x-y=2 and x+y=-2 sove by graphing please and show the solution

Answer:

Step-by-step explanation:

Let x represent the number of batches of soap that Lilth makes.

Let y represent the number of batches of lotion that Lilth makes.

It takes her 20 minutes(20/60 = 1/3 hours) to make a batch of soap and 35 minutes(35/60 = 7/12 hours) to make a batch of lotion. Lilth has 20 hours available to make soap and lotion. This means that

x/3 + 7y/12 = 20

4x + 7y = 240- - - - - - - - - - -1

The cost of producing each batch are $5 for the soap and $15 for the lotion. The materials to make the soap and lotion must cost at most $325. This means that

5x + 15y ≤ 325 - - - - - - - - -2

4x = 240 - 7y

x = (240 - 7y)/4

Substituting

5(240 - 7y)/4 + 15y ≤ 325

(1200 - 35y)/4 + 15y ≤ 325

1200 - 35y + 60y ≤ 1300

25y ≤ 1300 - 1200

25y ≤ 100

y ≤ 100/25

y ≤ 4

4x + 7 × 4 = 240

4x + 28 = 240

4x = 212

x = 212/4 = 53

Therefore, the solution (53, 4) means that she would make at most 53 batches of soap and at most 4 batches of lotion

Answer:

Hope this helps you.

The answer is 61, x+40+5x+14=180, so x equals 21. 5(21)+14 ends up equaling 119, so 180-119 equals 1

The value of x is [tex]5.625[/tex]

Explanation:

Since, from the figure we can see that, a ray bisects the angle of a triangle.

Then, the angle bisector theorem states that, "if a ray bisects an angle of a triangle, then it divides the opposite sides of the triangle into segments that are proportional to the other two sides".

Thus, we have,

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

where [tex]AC=4, BC=7.5, AD=3[/tex] and [tex]DB=x[/tex]

Substituting the values, we get,

[tex]$\frac{4}{7.5}=\frac{3}{x}$[/tex]

Simplifying, we have,

[tex]4x=22.5[/tex]

Dividing both sides by 4,

[tex]x=5.625[/tex]

Thus, the value of x is [tex]5.625[/tex]

Answer:

$22.50

Step-by-step explanation:

I think the unit of the sand sold is actually in cubic inches and not square inches.

V = L*B*H

V = 2.5 * 3 * 6

V = 45 in³

If 1 in³ = $0.50

    45 = x

x = 45 * $0.50

x = $22.50

Total amount paid by Rita is $98.79

Step-by-step explanation:

Total Amount = 89 + 9.79 = $98.79

Answer:

The carpenter will not be able to buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

Step-by-step explanation:

Given:

Amount a carpenter can spend at most = $250

The inequality to represent the amount he can spend on each type of board is given as:

[tex]8x+12y<250[/tex]

where [tex]x[/tex] represents  '2 by 8 boards' and [tex]y[/tex] represents '4 by 4 boards'.

To determine whether the carpenter can buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

Solution :

In order to check whether the carpenter can buy 12  '2 by 8 boards' and 14 '4 by 4 boards' ,  we need to plugin the [tex]x=12[/tex] and [tex]y=14[/tex] in the given inequality and see if it satisfies the condition or not or in other words (12,14) must be a solution for the inequality.

Plugging in  [tex]x=12[/tex] and [tex]y=14[/tex] in the given inequality

[tex]8(12)+12(14)<250[/tex]

[tex]96+168<250[/tex]

[tex]264<250[/tex]

The above statement can never be true and hence the carpenter will not be able to buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

The above statement can never be true and hence the carpenter will not be able to buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

Given that,

A carpenter has at most $250 to spend on lumber,

The inequality 8x + 12y < 250 represents,

The numbers x of 2 by 8 boards,

And the numbers y 4 by 4 boards.

We have to find,

The carpenter can buy can the carpenter buy twelve 2 by 8 boards and fourteen 4 by 4 boards.

According to the question,

The numbers x of 2 by 8 boards,

And the numbers y 4 by 4 boards.

Inequality [tex]8x + 12y < 250[/tex]

This means that a 2-by-8 board cost $8 each, while a 4-by-4 board cost $12 each.

x = 12 2-by-8 boards

y = 14 4-by-4 boards

In order to check whether the carpenter can buy 12  '2 by 8 boards' and 14 '4 by 4 boards' .

