A bus travels 12 miles west and 16 miles south from its original location. How far is the bus from the original location?

Answer:

x = 3

Step-by-step explanation:

Given

3x + 6x + 14 = 41, that is

9x + 14 = 41 ( subtract 14 from both sides )

9x = 27 ( divide both sides by 9 )

x = 3

Answer:

x=3

Step-by-step explanation:

3x+6x+14=41

9x + 14 = 41

    - 14 = - 14

9x = 27

x=3

Answer: Tessa's account balance is $-15.

Step-by-step explanation: Given that Tessa had $90 in her checking account. She paid her cable/internet bill for $75.She deposited $50 from her part-time job before writing a check for $80 to pay her credit card bill.

The remaining amount is calculated as: -

Balance = 90 + 50 - 75 -80

Balance = $-15

Hence, the account balance is $-15.

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Answer:

A

Step-by-step explanation:

Since the least square curve fit method is a flexible method for approximating the best fit to a given set of data points using several mathematical models, all of these models are suitable.

The applicable model for the least square curve fit depends on the type of data being analyzed. In this case, the question mentions a sinusoidal model as one of the options. Therefore, a least square curve fit can fit data points to a sinusoidal model, which includes sine and cosine functions. However, it may not necessarily be able to fit the data points to an exponential model, polynomial model of appropriate order, or power curve.
Least square curve fit can fit the data points to the following models:

a) sinusoidal model (including sine and cosine functions)
b) exponential model
c) polynomial model of appropriate order
d) power curve (\(y=c1x^(c2)\))

All of these models are applicable because the least square curve fit method is a versatile technique for approximating the best fit to a given set of data points using different mathematical models.

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Since the least square curve fit method is a flexible method for approximating the best fit to a given set of data points using several mathematical models, all of these models are suitable.

The applicable model for the least square curve fit depends on the type of data being analyzed. In this case, the question mentions a sinusoidal model as one of the options. Therefore, a least square curve fit can fit data points to a sinusoidal model, which includes sine and cosine functions. However, it may not necessarily be able to fit the data points to an exponential model, polynomial model of appropriate order, or power curve.
Least square curve fit can fit the data points to the following models:

a) sinusoidal model (including sine and cosine functions)
b) exponential model
c) polynomial model of appropriate order
d) power curve (\(y=c1x^(c2)\))

All of these models are applicable because the least square curve fit method is a versatile technique for approximating the best fit to a given set of data points using different mathematical models.

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Answer:

B

Step-by-step explanation:

In order the angles <C and <F are shared, then <B and <E, then the side equaling 10. This together proves that this triangle is congruent because of AAS (angle,angle,side) a triangle congruency rule.

Answer:

30 x 3 - 80 is 10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Eight less than three times a number is 10.

Answer:

Look it out for me

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

1/2(8x-6) = -1/3(9x-12)   distribute

4x-3 = -3x+4                 add 3x to both sides

7x-3 = 4                        add 3 to both sides

7x = 7                            divide by 7 on both sides

x = 1

By solving the improper fractions, there are 18 water stations in all.

This problem can be solved by two methods:

Method 1 :

First of all, calculate 13²/₃ miles in fraction. The value is 13.5 miles. Then calculate 3/4 mile in fraction. The value is .75 miles.

Now divide 13.5 miles by 0.75 miles.

13.5 ÷ 0.75 = 18

So, 18 water stations are there in all.

Method 2 :

Convert 13 ¹/₂ miles into an improper fraction from 27/2 miles.

Now, again divide 27/2 miles by 3/4.

27/2 ÷ 3/4 = ²⁷/₂ ₓ ⁴/₃ = 18

So, 18 water stations are there in all.

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Answer:

Below

Step-by-step explanation:

8 is classified as a rational number because it can be made into a fraction. 8.8 = 8 8/10 = 88/1

Because xanthan gum solutions are highly pseudoplastic (shear thinning) but not thixotropic, the initial viscosity is instantly rebuilt after high shearing.

A hypothesis is a theory put up to explain a phenomena. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are often based on prior findings that cannot be adequately explained by the current body of knowledge. A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis).

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The three properties of a subspace must be demonstrated for the set of all vectors orthogonal to w, indicated as w?, in order to demonstrate that it is a subspace of Rn.

In mathematics, objects with both magnitude and direction are called vectors. The vector's size is determined by the magnitude. It is shown as a line with an arrow, where the length of the line indicates the vector's magnitude and the arrow points in the desired direction. In addition, it goes by the names Euclidean vector, Geometric vector, Spatial vector, or just "vector."

The term "orthogonal" in mathematics denotes a direction at a 90° angle. If two vectors are perpendicular to one another and the result of the dot product analysis is zero, then the vectors are said to be orthogonal.

a) Let u be any component of w and choose any z in w. Since z and w are orthogonal to one another, zu = 0. Now, let cz be the result of c and z for any scalar c. The equation (cz)u = c(zu) = c * 0 = 0 is known. As u was an arbitrary element of w, this demonstrates that cz is orthogonal to u and therefore cz is in w?

b) Let u be any component of w and consider z1 and z2 in w. Both z1u and z2u are known to be zero. Given that the first argument of the dot product is linear, we know that (z1 + z2)u = z1u + z2u = 0 + 0 = 0. As u was an arbitrary member of w, this demonstrates that z1 + z2 is orthogonal to u and that z1 + z2 is in w?

c) We have demonstrated that w? is closed under addition and scalar multiplication from a and b. We observe that the zero vector is obviously orthogonal to any vector in w and is thus in w? to demonstrate that it contains the zero vector. This demonstrates that w? is a subspace of Rn since it satisfies all three characteristics of a subspace.

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the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

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Answer:

5b

Step-by-step explanation:

13b-8b=b(13-8) = 5b

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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The probability of getting all heads in three-coin tosses is 1/8 or 0.1251. This means that there is a 12.5% chance that all of Zack’s tulips will be pink.

We know that the formula for finding a probability for any outcome is:

Probability = Number of favorable outcomes ÷ Total number of outcomes.

We know that, when a coin is tossed one time then, there are two sample space: {H,T}.

This means that we can get either a head or a tail when a coin is tossed once. Now, since the coin has been tossed 3 times, hence:

The total number of possible outcomes = 2³ =8

This is due to the fact that there are a total of 2ⁿ possible outcomes when a coin is tossed n times.

The eight outcomes would be as follows:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

We are asked to find the probability of getting three heads, or tulips be pink. Therefore,

Probability = 1/8.

Therefore, there are 12.5% chances that all of the Zack's tulips would be pink.

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Complete question is:

Read the story. Zack planted an assortment of tulip bulbs in his garden. half of them were pink tulips. this morning, he noticed that 3 of the tulips had started to sprout. how likely is it that all of them will be pink? Zack simulates the situation by flipping a coin 3 times. Each time the coin lands on heads, it represents a pink tulip.

This table shows the results of 100 trials:

number of heads flipped   0   1   2   3

number of trials                  12 37 38 11

Based on zack's results, what is the probability that all of the tulips will be pink?

Answer:

what are the options?

Step-by-step explanation:

Answer:

0 is a rational, whole, integer and real number. Some definitions include it as a natural number and some don't (starting at 1 instead).

Step-by-step explanation:

Hope this helps

Considering the expression of a line, the gradient or slope is zero and the line is horizontal.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (4, 7) and (x₂, y₂)= (9, 7), the slope m can be calculated as:

m= (7 -7)÷ (9 -4)

m= 0÷ 5

m= 0

Finally, the gradient or slope is zero.

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The correct statement regarding the residuals is given as follows:

Yes, the residuals are relatively small.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence, on the graph, the residuals are given by the vertical distance between each point on the line.

The points are close to the line in this problem, meaning that the residuals are small and the model is a good fit.

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Câu trả lời:

26,2 cm

Giải thích từng bước:

Độ dài của một cung tính bằng radian được cho là:

L = θr

Ở đâu ; θ = góc trung tâm; r = Bán kính

θ = π / 3; r = 25cm

Độ dài của cung = π / 3 * 25

Chiều dài cung = 26,179938

Chiều dài cung = 26,2 cm

The optimal solution is X1 = 15, X2 = 20, and X3 = 16. The profit can increase to $612 if the profit for X2 increases to $24. The profit will increase by $4 if the right-hand side of constraint 3 is increased by 10 units. The profit will decrease by $12.5 if the right-hand side of constraint 2 is decreased by 5 units, but the higher bound on this decrease is $0.

The original LP problem can be constructed by looking at the "Solution" and "Dual" rows of the table. The "Solution" row shows the values of the decision variables in the optimal solution. The "Dual" row shows the dual values of the constraints. The dual value of a constraint is the amount by which the objective function can increase if the constraint is relaxed by one unit.

The constraints with slack are constraints 1 and 3. These constraints are not binding in the optimal solution, which means that they could be relaxed without changing the value of the objective function. The slack for constraint 1 is 52, which means that 52 units of the resource represented by constraint 1 are unused in the optimal solution. The slack for constraint 3 is 50, which means that 50 units of the resource represented by constraint 3 are unused in the optimal solution.

The optimal solution is computed by setting the decision variables equal to the values in the "Solution" row and then solving the resulting system of equations. In this case, the system of equations is:

X1 + X2 + X3 = 210

4X1 + 2X2 = 200

2X1 + 5X3 = 170

Solving this system of equations yields X1 = 15, X2 = 20, and X3 = 16.

If the profit for X2 increases to $24, then the dual value of constraint 2 will increase to 4. This means that the objective function can increase by $4 if constraint 2 is relaxed by one unit. In other words, if we increase the right-hand side of constraint 2 by one unit, then the optimal solution will change and the profit will increase by $4.

If the right-hand side of constraint 3 is increased by 10 units, then the dual value of constraint 3 will increase by $10. This means that the objective function can increase by $10 if constraint 3 is relaxed by one unit. In other words, if we increase the right-hand side of constraint 3 by 10 units, then the optimal solution will not change and the profit will increase by $10.

If the right-hand side of constraint 2 is decreased by 5 units, then the dual value of constraint 2 will decrease by 2.5. This means that the objective function will decrease by $2.5 if constraint 2 is relaxed by one unit. However, the dual value of constraint 2 is also bounded below by 0. This means that the profit can only decrease by $2.5 if constraint 2 is relaxed by one unit.

In conclusion, the bounds of the right-hand-side values and the dual prices are related to the feasibility of the solutions. If the right-hand side value of a constraint is less than the dual price of that constraint, then the constraint is infeasible. If the right-hand side value of a constraint is equal to the dual price of that constraint, then the constraint is binding in the optimal solution. If the right-hand side value of a constraint is greater than the dual price of that constraint, then the constraint is not binding in the optimal solution.

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\(\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}\)

\(\Huge \textsf{Step-by-step explanation}\)

\(\LARGE \bold{\textsf{Step 1: Assign Variables}}\)

\(\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}\)

\(\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}\)

\(\large \bold{ \textsf{From the problem, we know that:}}\)

\(\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}\)

\(\large \bold{ \textsf{We can use this information to write two equations:}}\)

\(\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}\)

\(\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}\)

\(\LARGE \bold{\textsf{Step 3: Solve the system of equations}}\)

\(\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}\)

\(\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}\)

\(\large \textsf{Simplifying this expression gives us:}\)

\(\textsf{10\textit{p} + 10 = 260}\)

\(\large \textsf{Subtracting 10 from both sides:}\)

\(\textsf{10\textit{p} = 250}\)

\(\large \textsf{Dividing both sides by 10}\)

\(\textsf{\textit{p} = 25}\)

\(\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}\)

\(\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}\)

\(\large \textsf{So, 25 pizzas and 80 sodas were sold.}\)

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The correct example of choosing a random sample from the target population of 100 students, where 40 are boys and 60 are girls, is option C.

Option C states that the group is separated into groups of boys and girls, and then 5 boys and 5 girls are randomly chosen from each group. This method ensures that both boys and girls are represented in the sample, and the random selection process helps to reduce bias.

Option A, choosing every other person on an alphabetical list of names, may introduce bias if the names are not randomly ordered or if there is any pattern to the list.

Option B, separating the group into groups of boys and girls and randomly choosing 5 boys and 5 girls from each group, is the correct method described in option C.

Option D, tossing a number cube for each name on the list and choosing those names that correspond to a 2, 4, or 6, does not guarantee a representative sample, as it introduces randomness based on the outcome of the number cube toss.

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