1. Jim is tracking the progress of his plant’s growth. Today the plant is 8cm high. The plant grows 3.5cm per day. What will the height of the plant be on day 28? (Hint: “today” is day 0).
"The plant grows 3.5 cm per day" means that the function grows by 3.5 cm each day. We can make a function like this:
y = 8 + 3.5x
Day 0 -> Day 28 is +28 days, so plug-in x with 28 to find out how much it would have grown in 28 days PLUS the original height of the plant, 8 cm.
y = 8 + 3.5(28) <-- see how I replaced x with 28
Simplify
y = 8 + 98 = 106 cm at day 28
2. The average inflation rate of the U.S. dollar over the last six years is 2.8% per year. If a new car cost $29,000 six years ago, how much would it cost today?
2015, 2016, 2017, 2018, 2019, 2020, 2021
Just to help you imagine the years, we need to find the car's value from $29,000 in 2015 to 2021 using the idea that the car's value increases by 2.8 percent. What does 2.8 percent mean and how do we use this information to find out how much it increases? We need to convert this to a decimal so we can multiply it by 29,000 easily. First, convert 2.8% to a decimal = 0.028. Then we have to add 1 to 0.028. Why? Because we need to make sure that we still have the original 100% of the 29,000. If we forget the 1 then we're just finding 2.8% of 29,000! So, now we know that our multiplier by each year is 1.028. Now we have to multiply.
29,000 x (1.028)^6 (we have a power of 6 because remember, we are multiplying the 1.028 every year, and there are 6 years!)
Simplify: 34,226.0425 that rounds to 34,226.0425 dollars
3. The population of Mickey Village is 48,000 today. Every other year the population increases by 1,550 people. In approximately how many years will the population exceed 70,000 people?
The details of this question are confusing, so I won't answer this. Sorry, I'm really short on time. I hope I could help the best I could.
A cereal company makes a cereal from two ingredients: wheat and oats. Each ingredient provides two essential nutrients: vitamin A and vitamin B. The company wants to know how many ounces of wheat and oats to include in each box of cereal so that the minimum requirements of 48 milligrams of vitamin A and 20 milligrams of vitamin B are satisfied. An ounce of wheat provides 10.5 milligrams of vitamin A and 2.4 milligrams of vitamin B. An ounce of oats provides 6 milligrams of vitamin A and 1.8 milligram of vitamin B. An ounce of wheat costs $0.05 and an ounce of oats costs $0.10. The company wants to minimize the total cost of production.
Find the solution to this problem using the Simplex method.
Answer:
z (min ) = 0.4167 $
x = 8,33 oz
y = 0
Step-by-step explanation:
Table:
Vitamin A Vitamin B Cost $/oz
Wheat (x) 10.5 2.4 0.05
Oats (y) 6 1.8 0.10
Requirements 48 (mg) 20 (mg)
Requirements 1,693 (oz) 0,7054 (oz)
The problem is minimized z subject to two constraint
z = 0.05*x + 0.1*y to minimize
Subject to:
Requirement of Vitamin A
10.5*x + 6 * y ≥ 48
Requirement of Vitamin B
2.4*x + 1.8*y ≥ 20
x≥0 y≥0
Using the on-line solver AtomZmaths and after 3 iterations the solution is:
z (min ) = 0.4167 $
x = 8,33 oz
y = 0
If a dog eats 1/4 pound of food each day, how many days will it take the dog to eat a 5 pound bag of food?
Answer:
20 days
Step-by-step explanation:
0.25 pound of food is eaten in 1 day
1 pound of food is eaten in 1 / 0.25
5 pound of food is eaten in 5/0.25 = 20 days
Rewrite by completing the square f(x) = x2 - 6x +43
Answer:
f(x) = (x - 3)^2 + 34
Step-by-step explanation:
PLZZZ HELP!!!!!!!!!1
What is the median and Q1 of the data set represented on the plot?
Median = 30; Q1 = 20
Median = 33; Q1 = 20
Median = 30; Q1 = 25
Median = 33; Q1 = 25
Answer:
i cant put the picture
Step-by-step explanation:
d. Median=33;Q1=25 the median is represented by the line in between the two boxes. Q1 is represented by the line on the far left of the box in the picture Q1 is marked for quadrent 1 and m is for median
In triangle ABC, m∠A=(2x+2)∘, m∠C=54∘, and the exterior angle at B is (4x)∘.
Triangle A B C. Angle A is 2 X plus 2 degrees, angle C is 54 degrees, & the exterior angle at B is 4 X degrees.
What is the measure of angle A?
