Eastern Manufacturing is involved with several situations that possibly involve contingencies. Each is described below. Eastern’s fiscal year ends December 31, and the 2024 financial statements are issued on March 15, 2025.

Step-by-step explanation:

so, this sounds like the blimp is located between the stadium and the planetarium.

we have a triangle :

the ground distance between the stadium and the planetarium is the baseline.

and the 2 lines of sight from the blimp on one side to the stadium and on the other side to the planetarium are the 2 legs.

we know the height of this triangle is 600 ft.

the angle of depression down to the stadium is 37°. which makes the inner triangle angle at the ground point at the stadium also 37°.

and the angle of depression down to the planetarium is 29°. which makes the inner triangle angle at the ground point at the planetarium also 29°.

and because the sum of all angles in a triangle is always 180°, we know the angle at the blimp is

180 - 37 - 29 = 114°

in order to solve this triangle, we need to split it into 2 right-angled triangles by using the height of the main triangle as delimiter.

we get a stadium side and a planetarium side triangle.

the baselines (Hypotenuses) of the 2 triangles are the corresponding lines of sight from the blimp.

the height of the large triangle is also a height and a leg in each small triangle.

and the stadium side part of the large baseline (between ground point and intersection with the height) is the second leg for the stadium side triangle.

and correspondingly, the planetarium side part of the large baseline (between ground point and intersection with the height) is the second leg for the planetarium side triangle.

the inner blimp angle of the stadium side triangle is

180 - 37 - 90 = 53°

and the inner blimp angle of the planetarium side triangle is

180 - 29 - 90 = 61°

now we can use the law of sine to get the lengths of the 2 parts of the baseline of the large triangle.

and when we add these 2 numbers we get the distance between stadium and planetarium.

law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being opposite of the associated angles.

for the stadium side triangle we get

part1/sin(53) = 600/sin(37)

part1 = 600×sin(53)/sin(37) = 796.226893... ft

for the planetarium side triangle we get

part2/sin(61) = 600/sin(29)

part2 = 600×sin(61)/sin(29) = 1,082.428653... ft

the distance between the stadium and the planetarium is

part1 + part2 = 1,878.655546... ft

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

There are a total of 25 marbles in the bag.

The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.

Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.

The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.

To find the probability of both events occurring together, we multiply their individual probabilities:

8/25 x 1/8 = 1/25

Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.

Answer:

Is there any answer choices? If not I would think its 5$

                                                                                      5$

                                                                                      4$

Step-by-step explanation:

Answer:

\(16\sqrt{2}\)

Step-by-step explanation:

The given triangle shown is a 45-45-90. We can use this picture attached to figure out BC.

n in this case is 16ft

Based on the picture, we can get BC's length, which is n\(\sqrt{2}\)

BC = \(16\sqrt{2}\)

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Answer:

creature

Step-by-step explanation:

it's definitely creature

Answer:

Hello! answer: u = 17

Step-by-step explanation:

answer is 17 because... 17 × 2 = 34 and 34 - 9 = 25 Hope that helps!

Answer:

u=17

Step-by-step explanation:

2u-9=25

2u=34

u=17

Answer:

each friend gets 200 books

Step-by-step explanation:

1,000÷5=200

The volume of the solid that lies within the sphere x² + y² + z² = 16 above the xy plane is (64√2π)/3   .

In the question ,

it is given that ,

the equation of the sphere is x² + y² + z² = 16 ;

and the equation of the cone is z = √(x² + y²) ;

In the spherical coordinate , the required solid ;

= {(ρ , φ , θ) ; 0 ≤ ρ ≤ 4 ; π/4 ≤ φ ≤ π/2 ; 0 ≤ θ ≤ 2π }

Volume of the sphere can be written by the interval :

Volume = \(\int\limits^{\pi/2 }_{\pi /4} \int\limits^{2\pi }_0 \int\limits^4_0 \(\rho\)^{2} sin\varphi .d\(\rho\).d\varphi .d\theta\)

Volume = \(\int\limits^{\pi/2 }_{\pi /4} \int\limits^{2\pi }_0 [\frac{p^{3} }{3}]^{4}_{0} .sin\varphi .d\(\rho\).d\varphi .d\theta\)

Simplifying further ,

we get ;

= (64/3)×(-0 + 1/√2)×(2π)

= (64√2π)/3

Therefore , the Volume of the Solid is (64√2π)/3  .

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Step-by-step explanation:

x²+2x+1

x²+x+x+1

x(x+1)1(x+1).

(x+1)(x+1)

x=-1. , x=-1

Answer:

\(\displaystyle \boxed{\text{\sf \Large x=-1}}\)

Step-by-step explanation:

Add 1 to both sides

\(x^2+2x+1=0\)

Use quadratic formula with a=1, b=2, c=1

\(\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}\)

\(\displaystyle x= \frac{-(2) \pm \sqrt{(2)^2-4(1)(1)} }{2(1)}=-1\)

Awnser would be family a

Answer:

$ 6.20 Cents

Step-by-step explanation:

17 - 5.50= 11.5

11.50 - 5.30= 6.2

Add A Zero at the end

You Get 6.20

the CPI to the nearest tenth in 1950 was 24.06.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, a bottle of dishwashing detergent cost $0.31 in 1950 and In 1970, a bottle of dishwashing detergent cost $0.50

Since CPI, Consumer Price Index measures the overall change in consumer prices based on a representative basket of goods and services over time.

The price of dishwashing detergent increased at the same rate as the CPI from 1950 to 1970.

So,

0.50 / 0.31 = CpI for 1970/ CPI for 1950

Since CPI in 1970 is 38.80

CPI in 1950 = 0.62 * 38.80

CPI in 1950 = 24.056

Therefore,  the CPI to the nearest tenth in 1950 was 24.06.

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Complete question:

In 1970, a bottle of dishwashing detergent cost $0.50. To answer each of the parts below, assume that the consumer price index (CPI) was 29.6 in 1960, 38.8 in 1970, and 82.4 in 1980.

If the price of dishwashing detergent increased at the same rate as the CPI from 1970 to 1980, how much did a bottle of dishwashing detergent cost in 1980? By how much did the price of a bottle of dishwashing detergent increase from 1970 to 1980?

Symmetry means,  hmmm usually a mirror image.

So when something is symmetry to another, is a way to say, one is the mirror image of the other, or namely they're just identical twins.

Now, if know that B is the midpoint, by definition is cutting AC into two equal halves, so AB is the mirror image of BC, so they're identical twins, there are no flaws, Q.E.D.

Check the picture below.

The Venn Diagram for these given sets is graphed at the end of the answer.

A Venn Diagram uses circles to show if elements belong to one set, or multiple sets, in the intersection.

For this problem, we have that:

The Venn Diagram showing this is inserted at the end of the answer. There are a two erasers marks because of typing mistakes on my part.

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Answer:

Step-by-step explanation:

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

Answer:

20 for both

Step-by-step explanation:

hope this helps

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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Answer:

0.0909

Step-by-step explanation:

4 blue + 5 red + 3 black = 12 chips in total.

p=probability

1st draw:

p (blue) = 4/12

there are now 11 chips in the bag, 4-1 =3 are blue.

2nd draw?

p (blue) = 3/11

probability of pulling one blue chip followed by another blue chip is:

(4/12) X (3/11) = (4X3)/12X11)

= (12)/(132)

= 1/11

0.0909

Answer:

Step-by-step explanation:

Given ΔABC and ΔADB, since both triangles are right angled triangles then the following are true.

From ΔADB, AB² = AD²+BD²

Given AB = 24 and AD = 16

BD² = AB² - AD²

BD² = 24²-16²

BD² = 576-256

BD² = 320

BD = \(\sqrt{320}\)

BD = 17.9

from ΔABC, AC² = AB²+BC²

SInce AC = AD+DC and BC² = BD² + DC² (from ΔBDC )we will have;

(AD+DC)² = AB²+ (BD² + DC²)

Given AD = 16, AB = 24 and BD = 17.9, on substituting

(16+DC)² = 24²+17.9²+ DC²

256+32DC+DC² =  24²+17.9²+ DC²

256+32DC = 24²+17.9²

32DC = 24²+17.9² - 256

32DC = 640.41

DC = \(\frac{640.41}{32}\)

DC = 20.01

Remember that AC = AD+DC

AC = 16+20.01

AC = 36.01

Answer:

x = 3.4

Step-by-step explanation:

Step 1: Isolate x

0.5x = 1.7

Step 2: Divide both sides by 0.5

x = 3.4

And we have our final answer!

Answer: x=3.4

Step-by-step explanation:

\(0.5x+4.2=5.9\)

multiply both sides by 10

\(5x+42=59\)

subtract 42 on both sides

\(5x=17\)

divide 5 on both sides

\(x=\frac{17}{5}\) or

Simplify

x= 3.4

The geometric center of the graph under the function is 5/3

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

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The value of x is 3 and  -3 respectively.

Given that;

From equation (1)

4x+60 < 72  

First, collect like terms

4x < 72 - 60

subtract like terms

4x < 12

Make 'x' the subject

x < 12/ 4

x < 3

For equation (2)

14x +11 <-31

collect like terms

14x < -31 - 11

14x < -42

Make 'x' the subject

x < -42/ 14

x < -3

Thus. the value of x is 3 and  -3 respectively.

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Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

Transversion is known as point mutation in DNA.

Transversion is a term used in molecular biology. It refers to a point mutation in DNA in which a single (two ring) purine (A or G) is changed for a (one ring) pyrimidine (T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ionizing radiation or alkylating agents. It can only be reversed by a spontaneous reversion.

So, here 5'AGCCTAC3' we can replace (A or G) with (T or C)

So, the answer should be :

5'ATCCTAC3'

Here we have replaced G with T and other things are same

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The full question will be like this

Assume that a wild-type sequence is 5'AGCCTAC3'. Indicate the sequence that might be produced by a transversion. Which of the following sequences might be produced by a transversion?

A) 5'AGTCTAC3'

B) 5'AGCCGCCGCCGCCTAC3'

C) 5'AGCCCAC3'

D) 5'ATCCTAC3'

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Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.