In the following problem, which step uses the additive identity to get to the next step?

-18 + 73 + 18
-18 + 18 + 73
0 + 73
73

Answer:

Step-by-step explanation:

width is 255/15=17

perimeter = 17*2+15*2=64

EZ

There is no danger of a collision, as the two paths will never met, due to the negative discriminant of the quadratic function.

A quadratic equation is modeled by the general equation presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given by the equation as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:

The equations for this problem are given as follows:

Replacing the first equation into the second, we have that:

x + x² + 1 = -4

x² + x + 5 = 0.

The coefficients are:

a = 1, b = 1, c = 5.

Hence the discriminant is of:

Δ = 1² - 4 x 1 x 5

Δ = -19.

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The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

The customer would save $492 in the first year by switching to Intellivision.

The customer would save $207 in the second year by switching to Intellivision.

For the third year, it would be cheaper to stick with ElectroniSource.

To calculate the savings for the first year, we need to find the total cost for ElectroniSource and compare it to the flat fee from Intellivision for all three services.

The savings for the first year by switching to Intellivision would be:

$1,632 - $1,140 = $492

Therefore, the customer would save $492 in the first year by switching to Intellivision.

After the first year, Intellivision raises the rates by 25%. So the new flat fee for the second year would be:

$95 + ($95 x 25%) = $118.75

The savings for the second year by switching to Intellivision would be:

$1,632 - $1,425 = $207

Therefore, the customer would save $207 in the second year by switching to Intellivision.

For the third year, Intellivision raises the rates by 16% compared to the second year. So the new flat fee for the third year would be:

$118.75 + ($118.75 x 16%) = $137.78

Therefore, for the third year, it would be cheaper to stick with ElectroniSource, which costs $1,632 for the year, compared to Intellivision, which costs $1,653.36 for the year.

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The given inequality is

The given coordinates are (7,4), (3.8, 4) and (0,9).

Let's evaluate each coordinated pair in the inequality to see which one satisfies it.

For (7,4).

Since 3 is not more than 8, we say (7,4) is not a solution.

For (3.8, 4).

Since -0.2 is not more than 8, we say (3.8, 4) is not a solution.

For (0,9).

Since -9 is not more than 8, we say (0,9) is not a solution.

The variance of the scores in a sample tends to be less than or equal to the variability of the scores in the population from which the sample was obtained.

When we take a sample from a population, it is expected that the variability within the sample will be somewhat representative of the variability in the population. However, due to the random nature of sampling, there is a chance that extreme scores or outliers in the population may not be fully captured in the sample, resulting in slightly reduced variability. Therefore, the sample variance typically provides an estimate that is close to the population variance but is generally smaller due to the potential sampling variability.

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Answer:

4ln x +ln 3-lnx

4ln x -ln x+ln3

3ln x+ln 3

ln(3x+3)is equivalent.

Answer:it’s 3

Step-by-step explanation: imma big brain

Answer:

3

Step-by-step explanation:

the answer on edge

Step-by-step explanation:

5 meters = 50 decimeters (10 decimeters per meter)

500 centimeters (100 centimeters per meter)

5000 millimeters (1000 millimeters per meter)

I HOPE IT HELPS YOU

The correlation coefficient measures the proportion of the dependent variable's overall fluctuation that the independent variable adequately captures.

The relationship between two parametric variables is represented by the correlation coefficient. It ranges from -1 to +-1. It means there is no correlation between the two variables when it is 0. When it is 1 or 1, there is a significant correlation between the variables.

Determinant coefficient: It shows how much of the variance in the dependent variable can be accounted for by the independent variable. It ranges from 0 to 1 and is represented by the symbol R2.

As a result: b) The coefficient of determination is the proportion of the dependent variable's variation that can be attributed to the independent variable.

Answers that are incorrect:

a) A linear regression is one that employs a regression formula with the form y=ax=b.

c) Correlation is a metric for determining how two variables are related.

d) The statistical technique of regression is used to build mathematical models that link two or more variables.

Option B is the proper response, thus.

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Step-by-step explanation:

To write this line in the slope-intercept (y=mx+c) form, all we need in addition to the information given is the slope. Since we know the x-intercept and y-intercept,

then slope = value of y-intercept ÷ (- value of x-intercept)

                  = ¹/₂

∴ the line is y = ¹/₂ x - 1

Answer: the first equation is the answer.

Step-by-step explanation: As you can see the first equation is 5/7=15/21. The are proportional because 5*3=15 and 7*3=21. If they are multiplied or divided by the same number, then they are proportional. It does not work with adding, subtracting or flipping.

