{1}{4x}\right)\,dx[/tex]

Answer:

a = 12

Step-by-step explanation:

Multiply the equation by the inverse of the coefficient of "a".

4·(1/4)a = 4·3

1·a = 12 . . . . . . simplify

a = 12

It would be located at (1, 3). Hope this helps!

Answer:

1,3

Step-by-step explanation:

[tex]P_{ELPJ} = EK+ES+LU+LK+PV+PU JS+JV \\ \Leftrightarrow P_{ELPJ} = 2EK + 2LU + 2PV + 2JS = 2 \times 2 + 2 \times 4 + 2 \times 1 + 2 \times 2 = 18[/tex]

this is an isosceles triangle two sides are the same

so there are 180° in a triangle

180-58= 122 now divide this by two because the last two angles are equal

122/2=61° =x°

Answer:

The volume would be 1 1/4 cubic inches.

Step-by-step explanation:

To find this, multiply all three numbers together because the formula for volume is length multiplied by width multiplied by height.

V = lwh

V = (1/4)(1 1/4)(4)

V = 1 1/4

Let

[tex]\theta=\sin^{-1}\dfrac x2\implies\sin\theta=\dfrac x2[/tex]

Recall that

[tex]\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\dfrac{x^2}4}[/tex]

Then

[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac{\frac x2}{\sqrt{1-\frac{x^2}4}}[/tex]

[tex]\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac x{\sqrt{4-x^2}}[/tex]

Final answer:

To find tan(sin⁻¹(x/2)), we use the relationship between the sides of a right triangle, leading to the solution tan(θ) = x/√(4 - x²).

Explanation:

The question "what is tan(sin-1(x/2))" involves understanding inverse trigonometric functions and their properties. To solve this, we can create a right-angled triangle where the angle θ has a sine value of x/2. According to the Pythagorean theorem, if one side (opposite) is x and the hypotenuse is 2, the adjacent side can be calculated as √(4 - x²). Thus, tan(θ) = opposite/adjacent = x/√(4 - x²).

Answer:

-1/2=x

Step-by-step explanation:

-9 + x = 5x - 7

     -x      -x

-9=4x-7

+7         +7

-2=4x

-2/4 =4x/4

-1/2=x

Answer:

b) 15

Step-by-step explanation:

Given that,

Total people = 100

% of people prefer vanilla = 25%

Number of people prefer vanilla out of 100 = 25% of 100

=> 25/100 * 100 = 25

% of people prefer swirl = 35%

Number of people prefer swirl out of 100 = 35% of 100

=> 35/100 * 100 = 35

% of people prefer chocolate = 40%

Number of people prefer chocolate out of 100 = 40% of 100

=> 40/100 * 100 = 40

The number of more people preferring chocolate over vanilla =  40 - 25

=> 15 so option b is correct

Answer:

The answer is B (15)

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

ΔACD is 3 times the size of ΔABE, so the dilation uses a scale factor of 3. That only leaves choices A, D, and E.

Dilation about point A leaves point A in the same place, so choice E can be eliminated on that basis. (There is only one point A, and not a translated version, consistent with choice A.)

Point C in the larger triangle corresponds to point B in the smaller triangle, and is 4 units down from it. Hence the description of D makes sense.

___

We hope you can see that choosing correct answers in multiple-choice questions is as much about consistency and reasonableness as it is about knowing how to work the problem. You do have to understand what the problem is asking and what the answers are saying about it.

Answer:

25m + 10b = 400

Step-by-step explanation:

Total amount that can be earned = $ 400

Amount earned on mowing a lawn = $ 25

Amount earned per hour on babysitting = $10

Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m

Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b

Total amount earned = Amount earned from mowing m lawns + Amount earned from babysitting for b hours

Using the values from above, we can set up the equation as:

400 = 25m + 10b

or

25m + 10b = 400

This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.

You can solve for 'x' in the equation 'ax = 7' by dividing both sides of the equation by 'a'. The result is 'x = 7/a'. This is based on the principle of maintaining equation equality through similar operations on both sides.

To solve for

x

in the equation

ax = 7

, you need to isolate the variable, x. This is done by

dividing

both sides of the equation by 'a'. This leaves x = 7/a. Therefore, you can find 'x' by dividing both sides of the equation by 'a'.

This process is based on the principle of equality.

You can maintain the equality of the equation by doing the same mathematical operation to both sides. Consequently, by dividing both sides by 'a', you successfully solve for x without disrupting the balance of the equation.

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Answer:

Hemisphere radius = 3 inch

Sphere volume = 4/3 • π • radius^3

Sphere volume = 4/3 • π • 27

Sphere volume = 113.0973355292 cubic inches

Cylinder Volume = π • radius^2 • height

Cylinder Volume = π • 9 * 10

Cylinder Volume = 282.7433388231 cubic inches

TOTAL VOLUME = 113.10 + 282.74 cubic inches

TOTAL VOLUME = 395.84 cubic inches

Step-by-step explanation:

Answer: 126π in.³

Step-by-step explanation:

If I'm not wrong, there's no change in the measurement...  I think it's D.  since there's no visible change in the angle measurement. If it asked the coordinates then maybe I could elaborate. This question is confusing though. :/

The measure of angle Z after the transformation is D) 103°.Therefore , D.) 103​ is correct .

A translation does not change the measure of angles, so the measure of angle Z after the transformation is the same as the measure of angle Z before the transformation, which is 103°.

Image verification:

The image you sent shows a kite with the following angle measures:

Angle W = 96°

Angle X = 58°

Angle Y = 103°

Angle Z = 103°

The kite is translated up 3 units and 4 units to the right, which does not change the measure of any of the angles.

Therefore, the measure of angle Z after the transformation is still 103°.

Answer

the answer is 6/10 or 0.6

Step-by-step explanation:

6/10 (3/5) because you have to share the amount of bags into the ratio of friends which would give you 0.6 or 6/10 simplified to 3/5

Answer:

8. A'(-1/2, 1), B'(0, 0), C'(1, 1 1/2)

10. 20°, 60°, 100°

Step-by-step explanation:

8. Point B is at the origin, the center of dilation, so its coordinates remain unchanged. The coordinates of A and C are each multiplied by the scale factor, 1/2.

A' = (1/2)A = (1/2)(-1, 2) = (-1/2, 1)

C' = (1/2)C = (1/2)(2, 3) = (1, 3/2)

__

10. The total number of ratio units is 1+3+5 = 9. The total of angle measures in any triangle is 180°. So, each of the "ratio units" must stand for 180°/9 = 20°. Then the angles are ...

1 · 20° = 20°

3 · 20° = 60°

5 · 20° = 100°

Solve for x in 5x - 3y = 18

x = 3(6 + y)/5

Substitute x = 3(6 + y)/5 into 3x + 3y = 30

9(6 + y)/5 + 3y = 30

Solve for y in 9(6 + y)/5 + 3y = 30

y = 4

Substitute y = 4 into x = 3(6 + y)/5

x = 6

Therefore,

x = 6

y = 4

The solution to the system of equations is x = 6 and y = 4.

Step 1: Add the two equations.

5x - 3y = 18

3x + 3y = 30

8x = 48

Step 2: Solve for x.

8x = 48

x = 6

Step 3: Substitute x = 6 into one of the original equations to solve for y.

5(6) - 3y = 18

30 - 3y = 18

-3y = -12

y = 4

Answer:

B) 11:35 a.m.

Final answer:

The bottle will be half full at 11:50 PM, which is ten minutes before it is completely full at midnight, due to the exponential growth doubling the contents every ten minutes.

Explanation:

The question involves understanding exponential growth, specifically the doubling time of a population or, in a more tangible sense, the filling of a jar (or bottle). Given that a bottle doubles the amount inside every ten minutes and is full at midnight, we can calculate when the bottle will be half full by working backwards from the endpoint.

If the bottle is full at midnight, then it was half full at 11:50 PM, since the contents double every ten minutes. This reveals a common misunderstanding in our intuition about exponential growth, where significant change occurs in the final moments before reaching capacity.

In summary, to find out when the bottle will be half full, simply subtract a single doubling interval (ten minutes) from the time when the bottle is known to be full.

The lateral area and surface area of the cuboid are 72 square feet and 142 square feet, respectively. The lateral area and surface area of the prism are 42 square cm and 62 square cm, respectively.

To find the lateral area and surface area of the given cuboid and prism, we need to use the formulas for each.

For the cuboid:
1. Lateral Area: The lateral area of a cuboid can be found by adding the areas of its four side faces. Since the cuboid has a length of 7 feet, a breadth of 5 feet, and a height of 3 feet, we can calculate the lateral area as follows:
- Side 1: length * height = 7 feet * 3 feet = 21 square feet
- Side 2: breadth * height = 5 feet * 3 feet = 15 square feet
- Side 3: length * height = 7 feet * 3 feet = 21 square feet
- Side 4: breadth * height = 5 feet * 3 feet = 15 square feet
The total lateral area is the sum of these four areas: 21 + 15 + 21 + 15 = 72 square feet.

2. Surface Area: The surface area of a cuboid is found by adding the areas of all six faces. In addition to the lateral area, we need to include the areas of the top and bottom faces. Using the dimensions of the cuboid, we can calculate the surface area as follows:
- Top face: length * breadth = 7 feet * 5 feet = 35 square feet
- Bottom face: length * breadth = 7 feet * 5 feet = 35 square feet
The total surface area is the sum of these six areas: 72 (lateral area) + 35 (top face) + 35 (bottom face) = 142 square feet.

Now, for the prism:
1. Lateral Area: To find the lateral area of the prism, we need to find the perimeter of the base and multiply it by the height of the prism. Since the prism has a base with a length of 5 cm and a breadth of 2 cm, the perimeter is: 2 * (length + breadth) = 2 * (5 cm + 2 cm) = 2 * 7 cm = 14 cm.
The lateral area is obtained by multiplying the perimeter by the height: 14 cm * 3 cm = 42 square cm.

2. Surface Area: The surface area of the prism is the sum of the lateral area and twice the area of the base. Since the base is a rectangle with a length of 5 cm and a breadth of 2 cm, its area is: length * breadth = 5 cm * 2 cm = 10 square cm.
The surface area is then calculated as: 42 (lateral area) + 2 * 10 (area of the base) = 42 + 20 = 62 square cm.

To determine the dimensions of the wall, we set up an equation using the given area and the fact that the wall's height is 2/3 of its length. Solving for length and height, we find that the length is 30 feet and the height is 20 feet.

The question asks to determine the length and height of a wall that Leo wants to paint, given that the area of the wall is 600 square feet, and the height is 2/3 of its length. To solve this, we will set up an equation to represent the relationship between the length and height and use the area to find the specific dimensions.

Let's use L to represent the length of the wall and H to represent the height. According to the given information, H = (2/3)L. The area of a rectangle is calculated by multiplying its length by its height, so we can set up the equation:

Area = L \H = 600 sq ft

Substituting the height with its relation to length, we get:

600 = L \(2/3)L

Dividing both sides by L and then by 2/3, we find that:

L² = 600 \(3/2)

L² = 900

L = 30 ft (since length must be positive)

Now, to find the height:

H = (2/3)\L = (2/3) \ 30 = 20 ft

So, the length of the wall is 30 feet and the height is 20 feet.