What reason explains why the m∠Q = 115°?

The object's position function is y = 2.5t² - 2t derived using kinematic equations. The speed at time t is |-2 + 5t| m/s where t is the time.

This is a problem of mechanics related to the motion of the object under the influence of a force. First, we need to calculate the acceleration using the formula F=ma. This gives us the acceleration as a = F/m = 20N/4kg = 5m/s². The object is moving upwards so this force is in the positive y direction.

The initial velocity vector is given as vs0d − i2j. The i-component represents the x-direction, and the j-component represents the y-direction. Thus, the initial speed is sqrt((0d)² + (−2)²) = 2 m/s. However, given that this velocity is in the negative y-direction, we determine its initial speed to be -2 m/s.

Now, we can determine the position function for the y-direction using the equation y = y0 + v0y*t + 0.5*a*t², where y0 represents the initial position (origin), v0y is the initial velocity in the y-direction (-2m/s for this case), a is the acceleration (5 m/s²), and t is time. Substituting these values, the equation becomes y = 0 – 2t + 0.5*5t² = 2.5t² - 2t.

For the speed at time t, you can utilize the velocity's magnitude in the y-direction using v = v0y + a*t = -2 m/s + 5t The magnitude ||v|| = sqrt((0)² + (-2 + 5t)²) = |-2 + 5t| m/s as speed is always positive.

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We determined the object's position function to be [tex]\[ \matbf{r}(t) = -t \mathf{i} + 2t \mathf{j} + \frac{5t^2}{2} \mathf{k} \][/tex] and its speed at time t to be |v(t)| = [tex]\sqrt{5 + 25t^2}[/tex]. The calculations involved using Newton's second law and integrating the acceleration and velocity.

To find the position function and speed of the object under the given conditions, we need to use the principles of Newtonian mechanics. Let's break it down step-by-step.

Step 1: Find the acceleration

Given:

- Force ( F = 20 N ) upward

- Mass  (m = 4 kg)

Using Newton's second law (F = ma) , we can find the acceleration:

[tex]\[ \mthbf{a} = \frac{\mahbf{F}}{m} \][/tex]

Since the force is acting directly upward (which we'll take as the ( z )-direction):

F = 20k

Thus,

[tex]\[ \mahbf{a} = \frac{20 \matbf{k}}{4} = 5 \mahbf{k} \][/tex]

So, the acceleration is:

a = 5k

Step 2: Find the velocity function

The initial velocity is given as:

[tex]\[ \matbf{v}(0) = -\matbf{i} + 2\matbf{j} \][/tex]

Acceleration is constant, so we can integrate to find the velocity function:

[tex]\[ \matbf{v}(t) = \mathf{v}(0) + \mathf{a} t \][/tex]

Substituting the known values:

[tex]\[ \mathf{v}(t) = (-\matbf{i} + 2\matbf{j}) + 5 t \mahbf{k} \][/tex]

Thus,

[tex]\[ \matbf{v}(t) = -\matbf{i} + 2\matbf{j} + 5t \mthbf{k} \][/tex]

Step 3: Find the position function

To find the position function, integrate the velocity function:

[tex]\[ \mahbf{r}(t) = \mathf{r}(0) + \int \mathf{v}(t) \, dt \][/tex]

Given that the object starts at the origin:

r(0) = 0

Integrating the velocity function:

[tex]\[ \mathf{r}(t) = \int (-\mathf{i} + 2\matbf{j} + 5t \mathf{k}) \, dt \][/tex]

[tex]\[ \mahbf{r}(t) = (-\matbf{i}t) + (2\matbf{j}t) + \left( \frac{5t^2}{2} \matbf{k} \right) \][/tex]

Thus, the position function is:

[tex]\[ \matbf{r}(t) = -t \mathf{i} + 2t \mathf{j} + \frac{5t^2}{2} \mathf{k} \][/tex]

Step 4: Find the speed at time ( t )

Speed is the magnitude of the velocity vector:

[tex]\[ \mathb{v}(t) = -\mathf{i} + 2\matbf{j} + 5t \mathb{k} \][/tex]

Calculate the magnitude:

[tex]\[ \text{Speed} = |\mathbf{v}(t)| = \sqrt{(-1)^2 + (2)^2 + (5t)^2} \][/tex]

[tex]\[ \text{Speed} = \sqrt{1 + 4 + 25t^2} \][/tex]

[tex]\[ \text{Speed} = \sqrt{5 + 25t^2} \][/tex]

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:

D itll go from 87.5 to 70, so it'll drop by 17.5

Step-by-step explanation:

Answer:

The answer is actually D

Step-by-step explanation:

This is true because when you add the scores together you get 350 and then you divide that number by however many data numbers there are in the set.

86+84+90+90=350

because there are 4 numbers in the data set you so divide 350 by 4 which equals 87.5

Then he scores a 0 on the quiz, it will indeed affect the mean.

You add the numbers 86+84+90+90+0 still equals 350, however, instead of 4 numbers in the data set it's 4 because of the zero.

Instead of dividing by 4, you divide by 5

350 divided by 5 equals 70.

the original MEAN was 87.5 and now it is 70, so that means that it decreased by 17.5. there's is your answer. The answer is D 17.5

Answer:

It's descriptive.

Step-by-step explanation:

inferential statistic, means we are inferring based on a sample of our population. Many times we need to infer because the data we need to collect is too large, i.e. the population is too large e.g. the average age of high school students in the US. so we take a sample, a portion of this population and we calculate their mean age. If our sample is random enough, we can "infer" to a certain degree of accuracy the mean

But descriptive statistics, describes the data. They are numbers used to summarise and describe a data. 60% describes the data.

To make at least a 25% profit, Cameron should charge a minimum of $1.22 per bag for the mixed candy. The cost per bag is found by adding the total cost of candy corn and M&Ms, then multiplying by 125% and dividing by the number of bags to distribute the cost and profit evenly.

The student's question involves calculating the minimum selling price for candy bags to achieve a certain profit margin, which is a common type of problem in Mathematics, specifically in the field of algebra and business mathematics.

To find the least price Cameron can charge for each of the thirty bags to make at least a 25% profit, we first calculate the total cost of the candy. Cameron bought twelve pounds of candy corn at 79 cents a pound and eighteen pounds of M&Ms at $1.09 a pound.

Now, we calculate the total cost including the desired 25% profit.

Total cost with profit: $29.10 × (1 + 0.25) = $36.375

Since Cameron is making thirty bags, we divide the total cost with profit by the number of bags.

Minimum selling price per bag: $36.375 / 30 bags = $1.2125

However, as prices are generally rounded to the nearest cent, the minimum charge per bag would be $1.22 to ensure a 25% profit.

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:

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.

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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:

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

Answer:

-15x^4y

Step-by-step explanation:

(-3x^3y^2)(5xy^-1)

-15x^4y^2/y

-15x^4y

Answer:

C.  -15x^4y.

Step-by-step explanation:

(-3x^3y^2) (5xy^-1)

= -3*5 x^(3+1)y^(2 - 1)

= -15x^4y.

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: The limit does not exist.

Step-by-step explanation: The limit of a piecewise function f(x) as it approaches "a" will exist if and only if the value of the limit of f(x) as x approaches "a" from the left is the same with the value of the limit of f(x) as x approaches "a" from the right.

From the given question the value are not the same. We have 5 (limit from the left) and -3 (limit from the right). So, we can conclude that the limit of f(x) as x approaches "a" does not exist.

Answer:

a) The probability is 0.3

b) The probability is 0.1

c) The probability is 0.35

Step-by-step explanation:

Lets call S1 and S2 the events ' he must stop at signal 1 ' and 'he must stop at signal 2' respectively.

a) We know that

0.65 = P(S1 ∪ S2) = P(S1) + P(S2) - P(S1 ∩ S2) = 0.4+0.55-P(S1 ∩ S2) = 0.95 - P(S1 ∩ S2)

Hence P(S1 ∩ S2) = 0.95-0.65 = 0.3

It stops at both signals with probability 0.3

b) Note that, due to the theorem of total probability we have

0.4 = P(S1) = P(S1 ∩ S2) + P(S1 ∩ S2^c) = 0.3 + P(S1∩S2^c)

Where S2^c is the complementary event of S2. Therefore

P(S1∩S2^c) = 0.4-0.3 = 0.1

The probability to stop at the first signal but not at the second one is 0.1

c) The probability of stopping at exactly one signal is equal at the sum of the probabilities of stopping only at the first signal and the probability of stopping only at the second one.

