Answer:
Part 1) John’s situation is modeled by a linear equation (see the explanation)
Part 2) [tex]y=100x+300[/tex]
Part 3) [tex]\$12,300[/tex]
Part 4) [tex]\$2,700[/tex]
Part 5) Is a exponential growth function
Part 6) [tex]A=6,000(1.07)^{t}[/tex]
Part 7) [tex]\$11,802.91[/tex]
Part 8) [tex]\$6,869.40[/tex]
Part 9) Is a exponential growth function
Part 10) [tex]A=5,000(e)^{0.10t}[/tex] or [tex]A=5,000(1.1052)^{t}[/tex]
Part 11) [tex]\$13,591.41[/tex]
Part 12) [tex]\$6,107.01[/tex]
Part 13) Natalie has the most money after 10 years
Part 14) Sally has the most money after 2 years
Step-by-step explanation:
Part 1) What type of equation models John’s situation?
Let
y ----> the total money saved in a jar
x ---> the time in months
The linear equation in slope intercept form
y=mx+b
The slope is equal to
[tex]m=\$100\ per\ month[/tex]
The y-intercept or initial value is
[tex]b=\$300[/tex]
so
[tex]y=100x+300[/tex]
therefore
John’s situation is modeled by a linear equation
Part 2) Write the model equation for John’s situation
see part 1)
Part 3) How much money will John have after 10 years?
Remember that
1 year is equal to 12 months
so
[tex]10\ years=10(12)=120 months[/tex]
For x=120 months
substitute in the linear equation
[tex]y=100(120)+300=\$12,300[/tex]
Part 4) How much money will John have after 2 years?
Remember that
1 year is equal to 12 months
so
[tex]2\ years=2(12)=24\ months[/tex]
For x=24 months
substitute in the linear equation
[tex]y=100(24)+300=\$2,700[/tex]
Part 5) What type of exponential model is Sally’s situation?
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]P=\$6,000\\ r=7\%=0.07\\n=1[/tex]
substitute in the formula above
[tex]A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}[/tex]
therefore
Is a exponential growth function
Part 6) Write the model equation for Sally’s situation
see the Part 5)
Part 7) How much money will Sally have after 10 years?
For t=10 years
substitute the value of t in the exponential growth function
[tex]A=6,000(1.07)^{10}=\$11,802.91[/tex]
Part 8) How much money will Sally have after 2 years?
For t=2 years
substitute the value of t in the exponential growth function
[tex]A=6,000(1.07)^{2}=\$6,869.40[/tex]
Part 9) What type of exponential model is Natalie’s situation?
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]P=\$5,000\\r=10\%=0.10[/tex]
substitute in the formula above
[tex]A=5,000(e)^{0.10t}[/tex]
Applying property of exponents
[tex]A=5,000(1.1052)^{t}[/tex]
therefore
Is a exponential growth function
Part 10) Write the model equation for Natalie’s situation
[tex]A=5,000(e)^{0.10t}[/tex] or [tex]A=5,000(1.1052)^{t}[/tex]
see Part 9)
Part 11) How much money will Natalie have after 10 years?
For t=10 years
substitute
[tex]A=5,000(e)^{0.10*10}=\$13,591.41[/tex]
Part 12) How much money will Natalie have after 2 years?
For t=2 years
substitute
[tex]A=5,000(e)^{0.10*2}=\$6,107.01[/tex]
Part 13) Who will have the most money after 10 years?
Compare the final investment after 10 years of John, Sally, and Natalie
Natalie has the most money after 10 years
Part 14) Who will have the most money after 2 years?
Compare the final investment after 2 years of John, Sally, and Natalie
Sally has the most money after 2 years
Ten identical slips of paper each contain one number from one to ten, inclusive. The papers are put into a bag and then mixed around.
Which statements about the situation are true? Check all that apply.
P(6) = P(1)
P(5) = One-half
P(>10) = 0
P(1 < x < 10) = 100%
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
If A ⊂ S; A could be {1, 3, 5, 7, 9}
Answer: A, C, E, F
Step-by-step explanation:
Answer: A, C, E, F
Step-by-step explanation:
There are 25 bananas that will be cut and divided evenly between 4 loaves of bread. How many bananas go into each loaf? Choose the correct answer from the choices below.
6 3⁄4 bananas per loaf
6 1⁄4 bananas per loaf
5 3⁄4 bananas per loaf
5 1⁄4 bananas per loaf
5 1⁄2 bananas per loaf
Answer: 6 1/4
Step-by-step explanation: 25 divided by 4 = 6 1/4
Of the 15 year olds at karate school 8 have black belts in 20 had Brown belts among 16 year olds 10 have black belts in 17 have Brown belts. which age group has a higher ratio of black belts to Brown belts
Answer:
16 year olds had the higher ratio of black belts to brown belts.
