the branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. she argues that this will reduce the average traveling time (a round trip) to 4.5 minutes. is she correct? if your answer is negative, then what will the average traveling time be?

Answer:

C) g(x) = f(x) + 4

Step-by-step explanation:

A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A

-anumber would slide the function DOWN instead.

As for the other answers:

A) the 3multiplied in front is a vertical STRETCH.

D) the 1/2 multiplied in front is a vertical shrink (smash)

B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.

Answer:

f(5.5) = -26.5

Step-by-step explanation:

f(5.5) = -5x+1

f(5.5) = -5(5.5) +1

f(5.5) = -26.5

Factorial notation is used to represent the product of a series of descending positive integers, and is denoted by an exclamation mark.

For example, 5! represents 5 x 4 x 3 x 2 x 1, which equals 120. If the study involves counting the number of ways a certain group of items can be arranged, factorial notation may be used to express the total number of possible arrangements. However, without knowing the specifics of Dr. Elder's study, it is impossible to provide the correct factorial notation. Therefore, I would recommend providing more details about the study in order to receive a more accurate answer.

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Answer:

g(x) = 2x - 3

Step-by-step explanation:

I hope this answers your question(s). Have a good weekend!

To find Cox and Cgd, various measurement techniques can be used, such as impedance measurements, small-signal AC analysis, and high-frequency models.

Cox and Cgd are parameters in bipolar junction transistor (BJT) modeling.

Cox is the output capacitance and Cgd is the drain-to-gate capacitance. These capacitances affect the high-frequency behavior of the transistor and play an important role in circuit design and analysis.

The exact method depends on the type of transistor, the operating conditions, and the level of accuracy desired. In general, specialized equipment and a good understanding of circuit analysis and BJT modeling are required to accurately determine Cox and Cgd.

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Answer:

$ 12 000.

Step-by-step explanation:

(175 000 + 225 000) * .03 =

Answer:

\(x = 1.48 \: and \: y = - 1.38\)

Step-by-step explanation:

\(first \: equation\)

\(x - 4y = 7\)

\(second \: equation\)

\(5x + y = 6\)

\(from \: equation \: 1 \\ make \: x \: the \: subject \: of \: formula \\ x = 7 + 4y\)

\(x =7 + 4y \: {equation \: 3}\)

\(substitutefor \: x \: in \: equation \: 2\)

\(5x + y = 6 \\ 5(7 + 4y) + y = 6 \\ 35 + 20y + y = 6 \\ 35 + 21y = 6 \\ 21 y = 6 - 35 \\ 21y = - 29 \\ \)

\(y = \frac{ - 29}{21} \)

\(y = - 1.38\)

\(subsitute \: for \: y \: into \: equation \: 3\)

\(x = 7 + 4y \\ x = 7 + 4( - 1.38) \\ x = 7 - 5.52 \\ x = 1.48\)

Answer:

The answer is 1,328

Step-by-step explanation:

The number of ounces that she weighs will be 1328 ounces. Then the correct option is D.

Conversion means converting the same thing into different units.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

If a child weighs 83 pounds. We know that in one pound, there are 16 ounces.

Then the number of ounces that she weighs will be

⇒ 83 x 16

⇒ 1328 ounces

Then the number of ounces that she weighs will be 1328 ounces. Then the correct option is D.

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Answer:

A.

Step-by-step explanation:

'The difference' means minus or subtraction. 'plus' and 'increased' are both for addition.

Brainliest please!

The points on the ellipse 4x^2 + y^2 = 4 that are farthest away from the point (1, 0) are (x, y) = (0, -2) with the smaller y-value and (x, y) = (0, 2) with the larger y-value.

