For those who are on Plato and have done this tutorial,please tell me the answer to this question. And it can't be equilibrium,because I tried that and it didn't work.

The number of dollars Laura should pay at the dinner party is $84.

Given that, the last time Laura hosted a fancy dinner party for her friends, she spent $108 to feed 9 people. This time, there will be only 7 people at the dinner party.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the number of dollars paid by Laura for 7 people be x.

Now, 9:108::7:x

⇒9x=108×7

⇒x=12×7

⇒x=84

Therefore, the number of dollars Laura should pay at the dinner party is $84.

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Answer:

y = 9

Step-by-step explanation:

-2y + 6 = -12

       -6     -6

-2y = -18

divide both sides by -2

y = 9

Hope this Helps!!!

Answer: y = -3

Step-by-step explanation:

Answer: the Dorians were far less advanced then the Mycenaean Greeks; economy collasped and trade stopped

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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The number of hours of overtime paid each week is an illustration of a geometric progression

The explicit rule is \(T_n = 20 * 1.5^{n-1}\)

The hours are given as:

20, 30, 45, and 67.5

The above function is a geometric function, and it is represented as:

\(T_n = ar^{n -1}\)

Where:

\(a = 20\) --- the first term

And we have:

\(r = \frac{30}{20}\)

\(r =1.5\)

So, we have:

\(T_n = 20 * 1.5^{n-1}\)

Hence, the explicit rule is \(T_n = 20 * 1.5^{n-1}\)

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Answer: the ordered pair negative 3 over 8, negative 5 over 8

Step-by-step explanation:

Answer:

dis look like it from flvs lol um imma try nd help out alright

uhhh um itz a bit hard so imma take a guess imma go with b

Step-by-step explanation:

nd since ur running low on points u can go to my account answer my questions with 2+2+4+5=13 or somethin like dat or take a guess

Answer:

\(P(head) = 0.5600\)

Step-by-step explanation:

Given

\(n = 500\) -- number of toss

\(head = 280\) --- outcomes of head

See comment

Required

Empirical probability of head

This is calculated as:

\(P(head) = \frac{n(head)}{n}\)

\(P(head) = \frac{280}{500}\)

\(P(head) = 0.5600\)

Answer:

Step-by-step explanation:

5/2

The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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Answer:

15

Step-by-step explanation:

.

Answer: 15

Step-by-step explanation:

This is the same as writing y = sqrt(4(x+5)) - 1

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

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

The northerly component of the wind blowing at 15 m/s from the South East is approximately 10.605 m/s.

To determine the northerly component of a wind blowing from the South East, we need to consider the direction from which the wind is coming and its magnitude.

A wind blowing from the South East means it is coming from the South East direction towards the opposite direction, which is the North West. Since the wind is coming from the South East, we can say it has a southeasterly direction.

To find the northerly component, we need to break down the wind vector into its north and east components. The northerly component represents the part of the wind that is directed towards the north.

If we assume that the wind is blowing at an angle of 45 degrees with respect to the North, we can use trigonometry to find the components. Since the wind is blowing at 15 m/s, we can consider it as the hypotenuse of a right triangle.

The northerly component can be found using the sine of the angle:

Northerly Component = Wind Speed * sin(Angle)

Northerly Component = 15 m/s * sin(45°)

Using the value of sin(45°) (which is √2 / 2 ≈ 0.707), we can calculate the northerly component:

Northerly Component ≈ 15 m/s * 0.707

Northerly Component ≈ 10.605 m/s

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Answer:

To convert pounds to rands, you need to know the current exchange rate between the two currencies. Once you have the exchange rate, you can multiply the number of pounds by the exchange rate to get the equivalent amount in rands.

For example, if the exchange rate is 1 GBP = 20 ZAR and you want to convert 100 pounds to rands, you would multiply 100 by 20, which equals 2000 rands.

Step-by-step explanation:

By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.

The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.

As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.

Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"

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Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.

To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.

First, let's simplify the equation:

2^x - 2 = 8^4

We know that 8 can be expressed as 2^3, so we can rewrite the equation as:

2^x - 2 = (2^3)^4

Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:

2^x - 2 = 2^(34)

Simplifying the right side of the equation:

2^x - 2 = 2^12

Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:

x = 12

Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.