In the equation 2X1 + 3X2 ≥ 20, there are no units of the resource that are unused.

If X1 = 5 and X2 = 4, then the left-hand side of the constraint equation becomes:

2X1 + 3X2 = 2(5) + 3(4) = 10 + 12 = 22

Since this value is greater than or equal to 20 (the right-hand side of the constraint equation), we know that the constraint is satisfied with this choice of X1 and X2.

To determine how many units of the resource are unused, we can look at the difference between the left-hand side of the constraint equation and the actual amount of the resource used. In this case, the actual amount of the resource used is:

5 units of X1

4 units of X2

So the total resource used is:

2(5) + 3(4) = 10 + 12 = 22

Therefore, the number of units of the resource that are unused is:

20 - 22 = -2

This means that there is no unused resource. In fact, the resource is being overused by 2 units. This violates the constraint equation, which requires that the left-hand side be greater than or equal to 20. In this case, the left-hand side is 22, which is greater than 20, but it should not exceed the available resource limit of 20.

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Answer:

It is 25 units

Step-by-step explanation:

The triangles are equal

Answer:

25 Units.

Step-by-step explanation:

The Triangles are equal and have the same area. Therefore, the longest side of ΔDEF and ΔABC will measure the same.

Answer:

(1,5)

Step-by-step explanation:

\(4x + 1 = 2x + 3 \\ 2x = 2 \\ x = 1 \\ y = 5\)

Answer:

-6-3

Step-by-step explanation:

Answer:

the slope is 2 and a=8 b=6

Step-by-step explanation:

A) the equation of a plane has three parameters: "a," "b," and "c."

B) Replace "x" and "y" with the specific values you have, and then calculate the corresponding value of "z." This prediction would give you an estimate of the z-value on the plane for the given x and y-values.

a) If the data points all fell approximately on a plane, a common function used to model such data is the equation of a plane in three-dimensional space. The general equation of a plane can be written as:

z = ax + by + c

In this equation, "z" represents the dependent variable (the value we want to predict), while "x" and "y" represent the independent variables (the given x and y-values). The coefficients "a," "b," and "c" are the parameters of the model.

The parameter "a" represents the weight or influence of the x-variable on the plane's orientation. It determines how much the plane changes in the z-direction as the x-value increases.

Similarly, the parameter "b" represents the weight or influence of the y-variable on the plane's orientation. It determines how much the plane changes in the z-direction as the y-value increases.

The parameter "c" is the intercept term, which represents the height of the plane above the xy-plane (when both x and y are zero).

Therefore, the equation of a plane has three parameters: "a," "b," and "c."

b) To use the model to predict a z-value corresponding to given x and y-values, you would substitute the known values of x and y into the equation of the plane:

z = ax + by + c

Replace "x" and "y" with the specific values you have, and then calculate the corresponding value of "z." This prediction would give you an estimate of the z-value on the plane for the given x and y-values.

It's important to note that this modeling assumes a linear relationship between the variables x, y, and z. If the relationship is nonlinear, you may need to consider alternative models, such as polynomial regression or other nonlinear regression technique

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The composite functions are fg(x) = (8x - 3)(x + 4); f/g(x) = (8x - 3)/(x + 4) and fg(2) = 78; f/g(2) = 2.17

The quadratic function in standard form is f(x) = 2x² + 2x - 4

Given that

f(x) = 8x - 3

g(x) = x + 4

So, we have

fg(x) = (8x - 3)(x + 4)

f/g(x) = (8x - 3)/(x + 4)

The value of x is 2

So, we have

fg(2) = (8(2) - 3)(2 + 4)

f/g(2) = (8(2) - 3)/(2 + 4)

Evaluate

fg(2) = 78

f/g(2) = 2.17

Here, we are given the table of values

The quadratic function can be calculated using

f(x) = a * product of (x - roots)

So, we have

f(x) = a(x + 2)(x - 1)

Using the function values, we have

a(0 + 2)(0 - 1) = -4

Evaluate

a = 2

So, the function is

f(x) = 2(x + 2)(x - 1)

Expand

f(x) = 2x² + 2x - 4

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Davidson has just arrived at the foothills of the Rockies and is on a cross-country motorcycle trip. He intends to take an hour longer on the east side of the 245 km trip than on the west side of the 225 km trip. On the downhill side, he intends to average 20 km/h more to achieve this. The trip through the Rockies will take approximately 17.375 hours.

Let the speed of the motorcycle on the west side of the trip be x km/h.

So, the time required to complete the 225 km trip will be:

Time for the west side of the trip = 225/x

Let the speed of the motorcycle on the east side of the trip be x + 20 km/h.

So, the time required to complete the 245 km trip will be:

Time for the east side of the trip = 245 / (x + 20)

We know that the time Davidson takes on the east side of the trip will be an hour longer than on the west side. Therefore, we can form the following equation:

245/(x + 20) = 225/x + 1

Multiplying both sides by x(x + 20),

we get:245x = 225(x + 20) + x(x + 20)

Simplifying the equation:20x = 400x = 20 km/h

Time taken on the west side of the trip is 225/20 = 11.25 hours

Time taken on the east side of the trip is 245/40 = 6.125 hours

So the total time for the trip through the Rockies is 11.25 + 6.125 = 17.375 hours, or about 17 hours and 22.5 minutes (rounded to the nearest minute).

Therefore, the trip through the Rockies will take approximately 17.375 hours.

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Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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The greatest number of bags required to pack the items such that 10 bags remain empty is 2,400 bags.

To find the greatest number of bags required to pack the items such that 10 bags remain empty, we need to determine the number of items in each bag.

Let's assume the number of items in each bag is x.

The total number of bottles of sanitizer is 240, the total number of face shields is 480, and the total number of masks is 600.

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

Number of bags for sanitizers: 240 / x

Number of bags for face shields: 480 / x

Number of bags for masks: 600 /x

Since the number of bags for each item type must be equal, we can set them equal to each other:

240 / x = 480 / x = 600 / x

To find the greatest number of bags, we need to find the least common multiple (LCM) of the three fractions.

The LCM of 240, 480, and 600 is 2,400.

So, x = 2,400.

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This system of linear Equations gives us c = 2, b = 2, and a = -1. Therefore, the coordinate vector of 1+4t+6t2 relative to the basis S is [-1, 2, 2].

(a) To find the coordinate vectors of each polynomial with respect to the standard basis for P2, we simply need to write each polynomial as a linear combination of the standard basis vectors {1, t, t2}.

1+t = 1(1) + 1(t) + 0(t2) = [1, 1, 0]

12t+02 = 1(0) + 2(t) + 1(t2) = [0, 2, 1]

1+t+3t2 = 1(1) + 1(t) + 3(t2) = [1, 1, 3]

(b) To show that the polynomials are linearly independent, we need to show that the only solution to the equation a(1+t) + b(12t+02) + c(1+t+3t2) = 0 is a = b = c = 0.

We can rewrite the equation as a system of linear equations:

a + c = 0

b + c = 0

3c = 0

From the third equation, we can see that c must be 0. Substituting this into the first two equations gives us a = b = 0. Therefore, the only solution to the equation is a = b = c = 0, which shows that the polynomials are linearly independent.

(c) S must be a basis for P2 because it is a set of three linearly independent vectors in P2. This means that S spans P2 (i.e., any polynomial in P2 can be written as a linear combination of the polynomials in S) and that S is the smallest possible set of vectors that spans P2.

(d) To find the coordinate vector of 1+4t+6t2 relative to the basis S, we need to solve the equation a(1+t) + b(12t+02) + c(1+t+3t2) = 1+4t+6t2 for a, b, and c.

Expanding the left side of the equation and comparing coefficients with the right side, we get:

a + b + c = 1

b + c = 4

3c = 6

Solving this system of linear equations gives us c = 2, b = 2, and a = -1. Therefore, the coordinate vector of 1+4t+6t2 relative to the basis S is [-1, 2, 2].

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The number of possible combinations of 8 objects taken 6 at a time is 28. Then the correct option is D.

Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

The number of possible combinations of 8 objects taken 6 at a time.

Then the number of the combination is given as

\(\rm ^8C_6 = \dfrac{8!}{(8-6)! 6!}\\\\\\^8C_6 = \dfrac{8 \times 7 \times 6!}{2 \times 1 6!}\\\\\\^8C_6 = 7 \times 4\\\\\\^8C_6 = 28\)

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Answer:

rise over run (change in y divided by change in x)

so it would go as follows

\(\frac{(3-1)}{(4-9)}\)

= \(\frac{2}{-5}\)

= \(-\frac{2}{5}\)

Answer: - (2/5)

Step-by-step explanation:

(y2-y1) / (x2- x1) =

(1-3) / (9-4)

= - (2/5)