Plugin the and in the given inequality and see if it satisfies the condition or not or in other words (12,14) must be a solution for the inequality.

Putting x=12 and y=14 in the inequality,

[tex]8(12) + 12(14) <250\\96+168<250\\264<250[/tex]

Hence, The above statement can never be true and hence the carpenter will not be able to buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

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Answer: the length of the smallest side is 11 feet.

the length of the medium side is 27 feet.

the length of the longest side is 28 feet.

Step-by-step explanation:

Let x represent the length of the smallest side.

Let y represent the length of the middle side.

Let z represent the length of the longest side.

The perimeter of a triangular garden is 66 feet. This means that

x + y + z = 66 - - - - - - - - - -1

if the middle length side is 5 feet greater than twice the length of the smallest​ side, it means that

y = 2x + 5

The longest side is 5 feet less than 3 times the length of the smallest side. It means that

z = 3x - 5

Substituting y = 2x + 5 and z = 3x - 5 into equation 1, it becomes

x + 2x + 5 + 3x - 5 = 66

6x = 66

x = 66/6 = 11

y = 2x + 5 = 2 × 11 + 5

y = 27

z = 3x - 5 = 3 × 11 - 5

z = 28

The length of the three sides of the triangular garden is 11 feet, 27 feet, and 28 feet.

The perimeter of a triangle is the sum of the lengths of its three sides. Let's assume the length of the smallest side is x. According to the given information, the middle length side is 5 feet greater than twice the length of the smallest side, so it can be expressed as 2x + 5. The longest side is 5 feet less than 3 times the length of the smallest side, so it can be expressed as 3x - 5.

Now, since the perimeter of the triangle is 66 feet, we can set up the equation:

x + (2x + 5) + (3x - 5) = 66

Simplifying this equation, we get:

6x = 66

Dividing both sides by 6, we get:

x = 11

So the length of the smallest side is 11 feet. The middle length side is 2x + 5 = 2(11) + 5 = 27 feet. The longest side is 3x - 5 = 3(11) - 5 = 28 feet.

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Answer:

The French restaurant did not use cream this year, due to a menu update.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of cream used by a French restaurant last year = 92.870 ounces

Amount of cream used by the French restaurant this year = 100% less

2.  How much cream did the restaurant use this year?

The answer is zero and we calculated it this way:

92,870 - 100% (92,870) = 92,870 - 92,870 * 1 = 92,870 - 92,870 = 0

The French restaurant did not use cream this year, due to a menu update.

Answer:60%

Step-by-step explanation: i know its correct bc i got it wrong and it told me the answer

Answer: Outsourcing Processes

Step-by-step explanation:

The inefficient use of resources and delays in production in Ucon Inc. that needs to be resolved by hiring external agencies to perform some operations would be resolved by the adoption of outsourcing processes strategy.

It's most likely the strategy employed here because external agencies performing certain operations in a company means they are outsourced to help the company overcome certain challenges.

Answer:

1

Step-by-step explanation:

The probability of selecting (at least)3 jacks out of a shuffled deck of 51  cards is 1. This is because in every shuffled deck of 51 cards, we are certain to find at least 3 jacks and this is 100% certain. So, the probability of selecting (at least) 3 jacks P(J)= 100% = 100/100 = 1    

Answer:

1

Step-by-step explanation:

The probability of selecting (at least)3 jacks out of a shuffled deck of 51  cards is 1. This is because in every shuffled deck of 51 cards, we are certain to find at least 3 jacks and this is 100% certain. So, the probability of selecting (at least) 3 jacks P(J)= 100% = 100/100 = 1    

Answer:

the expression that shows the number of noodles Julia uses to make 9 necklaces and 20 wreaths

  = (9 [tex]\times[/tex] n ) + (20 [tex]\times[/tex] (3/5)n) = 9n + 12n = 21n

Step-by-step explanation:

i) there are n noodles in a necklace

ii) there are 9 necklaces

iii) therefore the number of noodles used to make the nine necklaces = 9 [tex]\times[/tex] n = 9n

iv) there are 3/5 noodles in a wreath

v) there are 20 wreaths

vi) therefore the number of noodles used to make the nine necklaces

     = 20 [tex]\times[/tex] (3/5)n = 12n

vii) the expression that shows the number of noodles Julia uses to make 9 necklaces and 20 wreaths

  = (9 [tex]\times[/tex] n ) + (20 [tex]\times[/tex] (3/5)n) = 9n + 12n = 21n

Answer:

[tex]y=x/4+30[/tex]

Step-by-step explanation:

Let x be the normal time it takes for her to commute. We know that if she was 30min late, this would had 30 min to the journey. She takes a different route, she can travel four times faster than the normal route.

Therefore the normal time of commute will be 4 times less:

[tex]y=x/4+30[/tex]

This equation states that the commute time will be four times faster and adding the 30min that she is late.

Y is equals to one fourth times x plus thirty, y = 4x + 30.

Given that,

Jorie normally leaves work at 5:00 pm, but she is leaving work 30 minutes late today.

She decides to make up time by taking the toll road instead of side streets. She can travel four times faster by taking the toll road.

We have to determine,

Create an equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late.

According to the question,

Let x represent the number of minutes her normal commute takes when she leaves on time.

She was 30min late, this would had 30 min to the journey. She takes a different route, she can travel four times faster than the normal route.

Therefore,

The normal time of commute will be 4 times less,

[tex]y = 4x +30\\\\[/tex]

Hence, The commute time will be four times faster and adding the 30min that she is late.

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Answer:

A. Increasing cash, which will increase asset turnover

C.Increase assets, which will increase asset turnover and profit margin

Step-by-step explanation:

A reduction in inventory will improve business performance by increasing the efficiency of the company..

return of equity (ROE) can be calculated by: net profit/shareholder equity.

where share holder equity can be calculated by company assets minus debts.

Therefore ROE = Net profit/ (Assets - debts)

With, this formula, it can be deduced mathematically that, increasing ROE will Increase profit gain and  increase asset turnover.

ROE help company to estimate how management is using company assets to actualize profit. Reducing inventory is a reduction in the cost of procurement of goods needed by the company. this eventually increase the cash income of the company.

Also, a reduction in company debts can drastically improve the ROE.

Final answer:

Brandi needs to score an 88 on her final exam, which counts as two tests, to achieve an average score of 80 for the course.

Explanation:

The question involves calculating the score Brandi needs on the final exam to achieve an average of 80 when the final counts as two tests. To solve this, we add the current scores, multiply the desired average by the total number of tests (including the two final exams counted as separate tests), and subtract the sum of the current scores from this product.

Current sum of scores: 75 + 80 + 74 + 63 + 92 = 384
Number of tests, including the final counted twice: 5 + 2 = 7
Desired total of all scores: 80 (average) * 7 (tests) = 560

The score Brandi needs on the final is: 560 - 384 = 176.
Since the final counts as two tests, the necessary score for each portion of the final would be: 176 / 2 = 88.

Therefore, Brandi needs to score an 88 on her final exam to achieve an average score of 80.

Answer:

(A) The two events are Not Independent.

(B) The probability that Leah's luggage arrives in Denver is 0.695.

Step-by-step explanation:

Let F = Leah's first flight leaves on time and C = Leah's luggage will make the connecting flight.

Given:

P (F) = 0.15, P (C|F) = 0.95 and P (C|F') = 0.65

Here F' represents the events that Leash's first flight was not on time.

(A)

The events F and C are not independent.

For the luggage to make the connecting flight Leah's first flight must be on time.

As it is provided that the probability that the the luggage will make the connecting flight provided that the first flight is delayed is 0.65, i.e. there 0.35 probability that the luggage will not make the connecting flight.

Thus, implying that the two events F and C are dependent.

(B)

Compute the probability that Leah's luggage arrives in Denver as follows:

         P (D) = P (C|F) × P (F) + P (C|F') × P (F')

                 [tex]= (0.95\times0.15)+(0.65\times (1-0.15))\\=0.695[/tex]

Thus, the probability that Leah's luggage arrives in Denver is 0.695.

The first flight leaving on time and the luggage making the connection are dependent events. The probability that Leah's luggage arrives in Denver with her is 0.695.

A) In order to determine whether the first flight leaving on time and the luggage making the connection are independent events, we need to compare the probability of the luggage making the connection when the first flight is on time (0.95) to the probability of the luggage making the connection when the first flight is delayed (0.65).

If these probabilities are the same, then the events are independent.

However, since the probabilities differ, the events are dependent.

B) To find the probability that Leah's luggage arrives in Denver with her, we need to consider two scenarios:

We can then add these probabilities together to get the total probability: (0.15 * 0.95) + (0.85 * 0.65) = 0.1425 + 0.5525 = 0.695

The probability that a person who preferred a picnic responded by email is 2/3.

To find the probability that a person who preferred a picnic responded by email, we need to compare the number of email responses to the total number of responses. Let's assume the number of phone responses is x. Since the number of email responses is twice the number of phone responses, the number of email responses is 2x.

The total number of responses would be the sum of the email and phone responses, which is 2x + x = 3x.

The probability that a person who preferred a picnic responded by email would be the number of email responses divided by the total number of responses, which is 2x/3x = 2/3.

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To find the probability that a person selected at random who preferred a picnic responded by email, you take the 5% who responded by email and divide it by the total response percentage (30%). This results in a probability of 1/6, or approximately 16.67%.

We are given that 20% who preferred a picnic responded by phone and that the number of email responses was twice the number of phone responses. This means that 5% responded by email because twice 5% is 10%, and 10% plus the original 20% for phone responses gives us the 30% of people who responded in total. To find the probability that a randomly selected person who preferred a picnic responded by email, we can use relative frequency probability calculation.

The probability (P) can be expressed by the following equation:

P (Email | Picnic) = Number of people who preferred a picnic and responded by email / Total number of people who preferred a picnic

Given that the number of email responses is twice the number of phone responses, and knowing the percentage that corresponds to each mode of response:

To calculate the probability that the person responded by email, we take the proportion:

P (Email | Picnic) = 5% / 30%

After calculating this, we get: P (Email | Picnic) = 1/6 or approximately 0.1667, which is about 16.67%.

Answer:

a person travel 50 ft from the bottom to the top of the escalator

Step-by-step explanation:

An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30 degree angle

The escalator forms a right angle triangle

opposite to 30 degree angle is 25 feet. to find the distance from the bottom to the top of the escalator we find the hypotenuse

let x be the hypotenuse

[tex]sin(theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]sin(30)=\frac{25}{x}\\x sin(30)= 25\\x=\frac{25}{sin(30)} \\x=50\\[/tex]

a person travel 50 ft from the bottom to the top of the escalator

Using trigonometry, the person travels approximately 50 ft from bottom to top. So, the answer is (a) 50 ft.

To find the distance a person travels from the bottom to the top of the escalator, we can use trigonometric functions. Since the escalator rises at a 30° angle, we can use the sine function to find the vertical component of the distance traveled.

Let's denote the distance traveled from the bottom to the top of the escalator as ( d ).

We know that the vertical component of the distance traveled is [tex]\( d \cdot \sin(30°) \).[/tex]

Given that the height of the second floor is 25 ft, we have:

[tex]\[ d \cdot \sin(30°) = 25 \][/tex]

To find ( d ), divide both sides by ( sin(30°) ):

[tex]\[ d = \frac{25}{\sin(30°)} \][/tex]

Now, let's calculate:

[tex]\[ \sin(30°) \approx 0.5 \][/tex]

So:

[tex]\[ d = \frac{25}{0.5} = 50 \][/tex]

Therefore, the person travels approximately 50 ft from the bottom to the top of the escalator.

So, the correct answer is:

a) 50 ft

The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

Step-by-step explanation:

If the equation is y = A sin (B x + C) + D , where

∵ The amplitude is 4

∴ A = 4

∵ The period is 4π

∴  T= 4π ⇒ T = [tex]\frac{2\pi }{B}[/tex]

∵ The phase shift is [tex]-\frac{4}{3}\pi[/tex]

∴ C =  [tex]-\frac{4}{3}\pi[/tex]

∵ The vertical shift is -2

∴ D = -2

Substitute these values in the y = A sin( [tex]\frac{2\pi }{T}[/tex] t + C) + D

∴ y = 4 sin( [tex]\frac{2\pi }{4\pi }[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

- Simplify it

∴ y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

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Answer:

712/1 410/1

Step-by-step explanation:

theres a fraction for 712 and 410

Donna ate more popcorn than Jack.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

Donna ate 7/12 box of popcorn, and Jack ate 4/10 box of popcorn the boxes of popcorn.

Now, By using benchmark fraction we can determine who ate more popcorn as,

Here, Jack ate 4/10 box of popcorn.

⇒ 4/10

⇒ 2/5

And, Donna ate 7/12 box of popcorn.

⇒ 7/12

Take LCM of 5 and 12,

⇒ LCM {5, 12} = 60

Hence, We get;

⇒ 2/5 = 24/60

⇒ 7/12 = 35/60

Clearly, We get;

⇒ 7/12 > 2/5

Hence, Donna ate more popcorn than Jack.

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Answer:

It is True that all concepts rely on ratios meaning to provide a type of measurement because ratio compares one quantity to another

Step-by-step explanation:

Ratio shows how many times one quantity is to another

Answer:

it's division.

Step-by-step explanation:

Answer:

Amount of ribbon remaining with Lara is [tex]10\frac{1}{3}\ yard[/tex].

Step-by-step explanation:

Given:

Amount of ribbon Lara bought = [tex]8\frac{3}{10} \ yard[/tex]

[tex]8\frac{3}{10} \ yard[/tex] can be Rewritten as [tex]\frac{83}{10}\ yard[/tex]

Amount of ribbon Lara bought = [tex]\frac{83}{10}\ yard[/tex]

Amount of ribbon used to tie a package = [tex]1\frac{2}{5} \ yard[/tex]

[tex]1\frac{2}{5} \ yard[/tex] can be Rewritten as [tex]\frac{7}{5}\ yard[/tex]

Amount of ribbon used to tie a package = [tex]\frac{7}{5}\ yard[/tex]

Amount of ribbon used to make bow= [tex]2\frac{1}{3} \ yard[/tex]

[tex]2\frac{1}{3} \ yard[/tex] can be Rewritten as [tex]\frac{7}{6}\ yard[/tex]

Amount of ribbon used to make bow = [tex]\frac{7}{6}\ yard[/tex]

We need to find the amount of ribbon remaining with Lara.

Solution:

Now we can say that;

Amount of ribbon remaining with Lara can be find by subtracting Amount of ribbon used to tie a package and Amount of ribbon used to make bow from Amount of ribbon Lara bought.

framing in equation form we get;

Amount of ribbon remaining = [tex]\frac{83}{10}-\frac{7}{5}-\frac{7}{6}[/tex]

Now we will make the denominator common using LCM.

LCM of 5,6,10 is 30

So we get;

Amount of ribbon remaining = [tex]\frac{83\times3}{10\times 3}-\frac{7\times6}{5\times6}-\frac{7\times5}{6\times5}=\frac{249}{30}-\frac{42}{30}-\frac{35}{30}[/tex]

Now the denominator are common so we will solve the numerator we get;

Amount of ribbon remaining = [tex]\frac{249-42-35}{30}= \frac{172}{30}[/tex]

Now Given:

Amount of ribbon Joe gave = [tex]4\frac{3}{5}\ yard[/tex]

[tex]4\frac{3}{5}\ yard[/tex] can be rewritten as [tex]\frac{23}{5}\ yard[/tex]

Amount of ribbon Joe gave = [tex]\frac{23}{5}\ yard[/tex]

Now we can say that;

Amount of ribbon remaining with her = [tex]\frac{172}{30}+\frac{23}{5}[/tex]

Now again we will make the denominator common using LCM we get;

Amount of ribbon remaining with her = [tex]\frac{172\times1}{30\times1}+\frac{23\times6}{5\times6} = \frac{172}{30}+\frac{138}{30}[/tex]

Now denominators are common so we will solve the numerators we get;

Amount of ribbon remaining with her = [tex]\frac{172+138}{30}=\frac{310}{30}=\frac{31}{3}\ yard \ \ Or \ \ 10\frac{1}{3}\ yard[/tex]

Hence Amount of ribbon remaining with her is [tex]10\frac{1}{3}\ yard[/tex].

Final answer:

To find out how much ribbon Laura now has, we start with her initial amount, subtract the yardage used in two activities, and add the amount received from Joe, combining fractions and whole numbers to reach the final total yardage.

Explanation:

To calculate the amount of ribbon Laura has after her transactions, we need to perform a few steps involving addition and subtraction of mixed numbers, and then convert that number to a single unit if necessary. Here is how we solve this:

Start with the total ribbon Laura bought: 8 3/10 yards.

Subtract the ribbon used to tie a package: 1 2/5 yards.

Also, subtract the ribbon used to make a bow: 2 1/3 yards.

Add the ribbon given by Joe: 4 3/5 yards.

Combine the fractions and whole numbers separately for precision.

Finally, add or subtract the totals to find out how much ribbon Laura now has.

Let's do the math:

Laura's total ribbon after using some and receiving more from Joe is:

8 3/10 (initial amount) - 1 2/5 (package) - 2 1/3 (bow) + 4 3/5 (from Joe) = Laura's current ribbon amount.
Simplify the fractions and calculate:

Step by step:

Convert mixed numbers to improper fractions or work directly with mixed numbers.

Find common denominators for the fractions.

Add and subtract the fractions.

Add and subtract the whole numbers.

Combine the totals.

We'll end up with a total that represents the yardage of ribbon Laura has left.

Answer:

[tex]\displaystyle \sqrt{3}\:sec.[/tex]

Step-by-step explanation:

[tex]\displaystyle -54 = -18x^2 → \frac{-54}{-18} = \frac{-18x^2}{-18} \\ \\ 3 = x^2 → \sqrt{3} = x[/tex]

I am joyous to assist you anytime.

Answer: [tex]t_{n}=-15+9(n-1)[/tex]

Step-by-step explanation:

The formula for finding the nth term of an arithmetic sequence is given as:

[tex]t_{n}=a+(n-1)d[/tex]

[tex]a =[/tex] first term = -15

[tex]d =[/tex] common difference = -6 - (-15) = 9

[tex]n =[/tex] number of terms

substituting into the formula , we have :

[tex]t_{n} = -15+(n-1)9[/tex]

[tex]t_{n}=-15+9(n-1)[/tex]

Answer:

Step-by-step explanation:

1) the figure has 2 hemispheres and 1 cylinder.

2) The formula determining the volume of a hemisphere is expressed as

Volume = 4/3πr³

Where

r represents radius of the hemisphere.

π is a constant whose value is 3.14

The formula determining the volume of a cylinder is expressed as

Volume = 4/3πr³

Where

r represents radius of the cylinder

h represents the height of the cyinder.

3) volume of hemisphere = 4/3 × 3.14 × 2³ = 33.49mm³

Height of cylinder = 10 - (2+2) =6mm

Volume of cylinder = 3.14 × 2²× 6 = 75.36mm³

4) the composite volume is

2 × 33.49 + 75.36 = 142.34mm³

Answer:

Does each equation represent exponential decay or exponential growth?

Step-by-step explanation:

The best way to know if an equation represents an exponential growth or decay is to look a the base of the exponentiation. If the base is larger than 1, it will be an exponential growth. If the base is smaller than 1, it will be an exponential decay.

Answer:

1

Step-by-step explanation:

Final answer:

Martin Luther King Jr.'s phrase "Freedom at last" reflects the profound hope and vision for a future of racial equality and the end of segregation and discrimination in America, encapsulating the essence of his iconic "I Have a Dream" speech.

Explanation:

When Martin Luther King Jr. expressed the words "Freedom at last! Freedom at last! Thank God Almighty, we are free at last!", he was encapsulating the immense joy and the culmination of the struggle for civil rights and equality in America. This phrase symbolizes the hope and vision that one day, all people, regardless of race, would live in a society where they are judged by the content of their character and not the color of their skin. The phrase "Freedom at last" conveys a future where segregation, discrimination, and racial prejudice have been eradicated, and all of God's children—black men and white men, Jews and Gentiles, Protestants and Catholics—could join hands as equals.

The background of King delivering his keynote speech at the Lincoln Memorial highlights the reality that, a century after the Emancipation Proclamation, African Americans were still fighting against segregation and discrimination. King's vision was for the nation to truly live out its creed that "all men are created equal." His "I Have a Dream" speech, which included the powerful declaration of "Freedom at last," remains one of the most iconic speeches in American history and a defining moment in the Civil Rights Movement.

Answer:

D

Step-by-step explanation:

The area and the radius of a sphere are related by the formula:

A=4πr^2

Let’s say this is A1 and r1

Now the radius is tripled. This means r2 = 3r1

The new area thus becomes: A = 4 * (3r)^2 * π = 36πr^2

Comparing A1 and A2 , we can see that A2 = 9A1

Answer: the expected population in 1999 is 1412

Step-by-step explanation:

The population is decreasing in geometric progression. This is true because there is a common ratio between consecutive years.

Common ratio = 24500/35000 = 17150/24500 = 0.7

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 35000

r = 0.7

n = 10

The 9th term, T9 is

T9 = 35000 × 0.7^(10 - 1)

T9 = 35000 × 0.7^9

T9 = 1412

Answer:

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Step-by-step explanation: