abbi invested $1,000 in a certificate of deposit with a simple interest rate of 6% find the interest earned in 4 years. then find the total of principal plus interest.

Hey there! I'm happy to help!

In our problem, 100 is a certain percent of 80. When talking about percents, the word "is" means equals. Let's represent our certain percent with p and solve for it.

100=80p

Let's flip the equation around so p is on the left side.

80p=100

We divide both sides by 80.

p=1.25

As a percent, the increase is 125%.

Have a wonderful day!

Answer:

21.5

Step-by-step explanation:

h(t) = -16t^2 + 35t + 5,

Let t = 1.5

h(1.5) = -16 (1.5)^2 + 35(1.5) + 5

        =-16 *2.25 +52.5+5

      = -36+57.5

      = 21.5

Answer:

i think it is the third one but dont know just an educational geuss

Step-by-step explanation:

The given steps from the derivation of the quadratic formula are:

Step 3:  [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]

Step 4a: [tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 4b: [tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

The property "converting to a common denominator" justifies step 4b. So, option C: "converting to a common denominator" is correct.

The quadratic formula is as follows:

x = [-b ± (√b²+4ac)]/2a

This formula is derived from the quadratic equation [tex]ax^2+bx+c=0[/tex].

The standard quadratic equation is [tex]ax^2+bx+c=0[/tex]

Step 1: [tex]ax^2+bx=-c[/tex]

Step 2: Taking 'a' as common

[tex]a(x^2+\frac{b}{a}x)=-c[/tex]

Step 3: Adding [tex]\frac{b^2}{4a}[/tex] on both sides

[tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x)+\frac{b^2}{4a}[/tex]

⇒ [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]

Step 4a: Factoring the polynomial

[tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 4b: Converting to a common denominator

[tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

⇒ [tex]\frac{(-4ac+b^2)}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 5: Applying square root (on one side there is a square, so, on the other side it gets ±)

⇒ [tex]\frac{(-4ac+b^2)}{4a^2}=(x+\frac{b}{2a})^2[/tex]

⇒ ±[tex]\sqrt{\frac{(-4ac+b^2)}{4a^2}} =(x+\frac{b}{2a})[/tex]

⇒ [tex]x+\frac{b}{2a}[/tex] = ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

step 6: Subtacting [tex]\frac{b}{2a}[/tex] from both the sides

⇒ [tex]x=-\frac{b}{2a}[/tex] ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

⇒ x = [-b ± (√b²+4ac)]/2a

Thus, step 4b best explains or justifies the property "Converting to a common denominator".

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Answer:

A

Step-by-step explanation:

The first option is correct.

The 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Cost of a package with 8 AA batteries = $6.32

⇒ Cost of 1 AA battery of this package = [tex]\frac{6.32}{8}[/tex] = $0.79

And, cost of another package with 20 AA batteries = $16.00

⇒ Cost of 1 AA battery of another package = [tex]\frac{16}{20}[/tex] = $0.8

Hence, the 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

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Answer:

m = 0.421

Step-by-step explanation:

5.4(m-2)= -2(3m+3)     (expand parentheses by distributive property)

m(5.4) -2(5.4) = 3m(-2) + 3(-2)

5.4m - 10.8 = -6m - 6      (add 6m to both sides)

5.4m - 10.8 + 6m =  - 6

11.4m - 10.8 =  - 6   (add 10.8 to both sides)

11.4m = -6 + 10.8

11.4m = 4.8   (divide both sides by 11.4)

m = 4.8 / 11.4

m = 0.421

Answer:

m = 8/19

Step-by-step explanation :

5.4  (m-2) = -2 (3m +3)  

54/10 (m-2) = (3m +3)   as n = 1

2.3^3 /  2.5  (m-2) = (3m + 3)

4.868 (m-2) = (3m +3)

4.868 + 3 = (3m^2 * m-2)

8 / 9.5 * 2  

m = 8 / 19

Answer:

300 ft²

Step-by-step explanation:

Surface area= area of base + 4*area of triangle

a= 10 ft

h= 10 ft

Surface area:

Answer:

The radius is 1/6 m

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

1/162 * pi = 4/3 pi r^3

Divide each side by pi

1/162  = 4/3 r^3

Multiply each side by 3/4

3/4 *1/162  =3/4* 4/3 r^3

1/216 = r^3

Take the cube root of each side

(1/216)^ 1/3 = (r^3)^1/3

1/6 = r

The radius is 1/6 m

(3,2) isn’t a solution because it doesn't satisfy the equation also, the line on the graph doesn’t go through it .

We do same operations on both the sides so that equality of both expressions doesn't get disturbed.

Solving equations generally means finding the values of the variables used in it for which the considered equation is true.

The graph of the equation is given as y = -3/4x + 3.

We have to find if the point (3, 2) a solution to the equation.

So, we will subtitute the point to to satify the equation;

y = -3/4x + 3.

y = -3/4(3) + 3

y = -9 / 4 + 3

y = 3/3 = 1

Thus, (3,2) isn’t a solution because it doesn't satisfy the equation also, the line on the graph doesn’t go through it .

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Answer:

the guy is right

Step-by-step explanation:

Hey there! I'm happy to help!

We want to put this 0.002 into scientific notation, where you put it as a one digit number multiplied by 10 raised to a certain power.

If we move the decimal to the right 3 times, we will have 2. We will multiply this 2 by [tex]10^-^3[/tex] to show that it is still equal to 0.002.

So, the mass of the mustard seed is 2×[tex]10^-^3[/tex].

Now, we multiply this mustard seed mass by the number of mustard seeds to find the weight of all of the mustard seeds combined.

(2×[tex]10^-^3[/tex])×(4.3602×[tex]10^4[/tex])

Let's round 4.3602 to the nearest whole number, which is 4. We multiply those two together.

2×4=8

And we multiply the two exponents. When multiplying them, you add the numbers in the exponent. -3 and 4 combined gives us 1, and 10 the first power is just 10.

So, a good estimate for the mass of the mustard seeds is 80 grams, which is the same as (2×[tex]10^-^3[/tex])×(4×[tex]10^4[/tex])=8×[tex]10^1[/tex]

Have a wonderful day! :D

Answer:

Hey There!! The answer to this is B: The mass of a single seed can be written as

There are total of seeds in the jar

Total mass is the multiplication of these both numbers.

Since we want an estimate, we can use 4 instead of 4.3602 in the 2nd number.

The rule to multiply two numbers in scientific notation is:

So using this formula we multiply the 2 numbers and get answer as follows:

Thus, Answer choice B is right.

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

Jacob is 4 years old and his mother is 40 years old.

Step-by-step explanation:

Part 1: The linear equations are  and

Part 2: Solving the equations, we have,  and

Part 3: Jacob is 4 years old and his mother is 40 years old.

Explanation:

Part 1: Let j represent Jacob's age, and let m represent his mother's age.

It is given that, "Jacob's mother is three more than nine times as old as Jacob". Writing it as linear equation, we have,

It is also given that, "In eleven years, his mother will be five more than three times his age". Writing it as linear equation, we have,

Simplifying this, we get,

Thus, the linear equation is

The linear equations are   and

Part 2: Solving the linear equation, we get,

Substituting  in

Simplifying, we get,

Hence,

Substituting  in

Solving the equations, we have,  and

Part 3: Since, j represents jacob and m represents the jacob's mother

Thus, Jacob is 4 years old and his mother is 40 years old.

Answer:

y=¾(4x-20)

y=3x-15

Final answer= y - 3(x+12)

=y - 3x-36

=3x-15-3x-36

= -51

Answer:

The answer is -51

Step-by-step explanation:

Answer:

  m∠F = 66°

  m∠D = 57°

Step-by-step explanation:

It looks like you have ...

  ∠D = ∠E = (4x +1)°

  ∠F = (5x -4)°

The sum of the angles in the triangle is 180°, so we have ...

  2(4x +1) +(5x -4) = 180

  13x -2 = 180

  x = 182/13 = 14

Then the angle measures are ...

  ∠D = ∠E = (4(14) +1)° = 57°

  ∠F = (5(14) -4)° = 66°

__

m∠F = 66°

m∠D = 57°

Answer:

6 ÷ 6 + 6 x 6

Step-by-step explanation:

Hope this helps :D

Answer:

440 in²

Step-by-step explanation:

Answer:

(D) 440 in²

Step-by-step explanation:

We can find the surface area of this complex shape by breaking it down into two smaller shapes:

The base (with side lengths of 10, 10 and 2) and the top (with side lengths of 5, 5, and 8.)

Let's first find the surface area of the base.

The sides of the bass are [tex]10\cdot2 = 20[/tex] in², since there are 4 of these sides, the total side area here is [tex]20\cdot4 = 80[/tex] in².

The bottom of this prism has side lengths of 10 and 10, so [tex]10\cdot10=100[/tex].

There are two of these sides.

[tex]100\cdot2=200[/tex].

Let's add up the side lengths and the base lengths.

[tex]200+80=280[/tex]

We aren't done yet - if we see, the top part is taking away some of that surface area. To find how much it is taking away, we need to find the area of that side.

Note that the side on the base is the exact same as the top, who's side lengths are 5 and 5. So [tex]5\cdot5=25[/tex] in² are being taken away from the base, making it [tex]280-25 = 255[/tex]

Now let's find the surface area of the top.

The side, with lengths of 5 and 8, have a surface area of [tex]5\cdot8=40[/tex] in². Since there are 4 of these sides:

[tex]40\cdot4=160[/tex] in².

Now, the top of the box has side lengths of 5 and 5, so the surface area of that is [tex]5\cdot5 =25[/tex] in².

We don't want to find the area of the bottom of the top prism because that cuts into the base and technically is empty space = no surface area.

Let's add the top and the sides of the top box: [tex]160+25=185[/tex] in².

Finally, let's add the base and the top box surface areas together:

[tex]185 + 255 = 440[/tex]

So the total surface area of this design is 440 in².

Hope this helped (oh my god this took so long to write)

Answer:

a(n)= 120(1/2)^(n-1)

Step-by-step explanation:

60*x=120, x=60/120=1/2 so the sequence goes by a ratio of 1/2

a(n)=b(c)^n-1 and c=1/2. b= a(1)=120 so the formula is a(n)= 120(1/2)^(n-1)

Answer:120(1/2)^(n-1)

Step-by-step explanation:

60*x=120, x=60/120=1/2 so the sequence goes by a ratio of 1/2

a(n)=b(c)^n-1 and c=1/2. b= a(1)=120 so the formula is a(n)= 120(1/2)^(n-1)

Option 4 is correct, Teresita worked 15 hours during the second week.

Given that Teresita worked [tex]1\frac{1}{2}[/tex]  times the number of hours during the second week.

Therefore, she worked 1.5x hours during the second week.

The total number of hours she worked during the two weeks is given as 25.

So we can set up the equation:

x + 1.5x = 25

Combining like terms, we have:

2.5x = 25

Dividing both sides of the equation by 2.5, we get:

x = 25/2.5

x = 10

Therefore, Teresita worked 10 hours during the first week.

To find the number of hours she worked during the second week, we can substitute this value back into the equation:

1.5x = 1.5 × 10

= 15

Therefore, Teresita worked 15 hours during the second week.

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Answer:

Part A: 5 inches³.

Part B: 302 inches³.

Part C: Yes. Explanation below.

Step-by-step explanation:

Part A: The cookie sandwiches appear to be flat cylinders. The volume for a cylinder is pi * r^2 * h.

In this case, the h = 1 inch and r = 1.25 inches.

pi * 1.25^2 * 1

= pi * 1.5625

= 3.14 * 1.5625

= 4.90625.

So, the volume of a single cookie sandwich is about 5 inches³.

Part B: As stated before, the volume of a cylinder is pi * r^2 * h.

In this case, the r = 4.5 inches, and the h = 4.75 inches.

pi * 4.5^2 * 4.75

= 3.14 * 20.25 * 4.75

= 63.585 * 4.75

= 302.02875.

So, the volume of the food storage container is about 302 inches³.

Part C: Given the calculations from Parts A and B, Jenny will be able to transport all the cookie sandwiches in the food storage container. This is because there are 56 cookie sandwiches, each with a volume of 5 cubic inches. That means that the cookie sandwiches will take up 5 * 56 = 280 cubic inches of space. There is about 302 cubic inches of space in the container, so there will still be 22 cubic inches of air inside the container after the cookies are inside.

Hope this helps!

Answer:

Part A: 5 inches^3

Part B: 302 inches^3

Part C: Yes, Jenny will be able to transport all the cookie sandwiches in the food container. This is because there are 56 cookie sandwiches and they each have a volume of 5 cubic inches. So, 56 times 5 equals 280 cubic inches of space. There are 302 cubic inches inside the container, so all the cookie sandwiches will fit inside.

Answer:

Area = 2127.1 cm^2  (to the tenth)

Step-by-step explanation:

We may be missing the length of a side at the top of the picture.

However, we are given "a", so the sides of a regular hexagon can be calculated.

The side of a regular hexagon given "a" is

s = 2a/sqrt(3) = 28.61

Perimeter of hexagon

= 6s

Area of hexagon

= a*perimeter/2

= a*6s/2

= 3as

= 3a*2a/sqrt(3)

=2sqrt(3)a^2

= 2*sqrt(3)*24.78^2

= 2127.1 cm^2  (to the tenth)

Answer:

a) Grocery Store: $9.71

b) Other purchases: $6.71

Step-by-step explanation:

a) 485.72 x 0.02 = 9.71

b) 671.28 x 0.01 = 6.71

Don't forget the labels!!

Answer:

Slope = 1

Greatest value is positive infinite

Smallest value is negative infinite

Step-by-step explanation:

Function

Y=mx+c

Y=x

Answer:

[tex]f(1)=-48(-\frac{1}{4} )[/tex]

[tex]= 12[/tex]

[tex]f(n)=f(n-1)\:. (-\frac{1}{4} )[/tex]

OAmalOHopeO

Answer:

1.  Determined

2. area of study

3. artistic writing

Step-by-step explanation:

Hope this helps! <3

Answer:

✔ determined

✔ area of study

✔ artistic writing

Explanation:

Answer:

3x(x - 2)

Step-by-step explanation:

Both terms have a GCF (greatest common factor) of 3x so factoring that out, we get 3x(x - 2).

Answer:

3x ( x - 2 )

Step-by-step explanation:

First we hv to find wat is common in both of them.....

As we can see " 3x " is common in both of them

so....

If we take 3x from both the terms.... It will become....

3x square = 3x ( x )

-6x - 3x ( -2 )

Therefore the expression will become....

3 x square - 6x

= 3x ( x - 2 )

Hope this helps...

HAVE A GOOD DAY !!! ( no the biscuit ) (lol)

Answer:

Step-by-step explanation:

You didn't include any graphs, so I can't tell you which one it is. However, the graph of [tex]f(x)=\sqrt{x+5}[/tex] looks like this:

Hope this helps!

The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below and this can be determined by using the rules of transformation.

Given :

[tex]\rm f(x) = \sqrt{x+5}[/tex]

The following steps can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex]:

Step 1 - The rules of transformation can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex].

Step 2 - First draw the graph of [tex]\sqrt{x}[/tex] which is in the shape of a parabola.

Step 3 - Now, translate the graph in the left direction, So the function of the graph obtained is [tex]\rm f(x) = \sqrt{x+5}[/tex].

The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below.

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Answer:

460256

Step-by-step explanation:

35900 books equal to 7.8% of all copies sold

Total number of books:

Answer is 460256 in whole numbers

Answer:

Hello,

Step-by-step explanation:

The first number is

[tex]\dfrac{8}{12}[/tex]

The second number is

[tex]\dfrac{9}{12}[/tex]

Their sum is:

[tex]\dfrac{8}{12} +\dfrac{9}{12} =\dfrac{8+9}{12}=\dfrac{17}{12}[/tex]

Answer:

67

Step-by-step explanation:

it was a long proof...

follow the caption and steps and you'll understand it

proved...

Step-by-step explanation:

this is too easy method to solve this problem

Answer:

36

Step-by-step explanation:

(216) ^ (2/3)

Rewriting 216 as 6^3

(6^3) ^ (2/3)

We know that a^ b^c = a^ (b*c)

6 ^ (3*2/3)

6^2

36

Answer:

h(x + 1) = (x+3)(x-1)

Step-by-step explanation:

Simply plug the value of x+1 into the equation for x.

h(x) = x^2 - 4

h(x + 1) = (x + 1)^2 - 4

h(x + 1) = x^2 + 2x + 1 - 4

h(x + 1) = x^2 + 2x - 3

h(x + 1) = (x+3)(x-1)

Cheers.

Answer:

h(t)= t² - 2t -3

Step-by-step explanation:

h(x+1)= x²-4 is the given function

We can write it x²-4 as:

Substituting x+1  with  t. Then function is:

or