David has a bank account which pays interest at the rate of 1.5% per year, compounded annually. Determine what amount David must have in the bank, given that he would like to draw an annual salary of $32,635.15 from his account at the end of each year for 30 years. Round to the nearest cent.
a.
$783,760.48
b.
$979,054.50
c.
$1,225,080.50
d.
$795,516.88

Answer:

(2, 5)

Step-by-step explanation:

Given the 2 equations

y = x + 3 → (1)

- 2x + y = 1 → (2)

Substitute y = x + 3 into (2)

- 2x + x + 3 = 1

- x + 3 = 1 ( subtract 3 from both sides )

- x = - 2 ( multiply both sides by - 1 )

x = 2

Substitute x = 2 into (1) for corresponding value of y

y = 2 + 3 = 5

Solution is (2, 5)

Answer: y=5, x=2

Step-by-step explanation:

Answer: x = 1/6 or 1.6667

3x * 2 + 6x = 2

Multiply the numbers: 3 * 2 = 6

6x + 6x = 2

Add similar elements: 6x + 6x = 12x

12x = 2

Divide both sides by 12

12x / 12  =  2 / 12

Simplify

x = 1/6

Answer:  The required discriminant of the given quadratic equation is 60.

Step-by-step explanation:  We are given to find the discriminant of the following quadratic equation :

[tex]3x^2+6x=2\\\\\Rightarrow 3x^2+6x-2=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the discriminant of a quadratic equation [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by

[tex]D=b^2-4ac.[/tex]

For the given equation (i), we have

a = 3,  b = 6  and  c = -2.

Therefore, the discriminant of the given equation will be

[tex]D=b^2-4ac=6^2-4\times3\times(-2)=36+24=60.[/tex]

Thus, the required discriminant of the given quadratic equation is 60.

ANSWER

[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]

EXPLANATION

The given functions are

[tex]f(x) = {x}^{3} - 27[/tex]

and

[tex]g(x) = 3x - 9[/tex]

[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{3} - 27}{3x - 9} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ (x - 3)( {x}^{2} + 3x + 9) }{3(x -3 )} [/tex]

Cancel the common factors,

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} + 3x + 9 }{3} [/tex]

OR

[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]

Mode could work but I believe the best answer would be median.

Answer:

median

Step-by-step explanation:

Median is correct. One extreme outlier can "drag" the mean up or down, while it would have little or no effect on the median.

Answer:

  27

Step-by-step explanation:

The central angle of 120° is 1/3 of the entire circle of 360°, so the sector area is 1/3 of the circle area:

  1/3×81 = 27

The sector area is 27.

Answer:

a rectangle with two triangles.

Step-by-step explanation:

this way you will  be able to find the area of the rectangle then add it to the area of the two triangles.

Answer:

the correct answer is b

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

2+7=9

12+2=14

12+7=19

Answer:

No

Step-by-step explanation:

the sum of two sides has to be greater than the third side

2+7=9 9 isn't greater than 12

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (7, -4) and (7, 9). Substitute:

[tex]d=\sqrt{(7-7)^2+(9-(-4))^2}=\sqrt{0+13^2}=\sqrt{13^2}=13[/tex]

Used [tex]\sqrt{a^2}=a[/tex]

Answer:

a) yes they are similar

b)Proved below

c)Proved below

Step-by-step explanation:

a) rectangle 1 and 2 are similar by definition of similar rectangles.

Definition of similar rectangles states that two rectangles are similar if they have same shape but different sizes. The ratio between their corresponding sides are same, in this case as rectangle 2 is made by multiplying each dimension of Rectangle 1 by a

factor of k, where k>0 thus providing same proportion in length of different corresponding sides of two rectangles hence rectangle 1 and 2 are similar.

b) Perimeter of rectangle 1, P1= s1+ s2+ s3 + s4

As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore

  Perimeter of rectangle 2, P2= k.s1+ k.s2+ k.s3 + k.s4

Taking k common

                                                  = k(s1+ s2+ s3 + s4)

Substituting P1 in above expression

                                               P2  =k(P1)

Hence the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

c) Area of rectangle 1, A1= 2(s1)(s2)

As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore

Area of rectangle 2, A2= 2(k.s1)(k.s2)

                                       = 2k^2(s1)(s2)

                                        = k^2 [2(s1)(s2)]

Substituting A1 in above expression

                                        A2 = k^2(A1)

Hence the area of Rectangle 2 is k2 times the area of Rectangle 1 !

This is just a ONE STEP equation.

It is, because all you must do to solve for "x" is subtract 2

Answer:

one-step equation

x+2=14

x+2-2=14-2

x=12

Answer:

Multiply the length and the width of the shape together to get the area of the square or rectangle in square feet.

10 multiplied by 8 equals 80 square feet

Step-by-step explanation:

Got a 100 on it.

Final answer:

To cover a rectangular garden measuring 10 feet by 8 feet, multiply the length by the width to get an area of 80 square feet, which is the amount of material needed.

Explanation:

Calculating the Area of a Rectangular Garden

To determine the number of square feet required to cover your rectangular garden, you need to calculate the area of the garden. The area of a rectangle is found by multiplying the length by the width. In this case, the garden has a length of 10 feet and a width of 8 feet.

Steps to Calculate the Area

Measure the length and width of the garden using a measuring tape.

Multiply the length by the width to get the area in square feet: 10 feet (length) × 8 feet (width) = 80 square feet.

Therefore, you would need 80 square feet of material to cover the entire garden.

Answer:

Check the attached graph

Step-by-step explanation:

Given that slope of the line is m = 1

And the line passes through the point (-3,5).

Now we need to graph the line using above information. So begin by graphing the point (-3,5).

Slope means rise/run

Then slope = 1 means rise/run=1=1/1

means move point 1 unit up then 1 unit right

then new point is at (-2,6).

Now draw a line joining both points to get the final graph.

Answer:

Let's solve your system of equations by elimination.

8x+9y=48;12x+5y=21

Steps:

Multiply the first equation by 5,and multiply the second equation by -9.

5(8x+9y=48)

−9(12x+5y=21)

Becomes:

40x+45y=240

−108x−45y=−189

Add these equations to eliminate y:

−68x=51

Then solve−68x=51for x:

−68x /−68 = 51 /−68  (Divide both sides by -68)

x=  −3 /4

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

8x+9y=48

Substitute

−3 /4

8x+9y=48:

8( −3 /4 )+9y=48

9y−6=48 (Simplify both sides of the equation)

9y−6+6=48+6 (Add 6 to both sides)

9y=54

9y /9  =  54 /9  (Divide both sides by 9)   y=6

Answer:  x=  −3 /4  and y=6

Hope This Helps!  Have A Nice Day!!

37.5% as a fraction is 3/8.

Answer:

3/8

Step-by-step explanation:

To write a percent as a fraction, divide the percent by 100.

37.5% = 37.5/100

Now we reduce the fraction. First, multiply the numerator and denominator by 2 to get rid of the decimal in the numerator.

37.5% = 37.5/100 = 75/200

Both the numerator and denominator are divisible by 5, so we divide them by 5.

37.5% = 37.5/100 = 75/200 = 15/40

Both the numerator and denominator are divisible by 5 again, so we divide them by 5 again.

37.5% = 37.5/100 = 75/200 = 15/40 = 3/8

Answer: 37.5% = 3/8

The ratio in option (D), 15 boys to 40 girls is equivalent to 3 : 8.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

The given ratio of boy to girls is 3 : 8.

To find the equivalent ratio to 3:8.

Solve with the help of option,

(A)

15 boys to 55 girls.

The ratio 15 : 55 = 3 : 11

(B)

55 boys to 15 girls,

The ratio 55 : 15 = 11 : 3.

(C)

40 boys to 15 girls,

The ratio 40 : 15 = 8 : 3

(D)

15 boys to 40 girls,

The ratio 15 : 40 = 3 : 8.

The ratio of 15 boys to 40 girls is 3:8.

Hence, the correct option is (D).

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Answer:

see explanation

Step-by-step explanation:

(a)

Note the squared value in column 3 which is the square of 1 more than the row number, that is

row 2 → (2 + 1)² →3²

row 3 → (3 + 1)² → 4²

Find the square root of 676 = 26 → (25 + 1)² = 26²

Hence the row number is 25

(b)

The pattern in column 1 is [ row number × (row number + 2 ) + 1 ]

row number is n then n(n + 2) + 1 = n² + 2n + 1

Answer:

(2x)+3

Step-by-step explanation:

I'm sure most of you just want the answer, but if you want me to educate you, keep reading!!

The product of two and a number x can be written as 2x.

Three more than something means that we add 3 to it.

If we add 3 to 2x, we have 3+2x.

So in conclusion, the answer would be (2x)+3.

Hope this helps! :)

The final value will be 2x+3

Firstly,

∴If we add 3 to 2x, we have 3+2x.

So the answer would be (2x)+3.

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The initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.

The initial number of carbon-14 atoms in the organism at death can be calculated using the formula for exponential decay:

[tex]\[ N(t) = N_0 e^{-\lambda t} \][/tex]

where:

- [tex]\( N(t) \)[/tex] is the number of undecayed carbon-14 atoms at time [tex]\( t \),[/tex]

- [tex]\( N_0 \)[/tex] is the initial number of carbon-14 atoms at time \[tex]( t = 0 \[/tex]) (the time of death),

- [tex]\( \lambda \)[/tex] is the decay constant for carbon-14,

- [tex]\( t \)[/tex] is the time that has passed since the time of death.

 Given that after 5730 years (the half-life of carbon-14), the number of undecayed carbon-14 atoms is half the initial amount, we can write:

[tex]\[ \frac{N_0}{2} = N_0 e^{-\lambda \times 5730} \][/tex]

To find the decay constant [tex]\( \lambda \)[/tex], we use the half-life formula:

[tex]\[ \lambda = \frac{\ln(2)}{t_{1/2}} \][/tex]

 where [tex]\( t_{1/2} \)[/tex] is the half-life of carbon-14, which is 5730 years. Plugging in the values:

[tex]\[ \lambda = \frac{\ln(2)}{5730} \][/tex]

Now, we can solve for [tex]\( N_0 \)[/tex]using the information provided:

[tex]\[ 100 = N_0 e^{-\frac{\ln(2)}{5730} \times 573[/tex]

 Since [tex]\( e^{-\ln(2)} = \frac{1}{2} \)[/tex], the equation simplifies to:

[tex]\[ 100 = N_0 \times \frac{1}{2} \][/tex]

Solving for [tex]\( N_0 \):[/tex]

[tex]\[ N_0 = 100 \times 2 \][/tex]

[tex]\[ N_0 = 200 \][/tex]

 Therefore, the initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.

Answer:

The value of the single logarithm is -11 ⇒ answer B

Step-by-step explanation:

* Lets revise the rule of the logarithmic functions

# ㏒ a + ㏒ b = ㏒ ab  

# ㏒ a - ㏒ b = ㏒ a/b

# ㏒ a^n = n ㏒ a  

# ㏒ 1 = 0  

* Now lets solve the problem

∵ [tex]log_{b}(\frac{A^{5}C^{2}}{D^{6}})[/tex]

- Change the single logarithm to an expression by change the

  multiplication to addition and the division to subtraction

∵ [tex]log_{b}A^{5}=5log_{b}A[/tex]

∵ [tex]log_{b}C^{2}=2log_{b}C[/tex]

∵ [tex]log_{b}D^{6}=6log_{b}D[/tex]

∴ The single logarithm = [tex]5log_{b}A+2log_{b}C-6log_{b}D[/tex]

* Now lets substitute the values

∵ [tex]log_{b}A=3;===log_{b}C=2;===log_{b}D=5[/tex]

- Substitute the values into the expression

∴ The value = 5(3) + 2(2) - 6(5) = 15 + 4 - 30 = -11

* The value of the single logarithm is -11

The answer is .22222..., 3/10, .53, and 3/5.

Hope this helps!

Hello there!

The numbers in order from least to greatest are:

0.2222, 3/10, 0.53, 3/5

Start by turning all the numbers into either decimals. To do this, take the two fractions, 3/5 and 3/10 and divide them out.

3 divided by 5 = 0.6

3 divided by 10 = 0.3

Now let's look at our numbers again.

0.3, 0.222, 0.6, 0.53.

We know that 2 is less than 3, and 3 is less than 5, and 5 is less than 6, so lets rearrange the numbers into that order.

0.2222, 0.3, 0.53, 0.6

Now, convert any fractions that were converted into decimals back into their original forms.

0.2222, 3/10, 0.53, 3/5

This is your final answer. I hope this helps and have a great day!

Answer:

Step-by-step explanation:

I think you meant x^(3/2).  This breaks down in at least two ways:

[x^3]^(1/2), or √(x^3)m or √x³), or

[x^(1/2)]^3 = (√x)^3

To write [tex]x^{3/2}[/tex] in radical form, rewrite it as (√x)³or √(x³). This utilizes the relationship between fractional exponents and radicals.

To write [tex]x^{3/2}[/tex] in radical form, we can use the relationship between exponents and radicals. In general, the expression [tex]x^{a/b}[/tex] can be written in radical form as the b-th root of x raised to the power 'a'. So, applying this rule to the given expression.

[tex]x^{3/2}[/tex]

Step-by-Step Explanation:

Therefore, the radical form of [tex]x^{3/2}[/tex] is √x³ or (√x)³.

The answer is:

The area of this figure is 946 square inches.

We can see that the figure is composed by two rectangles with diferrent dimensions, so, to calculate the area of the entire figure.

So,

For the first rectangle, we have:

[tex]Base=7in\\Height=28in[/tex]

The area will be:

[tex]Area=Base*Height=7in*28in=196in^{2}[/tex]

For the second rectangle, we have:

[tex]Base=25in\\Height=30in[/tex]

The area will be:

[tex]Area=Base*Height=30in*25in=750in^{2}[/tex]

Now, calculating the area of the entire figure, we have:

[tex]TotalArea=FirstRectangleArea+SecondRectangleArea\\\\TotalArea=196in^{2}+750in^{2}=946in^{2}[/tex]

Have a nice day!

Answer:

C

Step-by-step explanation:

1 | 4   6   - 2

        4     10

  ------------------

   4   10    8 ← remainder

Answer:

Option C

Step-by-step explanation:

Given is a division in synthetic

We have to find the remainder

The divisor is x-1 and dividend is [tex]4x^2+6x-2[/tex]

By synthetic division we get the following:

1)     4    6   -2\\

             4    10\\

----------------------\\

      4    10    8=R

Thus remainder is 8

Answer:

The discount is 15% because 6/40 = 0.15 and a percent is multiplied by 100 so the answer is 15%.

To find the percentage discount, subtract the discount amount from the original price and divide by the original price, then multiply by 100.

To find the percentage discount, we need to calculate the amount of the discount first. The discount is given as $6, so we subtract $6 from the original price of $40 to get $34. To find the percentage, we divide the discount amount by the original price and multiply by 100. In this case, the discount percentage would be (6/40) * 100 = 15%.

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where are the expressions ?

Answer:

3x + 2

Step-by-step explanation:

Answer:

60 out of 250 children will prefer organized sports.

Step-by-step explanation:

We are given the results of a random survey of children between the ages of 13 and 18 about their favorite activity.

Based on these results, we are to find the number of children who will prefer organized sports if 250 children were asked about their favorite activity.

Children who will prefer organized sports = [tex]\frac{37}{155} \times 250[/tex] = 60

Answer:

Triangle

Step-by-step explanation:

Look at the shape of the red part

The shape of the triangle is the cross-section part of the given figure. Thus, option A is correct.

The cross-section part of the given figure could be the shape fro the inscribed figure.

Here we can see that the three-dimensional figure inscribed in the square is a cone.

The right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

But for the plane of the square, the triangle is the cross-section part of the given figure.

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There are 16 oz in a pound, so 2 lbs is 32 oz.

Answer: two pounds is equivalent to 32 ounces.

Step-by-step explanation: 1 pound is equal to 16 ounces, and since 2 is 1 two times, just multiply 16 by 2, 16x2=32 ounces

Answer:

The point (2,0) is outside the circle

Step-by-step explanation:

we have

[tex](x-2)^{2}+(y+3)^{2}=4[/tex]

[tex](x-2)^{2}+(y+3)^{2}=2^{2}[/tex]

This is the equation of a circle with center at (2,-3) and radius equal to 2 units

Using a graphing tool

Plot the circle and the given points and verify if the point lie outside  the circle

we have

[tex](1, -4 ),(0, -3),(2, 0),(2,-4)[/tex]

so

The point (2,0) is outside the circle

see the attached figure