Write each of the following expressions in the form Axmyn, where A is a real number and m and n are integers. 2x^2∙3yx^2

To reach their financial objective of having $130,000 accessible for their child's schooling when the youngster turns 18, the parents must set aside roughly $97,209.87 at 3% compound semiannually.

To determine how much money needs to be set aside to meet the financial goal of $130,000 for the child's education, we can use the compound interest formula:

\(A = P(1 + r/n)^(nt)\)

where A represents the future value, P represents the principal (or initial investment), r represents the annual interest rate, n is the frequency with which interest is compounded annually, and t represents the passage of time in years.

To solve for the principal, P, in this situation, we must first identify the principal, P.

\(P = A / (1 + r/n)^(nt)\)

Given that the child is currently 10 years old and will need the money in 8 years (at age 18), we have t = 8. The interest rate is 3%, which we need to express as a decimal (r = 0.03), and the interest is compounded semiannually, so n = 2.

Using these values and the desired future value of $130,000, we can calculate the required principal:

P = \(130000 / (1 + 0.03/2)^(2*8)\) = $97,209.87

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Given:

Account 1:

Principal amount (P)= x

Rate (R) = 7%

Account 2:

Principal amount (p) = x+800

Rate (R) = 13%

Total interest = $333

The simple interest is given as,

So, the amount in account 1 is x = $1145

Account 2: x+800= $1945

The interest in each account is,

Account 1 :

Account 2:

Based on the maximum taxable amount for social security in 2009, and the social security tax rate, the social security tax that Larry paid was $7,347.

The total amount paid by Larry as Social security tax can be found as;

= Maximum amount allowable for social security tax x Social security tax rate

The social security tax rate was 6.2% not 62.2%.

The social security tax was therefore:

= 118,500 x 6.2%

= $7,347

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Answer:

3

Step-by-step explanation:

The number of points to be removed from the graph is 2

from the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that

2 points have the same y coordinates

Another 2 points have the same y coordinates

For it to be a function, one of the 2 points must be removed each

So, we have the number of points to be removed from the graph is 2

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Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

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According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.

To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.

First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z1 = (264 - 264) / 75 = 0

z2 = (489 - 264) / 75 = 3

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .

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The expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Therefore, the expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

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Answer:

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Step-by-step explanation:

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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The final distance is 31 km.

Time, t = Distance, d/Velocity, v

Let's assume the ambulance drives a distance of x along the road, which leaves us 50-x on the road, after which it has reached the road.

It forms a triangle, after which we can use Pythagoras Theorem.

Using it, we get distance down the hill, d1, and we can calculate distance on the road remaining till the hospital, d2.

t = d1/v1 + d2/v2

 = \(\frac{\sqrt{x^{2} + 30^{2} } }{30} + \frac{50 - x}{120}\)

We need to minimise t. Therefore, we have to differentiate.

On differentiating and equating it to 0, we get the value of x as \(\sqrt{60} = 7.75\)

How far down the road should the vehicle aim to reach the road to reach the hospital at the minimum time?

\(= \sqrt{900 + 7.75^{2} } = 31 km\)

Thus, the final distance is 31 km.

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Answer:

I'd say edges

Answer:

B. 17

Step-by-step explanation:

The average rate of change is:

m_avg = (y₂ − y₁) / (x₂ − x₁)

m_avg = (100 − 49) / (10 − 7)

m_avg = 17

Answer:

Step-by-step explanation:

Solve the following expression.

Answer:

2 2/5 hours

Step-by-step explanation:

In 6 hours Brian can lay 1 slab of concrete

dividing both side by 6

in 6/6 hours Brian can lay 1/6 slab of concrete

Thus, in 1 hour  Brian can lay 1/6 slab of concrete

In 4 hours Greg can lay 1 slab of concrete

dividing both side by 4

in 4/4 hours Greg can lay 1/4 slab of concrete

Thus, in 1 hour  Greg can lay 1/4 slab of concrete

Thus, total part of slab laid by both in 1 hour when they work together

1/6 + 1/4 = 4+6/(6*4) = 10/24 = 5/12

5/12 of slab of concrete is laid by both of them in 1 hour

time taken to lay 5/12 of slab = 1 hour

dividing both side by 5/12

time taken to  5/12/ 5/12 of slab = 1/5/12 hour = 12/5 hours

time taken to 1/1 of slab = 12/5 hours = 2 2/5 hours

Thus,

it takes 2 2/5 hours to lay the full slab of concrete when Brian and Greg work together,

It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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The explicit formula for the sequence is an = 1,087(1/4)ⁿ⁻¹ .

Without calculating any terms before the nth term, the arithmetic sequence explicit formula is used to determine the nth term of an arithmetic sequence. The nth term of an arithmetic series whose initial term is "a" and common difference is "d" is determined by this formula: ann = a + (n - 1) d.

The following definition of the given sequence is recursive:

a1 = 1,087

an = (1/4) * an-1 for n > 1

a2 = (1/4) * a1 = (1/4) * 1,087 = 271.75

a3 = (1/4) * a2 = (1/4) * 271.75 = 67.9375

a4 = (1/4) * a3 = (1/4) * 67.9375 = 16.984375

We can see that each term is obtained by multiplying the previous term by 1/4. Therefore, the nth term can be expressed as:

an = (1/4)ⁿ⁻¹ * a1

Substituting a1 = 1,087, we get:

an = (1/4)ⁿ⁻¹  * 1,087

So the explicit formula for the sequence is an = 1,087(1/4)ⁿ⁻¹ .

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9514 1404 393

Answer:

  2.  4

Step-by-step explanation:

The "initial value" is the y-value corresponding to x=0. That is given in the first line of the table.

The initial value is 4.

$170 can be saved resulting in an actual net income of $0.

Answer:

x-intercepts:  (-1, 0) and (2, 0)

x-intercept:  (-3, 0)

Step-by-step explanation:

Given quadratic function:

\(f(x)=-4x^2+4x+8\)

The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ when y = 0

Therefore, to find the x-intercepts of the given function, set the function to zero:

\(\implies -4x^2+4x+8=0\)

Factor out -4:

\(\implies -4(x^2-x-2)=0\)

Divide both sides by -4

\(\implies x^2-x-2=0\)

Rewrite the middle term as -2x + x:

\(\implies x^2-2x+x-2=0\)

Factor the first two terms and the last two terms separately:

\(\implies x(x-2)+1(x-2)=0\)

Factor out the common term (x - 2):

\(\implies (x+1)(x-2)=0\)

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

\(\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}\)

Therefore, the x-intercepts are (-1, 0) and (2, 0).

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

Given quadratic equation:

\(-9 = x^2 + 6x\)

Add 9 to both sides:

\(\implies x^2+6x+9=0\)

Rewrite the middle term as 3x + 3x:

\(\implies x^2+3x+3x+9\)

Factor the first two terms and the last two terms separately:

\(\implies x(x+3)+3(x+3)=0\)

Factor out the common term (x + 3):

\(\implies (x+3)(x+3)=0\)

\(\implies (x+3)^2=0\)

Square root both sides:

\(\implies (x+3)=0\)

Solve for x:

\(\implies x=-3\)

Therefore, the x-intercept is (-3, 0).

As the function has a repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.  

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer:

the length of side X is 7.21

Answer:

  $2496

Step-by-step explanation:

You want to know the cost of carpeting a 18 ft by 24 ft room with carpet that costs $52 per square yard.

The dimensions of the room in yards are (18 ft)/(3 ft/yd) = 6 yd, by (24 ft)/(3 ft/yd) = 8 yd.

In square yards, the area is ...

  (6 yd)(8 yd) = 48 yd²

The cost of one square yard of carpet is $52, so the cost of 48 square yards will be 48 times as much.

  (48 yd²)($52/yd²) = $(48·52) = $2496

The total price to carpet the floor is $2496.

__

Additional comment

We're reluctant to call this the total price, as there are usually additional charges for tax, carpet pad, delivery, installation, removal and disposal of old flooring, and possibly additional materials such as tack strips or thresholds. Repairing mold or water damage, or leveling the floor, can also add cost.

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Answer:

False

Equivalent fractions are fractions with the same numerical value, basically fractions that are equal to each other.

Answer: false

Step-by-step explanation:

Answer:

Equation: \(143 + g = 180\)

\(g =37\)

Step-by-step explanation:

Given

The attached figure

Required

The equation to find g and the solution

From the attached: Angles ACD, DCE and ECB lie on a straight line.

Where

\(ACD = 90\)       \(DCE = 53\)     \(ECB = g\)

This means that:

\(ACD + DCE + ECB = 180\)

\(90 + 53 + g = 180\)

\(143 + g = 180\)

Subtract 143 from both sides

\(-143 + 143 + g = 180 - 143\)

\(g = 37\)

Answer:

r = 12

Step-by-step explanation:

-1.5(4-1r)=12

-6+1.5r=12

1.5r =18

r=12

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

416

Step-by-step explanation:

The front and back are triangles

a = 1/2 bh

a = 1/2(12)(8)

a = 48

We times this by 2 to find the front and the back.

96

Bottom

a = lw

a = 10 x 12

a = 12

120

Right and left sides

a = lw

a = 10 x10 = 100

Multiply this by 2 to find the right and the left sides.

200

Add the numbers together:

96 + 120 + 200 = 416

Helping in the name of Jesus.

To find the surface area of a three-dimensional object, you need to add up the area of all its faces.

This can be done using formulas specific to the shape of the object. For example, the surface area of a rectangular prism (a box) can be found using the formula SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the box, respectively. Other common three-dimensional shapes include spheres, cones, and cylinders, each with their own unique formulas for finding surface area. So, to answer your question, I would need to know what specific object you are referring to in order to provide an accurate answer about its surface area.

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