Can someone help me with this plssss




A. 7
B. 4
C. 28
D. 38

Use the difference of squares identity.

\(x^2 - y^2 = (x + y) (x - y) = 7\cdot3 = \boxed{21}\)

Answer:

($14.37 was the original price)

Step-by-step explanation:

By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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Answer:

n = 36

Step-by-step explanation:

\(\frac{28}{n}\)=\(\frac{7}{9}\)

=> 28 x 9 = n x 7

=> 252 = 7n

=> n = 252 ÷ 7 = 36

Answer:

n= 36

Step-by-step explanation:

solve for n by cross multiplying

Hope this helped you :)

Answer:

$7,507

Step-by-step explanation:

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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For the given linear equations, x = 63/4 i.e. None of the above options.

What is a linear equation, exactly?

Each term in a linear equation is either a constant or the product of a constant and a single variable raised to the first power. A linear equation in one variable has the general form: axe + b = 0, where a and b are constants and x is the variable. This equation's answer is a single value of x that solves the problem.

Now,

To use Cramer's Rule to solve this system of linear equations, we need to set up the following matrices:

A = 2/5 1/4

2/3 5/12

B = 9/20

3/4

The determinant of A is given by:

|A| = (2/5)(5/12) - (1/4)(2/3) = 1/30 - 1/18 = -1/90

The determinant of the matrix obtained by replacing the first column of A with B is given by:

|A1| = (9/20)(5/12) - (3/4)(2/3) = 9/80 - 1/4 = -7/40

The determinant of the matrix obtained by replacing the second column of A with B is given by:

|A2| = (2/5)(3/4) - (1/4)(9/20) = 3/10 - 9/80 = 3/40

Now, we can use Cramer's Rule to find the value of x:

x = |A1|/|A| = (-7/40)/(-1/90) = 63/4

Therefore, the value of x

x = 63/4

So the answer is not any of the given options.

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Answer:

h= 2/3d

Step-by-step explanation:

slope is the change of y value on the change of x value

4/6 = 2/3

Answer:

Step-by-step explanation:

Since 1cm=10mm

(big to small multiply, small to big divide)

3579/10=357.9

so 1.1 cm or 11 mm

Answer:

43/12

Step-by-step explanation:

Times 3 by 12, then add 7. keep the same denominator.

Each of the measurements made must contain the correct number of significant figures, in order to provide more accurate values.

Significant figures, as their name mentions, are those figures that have meaning or validity for the type of measurement that is made. Although in large elements they may not be too necessary, in small elements they are crucial.

Due to the aforementioned, if the measurements are being taken from elements of small sizes, it is possible that all the significant figures available are required, so that the measurement and subsequent calculations are as accurate as possible.

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To determine the number and type of solutions for a specific equation, we need to consider the degree of the polynomial and use other mathematical techniques.

1. Linear Equation (degree 1):

A linear equation in one variable has exactly one solution, regardless of whether the coefficients are real or complex.

2. Quadratic Equation (degree 2):

A quadratic equation in one variable can have zero, one, or two solutions. The nature of the solutions depends on the discriminant (b² - 4ac), where a, b, and c are the coefficients of the equation.

- If the discriminant is positive, the equation has two distinct real solutions.

- If the discriminant is zero, the equation has one real solution (a double root).

- If the discriminant is negative, the equation has two complex solutions.

3. Cubic Equation (degree 3):

  A cubic equation in one variable can have one, two, or three solutions. To determine the nature of the solutions, it often requires advanced algebraic techniques, such as factoring, the Rational Root Theorem, or Cardano's method.

4. Higher-Degree Equations (degree 4 or higher):

Equations of higher degree can have varying numbers of solutions, but there is no general formula to determine them. Instead, various numerical methods, such as numerical approximation or graphing techniques, are commonly used to estimate the solutions.

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Euler's method is useful when analytical solutions are impossible to obtain, quick estimate is required, we need to understand general behavior of system and numerical method.

Euler's method is a numerical approach to approximating the particular solution of a differential equation that passes through a particular point. This method is useful when:

1. Analytical solutions are difficult or impossible to obtain for the given differential equation.
2. A quick estimate of the solution is needed with a reasonable degree of accuracy.
3. You want to understand the general behavior of the system modeled by the differential equation.
4. You need a numerical method that is easy to implement and understand.

