the national debt is $22,000,000,000,000 and the population is 280,000,000. what is the amount of debt per person?

Step-by-step explanation:

\(y = 3 \csc( \frac{x}{5} ) \)

\( \frac{y}{3} = \csc( \frac{x}{5} ) \)

Multiply by 5 on both sides.

\(5 \times \frac{y}{3} = \csc(x) \)

Take the inverse of cosecant or arccsc of the function.

\(5 \: arccsc( \frac{y}{3}) = x\)

The trigonometric equation for​ x, where x is restricted to the given interval is x = 5 * arccsc(y/5)

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given

y = 3 CSC(x/5) for x in given domain

y/ 3 = CSC  (x/5)

CSC(x/5) = y/3

x/5 = arccsc(y/3)

x =  5* arccsc(y/3)

Therefore, "x = 5 * arccsc(y/5)" is the trigonometric formula when x is limited to the specified range.

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Let p be the amount of sales (in dollars) of phones.

Let c be the amount of sales (in dollars) of computers.

Equation 1: sales

    p + c = 2100

the amount of all sales is 2100

Equation 2: commission

   0.05p + 0.07c = 119

5% commission on phones plus 7% commission on computers totals to 119

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

Step-by-step explanation:

As,

In a constant term the power of the variable is zero, so it's degree is 0.

Eg:

\(4 {a}^{0} \)

Since,

\( {x}^{0} = 1\)

Hence,

4 × 1 = 4

Here, The value remains unchanged hence it is the constant variable.

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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On solving the provided question we can say that Manny would thus require 160 yards of fencing to surround the rectangular plot.

A boundary is a closed route that embraces, encircles, or delimits a two-dimensional form or length in one dimension. The perimeter of a circle or an ellipse is its outermost section. The perimeter calculation is used in a variety of real-world situations. The perimeter of a form is the radius of its edge. Discover how to calculate the perimeter by adding the lengths of the sides of various shapes. The perimeter of a shape may always be calculated by multiplying the lengths of its sides. The perimeter of a thing is the region that surrounds it. At your house, one example is an enclosed garden. The distance around anything is referred to as its perimeter. A 200-foot fence will be required for a 50-foot-by-50-foot yard.

P = 2(l + w), where l is the length and w is the width, gives the perimeter of a rectangle.

The length in this example is 35 yards, while the breadth is 45 yards. So,

\(P = 2(35 + 45)\\= 2(80)\\= 160 yards\\\)

Manny would thus require 160 yards of fencing to surround the rectangular plot.

As a result, option (b) 160 yards is the right answer.

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The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2

To solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:

8x²(x² - 4) = 0

Now we can use the difference of squares identity to factor the quadratic expression:

8x²(x + 2)(x - 2) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

8x² = 0 or x + 2 = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = -2 or x = 2

So the solution set for the equation is {0, -2, 2}.

To check the solution, we can substitute each value into the original equation and verify that it equals zero.

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Step-by-step explanation:

Start at -3    then begin adding 3's to get the next terms

-3   0    3    6    9  .....

Answer:

$600

Step-by-step explanation:

\(20\% \: of \: 750 \: is = \)

\( \frac{20}{100} \times 750\)

\( = 150\)

Subtract 150 from 750 to get discount price

\(750 - 150 \\ = 600\)

Therefore, the discount price is $600

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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Answer:

the gram

Step-by-step explanation:

casegunnell is my gram, follow if your a real g

Following are the calculation to the given points:

When the ABCD is parallelogram:

The properties of parallelogram:

\(\to \angle CBD = \angle ADB \\\\\)

\(\to \angle BCA = \angle DAC \\\\\)

When the Two-lines are parallel and alternate interior angles are equal:

\(\to \Delta BEC \cong \Delta AED \ \ \ \ \ \ \ \{ASA\} \\\\\to \overline {AE} \cong \overline{CE}\\\\ \to \overline{BE} \cong \overline{ED} \\\\\)

When the properties of congruent triangle.

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Answer:

Step-by-step explanation:

hours work restaurant - "r"

hours work yard - "y"

r + y \(\leq\) 15

r \(\geq\) 5

8r + 12y = 120 : (4) -----> 2r + 3y = 30

r = \(\frac{30 - 3y}{2}\)

\(\frac{30 - 3y}{2}\) \(\geq\) 5

30 - 3y ≥ 10

3y \(\leq\) 20

y ≤ 20/3

Answer:

it is 2^21

Step-by-step explanation:

Answer:

2^21

Step-by-step explanation:

add 3 and 18 together

dont change 2

Answer:

About 316,955 people

Step-by-step explanation:

The population of this city can be modeled with the formula \(P=I\cdot(1.05^t)\), where P represents the current population, I represents the initial population, and t represents the amount of time in years since the start of the model. Plugging in 145,201 for I and (2037-2021)=16 for t, we get:

\(P=145201\cdot(1.05)^{16}\approx145201\cdot2.18\approx 316955\)

Initial population=145,201

Total years=2037-2001=36

\(\\ \sf\longmapsto S=P\left(1+\dfrac{r}{100}\right)^t\)

\(\\ \sf\longmapsto S=145201\left(1+\dfrac{5}{100}\right)^{36}\)

\(\\ \sf\longmapsto S=145201\left(\dfrac{105}{100}\right)^{36}\)

\(\\ \sf\longmapsto S=145201(1.05)^{16}\)

\(\\ \sf\longmapsto S=145201(2.18)\)

\(\\ \sf\longmapsto S\approx 316955\)

Done

Answer:

$4.56

Step-by-step explanation:

2.85:5

multiply each side by 8/5

4.56:8

so it is $4.56 for 8 cookies

D i.e. {C, T, U, -, *} is the minimal complete set of relational algebra operations.

What is relational algebra?

Relational Algebra is a query language that takes a Relation as input and returns another Relation as output. Relational algebra provides the theoretical basis for relational databases and SQL. The necessary column data for a relation is projected via projection.

Now,

As Five basic operations in relational algebra are : Selection, Projection, Cartesian product, Union, and Set Difference and all these are present in

{C, T, U, -, *}.

Hence,

            D i.e. {C, T, U, -, *} is the minimal complete set of relational algebra operations.

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Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

The value of k = 2 by solving the given equation after substituting the values of f(x) and g(x).

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. Different types of equations includes linear, quadratic, cubic and others.

The given equation is:

g(x) = f(x) + k

Substitute f(x) = |x| + 3 and  g(x) = |x| + 5 in the above equation:

|x| + 5 = |x| + 3+ k

Substracting |x| from both sides gives:

5 = 3 + k

Substracting 3 from both sides gives:

2 = k

Therefore the value of k = 2.

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Answer:

12345824.4

Step-by-step explanation:

I'm not really sure. I just did 1240x637x15.63=12345824.4

answer:

53,445.1 gallons of water

Step-by-step explanation:

im not exactly sure but i looked up how to calculate gallons in a container and the website i went to told me to measure the interior length, width, and height which was already done, then it told me to multiply the length by width by height to get the volume of the container then it told me to divide the volume by 231 to get the number of gallons in the container, so 1,240* 637= 789,880* 15.63= 12,345,824.4÷231= 53,445.127272727272727272727272727 which rounded to the nearest tenth is 53,445.1, i honestly hope that this is right and that it helps

We know that

• She bought 13 packs of red rings.

• She bought 16 packs of yellow rings.

• She bought 14 packs of green rings.

• Each pack has 12 rings.

This problem is about multiplication, notice that each pack includes 12 rings, that means we need to multiply each pack by 12, in order to find the total number of rings of each color.

There are 156 red rings.

There are 192 yellow rings.

There are 168 green rings.

Now, we sum all these numbers to find the total

Answer:

  f(g(2)) = 51

Step-by-step explanation:

The expression f(g(2)) means you are to use g(2) as the argument for the function f(x).

__

The value of a function is found by substituting the argument value in the defining expression, then simplifying the result.

Here, we do that in steps, working outward from the innermost parentheses, as required by the Order of Operations.

  g(2) = 7(2^2) = 7·4 = 28 . . . . . put 2 where x is in g(x) = 7x^2, evaluate

  f(g(2)) = f(28) = 2(28) -5 = 56 -5 = 51 . . . . . . put 28 where x is in f(x) = 2x -5

  f(g(2)) = 51

_____

Many graphing calculators will let you define functions. You can use the calculator to compute the value for you. A spreadsheet can do the same thing.

Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

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The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer: Adams heart Beats 1,440 more times than Blake’s in 120 minutes.

Step-by-step explanation:

Adam: 74 x 120 = 8,880

Blake: 62 x 120 = 7,440

8,880 - 7,440 = 1,440

Answer:

1440

Step-by-step explanation: you multiply

74 x 120 and 62 x 120

8,880             7,440 then subtract the two

8,880 - 7,740 = 1,440

Step-by-step explanation:

the rink is a combination of a rectangle and 2 half-circles.

so, we need the areas of the rectangle and a full circle and add these 2 values.

the survivability is a little bit unclear. are the 9 ft the length of the arrow, or the whole width of the area ?

let's assume it is the first.

then the 9ft are the radius of the half-circles, and the width of the ice area is then the diameter of the circles and therefore twice the radius. 2×9 = 18ft.

the rectangle is simple :

Ar = 36×18 = 648 ft²

the formula for the area of a circle is

Ac = pi×r² = pi×9² = pi×81 = 254.4690049...ft²

this is rounded 254.5 ft²

as total area we have

648 + 254.5 = 902.5 ft²

Answer:

answer 4

Step-by-step explanation:

Answer:

x = 112, y = 68, z = 112

Step-by-step explanation:

y = 68

x = z = 180 - 68 = 112

Answer:

Sixteen

Step-by-step explanation:

My birthday was on Saturday and I turned 21 bro I hope you good

Answer:The present worth of the project for Bronson Building Inc is $6,389,137.

In order to calculate the present worth, follow these steps:

1. The given information is:

Initial cost (first cost) = $18,000,000

Annual revenue = $5,000,000

Annual expenses = $2,000,000

Net annual cash flow = Annual revenue - Annual expenses = $5,000,000 - $2,000,000 = $3,000,000

MARR = 11%

Project duration = 18 years

Sale price at the end of the project = $8,000,000

2. To calculate the present worth, we first need to find the present value of the net annual cash flows using the MARR as the discount rate. Then, we will add the present value of the sale price and subtract the initial cost.

Present value of net annual cash flows (PV_ACF) = Net annual cash flow * [(1 - (1 + MARR)^(-duration)) / MARR]

PV_ACF = $3,000,000 * [(1 - (1 + 0.11)^(-18)) / 0.11] = $3,000,000 * 7.696 = $23,088,000

3. Find the present value of the sale price at the end of the project.

Present value of sale price (PV_SP) = Sale price / (1 + MARR)^duration

PV_SP = $8,000,000 / (1 + 0.11)^18 = $8,000,000 / 6.146 = $1,301,137

4. Calculate the present worth of the project.

Present worth = PV_ACF + PV_SP - Initial cost

Present worth = $23,088,000 + $1,301,137 - $18,000,000 = $6,389,137

Step-by-step explanation: