Pranay's school is selling tickets to the annual talent show. On the first day of ticket sales the
school sold 9 senior citizen tickets and 10 student tickets for a total of $113. The school took in
$64 on the second day by selling 2 senior citizen tickets and 10 student tickets. What is the price
each of one senior citizen ticket and one student ticket?

Answer:

-1 - 4 i

Step-by-step explanation:

5 - (2 * i) - (2 * (3 + i)) =

-1 - 4 i

Answer:

  2973.5 liters

Step-by-step explanation:

You are being asked to find the volume of the largest possible container that has a given surface area. The volume will depend on the shape. If shape is not specified, we know a sphere has the largest volume for a given area.

__

The available area is ...

  ($100) / ($10/m²) = 10 m²

The area of a sphere with diameter d is ...

  A = πd²

Then the diameter for the given area is ...

  10 m² = πd²

  (10/π) m² = d² . . . . . divide by π

  √(10 m²/π) = d ≈ 1.78412 m . . . . . . diameter of the largest sphere

The volume of a sphere is given by ...

  V = 4/3πr³ = (π/6)d³

For the diameter found above, the volume of the sphere will be ...

  V = (π/6)(1.78412 m)³ ≈ 2.97354 m³

There are 1000 liters in a cubic meter, so the largest amount of water that can be contained is ...

  2.97354 m³ × (1000 L/m³) = 2973.54 L

The largest amount of water the container can hold is about 2973.5 liters.

Answer: Correct me if I am wrong, but this is how I think you should solve it.

Step-by-step explanation:

1. Simplify 8×5 to 40.

−2×(40+9)−6×7

2. Simplify 40+9 to 49.

−2×49−6×7

3. Simplify −2×49 to −98.

−98−6×7

4. Simplify 6×7 to 42.

−98−42

5. Simplify

−140

Your all done! Hope this helps.

Answer:

Step-by-step explanation:

The problem is concerned with angles 4 and 5, which lie between the lines given as parallel. They are on opposite sides of the line cutting across those parallel lines (the transversal), so they are ...

__

Being congruent angles, their measures are ...

_____

Additional comment

For questions like this, there are many descriptions that are true. It would be helpful to know the possible answer choices.

Answer:

Step-by-step explanation:

1) Opposite angles in a parallelogram are congruent, so angle B measures 82 degrees.

2) Opposite sides of a parallelogram are congruent, so 12=6x. Hence, x=2.

3) Opposite sides of a parallelogram are congruent, so by the alternate interior angles theorem, the answer is 62 degrees.

Answer:

see explanation

Step-by-step explanation:

the opposite angles of a parallelogram are congruent , then

∠ B = ∠ D = 82°

the opposite sides of a parallelogram are parallel and congruent , then

AD = BC , that is

6x = 12 ( divide both sides by 6 )

x = 2

∠ BCA and ∠ DAC are alternate angles and are congruent , then

∠ BCA = ∠ DAC = 62°

Answer:

P(A) = 13/18

P(B) = 7/18

Step-by-step explanation:

A) Sum greater than 5

If the sum needs to be >5, then it can be 6, 7, 8, 9, 10, 11, and 12.

There are 26 out of 36 events where the sum is >5, thus P(A) = 26/36 = 13/18.

B) Sum divisible by 4 or 6

The sum ranges from 2 to 12, there are two methods to calculate this:

B1) Method 1: Calculate the frequency one by one

The sums divisible by 4 or 6 are S = {4, 6, 8, 12}. There are 9 of them, n(S) = 14. Thus P(B) = 14/36 = 7/18.

B2) Method 2: Use the rule of not mutually exclusive events

Not mutually exclusive events (might also be called mutually inclusive) happens when two events can happen together at the same time. In this problem, the sum might be divisible by 4 and 6 at the same time, i.e. the number 12.

The common formula for not mutually exclusive events is P(A∪B) = P(A) + P(B) - P(A∩B). Nb: P(A) isn't talking about the previous problem, nor does P(B) talk about the second section as a whole; the terms P(A) and P(B) will be utilized next, explained with their uses.

P(A) = probability of the sum being divisible by 4, i.e. the number 4, 8 and 12

P(A) = (3+5+1) / 36 = 9/36 = 1/4

P(B) = probability of the sum being divisible by 6, i.e. the number 6 and 12

P(B) = (5+1) / 36 = 6/36 = 1/6

P(A∩B) = probability of the sum being divisible both by 4 and 6, i.e. the number 12

P(A) = 1 / 36 = 1/36

Here comes the use of formula P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 1/4 + 1/6 - 1/36 = 7/18

Nb: As you can see, both method B1 and B2 give the same answer. Method B1 is usually easier to use when facing simpler problems like this. I'd recommend using method B2 for more complex and difficult questions, such as when you can't visualize the problem with a table because there are too much sets of variables.

Image of table for reference: https://qph.fs.quoracdn.net/main-qimg-1283a98bd649f522986e2f91a592ffd3

Answer:

Length: 18 inches

Width: 6 inches

Step-by-step explanation:

l+w=24

l=3w    w=1w

3w+w=24

       w=6

Length: 3*6=18 inches

Width: 6 inches

Answer:

2(a+b)

Step-by-step explanation:

Answer:

3x +18+4x+15=180

7x+33=180

7x=180-33

7x=147

7x÷7=147÷7

x=21

Answer:

[tex]\boxed{\bf x = {21}^{o} }[/tex]

Step-by-step explanation:

We know that the sum of angles of a linear pair is always equal to 180°, they are also known as supplementary angles.

«•••••••••••••••«»•••••••••••••••»

Answer:

Heyyyy!!

The answer is 66.9

please read the explanation... it will help... I promise

Step-by-step explanation:

Okay... Here we go...

The context mentions that the two quadrilaterals are similar... meaning their sides are proportional...

So... you basically have to find the scale factor...

(the math itself is easier than the explanation...

51/16 = 3.1875 (that is the number we multiplied the sides of quadrilateral FGHI to get quadrilateral JKLM...

so to get side JK all you have to do is multiply that scale factor by side FG... which after the use of a calculator results in 66.9 (i rounded, and used a calculator... lol)

but yeah... i hope this helps...

Answer:

The first job pays more

Step-by-step explanation:

950 x 3 = One month pay = 2,850

2,859 x 12 = One year = 34,308 Per Year

Comparing them both

$45,000 One Year, First Job

$34,308 One Year, Second Job

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

In this question we must determine the lengths of the three sides of the triangle by Pythagorean theorem and then the area is determined by Heron's formula.

First, we determine the length of each side:

[tex]RS = \sqrt{(6-3)^{2}+(2-4)^{2}}[/tex]

[tex]RS = \sqrt{3^{2}+(-2)^{2}}[/tex]

[tex]RS = \sqrt{13}[/tex]

[tex]ST = \sqrt{(7-6)^{2}+(10-2)^{2}}[/tex]

[tex]ST = \sqrt{1^{2}+8^{2}}[/tex]

[tex]ST = \sqrt{65}[/tex]

[tex]RT = \sqrt{(7-3)^{2}+(10-4)^{2}}[/tex]

[tex]RT = \sqrt{4^{2}+6^{2}}[/tex]

[tex]RT = \sqrt{80}[/tex]

Now we calculate the area of the triangle by Heron's formula:

[tex]s = \frac{\sqrt{13}+\sqrt{65}+ \sqrt{80}}{2}[/tex]

s ≈ 10.306

[tex]A = \sqrt{10.306 \cdot (10.306 - \sqrt{13})\cdot (10.306 - \sqrt{65})\cdot (10.306 - \sqrt{80})}[/tex]

A ≈ 14.525

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

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Answer:

hope this will help you (✿^‿^)

Step-by-step explanation:

by Pythagorean theorem

h²=p²+b²

12²=9²+b²

b²=12²-9²

b=√63

b=7.9372

Answer:

answer is a

Step-by-step explanation:

u just look at 6 and 6.60 thats 1 and 10 every eraser but for 3 its 1.30

The area of the smallest box that a circular pizza will fit into = 1661 squared cm.

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.

The circular pizza requires the same amount of dough as the square pizza.

Area of the square pizza =40 cm * 40 cm

                                         = 1600 [tex]cm^{2}[/tex].

Area of circle= [tex]\pi\; r^{2}[/tex]

        1600     = 3.14 *[tex]r^{2}[/tex]

         [tex]r^{2}[/tex] = 510

        r= 22.58

       r = 23 cm approx.

Area of circle= [tex]\pi\; r^{2}[/tex]

                     = [tex]3.14 * (23)^{2}[/tex]

                     = 1661.06 squared cm

The area of the smallest box that a circular pizza will fit into = 1661 squared cm.

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[tex]8.92 ~ \text{cm}^2\\\\=8.92 \times \left( 1 ~ \text{cm} \right)^2\\\\=8.92 \times \left(10^{-2}~ \text{m} \right)^2~~~~~~;\left[1~ \text{cm} = \dfrac{1}{100}~ \text m} = 10^{-2}~ \text{ m} \right]\\\\=8.92 \times 10^{-4}~ \text{m}^2\\\\=0.000892~ \text{m}^2[/tex]

Answer:

The mean is greater than median

Step-by-step explanation:

Option D

Expression 3200(1.06)^t represents the enrollment of a high school t years after 2000 will increase by 6%.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

The given expression is as follows:-

=  3200 ( 1.06 ) [tex],^t[/tex]

Here when the time has increased the percentage is also increased by 6%.

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Answer:

7 things an investor should consider when picking stocks:

Trends in earnings growth.

Company strength relative to its peers.

Debt-to-equity ratio in line with industry norms.

Price-earnings ratio as an indicator of valuation.

How the company treats dividends.Effectiveness of executive leadership.

Step-by-step explanation:

Answer:

The positive solution is 1/2

Step-by-step explanation:

(4x+3)(6x-3) = 0

We can use the zero product property to find the zeros

4x+3 =0   6x-3 =0

4x =-3          6x = 3

x = -3/4           x = 3/6

x = -3/4             x = 1/2

The positive solution is 1/2

Answer:

[tex]2\sqrt{61\pi }[/tex]

Step-by-step explanation:

Let's find c by using the Pythagorean Theorem: [tex]10^2 + 12^2 = c^2[/tex] so [tex]c = \sqrt{10^2 + 12^2}[/tex]. I'm going to leave c like this so it is easier to multiply by [tex]\sqrt{\pi }[/tex]. [tex]c\sqrt{\pi } = \sqrt{10^2 + 12^2}\sqrt{\pi } = 2\sqrt{61\pi }.[/tex]

Hope this helped! :)

Answer:

last option, x = -1

Step-by-step explanation:

[tex]x^{2} + 2x + 1 = 0\\x_{1} = \frac{-2 + \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{2} = \frac{-2 - \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{1} = \frac{-2 + \sqrt{0} }{2}\\x_{2} = \frac{-2 - \sqrt{0} }{2}\\x = \frac{-2}{2} \\x = -1[/tex]

The value of x by using the Quadratic Formula is,

⇒ x = - 1

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Equation is,

⇒ x² + 2x + 1

Now, We can use the Quadratic Formula for x as;

⇒ x² + 2x + 1

⇒ x = - 2 ± √2² - 4×1×1 / 2

⇒ x = - 2 ± √4 - 4 / 2

⇒ x = - 2 / 2

⇒ x = - 1

Thus, The value of x by using the Quadratic Formula is,

⇒ x = - 1

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Answer:

m = 60

Step-by-step explanation:

log is another way to write an exponent.

Example:

exponent form:

7^2 = 49

log form:

log_7 (49) = 2



In your question, we need to change to exponent form, from log form.

log_5 (2m+5)=3

5 is the base. 3 is the exponent.

Now it can be solved.

5^3 = 2m+5

125 = 2m + 5

120 = 2m

60 = m

Find Q

Not safe

Apply Pythagorean theorem

PR²=4²+15²=16+225=241

Answer:

a) not safe

b) 15.5 ft (nearest tenth)

Step-by-step explanation:

Tan trig ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the given values into the formula and solving for x:

[tex]\implies \sf \tan(x)=\dfrac{4}{15}[/tex]

[tex]\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)[/tex]

[tex]\implies \sf x=14.9^{\circ}\:(nearest\:tenth)[/tex]

As 14.9° is not between 18° and 27°, the roof is not safe.

-------------------------------------------------------------------------------------------------

Pythagoras’ Theorem

[tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting the given values into the formula and solving for PR:

[tex]\implies \sf 15^2+4^2=PR^2[/tex]

[tex]\implies \sf 225+16=PR^2[/tex]

[tex]\implies \sf PR^2=241[/tex]

[tex]\implies \sf PR=\sqrt{241}[/tex]

[tex]\implies \sf PR=15.5\:ft\:(nearest\:tenth)[/tex]

Answer:

it should be C I did something very very similar to this but different questions

Answer:

 a) {-6, 2}

 b) -12

 c) minimum: -16

Step-by-step explanation:

I find a graphing calculator to be a big help. Its graph is attached.

a) The function can be factored as:

 f(x) = (x -2)(x +6)

The factors are zero at the x-intercepts: x = 2, x = -6.

b) The y-intercept is the function value when x=0. That is the constant in the function. The y-intercept is -12.

c) The leading coefficient of the function is positive, so its graph opens upward. The extreme value is a minimum. It is found on the axis of symmetry, at the x-value that is halfway between the x-intercepts: x = (2-6)/2 = -2. The function value there is ...

f(-2) = (-2-2)(-2+6) = -4(4) = -16

The minimum is f(-2) = -16.

Answer:

"quotient" indicates division

999 ÷ c = ?

Answer:

[tex]\frac{93458}{19435}[/tex] ≈ 4.81

Step-by-step explanation:

[tex]\frac{93458}{19435}[/tex] can not be simplified