58∘
112∘
28∘
68∘
Answer:
58°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two remote interior angles.
m∠A + m∠C = measure of exterior angle at B
2x + 2 + 54 = 4x
2x + 56 = 4x
2x = 56
x = 28
m∠A = 2x + 2 = 2(28) + 2 = 56 + 2 = 58°
Answer:
A
Step-by-step explanation:
Remark
<A + <C = the exterior angle.
Two remote interior angles = the exterior angle that neither connects to.
Remote means that the angles do not share any line in common with the remote angle. One of them might share a line extended with the exterior angle.
Equation
<A + <C = Remote angle connected to the supplement of B
Givens
m<A = 2x + 2
m<C = 54
Remote angle = 4x
Solution
2x + 2 + 54 = 4x Combine like terms on the left
2x + 56 = 4x Subtract 2x from both sides
56 = 4x - 2x
2x = 56 Divide by 2
x = 56/2
x = 28
Answer
<A = 2x + 2
<A = 2*28 + 2
<A = 56 + 2
<A = 58
Which value is included in the solution set for the inequality graphed on the number line?
4
3
2
-1
0 1 2
3
4
-5
O
-2.
ОО
03
Answer:
-5
Step-by-step explanation:
The number line is saying that the solution could be any number less than -2.
The value included in the solution set for the inequality graph on the number line is -5.
How to find the solution set of inequality graph on a number line?
The number line represents an inequality graph.
Let's use the range of value on the graph as x.
Therefore, the inequality on the number line will read as follows:
x < -2
Hence,
x less than -2 includes -3, -4, -5, -6, -7, -8 ..
Therefore, the value included in the solution set for the inequality graph on the number line is -5.
learn more on inequality graph here: https://brainly.com/question/1400037
Where can we use linear inequalities in real life?
Step-by-step explanation:
we can use it to solve age problems and Money problems e.t.c
Tyler sold a total of $115,000 of exercise equipment last month. If his commission is 6.5% of sales, how much commission did he earn?
A.
$2,342
B.
$7,475
C.
$12,719
D.
$115,065
Answer:
B
Step-by-step explanation:
Do 115000/100x6.5 You get 7.475k
College Math!!! I did the first half of the question, I just need the bottom half of it.
Answer:
-49
Step-by-step explanation:
[tex]\int _{-5}^{-2}\:\left(8\:w\left(r\right)-3\right)dr[/tex] = [tex]\int _{-5}^{-2}\:8\:w\left(r\right)dr[/tex] -3 (-2 -(-5)) = [tex]8 \int _{-5}^{-2}\:\:w\left(r\right)dr[/tex] -9 =8(-5) -9 = -49
2. Barnes and Noble bookstore is having a sale. Dr. Mumin's book sells for
$4 per copy. Dan Moyer's book sells for $1 per copy. Leannie spends $23
for 8 books'. How many copies of books from each author did she buy?
Mary has a stack of cards, 8 purple, 6 orange, 5 red and 7 black. If she has to choose a card, how many possible outcomes are there?
Answer: The amount of outcomes is 26 because you have 26 cards which are all possible to draw so they are the outcomes.
Step-by-step explanation:
Basic arithmetic really. 8+6+5+7 = 26. The color was just added to confuse u.
awnser plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
x = 12, x = -4.
Step-by-step explanation:
x² - 8x - 48 = 0.
This factors to (x - 12)(x + 4) = 0.
Proof:
(x - 12)(x + 4) = 0
first: x * x
outer: 4 * x
inner: -12 * x
last: -48.
first: x²
outer: 4x
inner: -12x
last: -48
x² + 4x - 12x - 48
x² - 8x - 48.
To find the zeros, take the individual pairs and find the values that make the equation 0.
x - 12 = 0
Add 12 to both sides.
x = 12.
x + 4 = 0
Subtract 4 from both sides.
x = -4.
Answer:
x= 4 + 2√5, x = 4 - 2√5
Step-by-step explanation:
So this is quadratics so you can solve it by completing the square and using the quadratic formula. The quadratic formula is x = (-b±√(b²-4ac)) / (2a).
hey guys i'm having a rough night and i can't figure out my homework rn i'm just too stress please help
Answer:
4a) Irrational
Step-by-step explanation:
The square root of 20 is irrational. There is no number that can multiplied by itself to equal 20.
For a better explanation, the square root of 25 is rational. 5 can be multipled two times to be equivalent to it. Meanwhile, 20 can't.
Help ASAP
What is the highest common factor of 180 and 168
Answer:
Its 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
make a factor tree, find the product of the prime factors, it will be 12.
prove that the points A(1 , -1 ) B(5, 2) C(9, 5) are collinear.
Answer:
AB= [tex]\sqrt(5-1)^2 +(2+1)^2 = \sqrt16+9 =5[/tex]
BC= [tex]\sqrt(5-9)^2 + (2-5)^2 = \sqrt16+9=5[/tex]
AC = [tex]\sqrt(1-9)^2 + (-1-5)^2 = \sqrt64+36 = 10[/tex]
So, AC = AB + BC
A, B, C are collinear points
Step-by-step explanation:
I hope this helps!
Solve the following equation for x. x^2 - 36 = 0
A. x=1 x=-36
B. x=-1 x=36
C. x=-6 x=6
D. x=-18 x=18
Answer:
The answer is C.x=6,x=-6
Step-by-step explanation:
Greetings!
x²-36=0x²-36+36=0+36.. add 36 both sidesx²=36... simplifyAn assumption
"In general, all equations of the form x² = a, where a is a positive number, will always give two solutions, namely x = - √a or x = √a."
Thus,
x= √ 36, x= - √ 36x=6, x=-6Find the missing length indicated
A) 25
B) 5
C) 8
D) 3
Given:
The figure of a triangle.
To find:
The missing length.
Solution:
Let x be the missing length.
Basic proportionality theorem(BPT): According to this theorem, if a line is parallel to the one side of a triangle then that the line intersects the other two sides of the triangle in the same ratio.
Using Basic proportionality theorem, we get
[tex]\dfrac{6}{8-6}=\dfrac{12-x}{x}[/tex]
[tex]\dfrac{6}{2}=\dfrac{12-x}{x}[/tex]
[tex]3=\dfrac{12-x}{x}[/tex]
[tex]3x=12-x[/tex]
Adding x on both sides, we get
[tex]3x+x=12[/tex]
[tex]4x=12[/tex]
[tex]x=\dfrac{12}{4}[/tex]
[tex]x=3[/tex]
The missing length is 3 Therefore, the correct option is D.
Please help me with this real quick
Answer: 7.5 miles
Step-by-step explanation:
think of it as a triangle; the bold line is the hypotenuse, or x.
8 |\ x
|_\ it's not a good triangle but you get the point
6
and then get out pythagorean theorem: a^2+b^2=c^2
put the numbers in: 8^2 + 6^2 = x^2
do some math:
64+36=x^2
100=x^2 (and then find square root)
10=x
BUT, it said each unit was 3/4 of a mile, so we must multiply 10 by 3/4 to get the actual distance, which is 7.5
please help, ill give brainliest
Answer:
hope this help you......
$265 worth of tickets were sold
Adult tickets cost $6
Child tickets cost $2.50
57 tickets were sold
Let x represent the number of adult tickets sold. Let y represent the number of child tickets sold.
Which equations represent the scenario? Select two equations.
Answer:
A and F, x=35
Step-by-step explanation:
The correct answers are :
A ) x + y = 57
F) 6x + 2.5ʏ = 265
\frac{5}{2}\mathrm{g}-\frac{1}{2}\mathrm{g}= 2 5 g− 2 1 g simlily
Answer:
ok
Step-by-step explanation:
measure of each exterior angle of a regular 30-gon?
7. An exterior angle of a regular polygon measures 22.5°. How many sides does it have?
8. An interior
Answer:
I'm not sure would love to help but dont know the answer
Find the area of each parallelogram
Please help with these thank you
Help pleaseeeeeeeeeeee
Answer;
Mark traveled at the highest velocity to Charleston
In a random sample of 10 residents of the state of Florida, the mean waste recycled per person per day was 2.1 pounds with a standard deviation of 0.59 pounds. Determine the 98% confidence interval for the mean waste recycled per person per day for the population of Florida. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
7.2x14.3 what is that?
Answer:
102.96
Step-by-step explanation:
Answer:
[tex]102.96[/tex]
Step-by-step explanation:
7 . 2
× 14 . 3
___________
²2 . 16
²28 . 80
72 . 00
____________
¹1¹02.96
Therefor, the answer is 102.96
What is the answer to this
Answer:
5 f
Re-order terms so that constants are on the left
. 5
5 f
solution
5 f
3.14(10)^(2)12
I cant figure this out
3.14(10)^2(12)
answer=3768
Simplify the polynomial, then evaluate for x = 2 . x + 3x ^ 2 + 2x - 3 - 4x ^ 2 + 6
Answer:
-x^2+3x+3
Step-by-step explanation:
if the evaluated answer is correct (but my answer above is correct) it would be -4+6+3 then the answer would be 5 but I am not sure
-7r^2= -329 square root property
9514 1404 393
Answer:
r = ±√47
Step-by-step explanation:
-7r^2 = -329 . . . . given
r^2 = 47 . . . . . divide both sides by -7 (multiplication property of equality)
r = ±√47 . . . . square root both sides (square root property of equality)
Answer:
This is what I got.
Step-by-step explanation: