The population of a city is 2,916. If the number of males is 240 more than the number of females, how many males and females are there in the city?
System of Equations: Solution:

Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

Answer:

31.5 inches

Step-by-step explanation:

If 2 centimeters is 9 inches, then 1 centimeter is 4.5 inches. Then, just multiply by 7.

As per the unitary method, there are 10 chairs and there are 2 tables.

In math the term called unitary method is known as  a process of finding the value of a single unit, and based on this value we can find the value of the required number of units.

Here we have given that tom and jerry have one day to work, but two tasks to focus on building chairs and tables.

Here we also know that  if tom spends all day building chairs, then he will make 16 chairs.

And if he instead devotes his day to building tables, then tom will make 4 tables.

Where as if jerry spends his day building chairs, then he will make 14 chairs on the other hand if he spends the day building tables, then he will make 7 tables.

Based on the given details, here by using the unitary method, for one day, he will product 10 chairs and 2 tables.

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Answer:

p = - 5

Step-by-step explanation:

–2.5p – 20 = 9p + 37.5

combine like terms:

- 2.5p - 9p = 37.5 + 20

simplify:

- 11.5p = 57.5

p = 57.5 / -11.5

p = - 5

Answer:

The answer is p = -5

Step-by-step explanation:

-2.5p - 20 = 9p + 37.5

(move constants to one side by adding 20 to both sides)

-2.5p = 9p + 57.5

(move all terms with the "p" variable to one side by subtracting 9 from both sides)

-11.5p = 57.5

(divide both sides by -11.5 to isolate the variable)

p = -5

Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

Answer:

\(2\sqrt{10}\)

Step-by-step explanation:

\(\sqrt{40}\)

\(\sqrt{4}\) x \(\sqrt{10}\)

2\(\sqrt{10}\)

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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The solution of calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity.

Present value (PV) is the current value of a future sum of money, discounted to reflect the time value of money and the risk of non-payment or default.

An annuity is a financial product that pays out a fixed stream of payments to an individual over a specified period of time.

According to the given information:

To calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity:

PV = (PMT / i) x (1 - \((1+n)^{-n}\))

Where:

PV = present value (the amount borrowed)

PMT = monthly payment

i = monthly interest rate (15% per annum / 12 months = 1.25%)

n = number of monthly payments (20 years x 12 months per year = 240 months)

First, we need to calculate the present value of the loan, which is the amount borrowed minus the down payment:

PV = R151 000.00 - R51 000.00

PV = R100 000.00

Next, we can plug in the values into the formula:

R100 000.00 = (PMT / 0.0125) x (1 - \((1+0.0125)^{-240}\))

Solving for PMT, we get:

PMT = R1,080.80

Therefore, the monthly payments on the mortgage bond will be R1,080.80.

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The correct answer is 8xy

Answer:

\((-\frac{1}{3},\frac{1}{2} )\) , \((-\frac{3}{2} ,3)\)

Step-by-step explanation:

2y = 3x + 1

y = 2x + 3

Graph 2y = 3x + 1.

Divide each term by 2 and simplify.

      \(y=\frac{3x}{2}+\frac{1}{2}\)

Rewrite in slope-intercept form.

      \(y=\frac{3}{2}x+\frac{1}{2}\)

Use the slope-intercept form to find the slope and y-intercept.

Find the values of m and b using the form y = mx + b.

       \(m=\frac{3}{2}\)

        \(b=\frac{1}{2}\)

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: \(\frac{3}{2}\)

y-intercept: \((0,\frac{1}{2} )\)

Any line can be graphed using two points. Select two x values, and plug them into the  equation to find the corresponding y values.

Find the x-intercept.

x-intercept(s):  \((-\frac{3}{2},0 )\)

y-intercept(s): (0, 3)

Create a table of the x and y values.

  _x_|_y_

  \(-\frac{3}{2}\)  |   \(0\)

     \(0\)  |   \(3\)

Graph the line using the slope and the y-intercept, or the points.

Slope: 2

intercept: (0, 3)

  _x_|_y_

  \(-\frac{3}{2}\)  |   \(0\)

     \(0\)  |   \(3\)

Graph y = 2x + 3

Use the slope-intercept form to find the slope and y-intercept.

Slope: 2

intercept: (0, 3)

x-intercept(s): \((-\frac{3}{2},0)\)

y-intercept(s): (0, 3)

Plot each graph on the same coordinate system.

Answer:B

Step-by-step explanation:

Answer:

Step-by-step explanation:

volume = 1/3 π r² h

where h = 15 yd.

           r = 5 yd.

plugin values into the equation:

volume = 1/3 π r² h

            = 1/3 * π * 5² * 15

            = 392.7 yd³

Answer:

A. 392•8yd^3

Step-by-step explanation:

After approximately 17.14 minutes, Rob will be closer to the top than Ashley.

Rob's distance from the top = 5.7 - 0.24t

Ashley's distance from the top = 4.5 - 0.17t

We want to find the time t when Rob's distance from the top is less than Ashley's distance:

5.7 - 0.24t < 4.5 - 0.17t

Now, we'll isolate the t variable by adding 0.17t to both sides and subtracting 4.5 from both sides:

0.07t > 1.2

t > 1.2 / 0.07

t > 17.14

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The coordinates of the final point after the reflections across the x-axis twice is (6, -4)

Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.

So reflecting (6,-4) across the x-axis gives us the point (6,4).

Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.

So reflecting (6,4) across the x-axis gives us the point (6,-4).

Therefore, the final point after both reflections is (6, -4).

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Answer: 5^5.

Step-by-step explanation: Using the equation x^a*x^b = x^(a+b), we find that 5^2*5^3 is equal to 5^5.

Answer:

y = 7

Step-by-step explanation:

y = 3(2-1) 2 + 1

y = 3(1)(2) + 1

y = 6 + 1

y = 7

The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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The plotting of the inequalities was done using geogebra online graphing calculator. The graph is attached.

Inequalities are the mathematical expressions in which both sides are not equal. It should be noted that in inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Inequality is an expression used to show the nonequal comparison of numbers and variables.

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12   (1)

2x + y < -5    (2)

Plotting the inequalities using GeoGebra online graphing calculator. The graph is attached

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The formula for nCk is ...

  nCk = n!/(k!(n -k)!)

It always works out that nC0 = 1 and nC1 = n, and the sequence of numbers across a row of the diagram is symmetrical about the center.

This means you only need to calculate one value to finish filling your diagram.

  4C2 = 4!/(2!(2!)) = (4·3)/(2·1) = 6

You will find the pattern to be ...

  each element in the diagram is the sum of the two above  it.

Answer:

anser is D

(f×f)(0)=-1

Step-by-step explanation:

(f×f)(x)=f(x)×f(x)

=(\(x^{2}\)-1)(\(x^{2}\)-1)

=\(x^{4}\)-2\(x^{2}\)+1

sub x=0

=\(0^{4}\)-2×\(0^{2}\)+1

=-1

Step-by-step explanation:

There is no diagram how can we answer

The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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The inverse function of the function f (x) = x - 12 is  f ⁻¹(x) = x + 12.

What is Inverse of a Function?

The inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by f⁻¹.

How do you find the inverse of a function?

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

We will use the concept of inverse function to find the inverse of the above function.

For the given function y = x - 12, express x in terms of y.

Now, y = x - 12

x = y + 12

To find the inverse of the function, swap x and y.

y = x + 12

Therefore, the inverse function of the function f (x) = x - 12 is  f ⁻¹ (x) = x + 12.

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it is false but 4 is not y-4x=0

Answer:

1) 0.53

2) 0.1615

Step-by-step explanation:

1) ______ + 0.37 = 0.9

______ = 0.9 - 0.37 = 0.53

2)______ - 0.0369 = 0.1246

______ = 0.1246 + 0.0369 = 0.1615

Answer:

1. 0.53

2.0.1615

Step-by-step explanation:

1.______+0.14+0.23=0.9

let the blank space be x

here,

x+0.14+0.23=0.9

or, x + 0.37=0.9

or, x=0.9- 0.37

: . x= 0.53

2. ______-0.0369 =0.1246

let the blank space be x

here,

x-0.0369= 0.1246

or,x=0.1246+0.0369

: . x= 0.1615

HOPE THIS HELPED.

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

-|3-5|-3=-|-2|-3=-2-3=-5

the answer is -5

the correct answer is A

Answer:

the answer is A

Step-by-step explanation:

be my friend please

Answer:

x = 9.6

Step-by-step explanation:

sin Q = 16/20 Q = 53.13° from the big triangle

16/20 = x/12

192 = 20x

x = 9.6