The ellipse equation is given as 4x² + y² = 4. We are required to find the points on this ellipse that are farthest away from the point (1, 0). Solution: Given, the equation of ellipse 4x² + y² = 4Putting (1, 0) on the equation, we get; 4(1)² + (0)² = 4 ⇒ 4 + 0 = 4, which is a point on the ellipse. So, (1, 0) is on the ellipse. Hence, we are required to find the point on the ellipse that is farthest away from the point (1, 0).Let's take the equation in the form of x²/a² + y²/b² = 1.4x² + y² = 4 => x²/(4/√4) + y²/(4/1) = 1Let a = 2/1 and b = 2/√4 = 1Hence, the semi-major axis is 2 and semi-minor axis is 1.We know that the distance between two points P(x1, y1) and Q(x2, y2) is given by √[(x2 − x1)² + (y2 − y1)²].For the farthest point from the given point (1, 0), we need to find the point on the major axis that intersects with the ellipse. This point will be on the top-right and bottom-left of the ellipse, at a distance of a from the center. And, the distance between this point and (1, 0) will be a distance of c from the center. As we have the value of a, we need to find c. We know that the value of c is given by √(a² − b²).Hence, c = √(a² − b²) = √(4 − 1) = √3.Now, let's find the farthest point from (1, 0) using the formulae above.We have a = 2 and c = √3. Therefore, the coordinates of the required points are:(x, y) = (1, √(3)) and (1, −√(3))So, the required points on the ellipse are (1, √(3)) and (1, −√(3)).Hence, (x, y) = (smaller y-value) is (1, −√(3)) and (x, y) = (larger y-value) is (1, √ (3)).

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The two points on the ellipse that are farthest away from (1,0) are (-1,0) and \(( \frac{ - 1}{3} , 2 \sqrt( \frac{2}{3})) \: or \: (\frac{ - 1}{3} , - 2 \sqrt( \frac{2}{3})) \)

How to find the points on the ellipse?

To find the points on the ellipse that are farthest away from the point (1,0), we first need to find the distance between the point (1,0) and any point (x,y) on the ellipse. The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula:\(d = \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\)

Using this formula, we can find the distance between (1,0) and any point (x,y) on the ellipse 4x² + y² = 4 as:\(d = \sqrt((x - 1)^2 + y^2)\)

To find the points on the ellipse that are farthest away from (1,0), we need to maximize this distance function subject to the constraint 4x² + y² = 4. To do this, we can use the method of Lagrange multipliers.

Let f(x,y) = (x - 1)² + y² be the distance function and g(x,y) = 4x² + y² - 4 be the constraint function. The Lagrange function is given by:

L(x,y,λ) = f(x,y) - λ g(x,y)

Taking the partial derivatives of L with respect to x, y, and λ and setting them to zero, we get:

2(x - 1) - 8λx = 0

2y - 2λy = 0

4x² + y² - 4 = 0

From the second equation, we get y(1 - λ) = 0, which gives us two cases:

Case 1: y = 0

From the third equation, we get 4x² = 4, which gives us x = ±1. Therefore, the two points on the ellipse with y = 0 that are farthest away from (1,0) are (1,0) and (-1,0).

Case 2: λ = 1

Substituting λ = 1 into the first and third equations, we get:

2(x - 1) - 8x = 0

4x² + y² - 4 = 0

Simplifying the first equation, we get x = -1/3. Substituting this into the second equation, we get \(y = ±2 \sqrt( \frac{2}{3})\)

. Therefore, the two points on the ellipse with λ = 1 that are farthest away from (1,0) are (-1/3, 2sqrt(2)/3) and \((-1/3, -2 \sqrt \frac{2}{3})\).

Thus, the two points on the ellipse that are farthest away from (1,0) are (-1,0) and

\(( \frac{ - 1}{3} , 2 \sqrt( \frac{2}{3})) \: or \: (\frac{ - 1}{3} , - 2 \sqrt( \frac{2}{3})) \)

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Correct question is "find the points on the ellipse 4x²+ y² = 4 that are farthest away from the point (1, 0). (x, y) = (smaller y-value) (x, y) = (larger y-value)."

Answer: DE = 17

Step-by-step explanation:

You can solve by similar triangle ratios or by pythagorean theorem:

AB/CD = CD/x

54/76.5 = 12/x

Solve for x:  54x = 12(76.5) = 918

x = 918/54 = 17

Or, because CDE is a right triangle:

\(12^{2} + 12^{2} = x^{2}\)

\(x^{2} = 288\\\)

x = \(\sqrt{288} = 17\)

Gentiana has $12 left to spend on the pizza pie as of the equation model.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,

Let the amount spend on pizza pie be x,
According to the question,
40 = 10 + 25% of 40 + 20% of 40 + x

40 = 10 + 40 × 0.25 + 40 × 0.20 + x
40 = 10 + 10 + 8 + x
x = 40 - 28
x = 12

Thus, Gentiana has $12 left to spend on the pizza pie as of the situation model.