That is P(S1 ∩ S2^c) + P(S1^c ∩ S2) = 0.1 + P(S1^c ∩ S2)

The same way as before:

0.55 = P(S2) = P(S1 ∩ S2) + P(S1^c ∩ S2) = 0.3 + P(S1^c ∩ S2)

Therefore

P(S1^c ∩ S2) = 0.55-0.3 = 0.25

And as a result, the probability of stopping at exactly one signal is 0.25 + 0.1 = 0.35.

The probability that he must stop at both signals 0.30.

The probability to stop at the first signal but not at the second one is 0.1.

The probability that he must stop at exactly 0.35.

Given that,

The probability that he must stop at the first signal is 0.4,

The analogous probability for the second signal is 0.55,

The probability that he must stop at at least one of the two signals is 0.65.

We have to determine,

What is the probability that he must stop.

According to the question,

F = Event that a certain motorist must stop at the first signal.

S = Event that a certain motorist must stop at the second signal.

P(S1 ∪ S2) = P(S1) + P(S2) - P(S1 ∩ S2) =0.65

0.4 +0.55 - P(S1 ∩ S2) = 0.65

0.95 - P(S1 ∩ S2) = 0.65

Hence, P(S1 ∩ S2) = 0.95 - 0.65 = 0.30

It stops at both signals with probability 0.30.

The probability that he must stop at both signals 0.30.

P(S1) = P(S1 ∩ S2) + P(S1 ∩ S2^c)

0.4 = 0.3 + P(S1∩S2^c)

Where S2^c is the complementary event of S2. Therefore

P(S1∩S2^c) = 0.4 - 0.3 = 0.1

The probability to stop at the first signal but not at the second one is 0.1.

= P(S1 ∩ S2^c) + P(S1^c ∩ S2)

= 0.1 + P(S1^c ∩ S2)

Then,

= P(S2) = P(S1 ∩ S2) + P(S1^c ∩ S2) = 0.5

= 0.3 + P(S1^c ∩ S2) = 0.5

Therefore,

P(S1^c ∩ S2) = 0.55 - 0.3 = 0.25

And the probability of stopping at exactly one signal is 0.25 + 0.1 = 0.35.

The probability that he must stop at exactly 0.35.

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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

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

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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:

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: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:

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:

Step-by-step explanation:

#2 the answer is B, -16/9

do 1/4-5/2

to do this, find the least common denominator. it's 4

1/4-10/4=-9/4

then divide 4 by -9/4. This is the same as 4*-4/9. That is -16/9

#3 the answer is A 9x/x-8

first factor the denominator of the first fraction using special products

x^2-6x-16=(x-8)(x+2)

if you look at the first fraction, you can simplify x+2 leaving you with the fraction 1/x+8

multiply that by 9x, and you get 9x/x-8

#4 the answer is C (2x+1)/2x^2

first add x/4 and 1/8

find the least common denominator. its 8

2x/8 + 1/8 is equal to (2x+1)/8

then multiply that by x^2/4 because dividing a fraction is the same as multiplying its reciprocal

you get (2x+1)/2x^2

#5 the answer is C (x-8)/(x+3)

using special products you can factor the numerator

x^2-4x-32 is the same as (x-8)(x+4)

then, using special products you can also factor the denominator

x^2+7x+12 is the same as (x+4)(x+3)

you can see that both the numerator and the denominator is multiplied by (x+4) you can simplify that. That leaves you with (x-8)/(x+3)

#7 the answer is D 3m

in the numerator in the second fraction, you can factor out 5m^2

leaving you with 5m^2(m-6)/5m^2. simplify the 5m^2 and the m-6

after you simplify both of those, you will get 3m

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:

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:

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:

[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.

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:

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: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.

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:

11. B

12. A

14. C

16. D

18. A

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 .