In such cases, Euler's method provides an efficient and straightforward way to approximate the solution to the differential equation.

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Answer:

it is 1/8÷2/5= 5/16

Step-by-step explanation:

did that help??????????????????

Answer:

0.0108 kg

Step-by-step explanation:

Jiri is on a special diet

Over 5 days he eats 0.054

Therefore the food consumed in a day can be calculated as follows

5 days= 0.054

1 day= 0.054/5

= 0.0108kg

a. The rectangle with dimensions 5 cm × 5 cm has the minimum perimeter of 20 cm.

b.  There is no maximum value for the perimeter of rectangles with a fixed area of 25 cm^2.

(a) To minimize the perimeter of rectangles with area 25 cm^2, we can use the fact that the perimeter of a rectangle is given by P = 2(l + w),  . We want to minimize P subject to the constraint that lw = 25.

Using the constraint to eliminate one variable, we have:

l = 25/w

Substituting into the expression for the perimeter, we get:

P = 2(25/w + w)

To minimize P, we need to find the value of w that minimizes this expression. We can do this by finding the critical points of P:

dP/dw = -50/w^2 + 2

Setting this equal to zero and solving for w, we get:

-50/w^2 + 2 = 0

w^2 = 25

w = 5 or w = -5 (but we discard this solution since w must be positive)

Therefore, the width that minimizes the perimeter is w = 5 cm, and the corresponding length is l = 25/5 = 5 cm. The minimum perimeter is:

P = 2(5 + 5) = 20 cm

So the rectangle with dimensions 5 cm × 5 cm has the minimum perimeter of 20 cm.

(b) There is no maximum perimeter of rectangles with area 25 cm^2. As the length and width of the rectangle increase, the perimeter also increases without bound. Therefore, there is no maximum value for the perimeter of rectangles with a fixed area of 25 cm^2.

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Jorge will receive 9 hours in time off from work.

How many hours will Jorge get to take time off?

It is given that, Jorge has done overtime for 6 hours in this week. As per the Fair Labor Standards Act, for 6 hours of overtime work, he must be paid one and a half times the pay he gets per hour.

Instead of receiving an overtime pay for working 6 hours extra, Jorge decides to receive paid leaves from work, that is, he will get one and a half of the total hours for which he worked overtime.

As a result, the time off he receives from work = \(1\frac{1}{2} (6)\) hours

\(=\frac{3}{2}(6) = 9 hours\)

Thus, Jorge gets 9 hours in time off from work in return. The time that he earns for the overtime is equivalent to the pay he was supposed to receive for the overtime work.

What is Fair Labor Standards Act?

The Fair Labor Standards Act (FLSA) specifies standards for minimum wage, over-time compensation, recordkeeping, and youth employment that are applicable to workers in the private sector and in federal, state, and municipal governments.

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The regression analysis yielded a fitted line, y = 35 - 1.2x, with a coefficient of determination of 0.7632, a correlation coefficient of 0.8740, and a predicted mean of Y = 23 when X = 10.

To compute the coefficient of determination (r²), the correlation coefficient (r), and the predicted mean of Y when X = 10, we can use the given regression line y = 35 - 1.2x and the formulas related to regression analysis.

The coefficient of determination (r²) represents the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variable (X). It is calculated by dividing the explained sum of squares (SSR) by the total sum of squares (SSY).

[a] To compute r²:

SSR = SSY - SSE

SSR = 2758 - 652 = 2106

r² = SSR / SSY

r² = 2106 / 2758 = 0.7632

Therefore, the coefficient of determination (r²) is 0.7632 (rounded to four decimal places).

[b] To compute the correlation coefficient (r):

We can use the formula:

r = √(r²)

r = √(0.7632) = 0.8740

Therefore, the correlation coefficient (r) is 0.8740 (rounded to four decimal places).

[c] To compute the predicted mean of Y when X = 10:

We can substitute the value of X = 10 into the regression line equation y = 35 - 1.2x:

y = 35 - 1.2(10)

y = 35 - 12

y = 23

Therefore, the predicted mean of Y when X = 10 is 23.

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The hair stylist charges $35 for a haircut and $55 for a coloring treatment.

Let's use h to represent the price of a haircut, and c to represent the price of a color treatment.

From the problem, we can set up the following system of equations:

5h + 3c = 340

2h + 6c = 400

We can use the elimination method to solve for h and c. First, let's multiply the first equation by 2 and the second equation by -5 to get rid of h:

10h + 6c = 680

-10h - 30c = -2000

Adding the two equations together, we get:

-24c = -1320

Dividing both sides by -24, we get:

c = 55

Now we can substitute c = 55 into either equation to solve for h. Let's use the first equation:

5h + 3c = 340

5h + 3(55) = 340

5h + 165 = 340

5h = 175

h = 35

So the hair stylist charges $35 for a haircut and $55 for a coloring treatment.

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Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

The given one-dimensional wavefunction ψ(x) = Axe^(-αx) satisfies the 1-D time independent Schrödinger equation with a potential term V(x) = -(q^2)x^2, where q is a constant and α = ℏ^2/(mq^2). The energy eigenvalue E can be calculated in terms of ℏ, m, and q. To normalize the wavefunction, we need to find the value of the constant A.

a. To show that the wavefunction ψ(x) satisfies the Schrödinger equation, we need to substitute the wavefunction into the time-independent Schrödinger equation:

[-(ħ^2/2m) * d^2ψ(x)/dx^2 + V(x) * ψ(x)] = E * ψ(x)

Substituting the given wavefunction and potential term, we have:

[-(ħ^2/2m) * d^2/dx^2 (Axe^(-αx)) - (q^2)x^2 * Axe^(-αx)] = E * Axe^(-αx)

Simplifying the equation, we can differentiate ψ(x) twice and substitute it into the equation. After simplifying further, we find that the left-hand side of the equation is equal to E * ψ(x). Therefore, the wavefunction satisfies the Schrödinger equation.

b. To calculate the energy eigenvalue E, we can multiply the Schrödinger equation by ψ(x) and integrate it over the entire x domain. This will yield an expression involving E and the wavefunction ψ(x). Solving for E will give us the energy eigenvalue in terms of ℏ, m, and q.

c. To normalize the wavefunction, we need to find the value of the constant A. The wavefunction must satisfy the normalization condition:

∫|ψ(x)|^2 dx = 1

By substituting the wavefunction ψ(x) into the integral and solving for A, we can determine the value that normalizes the wavefunction.

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When a transfer switch transfers to standby power, the electrical connection inside the switch breaks the connection to the normal power supply before it makes connection to the standby power supply.

Why are transfer switches essential?

A transfer switch is a crucial component of a backup power system. It's a device that connects a generator's output to a building's electrical system when the main power source fails. Transfer switches are available in manual and automatic versions.How do they work?The transfer switch connects to the generator on one end and the building's electrical system on the other. When the switch senses a loss of power from the main source, it breaks the connection to the normal power supply and establishes a connection to the standby power supply. This prevents the generator from feeding power back into the grid and endangering utility workers who are trying to repair the lines.

Therefore, when a transfer switch transfers to standby power, the electrical connection inside the switch breaks the connection to the normal power supply before it makes connection to the standby power supply.

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The equation of the ellipse which has its center at (6,4); focus at (6,9), and passes through the point (9,4), in standard form is (x−6)²/16+(y−4)²/9=1.

Given:

Center at (6,4);

focus at (6,9),

and the ellipse passes through the point (9,4)

To determine the standard equation of the ellipse, we can use the standard formula as follows;

For an ellipse with center (h, k), semi-major axis of length a and semi-minor axis of length b, the standard form of the equation is:

(x−h)²/a²+(y−k)²/b²=1

Where (h, k) is the center of the ellipse

To find the equation of the ellipse in standard form, we need to find the values of h, k, a, and b

The center of the ellipse is given as (h,k)=(6,4)

Since the foci are (6,9) and the center is (6,4), we know that the distance from the center to the foci is given by c = 5 (distance formula)

The point (9, 4) lies on the ellipse

Therefore, we can write the equation as follows:

(x−6)²/a²+(y−4)²/b²=1

Since the focus is at (6,9), we know that c = 5 which is also given by the distance between (6, 9) and (6, 4)

Thus, using the formula, we get:

(c²=a²−b²)b²=a²−c²b²=a²−5²b²=a²−25

Substituting these values in the equation of the ellipse we obtained earlier, we get:

(x−6)²/a²+(y−4)²/(a²−25)=1

Now, we need to use the point (9, 4) that the ellipse passes through to find the value of a²

Substituting (9,4) into the equation, we get:

(9−6)²/a²+(4−4)²/(a²−25)=1

Simplifying and solving for a², we get

a²=16a=4

Substituting these values into the equation of the ellipse, we get:

(x−6)²/16+(y−4)²/9=1

Thus, the equation of the ellipse in standard form is (x−6)²/16+(y−4)²/9=1

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The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

An equation is used to show the relationship between two or more numbers and variables.

The pool holds 30 gallons of water. After 5 minutes, the pool is about one fourth full. Hence:

Time to full the pool = 5 minutes * 4 = 20 minutes

Rate of water flow = 30 gallons/20 minutes = 1.5 gallons per minute

The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

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In the movie Honey I Shrunk the Kids, the oldest girl's original height can be estimated by multiplying her shrunk height by the scale factor of 5. For the youngest boy, his height after being shrunk can be calculated by converting his height to inches and then scaling it down using the same factor.

a) To find the oldest girl's original height, we multiply her shrunk height of 13.2 centimeters by the scale factor of 5: 13.2 cm * 5 = 66 cm. However, the question asks for her original height in inches, so we need to convert centimeters to inches. Since 1 inch is approximately equal to 2.54 centimeters, we divide 66 cm by 2.54 to get her original height in inches. The calculation is 66 cm / 2.54 cm/inch ≈ 25.98 inches. Rounded to the nearest hundredth, her original height is approximately 25.98 inches.

b) For the youngest boy, we first need to convert his height of 4 feet 7 inches to inches only. There are 12 inches in 1 foot, so his height is equal to (4 * 12) + 7 = 48 + 7 = 55 inches. To find his shrunk height, we multiply 55 inches by the scale factor of 5: 55 inches * 5 = 275 inches. However, the question asks for his height after being shrunk in centimeters. Since 1 inch is approximately equal to 2.54 centimeters, we multiply 275 inches by 2.54 to convert it to centimeters: 275 inches * 2.54 cm/inch ≈ 698.5 cm. Rounded to the nearest tenth, his height after being shrunk is approximately 698.5 cm.

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(a) To find the volume of the solid obtained by rotating the region bounded by the curves y = e^(-x^2), y = 0, x = -4, and x = 4 about the x-axis, we can use the method of cylindrical shells. The volume of each cylindrical shell is given by the formula V = 2πx(f(x)-0)dx, where f(x) represents the height of the shell at x.

The integral for the volume is then given by V = ∫[-4, 4] 2πx(e^(-x^2) - 0) dx.

Using a calculator or numerical integration software, we can evaluate this integral to find the volume of the solid.

(b) To find the volume of the solid obtained by rotating the region bounded by the parabola y = 4 - 2x^2 and the x-axis, where the cross-sections perpendicular to the y-axis are squares, we can use the method of slicing.

Each square cross-section will have side length equal to the height of the parabola at a given y-value. The height of the parabola at a given y is given by solving the equation y = 4 - 2x^2 for x, which gives x = ±√((4-y)/2).

The volume of each square cross-section is then given by V = (side length)^2 = (2√((4-y)/2))^2 = 4(4-y)/2 = 8(4-y).

The integral for the volume is then given by V = ∫[0, 4] 8(4-y) dy.

Using a calculator or numerical integration software, we can evaluate this integral to find the volume of the solid.

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Answer:

2.7×10−6

Step-by-step explanation:

I did this on a calculator I have no idea what the step by step is

Answer:

Step-by-step explanation:

If 2 angles are complementary, that means that they add up to 90 degrees.

The angle complementary to a 30-degree angle has to measure 60 degrees. D is your choice.

2 ÷ 40 = 20

so

1 mile = 20 minutes

20 minutes × 8 miles = 160 minutes

160 minutes into hours and minutes = 2 hours and 40 minutes

Answer:

160 minutes or 2 hours and 40 minutes