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Answer:  \(\sqrt{14}\)

Work Shown:

\(\text{x} = \text{geometric mean of A and B}\\\\\text{x} = \sqrt{A*B}\\\\\text{x} = \sqrt{2*7}\\\\\text{x} = \sqrt{14}\\\\\)

Answer:

A

Step-by-step explanation:

The formula for this type of interest is \(A=P(1+\frac{r}{n})^{nt}\), where A is the total amount, P is the initial investment, x is the interest rate, n is the amount of times that the investment is compounded a year, and t is the amount of years. Plugging in the numbers given, you get:

\(A=1800(1+\frac{0.025}{2})^{2\cdot 12}=\)

\(1800(1.0125)^{24}\approx 2425.23\)

Now, she invests this into a new account, and you can set up the following equation:

\(A=2425.23(1+\frac{0.04}{12})^{12\cdot 7}=\)

\(2425.23(1.0033333)^{84}\approx 3207.40\), or option A.

Hope this helps!

Answer:  12.5

18.75/1 ½ = 12.5

Answer:

07:45 or 7:45

Step-by-step explanation:

On a clock, the shorter hand shows the hour of the day, while the longer hand shows the minute. The clock is divided into 12 hours and 60 minutes. In this case, the shorter hand is between 7 and 8, and the minute hand is right at 45, meaning that the time is 07:45. Hope this helps!

The volume of the given triangular prism is 315 cm³.

The volume of a triangular prism, we need to multiply the base area of the triangular base by the height of the prism.

The triangular base has a base length of 5 cm and a height of 7 cm, and the height of the prism is 9 cm.

Calculate the area of the triangular base.

The area of a triangle can be calculated using the formula:

Area = (base length × height) / 2

Plugging in the values, we have:

Area = (5 cm × 7 cm) / 2

Area = 35 cm²

Calculate the volume of the prism.

The volume of a prism can be calculated by multiplying the base area by the height of the prism.

Volume = Base area × Height

Volume = 35 cm² × 9 cm

Volume = 315 cm³

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Answer:

2

Step-by-step explanation:

Degree of a term with one variable is the variable's exponent. With more than one variable, the degree is the sum of the exponents of the variables.

6xy-3x+y

The exponent of x is 1 and exponent y is 1

Then degree is 1+1=2

The number of cupcakes and brownies Fwam could have purchased is 1.75b + 4.50c ≤50.

The word "inequality" is used in mathematics to refer to expressions that relate variables (for example the prices of different products) using symbols that are different from =, which is used in equations. Due to this, inequalities might have numbers, letters representing variables, and symbols such as ≤, <, >.

1. List the variables

b = cupcakes

c = brownies

4.50 = price of the cupcakes

1.75 = price of the brownies

50 = total money

2. Relate the variables

1.75b + 4.50c ≤50

Each product should be multiplied by its price

The total money can be equal to or less than 50 (≤)

The products should be added

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Answer: This is the formula to find the volume of a triangular prism. V=1/4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4

Answer:

12/7 or E

Step-by-step explanation:

Answer: 1 5/7

Step-by-step explanation:

Answer:

x + m × y

$4.47

Step-by-step explanation:

The equation and computation is shown below:

Let us assume the cost of gallon be x

Increase each year be m

And, the number of years be y

So, the equation is

= x + m × y

The cost of gallon of gas in 16 years is

= $1.75 + $0.17 × 16

= $1.75 + $2.72

= $4.47

Answer:

Yes.

Step-by-step explanation:

The sum of two odd numbers is always even. The product of two or more odd numbers is always odd. The sum of an even number of odd numbers is even, while the sum of an odd number of odd numbers is odd.

The simplified form of the expression -8x^5 * 6x^9 is -48x^14. The expression -8x^5 * 6x^9 simplifies to -48x^14. The coefficient -48 is the product of the coefficients -8 and 6, and x^14 is obtained by adding the exponents of x.

The coefficient -8 and 6 can be multiplied to give -48. Then, the variables with the base x can be combined by adding their exponents: 5 + 9 = 14. Therefore, the simplified form of the expression is -48x^(14).

In this simplified form, -48 represents the product of the coefficients -8 and 6, while x^(14) represents the combination of the variables with the base x, with the exponent being the sum of the exponents from the original expression.

To simplify the expression -8x^5 * 6x^9, we can combine the coefficients and add the exponents of x.

First, we multiply the coefficients: -8 * 6 = -48.

Next, we combine the like terms with the same base (x) by adding their exponents: x^5 * x^9 = x^(5+9) = x^14.

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The R-squared value is approximately 0.458, meaning that 45.8% of the total variation in the crime rate can be explained by the poverty rate and median income in the model.

The sociologist is studying the crime rate in 31 New England cities as a function of poverty rate and median income. He found that the Sum of Squares Error (SSE) is 4,155,943 and the Sum of Squares Total (SST) is 7,675,381. To determine the proportion of variance explained by the model (R-squared), you can use the following formula:
R-squared = 1 - (SSE/SST)
R-squared = 1 - (4,155,943 / 7,675,381)
R-squared ≈ 0.458

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Answer:

4-i

Step-by-step explanation:

The complex conjugate means take the imaginary term and negate it

4+i becomes 4-i

4-i is the complex conjugate

a) The 3× 3 non-zero matrix A for solution vector \({\begin{bmatrix} 2\\ 4\\ 1\\\end{bmatrix} } \) , is equals to \({\begin{bmatrix} -2 & 1& 0\\ -1& -2& 10\\ 1& 2 & -9\\\end{bmatrix} } \).

b) The 3× 3 non-zero matrix A for solution vector \( {\begin{bmatrix} 1\\ 3\\ 5\\\end{bmatrix} } \) , is equals to \({\begin{bmatrix} 3 & -1& 0\\ -1& 2& -1\\ -5& 0 & 1\\\end{bmatrix} } \).

Matrix A is a square matrix with order 3×3 , which means it includes 3 rows and 3 columns. We have to determine the 3×3 non-zero matrix for each vector and are such that [2 4 1 ], [1 3 5 ] is solution of Ax = b. As we know the structure of a 3×3 matrix is look like as below, \({\begin{bmatrix} a & b& c\\ d& e& f\\ g& h & i \\\end{bmatrix} } \).

a) Vector, \(x = {\begin{bmatrix} 2\\ 4\\ 1\\\end{bmatrix} } \) is a solution of matrix Ax = b. So, here \(b = {\begin{bmatrix} 0\\ 0\\ 0\\\end{bmatrix}} \)

Now, Substitute all known values in above formula, \( {\begin{bmatrix} a & b& c\\ d& e& f\\ g& h & i \\\end{bmatrix} } {\begin{bmatrix} 2\\ 4\\ 1\\\end{bmatrix} } = {\begin{bmatrix}0\\ 0\\ 0\\\end{bmatrix}} \)

2a + 4b + c = 0

2d + 4e + f = 0

2g + 4h + i = 0

consider any values which satisfied the above equations, a = -2, b = 1 , c = 0

d = -1, e = -2, c = 10 ; g = 1, h = 2, i = -9

so, required matrix A is \({\begin{bmatrix} -2 & 1& 0\\ -1& -2& 10\\ 1& 2 & -9\\\end{bmatrix} } \).

b) Vector, \(x = {\begin{bmatrix} 1\\ 3\\ 5\\\end{bmatrix} } \) is a solution of matrix Ax = b. \(b = {\begin{bmatrix} 0\\ 0\\ 0\\\end{bmatrix} } \)

Now, Substitute all known values in above formula, \( {\begin{bmatrix} a & b& c\\ d& e& f\\ g& h & i \\\end{bmatrix} } {\begin{bmatrix} 1\\ 3\\ 5\\\end{bmatrix} } = {\begin{bmatrix} 0\\ 0\\ 0\\\end{bmatrix}}\)

a + 3b + 5 c = 0

d + 3e + 5f = 0

g + 3h + 5i = 0

consider any values which satisfied the above equations, a = 3, b = -1 , c = 0

d = -1, e = 2, c = -1 ; g = -5, h = 0, i = 1

so, required matrix A is \({\begin{bmatrix} 3 & -1& 0\\ -1& 2& -1\\ -5& 0 & 1\\\end{bmatrix} } \). Hence, required matrix is \({\begin{bmatrix} 3 & -1& 0\\ -1& 2& -1\\ -5& 0 & 1\\\end{bmatrix} } \).

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Complete question:

ion. 35. construct a 3 ×3 nonzero matrix for each vector and such that the vector

a) [2 4 1 ]

b) [1 3 5 ]

is a solution of Ax = b.

Answer:

q=13

Step-by-step explanation:

u=-3

q=2u^2 - 5

q=2(-3)^2 - 5

q= 2(9) - 5

q= 18 - 5

q=13

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer: 1. V≈603.19

2. V≈103.67

3. V≈513.13

Step-by-step explanation: i only know those sorry :(