tanja wants to establish an account that will supplement her retirement income beginning 10 years from now. find the lump sum she must deposit today so that $200,000 will be available at time of retirement, if the interest rate is 6%, compounded quarterly. (round to the nearest cent as needed)

In order to solve the system, we can compare both y values from each equation:

So the solution for this system is the pair (0, -4), that is, x = 0 and y = -4.

Given data:

The given mean is m=24.

The given standard devaition is s=0.62.

The given vallue is x=22.9.

The expression for the value of z is,

Refer the standard z-table.

The number of box required are,

Thus, the number of boxes are 288.

Each Jet Ski should sell for $8288.

What is selling price?

The amount a buyer pays for a good or service is known as the selling price. It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.

Let the selling price be x.

Therefore according to the question,

( x - 5600/ 5600) 100 = 48

=>  x - 5600 = 48 . 56

=> x = 2688 + 5600

=> x = 8288

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Answer:

600

Step-by-step explanation:

the total is 626 but round it to the nearest hundred is 600 because the rule 5 or more go up one more 4 or less stay at rest

In this case we have the point (-2,4), since this represents the x and y coordinates of the solution of the system of equations, then:

x= -2

y= 4

Let's create the pair of equations:

1. ax+by=c

2. ex+fy=g

Randomly let's define the values of the coefficients a, b, e and f:

a= 1

b=2

e= -1

f= 4

With these values and the known coordinates of the solution, let's replace into the expressions of the system of equations and solve for c and g, like this:

Answer:

Each bottle cost $0.20.  That is the unit rate

Step-by-step explanation:

[tex]\frac{5.00}{25}[/tex]

Answer:

Equation: 2x +2x +x -8= 4(x +2)

x= 16

Step-by-step explanation:

The perimeter is the total length of the sides of a particular shape or figure.

Given that the triangle and square have an equal perimeter,

Perimeter of triangle= perimeter of square

Since a square has 4 equal sides,

2x +2x +x -8= 4(x +2)

Let's solve the above equation.

Simplify and expand:

5x -8= 4x +8

Move x terms to the left of the equation, constants to the right.

5x -4x= 8 +8

x= 16

Thus, the value of x is 16.

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Answer:

x = 16

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

As the sides of a square are equal in length, the perimeter of a square is four times the length of one side.

[tex]\begin{aligned}\implies \textsf{Perimeter of the square}&=4(x+2)\\& = 4x+8\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Perimeter of the triangle}&=2x+2x+(x-8)\\&=4x+x-8\\&=5x-8\end{aligned}[/tex]

If the perimeter of the triangle and the perimeter of the square are equal then:

[tex]\begin{aligned}\implies\textsf{Perimeter of the triangle}&=\textsf{Perimeter of the square}\\5x-8&=4x+8\\5x-8-4x&=4x+8-4x\\x-8&=8\\x-8+8&=8+8\\x&=16\end{aligned}[/tex]

Therefore, the value of x is 16.

B) 12/13

1) In this triangle, the sine of angle A is given by the opposite leg over the hypotenuse, so we can write it out. Since the hypotenuse is opposite to the right angle:

Note that we simplified that original ratio 36/39 dividing both numerator and denominator by 3

2) Hence, the answer is B) 12/13

Answer:

15

Step-by-step explanation:

Speed= 230 per hour

Distance=3,647

Formula

Time=Distance upon speed

divide 230 into 3,647=15 time

You can only subtract or divide?

The probability that x≥5

P (x≥5) = P(5)+P(10)+P(15)+ P(20)

P (x≥5)= 0.1+0.25+0.1+0.15

P (x≥5)= 0.6

To write the equation of the line that passes through (10,80) (5,65)

we will use the formula;

x₁ = 10 y₁ = 80 x₂ = 5 y₂ = 65

substituting the above into the formula;

we will go ahead and simplify

y- 80 = 3(x - 10)

y- 80 = 3x - 30

y -3x -80 + 30 = 0

y - 3x - 50 = 0

The above is the equation of the line.

To write in a slope-intercept form simply means to write it in the form;

y = mx + b

where m is the slope and b is the intercept

Hence;

y = 3x + 50

The above is the equation of the line in a slope-intercept form

The exact solution of log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2) While x = 1 is 0.954.

Given:

log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2)

= log 3(x + 2)

putting x = 1

= log 3( 1 + 2 )

= log 3 . 3

= log 3 + log 3

= 0.477 + 0.477

=0.954

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First determine the common ratio between consecutive terms.

4.5/3 = 9/6 = 3/2

6.75/4.5 = 27/18 = 3/2

and so on. The [tex]n[/tex]-th term in the sequence is given by

[tex]a_n = 3 \cdot \left(\dfrac32\right)^{n-1}[/tex]

Solve for [tex]n[/tex] that gives the last term to find how many terms are in the sum.

[tex]n = 1 + \log_{3/2}\left(\dfrac{a_n}3\right)[/tex]

Plug in the last term.

[tex]n = 1 + \log_{3/2} \left(\dfrac{34.171875}3\right) = 1 + 6 = 7[/tex]

Then the sum of the first 7 terms of this sequence is

[tex]\displaystyle \sum_{n=1}^7 3 \cdot \left(\frac32\right)^{n-1} = 3\cdot\frac{1 - \left(\frac32\right)^7}{1-\frac32} = \boxed{\frac{6177}{44}} = 96.515625[/tex]

where we use the formula

[tex]\displaystyle \sum_{n=1}^k r^{n-1} = \frac{1-r^n}{1-r}[/tex]

The equation of the line passing through points  (0,1) and (2,2) will be y = ( 1 / 2) x + 1

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope= 2-1   /   2-0  =  1 /2

Now pick one of the points and put in for y and x use (2,2).

2= 1/2(2) +b

2=1 + b

2-1 =1-1 +b   subtract 1 from each side

1 = b   This is your y-intercept

The equation will be written as:-

y = ( 1 / 2) x + 1

Given any line, to find the slope of the line, follow the procedure below:

First, pick any two points (x1,y1) and (x2,y2) on the line.

Then, substitute the points into the formula for slope below:

You can use this method to find the slope of any given line.

Answer: x = 17

Step-by-step explanation:

         We can tell that these two angles are supplementary angles because we can use corresponding angles. See attached.

(x + 14)° + (9x - 4)° = 180°

x° + 14° + 9x° - 4° = 180°

14°- 4° + x° + 9x° = 180°

10° + 10x° = 180°

10x° = 170°

x = 17

The value of x is 15

Here, we want to get value of x

From the question, we have that AC = AD

This means that what we have is an isosceles triangle

Mathematically, the bases of an isosceles triangle have same angle

For triangle ACD; the measure of angle D and the measure of angle C is same

That means the value of x is 15 too

Since the two cylinders are congruent, it means that their dimensions are exactly the same thing.

In other words, the radius of cylinder 1 is the same as that of cylinder 2, and the height of cylinder 2 is the same as that of cylinder 1. This is what it means for two solid shapes to be congruent.

Now, to find the volume of cylinder 2, we apply the frmula for the volume of a tyical cylnder:

Now,

radius of cylinder 2 = radius of cylinder 1 = 3

height of cylinder 2 = 8

Thus: r = 3, h= 8

Therefore:

Therefore the volume of cylinder 2 is 72pi cubic units (Option D)

x = 36° (option C)

The adjacent angles in a parallelogram are supplementary. This means the sum of the angles is equal to 180 degrees

The adjacent angles in this paralllelogram are (4x + 2)° and 34°

(4x + 2)° + 34° = 180°

4x + 2 + 34 = 180

4x + 36 = 180

4x = 180 - 36

4x = 144

Divide both sides by 4:

4x/4 = 144/4

x = 36° (option C)

Answer:

a) The curved surface area is;

b) The volume of the cylindrical tank is;

Explanation:

Given that the cylindrical tank has height 15m and radius 7m.

The curved surface area of a cylinder can be calculated using the formula;

substituting the given values;

Therefore, the curved surface area is;

The volume of the cylindrical tank can be calculated using the formula;

Substituting the given values;

Therefore, the volume of the cylindrical tank is;

The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168° so option (A) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠J +  m∠L +  m∠K = 180°

m∠K = 180° - 78° -  90°

m∠K = 12°.

The exterior angle of k = 180- 12 = 168°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168°".

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The constant of proportionality that lies in all of the pairs of values that we have here is given as 17.5

This is the term that is used to refer to the ratio that is known for the fact that it helps to relate two values that are given in a proportional way.

For instance we are to find the constant proportionality of (9, 148.50)

This is given as 9 + 148.5 / 9

= 157.5 / 9

= 17.5

Then the second pair is (15 ,247.50)

In the same way 15 + 247.50 / 15 = 17.5

Hence we can see that the constant of proportionality in all of the pairs is 17.5

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Answer:

its 16.50 i literally just took the test trust me.

Step-by-step explanation:

9 x 16.50 = 148.50

15 x 16.50= 247.50

21  x 16.50 = 346.50!

hope this helps! =)

Given:

To write it in scientific notation:

It can be written as,

Hence, the scientific notation is,

we have that

3 years=3(12)=36 months

so

$2,400+$167(36)=$8,412

and

39,087-36,000=3,087 miles

so

$0.12*(3,087)=$370.44

therefore

The total cost is

$8,412+$370.44=$8,782.44

Answer: 16

Step-by-step explanation:

The perimeter of the triangle is [tex]2x+2x+x-8=5x-8[/tex].

The perimeter of the square is [tex]4(x+2)=4x+8[/tex].

Setting the perimeters equal to each other,

[tex]5x-8=4x+8\\\\x-8=8\\\\x=16[/tex]

A rational number between the two given ones is -2/5, such that:

-1/3 > -2/5 > -1/2.

Rememeber that a rational number is any number that can be written as a quotient between two integer numbers.

Here we want to find a rational number between -1/3 and 1/-2, we can rewrite the second one as -1/2.

Now we want to find a number x such that:

-1/3 > x > --1/2

Remember that:

-1/3 ≈ -0.33...

-1/2 ≈ -0.5

So a number between these two is -0.4 which can be written as -2/5 (this is also rational).

That is the number we wanted to find.

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Given the equation of the line in point-slope form:

Based on this, one point of the line is (-1, 3). Now, the slope-intercept form of the equation is:

Then, another point of the line is (0, 24/5) = (0, 4.8). Finally, the graph of the equation is: