Find the exact value of cot theta if csc theta = -4/3 and the terminal side of theta lies in Quadrant III.

Question is Incomplete; Complete question is given below;

3 rectangular prisms have a combined volume of 518 cubic feet. Prism A has 1/3 the volume of Prism B. Prisms B and C have equal volume.What is the volume. What is the volume of each prism.

Answer:

Volume of prism A is [tex]74\ ft^3[/tex] and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].

Step-by-step explanation:

Let the Volume of 3 prism be A,B,C.

Now Given:

3 rectangular prisms have a combined volume of 518 cubic feet.

so we can say that;

[tex]A+B+C=518 \ ft^3 \ \ \ \ equation \ 1[/tex]

Also Given:

Prisms B and C have equal volume.

[tex]B = C[/tex]

Also given:

Prism A has 1/3 the volume of Prism B.

so we can say that;

[tex]A=\frac{B}{3} = \frac{C}{3}\\\\B=C=3A[/tex]

Now Substituting the value of B and C in equation 1 we get;

[tex]A+B+C=518\\\\A+3A+3A=518\\\\7A=518[/tex]

Dividing both side by 7 we get;

[tex]\frac{7A}{7}=\frac{518}{7}\\\\A= 74 \ ft^3[/tex]

Now Substituting the value of A to find B and C we get;

[tex]B=C=3A=3\times74=222\ ft^3[/tex]

Hence Volume of prism A is [tex]74\ ft^3[/tex]  and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].

Answer:

Step-by-step explanation:

DE*s=BA  24*s=35 s=35/24

(3x+7)35/24=6x-5

35/8x+5/24=6x-5

          -5/24    -5/24

Answer:

d) Clothing prices decline because manufacturers shift to production in countries with lower wages.

Step-by-step explanation:

Demand is the quantity of goods or services consumers are able and willing and able to buy at a given price and at a particular time.

Movement along the demand curve also known as change in quantity demanded is an increase or decrease in the quantity demanded of goods or services due to change in the price of the good or service itself.

It is important to note that the only factor causing movement along the demand curve is change in the price of the product.

Answer:

a. contrapositive because it's the converse and inverse. True.

b. converse because it's the reverse of conditional statement. True.

c. That is false so it's not converse, inverse, or contrapositive.

The given statement is: If two angles form a linear pair, then they are supplementary. The inverse is true, the converse is false, and the contrapositive is true.

The given statement is: If two angles form a linear pair, then they are supplementary. Let's analyze the options:

a. If two angles are not supplementary, then they do not form a linear pair. This is the inverse of the given statement. It is true because if two angles do not add up to 180 degrees, they cannot form a linear pair.

b. If two angles are supplementary, then they form a linear pair. This is the converse of the given statement. It is false because two supplementary angles may or may not form a linear pair.

c. If two angles do not form a linear pair, then they are supplementary. This is the contrapositive of the given statement. It is true because if angles do not form a linear pair, that means they do not add up to 180 degrees, and hence, they must be supplementary.

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Answer:

Kim and Lauren have 5 more hours to reach Pennsylvania.

Step-by-step explanation:

Given,

Total distance = 680 miles

We have to find the number of hours taken by them to reach Pennsylvania.

Solution,

For Day 1:

Speed = [tex]60\ mi/h[/tex]

Time = 3 hrs

We know that the distance is equal to speed multiplied with time.

So the equation is;

[tex]Distance = 60\times3=180\ miles[/tex]

For Day 2:

Speed = [tex]65\ mi/h[/tex]

Time = 5 hrs

We know that the distance is equal to speed multiplied with time.

So the equation is;

[tex]Distance = 65\times5=325\ miles[/tex]

Now the total distance traveled in two  days is the sum of distance traveled in day 1 and distance traveled in day 2.

Distance traveled in 2 days = [tex]180+325=505\ miles[/tex]

So the remaining distance they have to travel is equal to total distance minus distance traveled in 2 days.

Remaining distance =[tex]680-505=175\ miles[/tex]

Now also given that the speed on day 3 is [tex]35\ mi/h[/tex].

So the time taken to cover the distance is equal to distance divided by speed.

[tex]\therefore time=\frac{175}{35}=5\ hours[/tex]

Hence Kim and Lauren have 5 more hours to reach Pennsylvania.

Answer:

The difference between the number of pages that Darla and Juan read are VI pages.

Step-by-step explanation:

Given:

Darla told her teacher that she had read XLV pages in her library book.

Juan said that he had read XXXIX pages.

Now, to get the difference between the number of pages that Darla read and Juan read.

As, we see the number of pages are in roman numeral symbols.

So, we convert them in numbers first to calculate:

Darla read = XLV pages.

Darla read = 45 pages.

Now,

Juan read = XXXIX pages.

Juan read = 39 pages.

So, to get the difference between the number of pages by subtracting:

[tex]45-39=6[/tex]

Thus, the difference between the number of pages = 6 pages.

Now, converting it into roman numerals:

6 pages = VI pages.

Therefore, the difference between the number of pages that Darla and Juan read are VI pages.

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

To solve this question I would use the sin rule.

The sin rule states that

[tex] \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) } [/tex]

Therefore if you substitute in your numbers you get:

[tex] \frac{a}{ \sin(90) } = \frac{15}{ \sin(60) } [/tex]

If you rearrange that you get:

[tex]a = \frac{15}{ \sin(60) } \times \sin(90) [/tex]

Therefore a = 17.3 Inches (to 3 sf)

This can also be done with basic trigonometry where you would get

[tex] \sin(60) = \frac{15}{h} [/tex]

Rearranging to

[tex]h = \frac{15}{ \sin(60) } [/tex]

meaning the answer is 13.7 inches

================================================

Work Shown:

h = unknown hypotenuse

sin(angle) = opposite/hypotenuse

sin(60) = 15/h

h*sin(60) = 15

h*sqrt(3)/2 = 15

h*sqrt(3) = 2*15

h*sqrt(3) = 30

h = 30/sqrt(3)

h = (30*sqrt(3))/(sqrt(3)*sqrt(3)

h = 30*sqrt(3)/3

h = (30/3)*sqrt(3)

h = 10*sqrt(3)

Answer:

[tex]Down\ payment = 7,344[/tex]

Step-by-step explanation:

Let x be the amount of 15% of gross income.

Given:

Jessica gross income = 48,960.00

She decided to use 15% amount as down payment.

We need to find the amount of 15% of gross income.

Solution:

Using percentage formula.

[tex]percentage = (\frac{Value}{Total\ value})\times 100[/tex]

Now we substitute 15 in the place of percentage and 48,960 in the place of Total value.

[tex]15=(\frac{x}{48960})\times 100[/tex]

Now, we apply cross multiplication rule.

[tex]x= \frac{48960\times 15}{100}[/tex]

[tex]x=48960\times 0.15[/tex]

[tex]x =7,344[/tex]

Therefore: Down payment is 7,344.

Final answer:

Jessica allocated $7,344 for the down payment on a house based on her 15% gross income allocation.

Explanation:

The budget that Jessica allocated for her down payment on a house is calculated as follows:

Calculate 15% of Jessica's gross income: 15% of $48,960 is $48,960 * 0.15 = $7,344.

Therefore, the budget that Jessica allowed for the down payment on a house is $7,344.

Step-by-step explanation:

Circumference of a circle = πD, where D is the diameter.

Diameter of circle 1 = 1.125

Circumference of circle 1 = π x 1.125

Diameter of circle 1 = 2.25

Circumference of circle 1 = π x 2.25

[tex]\texttt{Ratio of circumferences = }\frac{\pi \times 1.125}{\pi \times 2.25}\\\\\texttt{Ratio of circumferences = }\frac{1}{2}[/tex]

Circumference of circle 1 : Circumference of circle 2 = 1 : 2

Answer:

1:1

Step-by-step explanation:

Answer:length = 11 feet

Width = 5 feet

Step-by-step explanation:

Let L represent the length of the rectangular box.

Let W represent the width of the rectangular box.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The length of the batter's box on a softball field is 1 ft more than twice the width. It means that

L = 2W + 1

The areas of the batter's box is 55 ft^2. It means that

LW = 55

Substituting L = 2W + 1 into LW = 55, it becomes

W(2W + 1 ) = 55

2W² + W = 55

2W² + W - 55 = 0

2W² + 11W - 10W - 55 = 0

W(2W + 11) - 5(2W + 11) = 0

(W - 5) = 0 or 2W + 11 = 0

W = 5 or W = - 11/2

The width cannot be negative, hence, it is 5 ft

L = 2W + 1 = 2 × 5 + 1 = 10 + 1

L = 11 feet

Answer:

The answer to your question is picture 1

Step-by-step explanation:

- This is a quadratic equation, so we look for a parabola. The four graphs show parabolas.

- We can notice a negative sign before the term (x - 3)², which indicates that it is a down-parabola. We discard the second and the fourth pictures.

- Get the vertex

                         y = -(x - 3)² - 5

                         y + 5 = - (x - 3)²      Vertex = (-5, 3)  

                                                         because we change signs

- With all this information, we conclude that the answer is picture 1 because its vertex is (-5, 3)

Answer: 0.383 and 0.6671

Step-by-step explanation:

Take 22%, that is 0.22 to be probability of success.

That means "1-0.22 = 0.78" is the probability of failure.

When dealing with selection in probability mathematics, the combination equation is used.

Probability of selecting number 'r' as a successful outcome from a given number 'n' is given as

nCr * p^r * q^n-r

Where p is the probability of success= 0.22

q is the probability of failure= 0.78

n is the total number of sample =10

r is the varying outcome of number of success.

For the first question, number of success is asked to be everything more than 2, that is probability of choosing 3,4,5,6,7,8,9,10 people with a successful outcome (adults who will pay more for environmentally friendly product.)

Instead of going through the long process of checking probability of success for choosing 3,4,5,6,7,8,9,10 adults who will pay more, we can simply find the probability of choosing 0,1,2 adults who will pay more and subtract the answer from 1.

By doing this, we first check for probability of choosing 0 adult that will pay More and this is gotten by putting r=0 in our probability Formula. The Formula becomes

=10C0 * 0.22^0 * 0.78^10

=1 *1 * 0.0834= 0.0834

Hence, Probability of Choosing 0 adult that will Pay more is 0.0834

To Check for probability of choosing 1 adult that will pay more becomes

=10C1 * 0.22^1 * 0.78^9

=10 * 0.22 * 0.1069 = 0.2352

Hence, Probability of choosing 1adult that will pay more = 0.2352

To Check for the probability of choosing 2adults that will pay more becomes

=10C2 * 0.22^2 * 0.78^8

=45 * 0.0484 * 0.1370 = 0.2984

Therefore the total sum of choosing 0,1,2 adults that are willing to pay more becomes

= 0.0834+ 0.2352+ 0.2984 = 0.617

So to determine the probability of choosing more than 2 adults, that is, 3,4,5,6,7,8,9,10 adults that are willing to pay more, we subtract 0.617 from 1.

This gives 1-0.617 = 0.383

Hence, probability of choosing more than 2 people that are willing to pay more than 2 = 0.383.

To determine the probability of choosing between two and five people inclusive, we follow the same probability formular but r becomes 2,3,4,5 differently.

For probability of choosing 2 adults, we already calculated it to be 0.2984 earlier.

For probability of choosing 3 adults, it becomes

10C3 * 0.22^3 * 0.78^7

=120* 0.0106 * 0.1757 = 0.2235

For the probability of choosign 4 adults, it becomes

10C4 * 0.22^4 * 0.78^6

= 210 * 0.0023 * 0.2252 = 0.1088

For the probability of choosing 5 adults, it becomes

10C5 * 0.22^5 * 0.78^5

= 252 * 0.0005 * 0.2887 = 0.0364

Hence, the probability of choosing between 2 and 5 adults becomes

0.2984 + 0.2235 + 0.1088 + 0.0364 = 0.6671

To find the probability of the number of adults who would pay more for environmentally friendly products, use the binomial probability formula.

To find the probability of the number of adults who would pay more for environmentally friendly products, we need to use the binomial probability formula.

The formula is: P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where:

Let's calculate the probabilities for the given scenario:

P(X > 2) = 1 - P(X <= 2)

P(X between 2 and 5 inclusive) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Answer: A) Stratified random sampling

Step-by-step explanation:

Since , the researchers divided college students into the four classes (freshman, sophomore, junior, and senior) and then took a random sample of students from each class.

That means each category is participating in the sample.

It means , they used stratified sampling method where each class denotes a strata.

Here ,  each category participates in researcher's analysis.

Hence, the correct answer is A) Stratified random sampling .

Answer:

1,440,000 cubic feet

Step-by-step explanation:

Proportions

We are told that 90% of the volume of an iceberg is below water. It means that 10% is above water. The proportion between the sunk/floating volumes is 90/10=9. The underwater volume of the iceberg is 9 times the above water volume. Thus, the volume of the iceberg below water is 9*160,000 = [tex]\boxed{1,440,000\ cubic feet}[/tex]

The volume of the iceberg below water is 1,440,000 cubic feet.

To determine the volume of the iceberg below the water's surface, we can use the fact that 90% of the iceberg's total volume is submerged underwater.

We are given that the volume of the part above water is 160,000 cubic feet.

Let V be the total volume of the iceberg and V_sub be the volume submerged below the water.

We can set up the following equation based on the given information:

V_sub = 0.9 * V

We know that V_sub + V_above = V, where V_above is the volume above the water's surface. We are given that V_above is 160,000 cubic feet, so we can rewrite the equation as:

V_sub + 160,000 = V

Now, substitute the expression for V_sub from the first equation:

0.9 * V + 160,000 = V

To isolate V_sub, subtract 160,000 from both sides of the equation:

0.9 * V = V - 160,000

Now, subtract V from both sides:

0.9 * V - V = -160,000

0.1 * V = -160,000

Now, divide both sides by 0.1 to find V_sub:

V_sub = (-160,000) / 0.1 = -1,600,000 cubic feet

However, it's important to note that the volume cannot be negative, and this result doesn't make physical sense.

This suggests there might be an issue with the given information or calculations.

For similar question on volume.

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Answer:

P(A' U B) = 84/100

Step-by-step explanation:

We have, P(A) = 86/100

P(B) = 79/100

P(A') = 7/50

P(A U B) = 95/100

-: P(A intersection B) = P(A) + P(B) - P(A U B)

P(A intersection B) = 86/100 + 79/100 - 95/100

P(A intersection B) = (86+79-95)/100 = (165-95)/100

P(A intersection B) = 70/100

Now, P(A' U B) = P(A') + P(A intersection B)

P(A' U B) = 7/50+70/100

P(A' U B) = (7*2+70)/100 = (14 + 70)/100

P(A' U B) = 84/100

Answer:

f(x) = 100(0.50)x

Step-by-step explanation:

f(1) = 100(0.50)1

f(2) = 100(0.50)2

Therefore f(x) = 100(0.50)x

Answer:

42 liters

Step-by-step explanation:

Set up the ratios as fractions.

6/7 = 36/x

To get the volumes multiply the 6 and the 7 by 6.

This is how you got the 36 for the first volume.

The volume of the second container is 42.

7 x 6 = 42

Answer:

the choice of consumers regarding what to purchase to satisfy their wants and the choice of producers regarding what to produce to maximize profits.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total number of ducks in the pond is 75. 25 ducks are marked as a winner.

Probability is expressed as number of possible outcomes/total number of outcomes.

if you take 2 ducks out but don't replace them, the probability that the first duck that you took out is a winner is

25/75 = 1/3

The total number of ducks left would be 74 and the number of winners would be 24.

the probability that the second duck that you took out is a winner is

24/74 = 12/37

Therefore, the probability that both are winners is

1/3 × 12/37 = 4/37

Answer:

152.6$

Step-by-step explanation:

35*4=140

Need to find the new amount since it was decreased by 18%

35*18/100=6.30

6.30+6.30

12.6

140+28.7=152.6

Answer: he invested $6000 in the account earning 5% interest and $2100 in the other account earning 2% interest

Step-by-step explanation:

Let x represent the amount invested in the account earning 5% interest.

Let y represent the amount invested in the account earning 2% interest.

In an account earning 5% interest, George invested $1800 more than twice the amount he invested in an account earning 2%. It means that

x = 2y + 1800

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

Assuming the duration for both investments is 1 year,

The interest on the first account would be

I = (x × 5 × 1)/100 = 0.05x

The interest on the second account would be

I = (y × 2 × 1)/100 = 0.02y

George earned a total of $342 in simple interest from two separate accounts. This means that

0.05x + 0.02y = 342 - - - - - - - - - - 1

Substituting x = 2y + 1800 into equation 1, it becomes

0.05(2y + 1800) + 0.02y = 342

0.1y + 90 + 0.02y = 342

0.1y + 0.02y = 342 - 90

0.12y = 252

y = 252/0.12 = 2100

x = 2y + 1800 = 2 × 2100 + 1800 = $6000

Answer:tony was billed for 154 minutes.

Step-by-step explanation:

Let x represent the number of minutes for which Tony was billed.

For his long distance phone service, Tony pays an $8 monthly fee plus 6 cents per minute. Converting 6 cents to dollars, it becomes 6/100 = $0.06

This means that if he made x minutes of long distance call in a month, the total cost would be

8 + 0.06x

Last month, Tony's long distance bill was $17.24. It means that

8 + 0.06x = 17.24

0.06x = 17.24 - 8 = 9.24

x = 9.24/0.06

x = 154

Answer:

Sum = 1,023

Step-by-step explanation:

The given series is:

1 + 2 + 4 + 8 + ........ + a₁₀

The given series is a geometric series.

It is required to find the sum of the first 10 terms

The sum to n terms of a geometric series given by:  [tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex]

Where: a = the first term = 1

            r = common ratio = 2/1 = 2

           n = number of terms = 10

So,

[tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex] = [tex]\frac{1*(2^{10} -1)}{2-1} = 2^{10} -1 = 1024 - 1 = 1,023[/tex]

So, the summation of the series = 1,023

1/3 shows the spots that are black as compared to all the spots

Step-by-step explanation:

The simple fraction will consist of number of black spots as numerator and the total number of spots on the dog in denominator.

Given

Number of black spots = b = 8

Number of white spots = w = 13

Number of Gray spots = g = 3

Total spots are:

[tex]t=b+w+g = 8+13+3 = 24[/tex]

So the fraction will be:

[tex]\frac{Number\ of\ black\ spots}{Total\ spots}\\= \frac{b}{t}\\=\frac{8}{24}\\= \frac{1}{3}[/tex]

Hence,

1/3 shows the spots that are black as compared to all the spots

Keywords: Fractions, sum

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Answer:

[tex]\displaystyle y=- \frac{1}{2}x-3[/tex]

(first option)

Step-by-step explanation:

Linear Functions

They can be defined by knowing two points on them or a point and the slope of the line. The portion "a" of the piecewise function must have these conditions, only by looking at the graph

* It must be decreasing, the slope must be negative

* It must be defined for x<-2, because for x>-2, the function is defined by another piece.

* It must pass through the point (-2,-2)

Options 2 and 4 are immediately discarded, since x>2

Testing it (-2,-2) belongs to

[tex]\displaystyle y=- \frac{1}{2}x-3[/tex]

[tex]\displaystyle y=- \frac{1}{2}(-2)-3=1-3=-2[/tex]

The point (-2,-2) belongs to this function, so it's the correct choice. Let's verify the last function

[tex]\displaystyle y=- \frac{1}{2}x-6[/tex]

[tex]\displaystyle y=- \frac{1}{2}(-2)-6=-5[/tex]

This is not the point we are testing, so the portion of the graph labeled "a" is

[tex]\boxed{\displaystyle y=- \frac{1}{2}x-3}[/tex]

(First option)

Answer:A=183cm^

Step-by-step explanation:

The area of square is :

Let s be side

A= s^2

144= s^2

Square both side

Therefore

s=sqrt(144)

s=12 cm

The perimeter of the square is : 4× s= 4×12= 48cm

So the perimeter of the square is equal to the circumference of the circle.

The equation will be:

4×s=2×pi×r

4×12=2× (22/7)×r

r=48/6.29

r=7.63

Area of a circle is:

A=pi× r^2

A= (22/7) × (7.63)^2

A=182.9674cm^2

A=183cm^

Final answer:

To find the area of the largest circle from a string around a square, calculate the square's perimeter to get the string's length, which is also the circle's circumference. Then determine the circle's radius and use it to calculate the circle's area, which rounds to 183 square units.

Explanation:

To find the area of the largest circle that can be formed from a piece of string that fits around a square with an area of 144, first we must determine the perimeter of the square. Since the area of the square (A) is 144, the side length (s) can be found by taking the square root of the area: s = √A = √144 = 12. Therefore, the perimeter (P) of the square is P = 4s = 4 × 12 = 48.

The string that fits around the square is the same length as the perimeter, so it will also be 48 units long. This string will become the circumference (C) of the circle. The formula for the circumference of a circle is C = 2πr, where π is approximately 3.14 and r is the radius of the circle. We can solve for r by setting the circumference equal to the length of the string: C = 2πr = 48 → r = 48 / (2π) → r ≈ 7.64. So the radius of the circle is approximately 7.64 units.

Finally, to find the area (A) of the circle, we use the formula A = πr². Substituting the value of the radius, we get A = π × (7.64)² ≈ 183.47. However, since we need to round to the nearest whole number, the largest circle area is approximately 183 square units.

Step-by-step explanation:

Given  

    2. and w = max (10,w)

From the first equation we get that w= 20

and it also satisfies the second equation.

∴ The value of min(10,w) = min(10,20) ∵w=20

                                        = 10

Considering both conditions, our w value could be 10 or greater. As we are looking for the minimum value between 10 and w, the result of min(10, w) will be 10.

Let's look at the two provided conditions:

Since both conditions suggest that w could be a value 10 or greater, the exponent w in min(10, w) will be at least 10. However, because we're finding the minimum between 10 and w, the value of min(10, w) will be 10.

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Answer:

11. B

12. A

14. C

16. D

18. A

Answer:

Option C) -cosu is correct

Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]

Step-by-step explanation:

Given expression is [tex]cos(u+\pi)[/tex]

To find the value of the given expression :

By using the formula [tex]cos(A+B)=cosAcosB-sinAsinB[/tex]

Substitute A=u and [tex]B=\pi[/tex] in the above formula we get

[tex]cos(u+\pi)=cosucos\pi-sinusin\pi[/tex]

[tex]=cosu(-1)-sinu(0)[/tex]  ( here [tex]cos\pi=-1[/tex] and [tex]sin\pi=0[/tex] )

[tex]=-cosu-0[/tex]

[tex]=-cosu[/tex]

[tex]cos(u+\pi)=-cosu[/tex]

Therefore option C) -cosu is correct

Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]

Answer:

Option B) False            

Step-by-step explanation:

We define the following terms:

Range:

It is the difference between the minimum and maximum value of data.

It is effected by presence of outliers.

Interquartile range:

It is the difference between the third quartile and the first quartile of data.

Variance:

[tex]\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

It is a measure of spread of the data. It is effected by presence of outliers as they increase the variation in the data.

Thus, the given statement is false.