To model the growth of a savings account with an exponential function, we will use the formula to calculate the amount of money, A(t), accumulated after a certain number of years, t, given an initial principal amount, P, and an annual interest rate, r.
The standard formula for exponential growth in the context of compound interest is as follows:
\[ A(t) = P (1 + r)^t \]
where:
- \( A(t) \) represents the amount of money in the savings account after \( t \) years.
- \( P \) is the principal amount initially deposited into the account.
- \( r \) is the annual interest rate (expressed as a decimal).
- \( t \) represents the time in years.
For your savings account, you start with $400 (the principal amount, \( P \)), and it gains 3% interest every year (the annual interest rate, \( r \)).
Let's assign the given values to their respective variables in the formula:
- \( P = \$400 \)
- \( r = 3\% = 0.03 \) (since 3% as a decimal is 0.03)
Inserting these values into the formula yields the specific exponential function for this savings account:
\[ A(t) = \$400 (1 + 0.03)^t \]
This equation represents the amount of money that will be in the savings account after any number of years, \( t \), based on the continuous application of a 3% annual interest rate.
1. Which numbers below are equivalent to 13.4? Select all that apply.
a.
b. 0.134%
c. 13.4%
d. 134%
e. 1340%
Answer:
1340%
Step-by-step explanation:
Answer:
b and also whats a
Step-by-step explanation:
multiply the following: 6z^2(7z^2+3z-2)
To multiply the expression 6z^2 by the trinomial (7z^2+3z-2), distribute 6z^2 across each term in the trinomial to obtain 42z^4 + 18z^3 - 12z^2.
Explanation:The student has asked to multiply the expression 6z2 by the trinomial (7z2+3z-2). To solve this problem, we'll apply the distributive property, which entails multiplying the term outside the parenthesis by each term inside the parenthesis.
Multiply the term 6z2 by 7z2, which gives 42z4.Multiply 6z2 by 3z, yielding 18z3.Finally, multiply 6z2 by -2 to get -12z2.Combine all the products to get the final expanded expression: 42z4 + 18z3 - 12z2.
The product of [tex]\(6z^2\)[/tex] and [tex]\(7z^2 + 3z - 2\)[/tex] is [tex]\(42z^4 + 18z^3 - 12z^2\)[/tex].
To multiply [tex]\(6z^2\)[/tex] by the trinomial [tex]\(7z^2 + 3z - 2\)[/tex], you need to distribute [tex]\(6z^2\)[/tex] to each term inside the parentheses. Here's how you can do it stepwise:
1. Multiply [tex]\(6z^2\)[/tex] by the first term of the trinomial [tex](\(7z^2\))[/tex]:
[tex]\[ 6z^2 \cdot 7z^2 = 42z^4 \][/tex]
2. Multiply [tex]\(6z^2\)[/tex] by the second term of the trinomial [tex](\(3z\)):[/tex]
[tex]\[ 6z^2 \cdot 3z = 18z^3 \][/tex]
3. Multiply [tex]\(6z^2\)[/tex] by the third term of the trinomial [tex](\(-2\))[/tex]:
[tex]\[ 6z^2 \cdot (-2) = -12z^2 \][/tex]
Now, combine these results:
[tex]\[ 6z^2(7z^2 + 3z - 2) = 42z^4 + 18z^3 - 12z^2 \][/tex]
So, the product of [tex]\(6z^2\)[/tex] and [tex]\(7z^2 + 3z - 2\)[/tex] is [tex]\(42z^4 + 18z^3 - 12z^2\)[/tex].
The graph shows that f(x)=(one-third) Superscript x is translated horizontally and vertically to get the function (one-third) Superscript x minus h.
On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes through (negative 1, 3), (0, 1), (1, 0.3). g (x) decreases in quadrant 1 into quadrant 4. It crosses the x-axis at (4, 0), and goes through (5, negative 2).
What is the value of k?
−5
−3
3
5
It is the number 3.
What is the slope of the line?
3(y - 1) = 2x + 2
Choose 1 answer:
Answer:
2/3
Step-by-step explanation:
3(y - 1) = 2x + 2
3y - 3 = 2x + 2
3y = 2x + 5
3y/3 = 2x/3 + 5/3
y = 2/3x + 5/3
Does that help?
please answer correctly, will mark brainliest
Answer:
Since the values vary from 0.5 to 4.5, let's take 5 intervals of width 1 unit each
(Lower boundary is included, upper boundary is not)
Average
no. of --------> frequency
movies
_______ __________
0 - 1 --------------> 1
1 - 2 --------------> 5
2 - 3 --------------> 5
3 - 4 --------------> 2
4 - 5 --------------> 1
For frequencies, just count the data values in each interval
A baker me 5 pounds of the dough 8/9 of the dough to make sandwich rolls how much of the dough is left over
Answer:
4.444...
Step-by-step explanation:
To do this question you find out 8/9 of 5
8/9 x 5
The method is: you divide by the denominator (bottom number of a fraction) and multiply by the numerator ( top number of a fraction)
= 5 ÷ 9 = 0.555…
= 0.555 x 8 = 4.444 recurring.
Answer:
[tex]4\frac{1}{9}[/tex]
Step-by-step explanation:
[tex]\frac{5}{1}[/tex] - [tex]\frac{8}{9}[/tex][tex]\frac{45-8}{9}[/tex] = [tex]\frac{37}{9}=4\frac{1}{9}[/tex]
HURRY
What is the length of a diagonal of a cube with a side length of 3 cm?
StartRoot 18 EndRoot cm
StartRoot 27 EndRoot cm
StartRoot 33 EndRoot cm
StartRoot 38 EndRoot cm
For the given cube, the length of the diagonal is given by:
[tex]d = \sqrt{27} cm[/tex]
How to find the diagonal of the cube?
For a cube of side length S, the diagonal of the cube is given by the expression:
[tex]d = \sqrt{S^2 + S^2 + S^2} = \sqrt{3}*S[/tex]
In this case, the side length is equal to 3cm, replacing that we get:
[tex]d = \sqrt{3*S^2} = \sqrt{3*(3)^2} cm = \sqrt{27} cm[/tex]
The correct option is the second one, counting from the top.
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100% - 9/10
Pleeaaase help
Answer:
-0.8 or 991/10
(also it can be 10%)
Step-by-step explanation:
991
——— = 99.10000
10
Step by step solution :
Step 1 :
9
Simplify ——
10
Equation at the end of step 1 :
9
100 - ——
10
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 10 as the denominator :
100 100 • 10
100 = ——— = ————————
1 10
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
100 • 10 - (9) 991
—————————————— = ———
10 10
Final result :
991
——— = 99.10000
10
The value of expression 1/10.
Given that we need to solve expression 100% - 9/10,
To explain the calculation of "100% - 9/10," let's break it down step by step:
First, let's simplify the fraction 9/10. This fraction represents a ratio where the numerator (9) is the number of parts, and the denominator (10) is the total number of parts.
In this case, it means that we have 9 parts out of a total of 10 parts.
Next, we need to calculate the percentage equivalent of 9/10. To do this, we can multiply the fraction by 100.
So, 9/10 × 100 = 90%.
This means that 9/10 is equivalent to 90%.
Finally, we subtract 90% from 100%. Since 100% represents the whole or the entirety, subtracting 90% from it gives us the remaining percentage.
Mathematically, 100% - 90% = 10%
10% = 1/10
Therefore, 100% - 9/10 equals 10%.
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2. Apple Strudle muffins
Makes 12 muffins
You are having 14 people for brunch and each person will eat 2 muffins. How
many muffins do you need? _ Adjust the recipe
I really need a answer right now, I have no idea how to do this please help
Answer:
Since there are 14 people who will eat 2 muffins each, you will need to make 28 muffins. To get this many muffins you will have to multiply the recipe by 2 1/3. Multiply each ingredient by 2 1/3 to make enough muffins
Step-by-step explanation:
Which equation could be used to
approximate the data in the scatter plot
below? *
a. y=-1.4x + 3.5
b. y = 1.4x - 3.5
c. y=-1.4x - 3.5
d. y = 1.4x + 3.5
Question in the picture:)
Given:
Set A represents rational numbers.
Set B represents integers.
Set C represents whole numbers.
To find:
Which of the value represents a value that could be placed in set C.
Solution:
Rational number is ratio of two numbers which of the form [tex]\frac{p}{q}, \ q\neq0[/tex].
Integer is a set of positive and negative numbers including zero.
Integers: {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}
Whole numbers are positive numbers with zero.
Whole numbers: {0, 1, 2, 3, 4, ...}
Option A: -10
-10 is a integer. So that, it is placed in set B not in set C.
Therefore, it is not true.
Option B: 2.5
2.5 can be written as [tex]\frac{5}{2}[/tex]. It is a rational number.
Rational number placed in set A.
Therefore, it is not true.
Option C: [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{4}[/tex] is a rational number.
Rational number placed in set A.
Therefore, it is not true.
Option D: [tex]\frac{12}{4}[/tex]
[tex]$\frac{12}{4}=3[/tex] (cancelling common factors)
3 is a whole number.
Whole numbers placed in set C.
Therefore, it is true.
Hence [tex]\frac{12}{4}[/tex] is the value that could be placed in set C.
Nolan drove 234 miles in 4 hours. On average, how fast did he drive in miles per
hour? Express your answer in simplest form.
Answer:
58.5 MilesStep-by-step explanation:
234 m = 4 hrs
Divide the total amount of miles to hours
234/4 = 58.5
58.5 m = 1 hr
I hope this helped you!
Answer:
12
Step-by-step explanation:
What is the hypotenuse of
1,2,3
8,7,6
15,20,25
PLZ NEED ANSWERS NOW
Use the figure to find the measure.
Area triangle DEF =
3/4
4/3
3
The area of triangle DEF cannot be determined without specific measurements for the base and height. To find the area of a triangle, use the formula \( \frac{1}{2} \times \text{base} \times \text{height} \), and be attentive to significant figures.
Explanation:To determine the measure of the area of triangle DEF, we would need specific information about the dimensions of the triangle, such as the base and the height. Without this information or a corresponding figure provided in the question, we cannot calculate the area. However, I can guide you on how to calculate it once you have the necessary dimensions.
To calculate the area of a triangle, the formula is \( \frac{1}{2} \times \text{base} \times \text{height} \). For example, if you have a triangle with a base of 166 mm and a height of 930.0 mm, the area would be \( \frac{1}{2} \times 166 \text{mm} \times 930.0 \text{mm} \). Make sure to convert the measurements to the same units if they are not already, and pay attention to the proper number of significant figures in your final answer.
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6.1712 rounded to the nearest tenth
Answer:
6.2
Step-by-step explanation:
Answer:
the answer is 6.2
5/8 divided by 1 1/3 in lowest form
HOPE THIS WILL HELP U...
Answer:
15/32
Step-by-step explanation:
5/8/1 1/3
Which can also be written as 5/8÷ 1 1/3
So let's solve
5/8÷4/3
So remember that the division will change to multiplication and 4/3 will also change to 3/4
5/8×3/4
15/32
This is the lowest form it can be since the two are not divisible by the same number
So the final answer is 15/32
how do you find the domain of f(x)= x over 2x^2-5x-3
Answer:
D = ]-∞ , -1/2[ U ]-1/2 , 3[ U ]3 , +∞[
Step-by-step explanation:
hello :
f(x) = x/(2x²-5x-3)
f exist for : 2x²-5x-3 ≠ 0
2x²-5x-3 = 0
∆ = b² -4ac a=2 and b= -5 and c= -3
∆ = (-5)² - 4(2)(-3) = 49 = 7²
X1 = (-b-√∆ )/2a = (5-7)/4 = -1/2
X2 = (-b+√∆ )/2a = (5+7)/4 = 3
the domain is : D = ]-∞ , -1/2[ U ]-1/2 , 3[ U ]3 , +∞[
-
find a formula for the nth term of the arithmetic sequence the first term is -2 and the common difference is 8
Answer:
a(n) = -2 + 8(n - 1)
Step-by-step explanation:
General formula is a(n) = a(1) + d(n - 1), where d is the common difference.
Here a(n) = -2 + 8(n - 1)
Answer:
a(n)=8n-10
Step-by-step explanation:
thats the answer if you are on Acellus :)
Question 7 (5 points)
A class of 24 students went on a picnic. They had a choice between having a turkey
sandwich or a vegetarian sandwich. Eighteen students selected turkey, and the rest
selected vegetarian. Write a ratio to compare the number of turkey sandwiches to the number of vegetarian sandwiches.
1:3
3:1
4:1
4:3
Answer:
B, 3:1
Step-by-step explanation:
18:6 is 3:1 if you divide both sides by 6
Final answer:
The correct ratio to compare the number of turkey sandwiches to vegetarian sandwiches is 3:1, with 18 students selecting turkey and 6 students selecting vegetarian sandwiches.
Explanation:
The correct ratio to compare the number of turkey sandwiches to the number of vegetarian sandwiches is 3:1.
First, determine that 18 students chose turkey sandwiches, which leaves 6 students choosing vegetarian sandwiches (24 total students - 18 turkey sandwiches).Next, calculate the ratio by dividing the number of turkey sandwiches by the number of vegetarian sandwiches, resulting in 18/6 = 3.Therefore, the ratio of turkey sandwiches to vegetarian sandwiches is 3:1.Type of Desserts Number of Students
Ice Cream 8
Cake 6
Banana Pudding 7
Apple Pie 4
Jell-O 3
Myles asked his classmates to name their favorite desserts. He displayed the results in the table here.
Which graph matches the data in the table?
A) A
B) B
C) C
D) D
if the picture was bigger i would be able to help could u get it a bit bigger
1.3 billion people live on?
Answer:
1.25
Step-by-step explanation:
In India
Answer: D
Step-by-step explanation:
1 dollar a day
Help me plz now this is very important
Answer:
A
Step-by-step explanation:
11-2.9= 8.1
so the right answer is of option A
A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Three marbles are randomly chosen from the bag.
What is the probability that there is at most one purple marble?
Answer:Not very great probability
Step-by-step explanation:
There is not a great probability because there are 8 yellow, 9 green, and 5 red. The less purple marbles there are, the less of a chance that a purple marble will be pulled from the bag because there are only three of the purple marbles.
Answer:
0.971
Step-by-step explanation:
i did it
PLEASE HURRY
Solve 12 – 15x > 22 to find out the solution set.
---------------------------------------------------------
12 – 15x > 22
Suntract 12 from both sides:
12-15x-12 > 22-12
Simplify:
15x > 10
Multiply both sides by -1 (reverse the inequality):
(15x)(-1)<(10)(-1)
Simplify:
15x < -10
Divide both sides by 15:
15x/15 < -10/15
Simplify:
x < -2/3
Your Answer Is x < -2/3
plz mark me as brainliest :)
Answer:
x < [tex]\frac{-2}{3}[/tex] OR x < -0.67
Step-by-step explanation:
The first step is to subtract 12 from both sides, like so:
12 - 15x > 22
-12 -12
__________
-15x > 10
Then, divide both sides by -15:
-15x > 10
x > [tex]\frac{-10}{15}[/tex]
Simplify:
x > [tex]\frac{-2}{3}[/tex]
When you multiply/divide by a negative number, you must flip the sign around. In this case, we divided by a negative number:
x < [tex]\frac{-2}{3}[/tex] OR x < -0.67
Find the length of the unknown side. Round your answer to the nearest whole number. (4 points)
Image of a right triangle with legs labeled 12 meters and 8 meters. Hypotenuse is unknown.
Group of answer choices
13 meters
14 meters
200 meters
208 meters
Answer:
The hypotenuse is 14 m to the nearest meter.
Step-by-step explanation:
By Pythagoras:
h^2 = 12^2 + 8^2
h^2 = 208
h = √208
h = 14.4 m.
Answer:
its 14! hope this helps
Step-by-step explanation:
Joe is building a fort for his little brother out of boxes. He is wondering how much room there will be inside the
40 in
20 in
20 in
30 in
60 in
How much space is inside the fort?
The number line shows four elevations in Death Valley National Park.Enter the difference ,in feet between the elevation at Zabriskie Point and Furnace Creek.
Given:
The number of elevations in Death Valley National Park is given below:
Zabriskie Point = 648 feet
Stovepipe Wells = 0 feet
Furnace Creek = -178 feet
Badwater Basin = -282 feet
To find the difference between the elevation at Zabriskie Point and Furnace Creek.
Formula
Difference means subtraction.a-(-b) = a+bSo,
The difference between the elevation at Zabriskie Point and Furnace Creek = (648-(-178)) feet
= 648+178 feet
= 826 feet
Hence,
The difference between the elevation at Zabriskie Point and Furnace Creek is 826 feet.
The elevation difference between Zabriskie Point and Furnace Creek in Death Valley National Park is 826 feet, obtained by adding the positive elevations.
To find the difference between the elevation at Zabriskie Point and Furnace Creek in Death Valley National Park, follow these steps:
Use the formula for subtracting negative numbers:
Difference = Elevation at Zabriskie Point - (Elevation at Furnace Creek)
Given elevations:
Elevation at Zabriskie Point = 648 feet
Elevation at Furnace Creek = -178 feet
Substitute these values into the formula:
Difference = 648 - (-178) feet
Remember that subtracting a negative is the same as adding the positive:
Difference = 648 + 178 feet
Perform the addition:
Difference = 826 feet
Therefore, the difference between the elevation at Zabriskie Point and Furnace Creek is 826 feet.
Parallel, intersecting or skew?
AB and BC.
AE and BF.
EF and AD.
Plane ABC and Plane ABF.
Plane AED and Plane BFC.
HELP!!!
Two lines are:
Parallel if they don't intersect and lie on the same planeIntersecting if...well, they intersect at one pointSkew if they don't intersect and they lie on two different planesSo, we have:
AB and BC intersect at point BAE and BF don't intersect, but both lie on the plane AEFBEF and AD don't intersect and don't lie on a common planeABC and ABF intersect on segment ABAED and BFC are parallel (they're both perpendicular to plane ABC)The relationships between the lines and planes depend on their orientation in space. Without diagrams, it's only possible to give general descriptions, suggesting various intersecting, parallel, or skew scenarios.
Explanation:Without diagrams or additional context, it's difficult to determine the relationships between the segments and planes, but I will provide general descriptions. Lines AB and BC appear to intersect if 'B' is the shared point between them. Lines AE and BF could be parallel, intersecting, or skew, depending on their orientation in space. Lines EF and AD again depend on their spatial orientation. Plane ABC and Plane ABF may intersect along line AB, if they are not the same plane. Plane AED and Plane BFC could also intersect, be parallel, or neither, depending on how the points are positioned in space.
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What is the surface area of the cone? Express your answer in terms of π.b
Given:
Radius of the cone = 5 ft
Slant height of the cone = 21 ft
To find:
The surface area of the cone
Solution:
Surface area of cone formula:
[tex]SA=\pi r^{2}+\pi r l[/tex]
where r is the radius and l is the slant height.
[tex]SA=\pi \times 5^{2}+\pi \times 5 \times 21[/tex]
[tex]SA=\pi \times 25+\pi \times 105[/tex]
[tex]SA=25 \pi+ 105 \pi[/tex]
[tex]SA=130 \pi[/tex]
The surface area of the cone is 130π square feet.
The total surface area of the cone is 130π square feet.
How to Calculate the Surface Area of a Cone
The surface area of a cone can be calculated using two main components: the base and the lateral (side) surface. If the radius of the base is r and the slant height is l, the formulas for these areas become essential.
The area of the base is found using the formula for the area of a circle: πr².The lateral surface area is calculated using: πrl, where l is the slant height.Therefore, the total surface area A of the cone is:
A = πr² + πrl
Calculate the surface area using the given values:
A =
Which pair of ratios form a proportion? 97 points
5 : 10 and 10 : 15
8 : 12 and 18 : 27
9 : 15 and 24 : 30
6 : 20 and 7 : 30
Answer:
8 : 12 and 18 : 27
Step-by-step explanation:
5:10 and 10:15 simplify to: 1:2 and 2:3
8:12 and 18:27 simplify to: 2:3 and 2:3
9:15 and 24:30 simplify to: 3:5 and 4:5
6:20 and 7:30 simplify to: 3:10 and 7:30
The ONLY pair of equal proportions is the second one (8 : 12 and 18 : 27), making it the right answer
Answer:
Second one:
8 : 12 and 18 : 27
Step-by-step explanation:
5 : 10 and 10 : 15
5/10 , 10/15
1/2 , 2/3
Not constant, so not proportional
8 : 12 and 18 : 27
8/12 , 18/27
2/3 , 2/3
Constant, so proportional
9 : 15 and 24 : 30
9/15 , 24/30
3/5 , 4/5
Not constant, so not proportional
6 : 20 and 7 : 30
6/20 , 7/30
3/10 , 7/30
Not constant, so not proportional