One year, the population of a city was 181,000. Several years later it was 150,230. Find the percent decrease.

The amount invested in the account that yields 10% simple interest is $1,000.

The amount invested in the account that yields 7% simple interest is $9,000.

The first step is to form a system of equations using the information provided in the question:

a + b = $10,000 equation 1

0.1a + 0.07b = 730 equation 2

Where:

a = amount invested in the account that yields 10% simple interest

b =  amount invested in the account that yields 7% simple interest

The elimination method would be used to solve the equations

Multiply equation 1 by 0.1

0.1a + 0.1b = 1000 equation 3

Subtract equation 2 from equation 3

0.03b = $270

Divide both sides of the equation by 0.03

b = $270 / 0.03

b = 9,000

Substitute for b in equation 1

a + 9,000 = 10,000

a = 10,000 - 9,000

a = 1000

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Answer:

Box A: -2x

Box B: 2/9

Step-by-step explanation:

Multiply 1/3 by each of the expressions above the rectangle.

Box A: 1/3 × (-6x) = -2x

Box B: 1/3 × 2/3 = 2/9

Answer:

49

Step-by-step explanation:

35+14=49

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32 inches more of tape students need.

Given that,

Students in Dave's science class are trying to build the tallest structure. Ten newspapers and two yards of tape are given to each group of kids. The decision is made by Dave's group to roll up each newspaper. Then, they use 4 inches of tape to seal each roll.

We have to find how many more inches of tape are there.

We know that,

1 yard is 36 inches.

So,

2 yards is 2 times 36 is 72 inches.

The inches of the tape they need is 10 times 4 is 40.

So,

72-40 is 32 inches

Therefore, 32 inches more of tape students need.

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The acceleration of the car three seconds before it comes to a stop is  -2.76 m/s² (Letter B).

Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.

In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.

For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x

The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you  should solve this quadratic function:

Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]

[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]

[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]

[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]

Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].

The acceleration can be found from the derivative of the velocity function. See below.

a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]

a(t)= -6*[tex]2\sqrt{3}[/tex]t+18

a(t)= [tex]-12\sqrt{3}[/tex]t+18

a(t)=-2.76

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Kinetic energy of a 64 kg object travelling at 12 m/s is 4.6kj.

Kinetic energy = KE = [tex]\frac{1}{2}mv^{2}[/tex]

Mass = m = 64 kg

Velocity = v = 12 m/s

KE = [tex]\frac{1}{2}*64*(12)^{2}[/tex]

    = 4608 J

1000 j = 1 kj

      1 j = 1/1000 kj

4608 j = 4608/1000 kj

          = 4.608 kj

Hence, kinetic energy is 4.6 kj.

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Using division operations and based on the rates of production, given, Machine D works the fastest.

The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).

The rate of production is the number of goods that can be produced during a given period of time.

The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.

There are, therefore, two ways of determining production rate.  Firstly, we can divide the total production by the hours consumed.

Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.

                           Units          Production     Rate of

                       Produced          Hours      Production

Machine A        10,000               15             667 cups per hour

Machine B       25,000              20           1,250 cups per hour

Machine C       30,000              30           1,000 cups per hour

Machine D       15,000               10            1,500 cups per hour

Thus, using division operation, Machine D produces at the fastest rate than the other three machines.

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                           Units          Production

                       Produced          Hours

Machine A        10,000               15

Machine B       25,000              20

Machine C       30,000              30

Machine D       15,000               10

Answer:

B

Step-by-step explanation:

(7x+2)(7x+2)

7x×7x=49

7x×2+2×7x=28x

2x2=4

Answer:

See below

Step-by-step explanation:

2 /1 5 = .1333

so   2/15 < .83

Answer: resource - trust me bro

Step-by-step explanation: Let x = the smaller numberLet 2x + 10 = the larger numberx(2x + 10) = 1002x^2 + 10x - 100 = 0Divide both sides of the equation by 2.x^2 + 5x - 50 = 0(x - 5)(x + 10) = 0x - 5 = 0 or x + 10 = 0x = 5 or x = -10, not a positive number2x + 10 = 2(5) + 10 = 20

Using the substitution method, the solution to the system of equations is: x = -4 and y = 12.

To solve a system of equations using the substitution method, find the value of one of the variables in one equation, then substitute it in the second equation and solve to find the value of the second variable.

Given the equations:

x + y = 8 --> eqn. 1

y = -3x --> eqn. 2

Substitute -3x for y into equation 1:

x + (-3x) = 8

x - 3x = 8

-2x = 8

-2x/-2 = 8/-2

x = -4

Substitute x = -4 into equation 2:

y = -3(-4)

y = 12

The solution is, x = -4 and y = 12.

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The exponential function that can model the amount of medication in Austin's body, y, x hours is of: [tex]y = 180(0.9)^x[/tex]

The definition of the exponential function is presented as follows:

[tex]y = a(b)^x[/tex]

The parameters a and b are listed as follows:

a is the amount when x = 0.

b is the rate of change.

Given that the initial dose was of 180 micrograms, hence the parameter a is;

a = 180.

After one hour, the concentration was of 162 micrograms, hence the parameter b is;

b = 162/180 = 0.9.

Hence the equation is:

[tex]y = 180(0.9)^x[/tex]

After six hours, the concentration is given as;

[tex]y = 180(0.9)^6[/tex]= 96 micrograms.

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Answer:

New: $44,840 Original: 47,200

Step-by-step explanation:

You have to multiply 47,200 by 95% or 0.95

The equation a+b+c+d=15 has infinite many solutions

From the question, the equation is given as

a+b+c+d = 15

From the above representation of the equation, we can see that:

When a linear equation that has more than one variable is given, the number of solutions cannot be quantified i.e. infinite number of solutions

Hence, the equation has infinite number of solutions

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Answer:

P(les than/equal to 3): ½

Answer:

f = 4/3

f = 1.3

f = 1 1/3

Step-by-step explanation:

Move all terms that don't contain f to the right side and solve.

The prime factorization of 48 is  2⁴  ×  3.

Those greater than one are known as prime numbers. They simply have two variables: the number itself and factor 1. This indicates that these numbers cannot be divided without leaving a remainder by any number other than 1 and the number itself.

Given:

The number is 48,

Factorize 48 we get 2 × 2  × 2  × 2 × 3

= 2⁴  ×  3

Therefore, the prime factorization of 48 is  2⁴  ×  3.

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The paper company can produce 25 notebooks for $285

From the question, the equation of the total cost is given as

Equation = 4x + 185

Rewrite as

Cost = 4x + 185

Express the equation as a cost function

So, we have the following representations

C(x) = 4x + 185

When the total cost is $285, we have

C(x) = 285

This gives

4x + 185 = 285

Subtract 185 from both sides

4x = 100

Divide by 4

x  = 25

Hence, the number of notebooks is 25

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The estimation of 719 x 26 is 14,000

Making a number simpler so that its value stays near to its original state is known as rounding. Although less exact, the outcome of rounding off a number is simpler to utilise.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

Estimation of 719 x 26

Now, Round off nearest hundred for 719 which is 700

i.e., Round 719 = 700

Now, Round off nearest hundred for 26 which is 20

i.e., Round 26 = 20

Hence, the estimation is 700 x 20 = 14,000.

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x-3=0

so x = 3

-(y-2)=0

so y = 2

vertex = (3,2)

Answer:

------------------------------

Using polar coordinates, volume of the given solid is, 32√3π.

What is volume of solid?

An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units

We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.

So, the volume is

[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]

[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]

[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]

[tex]32\sqrt{3}\pi[/tex]

Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].

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Answer: 1 hour and 30 minutes or 1.5 hours

Answer:

1 hour and 30 minutes

Step-by-step explanation:

Answer:

5 = 1

or

5 = 25

Step-by-step explanation:

I've seen two answers to this.

1. Since we are told 1 = 5, then 5 = 1.

One answer is 1 = 5

2. Since each number on the right is 5 times the number on the left, then 25 corresponds to 5, and 5 = 25.

Answer: 5=1 (The correct answer) 5=25 (The answer that makes sense but is not correct).

Step-by-step explanation:

Explanation for answer 1: It say's that 1 = 5.

Explanation for answer 2: If we follow the pattern of adding 5 each time we go up a number then 5 would equal 25.

The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.

Given,

The cost for one calendar = $8

The cost for one coffee mug = $12

Dominique must sell at least $800 of merchandise and it should include at least 60 coffee mugs.

Here,

x be the number of calendars and y be the number of coffee mugs;

We have to find an inequality which represents the given situation;

So,

The inequality be;

8x + 12y ≥ 800 and x ≥ 60

That is,

The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.

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