Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (6, 1) and (5, 4)

Answer:

17807cm2

Step-by-step explanation:

Surface area of a hexagonal prism is =( (3√3)/2) a^2 h

= 2.598 * 15.5^2 *28.5

= 2.598* 240.5* 28.5

=17807.34cm2

Answer:

-26

Step-by-step explanation:

a(6)=-2(6)-14

a(6)=-12-14

a(6)=-26

Hope this helped!

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The 6th value in the sequence = an=−2n−14 = -4.3

Take n = 6

⇒  a6 = -2·6 -14 = -12-14 = -26

∴ a= [tex]\frac{-26}{6}[/tex] = -4.3

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geomrietc, or harmonic sequence.

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Answer:

I think it is 5 but don't take my word for it

Step-by-step explanation:

I think you minus 20 - 15 which equals to 5 so 20 - 15 = 5 hopefully i was a little helpful just try that if its not correct i'm so sorry i will practice my math and answer this question again thank you for being so understanding                                                                

Answer:

Correct answer: Alex can finish the same job in 60 hours

Step-by-step explanation:

The appropriate equation for this situation is:

1/20 + 1/x = 1/15  => (x + 20) / 20x = 1/15 => 15 · (x + 20) = 20x =>

15x + 300 = 20x  => 5x = 300  => x = 300/5 = 60 hours

x = 60 hours

God is with you!!!

the equations are:

[tex]\[ c^2 = a^2 + b^2 \][/tex]

[tex]\[ a^2 = c^2 - b^2 \][/tex]

[tex]\[ b^2 = c^2 - a^2 \][/tex]

In a right triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. So, we have:

[tex]\[ c^2 = a^2 + b^2 \][/tex]

This equation represents the relationship among the side lengths of a right triangle.

Therefore, the equations are:

[tex]\[ c^2 = a^2 + b^2 \][/tex]

[tex]\[ a^2 = c^2 - b^2 \][/tex]

[tex]\[ b^2 = c^2 - a^2 \][/tex]

This completes the three relations among a, b, andc.

The complete Question is given below:

A right triangle has side lengths of a,b , and c units. The longest side has a length of c units. Complete each equation show three relations among a,b , and c .

Type the answers in the boxes below.

c^(2)= _____

a^(2)= _____

b^(2)= _____

Answer:

Domain  (0, ∞)  and Range (-∞, ∞).

Step-by-step explanation:

The domain of f(x) = 0.5^x is all values of x and the range is f(x)>0  as  0.5^x  cannot be negative or zero.

In interval form this is Domain is (-∞, ∞) and Range is  (0, ∞).

So its inverse has Domain  (0, ∞)  and Range (-∞, ∞).

The requierd domain (0, ∞) and range (-∞, ∞) of the inverse of f(x) = 0.5ˣ.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

The exponential function is given in the question, as follows:

f(x) = 0.5ˣ

Here the domain of f(x) = 0.5ˣ is all values of x and the range is f(x) > 0  as f(x) = 0.5ˣ  cannot be negative or zero.

In interval form, the Domain is (-∞, ∞) and the Range is (0, ∞).

As a result, its inverse has Domain (0, ∞) and Range (-∞, ∞)

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Answer:

Step-by-step explanation:

Triangle GHI is a right angle triangle.

From the given right angle triangle,

HI represents the hypotenuse of the right angle triangle.

With m∠H as the reference angle,

GH represents the adjacent side of the right angle triangle.

GI represents the opposite side of the right angle triangle.

To determine m∠H, we would apply

the Sine trigonometric ratio.

Sine θ = opposite side/hypotenuse. Therefore,

Sin H = 9/10 = 0.9

m∠H = Sin^-1(0.9)

m∠H = 64.2° to the nearest tenth.

Answer:

The company's daily fixed cost=$8000

The marginal cost per cycle=Slope=$ 25

Step-by-step explanation:

We are given that

Factory produces bicycle in a day=[tex]x_1=[/tex]100

Total cost,[tex]y_1=[/tex]$10,500

Factory produces bicycles in a day,[tex]x_2[/tex]=120

Total cost=[tex]y_2=[/tex]$11,000

There are two points (100,10500) and (120,11000)

Slope =[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the formula

[tex]m=\frac{11000-10500}{120-100}=\frac{500}{20}=25[/tex]

Slope-intercept form

[tex]y=mx+c[/tex]

Where m=Slope of line

c=y-intercept

Substitute the values

[tex]10500=25(100)+c[/tex]

[tex]10500=2500+c[/tex]

[tex]c=10500-2500=8000[/tex]

y-intercept=8000

Substitute the values in the equation

[tex]y=25x+8000[/tex]

Therefore, company's daily fixed cost=$8000

The marginal cost per cycle=Slope=$ 25

Answer:

1. Area of a square = (x^2)^2 = x^4

(each side is x^2, area of a square = side^2

so (x^2)(x^2) = x^4 )

2. when x = 5

area = 5^4 = 625

3. when x = 10

area = 10^4 = 10000

Step-by-step explanation:

Hope its right!

Final answer:

The area of a square mural where the side length is a perfect square, represented as x², can be expressed as A = x⁴, which simplifies the concept of multiplying the side length by itself twice.

Explanation:

The area of a mural square, where the side length is a perfect square represented as x to the power of 2 (x²), is calculated by squaring the side length. Therefore, if x itself is a perfect square, the area A of the square mural is given by A = x² * x², which simplifies to A = x⁴. Since the side length is a perfect square, x could be expressed as y² where y is an integer, resulting in the area being y⁴, where y⁴ represents the side length squared twice.

Answer:

The correct statements are:

To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement

To see the Reconciliation report, select View report after you've successfully reconciled the account.

EXPLANATION:

The steps to reconciling a bank account using QuickBooks Online include:

1. Click on the Gear button, then on “Tools” and then “Reconcile.”

2. Click on the drop-down menu under “Accounts” and select the account you want to reconcile.

3. Enter the “Ending balance” and “Ending date” based on your bank statement information.

4. Match transactions to your bank statement and check them off one by one.

5. Apply filters so transactions are easier to find.

6. Keep going until the “Difference” field is zero and you see the Success! page.

7. Select "View Report" from the Report period drop-down arrow to view your reconciliation report.

The two options that are correct regarding bank account reconciliation QuickBooks online are:

Quickbooks is an Accounting Application that aids in the collection, processing, analyses, and reporting of Accounting and Financial Information for organizations.

It is a tool that is very useful for business owners.

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Answer: 16 men

32 women

38 children

Step-by-step explanation:

Let x represent the number of men in the group.

Let y represent the number if women in the group.

Let z represent the number of children in the group.

A group of 86 people consist of men women and children. This means that

x + y + z = 86 - - - - - - - - - - - - 1

There are twice as many women than there are men. It means that

x = y/2

There are 6 more children than there are women. This means that

z = y + 6

Substituting x = y/2 and z = y + 6 into equation 1, it becomes

y/2 + y + y + 6 = 86

multiplying through by 2, it becomes

y + 2y + 2y + 12 = 172

5y = 172 - 12 = 160

y = 160/5 = 32

x = y/2 = 32/2

x = 16

z = y + 6 = 32 + 6

z = 38

There are 16 men, 32 women, and 38 children in the group.

Let the number of men be M, the number of women be W, and the number of children be C.

From the given information, we have the following equations:

W = 2M (Twice as many women as men)

C = W + 6 (6 more children than women)

The total number of people is given as 86:

M + W + C = 86

Substituting the values of W and C in terms of M into the third equation, we have:

M + 2M + (2M + 6) = 86

5M + 6 = 86

5M = 80

M = 16

Substituting the value of M in the first equation, we have:

W = 2(16) = 32

Finally, substituting the value of W in the second equation, we have:

C = 32 + 6 = 38

Therefore, there are 16 men, 32 women, and 38 children in the group.

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Final answer:

To calculate the cost, multiply the amount of turkey per student (0.3 pounds) by the number of students (100), then multiply the total pounds needed (30) by the cost per pound ($0.79), resulting in a total cost of $23.70 for turkey for 100 students.

Explanation:

The question asks us to calculate the cost of providing turkey to 100 students if each student requires 0.3 pounds of turkey, and turkey costs $0.79 per pound. To find the total amount of turkey needed, we multiply the amount each student gets by the total number of students: 0.3 pounds/student × 100 students. This calculation results in 30 pounds of turkey required for 100 students.

Next, to determine the total cost, we multiply the total pounds of turkey needed by the cost per pound: 30 pounds × $0.79/pound. This calculation gives us a total cost of $23.70 for the turkey.

Therefore, it will cost $23.70 to give turkey to 100 students.

Answer:   [tex]\dfrac{5}{9}[/tex]

Step-by-step explanation:

When we throw a die , Total outcomes =6

When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]

Given : Three fair dice are rolled, one red, one green and one blue.

Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed

By Permutations , the number of favorable outcomes = [tex]^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120[/tex]

The probability that the upturned faces of the three dice are all of different numbers = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{120}{216}=\dfrac{5}{9}[/tex]

The probability that the upturned faces of the three dice are all of different numbers  is [tex]\dfrac{5}{9}[/tex] .

Answer:

The answer to your question is 1.- (-3, 4)    2.-   (3, 1)  None of the choices

Step-by-step explanation:

1.- The solution of a system of equation by the graph method is the point in which the lines cross. In this graph we observe that this point is approximately

(-3, 4).

2.-

Equation 1   x + y = 4

Equation 2  x - y = 2

Solve by the combination method

                   x + y = 4

                  x  -  y = 2

                 2x    0  = 6

                        2x = 6

Solve for x

                          x = 6/2

                          x = 3

Substitute x in equation 1 to find y

                    3 + y = 4

Solve for y

                          y = 4 - 3

                          y = 1

Solution     (3, 1)                          

Answer:22in2

Step-by-step explanation:

Answer:

The correct option is second one i.e 24 units.

Therefore the height of the triangle is

[tex]NR=24\ units[/tex]

Step-by-step explanation:

Given:

An equilateral triangle has all sides equal.

ΔMNO is an Equilateral Triangle with sides measuring,

[tex]NM = MO = ON =16\sqrt{3}[/tex]

NR is perpendicular bisector to MO such that

[tex]MR=RO=\dfrac{MO}{2}=\dfrac{16\sqrt{3}}{2}=8\sqrt{3}[/tex] .NR ⊥ Bisector.

To Find:

Height of the triangle = NR = ?

Solution :

Now we have a right angled triangle NRM at ∠R =90°,

So by applying Pythagoras theorem we get

[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]

Substituting the values we get

[tex](MN)^{2} = (MR)^{2}+(NR)^{2}\\\\(16\sqrt{3})^{2}=(8\sqrt{3})^{2}+(NR)^{2}\\\\(NR)^{2}=768-192=576\\Square\ rooting\ we\ get\\NR=\sqrt{576}=24\ units[/tex]

Therefore the height of the triangle is

[tex]NR=24\ units[/tex]

Answer:

b 24

Step-by-step explanation:

Answer:

Discussed below.

Step-by-step explanation:

The headline states that 98% of all movies show imagery of drugs. There are a few assumptions that the wording can insinuate:

However, the story refers to a more specific statistic: that not 98% of all movies but 98% of the top movie rentals depicted drug use, drinking or smoking.

The key differences:

Thus, the headline misrepresents the content of the story which may lead one to make broader and misplaced conclusion about imagery of drugs in movies.

The headline accurately reflects the information provided in the news story, but the accuracy is dependent on the credibility and methodology of the government study.

The headline "Drugs shown in 98 percent of movies" accompanied a news story about a "government study" claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals.

First, it's important to note that the headline accurately reflects the information provided in the news story. However, the accuracy of the headline is dependent on the credibility and methodology of the government study being referenced.

Without additional information about the study, such as the sample size, selection criteria, and methodology, it is difficult to fully assess the accuracy of the headline. It's always important to critically evaluate the sources of information and consider multiple perspectives in order to draw accurate conclusions.

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Answer:

Step-by-step explanation:

The current global population is growing at an annual rate of 1.35 percent. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 6.1 × 10^9

r = 1.35% = 1.35/100 = 0.0135

t = 1

Therefore

A = 6.1 × 10^9(1 + 0.0135)^1

A = 6.1 × 10^9(1.0135)^1

A = 6182350000

The number of people that would be added is

6182350000 - 6100000000

= 82350000

If the world population were to keep growing at 1.35%, we number of people who would be added next year is 82,350,000 people.

The population of the world is growing at 1.35%. This means that next year, the number of people added will be 1.35% of the current population.

The current population is 6.1 billion so the number of people who will be added is:

= Population x Incremental rate

= 6,100,000,000 x 1.35%

= 82,350,000 people

In conclusion, 82,350,000 people will be added.

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Answer:

($13,300,$46,900)

Step-by-step explanation:

We are given the following in he question:

Mean, μ = $30,100

Standard Deviation, σ = $5,600

Chebyshev's Theorem:

[tex]1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%[/tex]

Thus, 89% of data lies within three standard deviation of mean.

[tex]\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900[/tex]

Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)

Answer: Leah has 15 stickers left for herself.

Step-by-step explanation:

Total number of stickers that Leah had initially is 50. Leah gave 1/2 of the stickers to her sister. This means that the number of stickers that Leah gave to her sister is

1/2 × 50 = 25 stickers

Of the amount left, she gave 2/5 to her friend. This means that the number of stickers that Leah gave to her friend is

2/5 × 25 = 10 stickers

Therefore, the number of stickers that Leah have left for herself is

50 - (25 + 15)

= 50 - 35

= 15

After giving away some of her stickers to her sister and friend, Leah has 15 stickers left for herself.

Leah initially had 50 stickers. She gave half of them to her sister, which left her with 50/2 = 25 stickers. Then, she gave away 2/5 of these remaining stickers to her friend.

To calculate how many she gave her friend, we multiply 25 * 2/5 = 10 stickers.

To find out how many Leah has left for herself, we subtract this from the number she had after giving stickers to her sister: 25 - 10 = 15 stickers.

So, Leah has 15 stickers left for herself.

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Answer:

option C

Step-by-step explanation:

In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon

The ration of spice mix over Cinnamon is

[tex]\frac{\frac{3}{4} }{\frac{5}{6} } =\frac{3}{4} \cdot \frac{6}{5} =\frac{9}{10}[/tex]

Let x be the spice mix per pound

make a proportion

[tex]\frac{9}{10} =\frac{1}{x}[/tex]

cross multiply

[tex]9x=10\\x=\frac{10}{9}\\x= 1 \frac{1}{9}[/tex]

option C is the answer

Answer:

23

Step-by-step explanation:

We take a methodical approach by considering the different possible values of b when asqrtb is the simplest form of sqrtn.

Case 1: b=1. We can't forget the perfect squares! If n=100, for example, then sqrt100 can be written as 10sqrt1. So, we must include the perfect squares from 10^2=100 up through 22^2 = 484. (All greater squares are greater than 500.) There are 13 such squares.

Case 2: b=2. If b=2, then we have asqrtb = asqrt2 = sqrta^2 x sqrt2 = sqrt2a^2. We still must have a {>_} 10, but now we need 2a^2 to be no greater than 500. This means that a^2 must be no greater than 250, so a can be 10, 11, 12, 13, 14, or 15. There are 6 such values.

Case 3: b=3. We then have asqrtb = asqrt3 = sqrt3a^2. Since 3a^2 {<_} 500, we know that a^2 is less than 167. We still need a {>_} 10, so there are only 3 values of a in this case: 10, 11, 12.

We skip b=4 because then asqrtb would not be in simplest form.

Case 4: b=5. We then have asqrtb = sqrt5a^2, and a=10 is the only possible value for this case.

For any greater value of b, the resulting value of n is greater than 500 when a {>_} 10. So, there are no more possible numbers asqrtb that satisfy the problem. Since each of the 13+6+3+1 = 23 possibilities listed above represent different simplified forms, they give us 23 different possible values of n that satisfy the problem.

There are infinitely many positive integers less than 500 that have square roots in the form of a√b, where a and b are integers with a≥10.

The number of such positive integers n is infinite, as there is no finite value for the count.

Here,

We are looking for positive integers n that are less than 500.

The square roots of these integers can be expressed in the form a√b.

And [tex]a\ge 10[/tex]

To find the number of positive integers less than 500 that have square roots in the form of a√b,

Analyze the possible values of a and b separately:

For a,

We know that it must be an integer greater than or equal to 1. So,

We have a total of a = 10, 11, 12  ..., and so on. (since a ≥ 10)

As for b,

it can be any perfect square less than or equal to 500.

Let's list a few examples:

b = 1, since 1√1 = 1

b = 4, since 1√4 = 2

b = 9, since 1√9 = 3

b = 16, since 1√16 = 4

...

b = 484, since 1√484 = 22

Now, we can count the number of possibilities for a and b.

We have an infinite number of possibilities for a, but b has a finite number of perfect squares less than or equal to 500.

There are 22 perfect squares within this range.

Therefore, the total number of positive integers n, with n < 500, that have square roots in the form of a√b is 22 x infinity = infinity.

Since there are infinitely many possible values for n,

Hence,

We can conclude that there is no finite value for the number of positive integers n that satisfies this condition.

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Answer:

Mona = 8, Shakira = 16

Step-by-step explanation:

S = 2m....m = S/2

2S + S = 24

3S = 24

S = 24/3

S = 8

Mona = 8

Shakira = 16

Answer:

3.75 gallons

Step-by-step explanation:

Answer:

Fx=N177.007

Step-by-step explanation:

Let us first concentrate on the central value. Take F0 = 325 and theta 0 = 57 degrees. Find the central value of Fx, in N

can be pu as thus from an online resource

To resolve forces into the horizontal component , we have

Fx=fCosФ

Fx=325Cos57

Fx=N177.007

Take Note that a force is that which tends to change a body's state of rest or uniform motion in a straight line.

Answer:

X=2y-3

Step-by-step explanation:

Let Rebecca's age be x

Let Anthony's age be y

Twice Anthony =2y

Rebecca's age (x) to be 3 years younger than twice Anthony's =2y-3

So, it's x=2y-3

Answer:

[tex]y=-\frac{74}{21}x+452[/tex]

Step-by-step explanation:

Given:

The level of a lake is falling linearly.

On Jan 1, the level is 452 inches

On Jan 21, the level is 378 inches.

Now, a linear function can be represented in the form:

[tex]y=mx+b[/tex]

Where, 'm' is the rate of change and 'b' is initial level

[tex]x\to number\ of\ days\ passed\ since\ Jan\ 1[/tex]

[tex]y\to Lake\ level[/tex]

So, let Jan 1 corresponds to the initial level and thus b = 452 in

Now, the rate of change is given as the ratio of the change in level of lake to the number of days passed.

So, from Jan 1 to Jan 21, the days passed is 21.

Change in level = Level on Jan 21 - Level on Jan 1

Change in level = 378 in - 452 in = -74 in

Now, rate of change is given as:

[tex]m=\frac{-74}{21}[/tex]

Hence, the function to represent the lake level is [tex]y=-\frac{74}{21}x+452[/tex]

Where, 'x' is the number of days passed since Jan 1.

Final answer:

The lake level can be represented by a linear function L(t) = -3.7t + 452, where L(t) is the lake level in inches and t is the time in days from January 1st.

Explanation:

To find a function representing the lake level as it drops linearly over time, we need to determine the linear equation that corresponds to the change in the lake level.

We are given that the lake level is 452 inches on January 1st and 378 inches on January 21st.

First, we will define the variables where L(t) is the lake level in inches and t is the time in days with t=0 corresponding to January 1st.

We are given two points on the linear function: (0, 452) and (20, 378), since January 21st is 20 days after January 1st.

Next, we calculate the slope of the line using the formula:

slope = (change in lake level) / (change in time) = (378 - 452) / (20 - 0) = -74 / 20 = -3.7 inches per day.

Now, we can use the slope and a point to write the equation of the lake level as a function of time in the slope-intercept form:

L(t) = mt + b

where m is the slope and b is the y-intercept. Plugging in the slope and the point (0, 452):

L(t) = -3.7t + 452

This equation represents the function of the lake level over time.

Answer:

She buy 0.5 pounds of black olives and 3.5 pounds of green olives.

Step-by-step explanation:

Given:

Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives.

Black olives cost three dollars a pound. Green olives cost five dollars a pound.

She spends $15.50.

Now, to find the pounds of olives she buy.

Let the pounds of black olives be [tex]x.[/tex]

And the pounds of green olives be [tex]y.[/tex]

So, total pounds of olives:

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

[tex]x=4-y[/tex]    ........( 1 )

As, given the cost of black olives $3 a pound.

And cost of green olives $4 a pound.

Now, the total money spends:

[tex]3x+4y=15.50[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]3(4-y)+4y=15.50[/tex]

[tex]12-3y+4y=15.50[/tex]

[tex]12+y=15.50[/tex]

Subtracting both sides by 12 we get:

[tex]y=3.5[/tex]

The green olives = 3.5 pounds.

Now, substituting the value of [tex]y[/tex] in equation (1):

[tex]x=4-y\\x=4-3.5\\x=0.5\ pounds.[/tex]

The black olives = 0.5 pounds.

Therefore, she buy 0.5 pounds of black olives and 3.5 pounds of green olives.

Final answer:

Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party, determined by solving a system of equations representing the total weight and cost of the olives.

Explanation:

How Many Pounds of Black and Green Olives did Susan Buy?

To determine how many pounds of black and green olives Susan bought, we need to create a system of equations based on the information provided:

Let x be the number of pounds of black olives Susan bought, and let y be the number of pounds of green olives.

The first equation will represent the total weight of olives:

1. x + y = 4 (since Susan bought 4 pounds of olives in total)

The second equation will represent the total cost of olives:

2. 3x + 5y = 15.50 (because black olives cost $3 per pound and green olives cost $5 per pound)

Now, let's solve this system of equations:

Multiplying the first equation by 3 gives us a new equation:
3x + 3y = 12

Now, we subtract this new equation from the second equation to find y:

(3x + 5y = 15.50) - (3x + 3y = 12)

2y = 3.50
y = 1.75

So, Susan bought 1.75 pounds of green olives. We can now substitute y into the first equation to find x:

x + 1.75 = 4
x = 4 - 1.75
x = 2.25

Therefore, Susan bought 2.25 pounds of black olives.

In conclusion, Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party.

Answer:

[tex]25\ seconds[/tex]

Step-by-step explanation:

Hi,

Time, speed and distance are related by a very simple formula:

[tex]Distance = Time \times Speed[/tex]

Which can easily be used here to solve the question.

To find the time, we require:

Speed:

This is given in the question as 4 ft/ sec.

Distance:

On a circle, the distance from the end of the circle to the centre is referred to as "Radius". We shall assume the radius here is [tex]r[/tex].

To calculate the radius, we can use the formula of the circumference: [tex]C = 2 \pi r[/tex]

Were are given that C = 628 feet.

Using the formula: [tex]r = \frac{628}{2 \pi} = 100\ feet[/tex]

The distance the boat needs to travel is 100 feet.

Time:

To calculate time, we alter the provided formula to: [tex]Time = \frac{Distance}{Speed}[/tex]

Substituting the values in this: [tex]Time = \frac{r}{4}[/tex]

[tex]Time = \frac{100}{4} = 25\ seconds[/tex]

The boat requires 25 seconds to travel from the edge of the pond to centre.