Step-by-step explanation:
15 year olds: 8/28 students had black belts
8/28 = 28.6% had black belts
16 year olds: 10/27 students had bald belts
10/27 = 37.0% had black belts
Which of the following does NOT describe a control group?
Answer:
D. a group of trees not given a new growth hormone
Step-by-step explanation:
Because everything is controlled I think
24 is 120% of what?, i need help so please tell ne the steps!?
Answer: it’s 20
We have, 120% × x = 24
or,
120/100 × x = 24
Multiplying both sides by 100 and dividing both sides by 120,
we have x = 24 × 100/120
x = 20
If you are using a calculator, simply enter 24×100÷120, which will give you the answer.
2)x-5)+2-3(5-2x)=16
Answer:
Step-by-step explanation:
hello :
2(x-5)+2-3(5-2x)=16
2x-10+2-15+6x =16
8x-23 =16
8x =39
x = 39/8
Which step is included in the graph of the function f(x)=[x-1]? (the brackets are ceiling functions symbols)
Answer:
The correct step is y = - 5 for, - 4 ≤ x < - 3.
Step-by-step explanation:
From the definition of a box function y = [x], we know that
y = 0 for, 0 ≤ x < 1
y = - 1 for, - 1 ≤ x < 0
y = - 2 for, - 2 ≤ x < - 1
Here, we are given another box function y = [x - 1], and we have to choose from options the steps which is included in the graph of the this function.
So, the correct step is y = - 5 for, - 4 ≤ x < - 3. (Answer)
HELP PLEASE What is the volume of this right cone?
O 384 pie cm
O 691 cm
1038 cm
2073 cm
The answer would be properly V = 1/3*pi*r²*h ..
V = 1/3*pi*12²*8 ..
V = 384*pi.
Hope it helps! ~
RealNameXHidden :0
Solve each system by elimination.
3) 9x - 5y = 13
- 4x + 5y = 22
Answer:
x=7, y=10. (7, 10).
Step-by-step explanation:
9x-5y=13
-4x+5y=22
-------------------
5x=35
x=35/5
x=7
9(7)-5y=13
63-5y=13
5y=63-13
5y=50
y=50/5
y=10
2 with an exponent of -2
Answer:
0.25
Step-by-step explanation:
2^-2=0.25
If the weight of a package is multiplied by 2/3 the result is 40 pounds. Find the weight of the package.
all you do is divide 40 by 2/3 to get the answer :D
Answer: Weight is 60
Explanation:
So lets look at what we are given:
w (weight) * 2/3 = 40 pounds
(short explanation is you times 40 by 3/2)
We want to solve for weight there are a few ways to do this but the easiest one is to times both sides of the equation by the reciprocal of 2/3. Which is 3/2. That will cancel our the 2/3 and leave only "w" on the left side.
w = 40 * 3/2
Panchito Pantera has 100 coins(Quarters and dime). He has a totalof $22.How many quarters does he have?? dimes??
There are 20 dimes and 80 quarters
Solution:
Let "d" be the number of dimes
Let "q" be the number of quarters
1 dime = $ 0.10
1 quarter = $ 0.25
Panchito Pantera has 100 coins
Therefore,
number of dimes + number of quarters = 100
d + q = 100 ----------- eqn 1
He has a total of $22. Thus we frame a equation as:
number of dimes x 0.10 + number of quarters x 0.25 = 22
[tex]d \times 0.10 + q \times 0.25 = 22[/tex]
0.1d + 0.25q = 22 --------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
d = 100 - q ------- eqn 3
Substitute eqn 3 in eqn 2
0.1(100 - q) + 0.25q = 22
10 - 0.1q + 0.25q = 22
0.15q = 22 - 10
0.15q = 12
Divide both sides by 0.15
q = 80
Substitute q = 80 in eqn 3
d = 100 - 80
d = 20
Thus there are 20 dimes and 80 quarters
what number is divisible by 2
Answer:4,6,8,10,12,14,16,18,20
Step-by-step explanation:
Basically all even numbers.
factor this expression completely. 18x^2 - 32
Answer:
2(3x - 4)(3x + 4)
Step-by-step explanation:
Factorizing the below expression requires factoring common term.
[tex]18 {x}^{2} - 32[/tex]
Obviously 2 is common to both 18 and 32. Thus, the answer is:
[tex] = 2(9 {x}^{2} - 16)[/tex]
=2(3x - 4)(3x + 4)
Answer:
the answer above was a little confusing to me so i thought i would just give the answer straight up: 2(3x+4)(3x-4)
Step-by-step explanation:
just did the test! :)
What is 19 3/5 -18 4/5=
Answer:
1 -1/5 is the answer #markasbrainliest
The equations in this sytem were added to solve for x. What is the value of x?
Negative 2 x + y = 8. 5 x minus y = negative 5. 3 x = 3.
x = negative 3
x = negative 1
x = 1
x = 3
Question:
The equations in this system were added to solve for x. What is the value of x? -2x+y=8 5x-y=-5 3x=3
Options:
x = negative 3
x = negative 1
x = 1
x = 3
Answer:
The value of x is 1
Solution:
Given system of equations are:
-2x + y = 8 ------- eqn 1
5x - y = -5 ------- eqn 2
The above equations are added to solve for "x"
Add eqn 1 and eqn 2
-2x + y + 5x - y = 8 - 5
Combine the like terms
-2x + 5x + y - y = 3
Add the like terms
3x + 0 = 3
3x = 3
Divide both sides of equation by 3
x = 1
Thus the value of x is 1
Answer:
x=1
Step-by-step explanation:
A right prism has a base that is an equilateral triangle. The height of the prism is equal to the height of the base. If the volume of the prism is 81, what are the lengths of the sides of the base?
Length of side of base is 5.45
Step-by-step explanation:
Step 1: Volume of a right prism = Area of the base × Height = 1/2 × base × height of base × height of prismHere, since the base is an equilateral triangle and it is given that height of the prism is equal to that of the base, measures of base and height are equal.
⇒ Volume = 1/2 × b × h × h (b and h are equal)
⇒ 81 = 1/2 × b³
⇒ b³ = 162
⇒ b = ∛162 = 5.45
What is the name of when the line of slope is on the x axis line
Answer:
X-axis
Step-by-step explanation:
the name of when the line of slope is on the x axis line is the x axis line.
Answer: intersect.
Step-by-step explanation:
Next Tuesday, Cordelia is catering a proposal dinner for her brother. If she wants to serve her macaroni and cheese at this dinner for 2, she will use _____ cup(s) of Parmesan cheese. The recipe includes that 1/2 Cups of Parmesan cheese serves 4 people.
Answer: [tex]\frac{1}{4}\ cups[/tex]
Step-by-step explanation:
For this exercise it is important to analize the information given in the exercise.
According to the data provided in the exercise, the recipe says that [tex]\frac{1}{2}\ cups[/tex] of Parmesan serves four people.
The, let be "x" the amount of cups of Parmesan cheese that Cordelia will use for her brother's proposal dinner.
In this case, since the proposal dinner is for two people, you can set up the following proportion:
[tex]\frac{4}{\frac{1}{2}}=\frac{2}{x}[/tex]
Finally, you must solve for "x" in order to find its value, as you can observe below:
[tex]8=\frac{2}{x}\\\\8x=2\\\\x=\frac{2}{8}\\\\x=\frac{1}{4}[/tex]
Therefore, knowing the value of "x", you can determine that Cordelia will use [tex]\frac{1}{4}\ cups[/tex] of Parmesan cheese for the proposal dinner.
just realized this is science not math O_o Determine if each description is mass or weight. Drag each description into the correct category.
This remains the same on the moon as on Earth.
This results from the pull of gravity.
This relates to the amount of matter in an object.
This will change in space.
mass(this is a category) weight (this is a category)
sorry i just realized its not mathematics O_o
This remains the same on the moon as on Earth. --> MASS
This results from the pull of gravity. --> WEIGHT
This relates to the amount of matter in an object. --> MASS
This will change in space. --> WEIGHT
mass is a SCALAR, weight is a VECTOR
Step-by-step explanation:
In physics:
- The mass of an object is a scalar quantity that gives a measure of the "amount of matter" in an object. It is an intrinsec property of the object, therefore its value does not depend on the location of the object.
- The weight of an object is the force of gravitational attraction exerted on the object. Being a force, it has a magnitude and a direction. Its magnitude is given by
[tex]F=mg[/tex]
where m is the mass of the object and g is the acceleration due to gravity at the location of the object. Therefore, its value depends on the location.
Now we can identify correctly each statement given:
This remains the same on the moon as on Earth. --> MASS
This results from the pull of gravity. --> WEIGHT
This relates to the amount of matter in an object. --> MASS
This will change in space. --> WEIGHT
mass is a SCALAR, weight is a VECTOR
Learn more about mass and weight:
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#LearnwithBrainly
Solve for t. 2:3 = 27:t
18
18.5
40.5
Answer:
2t = 81
t = 40.5 is the answer
answer is c
Simplify the expression. 5–3 • 7^0
Answer:
5-3x7^0
(5-3)7^0
2x1
2
Step-by-step explanation:
7^0 is 1
and do you want to chat
Answer:
5-3 x 7^0
5-3 x 0
5-0
5
Step-by-step explanation:
I cannot type a dot so x is multiply. PEMDAS so take care of your exponent first 7^0=0. Now we have 5-3 x 0 so your next step is multiplication take 3 x 0= 0. Now you have 5-0, and 5-0= 5
In the translation T of the graph below, use the figure to describe the following transformation. T -2 : (x, y)
(x - 9, y- 1)
(x - 6, y - 2)
(-2x - 6, -2y - 2)
See the explanation
Explanation:You haven't provided any figure, so I could help you in a general way providing my own figure which is attached below. In order to illustrate transformations, let's choose the third one:
[tex]T:(x - 6, y - 2)[/tex]
For this transformation, every point on the original figure is translated 6 units to the left and 2 units down. So quadrilateral ABCD is transformed into quadrilateral EFGH as follows:
[tex]A(10,4) \\ \\ B(14,2) \\ \\ C(14,6) \\ \\ C(10,-2) \\ \\ \\ E \rightarrow (10-6,4-2) \rightarrow (4,2) \\ \\ F \rightarrow (14-6,2-2) \rightarrow (8,0) \\ \\ G \rightarrow (14-6,6-2) \rightarrow (8,4) \\ \\ H \rightarrow (10-6,-2-2) \rightarrow (4,-4)[/tex]
Learn more:
Shifting graphs: https://brainly.com/question/10010217
#LearnWithBrainly
Answer:
The answer is (x - 6, y - 2)
Step-by-step explanation:
For this transformation, every point on the original figure is translated 6 units to the left and 2 units down. So quadrilateral ABCD is transformed into quadrilateral EFGH as follows:
What percent of 140 is 50.4?
Ο 27%
Ο
Ο 36%
Ενετούς
Ο
Ο 50%
Ο 63%
Answer:
36%.
Step-by-step explanation:
That is (50.4 / 140) * 100
= 0.36 * 100
= 36 %.
What is the square root of 59,13,2,and 7/2 rounded to the nearest tenth.
Answer:check the pic
Step-by-step explanation:
On a random Monday in the spring, 95% of students are present at school. If there are 589 students present, then how many total students are enrolled?
Answer:
620
Step-by-step explanation:
How do i get a equation that equals 24 using the numbers 8 3 5 and 1 with a 24 card using multiplication negative times division
Answer:
[(8-3)×5]-1=24
Step-by-step explanation:
[(8-3)×5]-1=24
[(5)×5]-1=24
[5×5]-1=24
[25]-1=24
25-1=24
24=24
Using the numbers 8, 3, 5, and 1 with multiplication, negative numbers, and division, you can form the equation (8 - 5) × 3 = 24.
How to get an Equation that equals a number?Sure, let's find an equation that equals 24 using the numbers 8, 3, 5, and 1 with the operations of multiplication, negative numbers, and division:
Equation: (8 - 5) × 3 = 24
See calculation below:
Start with the number 8 then subtract 5 to get 3.
Multiply 3 by 3 to get 9 and then multiply 9 by -1 to get -9.
Subtract -9 from 24 to get 33.
So, the equation (8 - 5) × 3 = 24 is achieved using the numbers and operations you specified.
Learn more about Equation on:
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two equivalent fraction for 3/12
Answer:
1/4 and 6/24
Step-by-step explanation:
3 divided by 3 equals 1. So then you have to do the same for the denominator. 12 divided by 3 equals 4. And you get 1/4.
Another is 3 x 2 = 6 and 12 x 2 = 24. 6/24
who ever answers right will get Brainlyeist!!!!! PLEASE HELP ME OUT!!!
3. Find the area of the triangle.
A. 21.2 in
B. 10.5 in
C. 21 in
D. 42 in
Answer:
C. 21 in² . . . . your answer selection is correct.
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
where b represents the base of the triangle, and h represents the height of the opposite vertex above that base.
The figure shows you that half the base is 3 in and the height is 7 in, so the area is ...
A = (1/2b)h = (3 in)(7 in) = 21 in² . . . . matches choice C
At the mall you spent a total of $170.86 if you bought two pairs of jeans for $39.95 each a jacket for $45.99 and shirts for
A total of $170.86 will be spent if you buy shirts for $44.11
Step-by-step explanation:
Step 1:
Let the cost of shirts be $x.
Given that, one pair of jeans costs $39.95, 2 pairs cost 2 * $ 39.95 which is $79.9. Jacket costs $45.99.
Step 2:
Create an equation with this given data.
$170.86 = $x + $79.9 + $45.99
Step 3:
Calculate the value of x from this equation to get the cost of shirts.
$170.86 = $x + $125.89
$x = $170.86 - $125.89
$x = $44.11