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A boxplot is a standardized way of displaying the distribution of data based on a five-number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”). It can tell you about your outliers and what their values are.

To draw a boxplot, we need to get the five numbers outlined in the definition above from the data provided. The data provided has to be arranged in ascending order. This is shown below:

Minimum Number: 63

Maximum Number: 100

Median: The median position is calculated using the formula

where n is the number of data in the set.

For the question provided, the number of terms is 12. Therefore, the median position is:

The 6.5th position is gotten by finding the average of the 6th and 7th terms. This is shown below:

First Quartile: The position of the first quartile is gotten using the formula:

The 3.25th position is gotten by multiplying the preceding term of the position by 0.25 and the following term by 0.75 and then finding the sum. This is done below:

Third Quartile: The position of the third quartile is gotten using the formula:

The 9.75th position is gotten by multiplying the preceding term of the position by 0.75 and the following term by 0.25 and then finding the sum. Since both the 9th and 10th terms are 91, then the value of Q3 is 91.

Boxplot

This is shown below:

Answer:

14.5 pounds of apples.

Step-by-step explanation:

$3.77 ÷ $.26 = 14.5

Apples = 14.5 pounds

Hope this helps! :)

Answer:

B. 10x -40

Step-by-step explanation:

To rewrite the expression 5(2x-8) using the distributive property, we need to separate the expression inside the parentheses and then multiply the two expressions by 5. The answer is: 10x-40.

Answer:

10

Step-by-step explanation:

The least common denominator can be found by finding the LCM of the 2 denominators:

First let's list the multiples of the first denominator :

10,20,30,40,50

Now let's list the multiples of the second denominator :

5,10,15,20,25

As we can see the lowest number that appears in both lists is 10.

Therefore 10 is the least common denominator.

Answer:

1

Step-by-step explanation:

17's only factors are 1 and 17 so the GCL is 1

Answer:

6 steps forward and 6 steps backward

Explanation:

12 steps in total - 6 + 6 = 12

Answer:

Step-by-step explanation:

Which price gives the store the maximum amount of revenue, and what is the ... When graphing the function f(x)=-x+5+12 on your graphing calculator, what is the ... Based on the graph, how many real number solutions does the equation x3 + ... is challenged to a game by a classmate, which statement below is correct in all ...

Missing: 836 ‎| Must include:

Answer:

none will be left over

Step-by-step explanation:

Which price gives the store the maximum amount of revenue, and what is the ... When graphing the function f(x)=-x+5+12 on your graphing calculator, what is the ... Based on the graph, how many real number solutions does the equation x3 + ... is challenged to a game by a classmate, which statement below is correct in all ...

Answer:7 x 10 ^1 is the right answer

Step-by-step explanation:

Hope this helps :)

There is the bacterial cell 7 × 10¹ times smaller than the amoeba cell which is the correct answer would be an option (B).

Scientific Notation is a way of writing down in the easy form of very large or very small numbers.

We have been given that a bacterial cell is around 5 × 10⁻⁶ m long, while an amoeba cell is about 3.5 × 10⁻⁴ m long.

To determine the number of times smaller is the bacterial cell than the amoeba cell.

⇒ amoeba cell / bacterial cell

⇒ 3.5 × 10⁻⁴ m / 5 × 10⁻⁶ m

Apply the division operation, and we get

⇒ 0.7 × 10⁻⁴ × 10⁶

Adding the exponents of the above terms

⇒ 0.7 × 10⁻⁴⁺⁶

⇒ 0.7 × 10²

⇒ 7 × 10¹

Hence, there is the bacterial cell 7 × 10¹ times smaller than the amoeba cell.

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Answer:

a. 17 1/2

b. 16 1/5

Step-by-step explanation:

a.

convert mixed numbers to fractions

5/1 2/7

5 x 7 / 1 x 2

= 35/2 and simplify

b.

convert mixed numbers to fractions

9/1 5/9

9 x 9 / 1 x 5

= 81/5

\(5 \div \dfrac 27 = 5 \times \left(\dfrac 27 \right)^{-1} = 5 \times \dfrac 72 = \dfrac{35}2\\\\\\9\div \dfrac 59 = 9 \times \left(\dfrac 59 \right)^{-1} = 9 \times \dfrac 95 = \dfrac{81}5\)

The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 5)² + (y - 1)² = 5²

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The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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