Answer:
z is 0.03
if you divide 0.06/2= 0.03
Step-by-step explanation:
Priya bought two plants for a science experiment. When she brought them home, the first plant was 5cm tall and the second plant was 4cm. Since then, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.
a. Which plant is taller at the end of 2 weeks? Explain your reasoning.
b. Which plant is taller at the end of 10 weeks? Explain your reasoning.
c. Priya represents this situation with the equation 5 + 0.5w = 4 + 0.75w, where w represents the end of week w. What does the solution to this equation, w = 4 represent in this situation?
d. what does the solution to the inequality 5 + 0.5w > 4 + 0.75w represent in this situation?
Answer:
a. After 2 weeks the first plant will be taller.
b. After 10 weeks the second plant will be taller.
c. After 4 weeks both the plant will be of the same height.
d. This is the condition for the height of the first plant is greater than that of the second plant.
Step-by-step explanation:
The first plant was 5 cm tall and the second plant was 4 cm.
Again, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.
So, the height of the first plant after W weeks will be (5 + 0.5W) cm. and the height of the second plant after W weeks will be (4 + 0.75W) cm.
a. After 2 weeks the first plant will be (5 + 2× 0.5) = 6 cm.
And after 2 weeks the second plant will be (4 + 2 × 0.75) = 5.5 cm
So, after 2 weeks the first plant will be taller.
b. After 10 weeks the first plant will be (5 + 10× 0.5) = 10 cm.
And after 10 weeks the second plant will be (4 + 10 × 0.75) = 11.5 cm
So, after 10 weeks the second plant will be taller.
c. If 5 + 0.5w = 4 + 0.75w, give w = 4 weeks, then this means that after 4 weeks both the plant will be of the same height.
d. If, 5 + 0.5w > 4 + 0.75w, then it means that this condition is for the height of the first plant will be more than the second plant. (Answer)
a. After 2 weeks: First plant: 6 cm (taller), Second plant: 5.5 cm b. After 10 weeks: First plant: 10 cm. Second plant: 11.5 cm (taller) c. Solution to 5+0.5w=4+0.75w is w=4, where both plants are equal in height (5 cm). d. Inequality 5+0.5w>4+0.75w indicates the first plant is taller before w=4 weeks.
a. To determine which plant is taller at the end of 2 weeks, let's calculate their heights:
- First plant after 2 weeks: [tex]\( 5 + 0.5 \cdot 2 = 5 + 1 = 6 \)[/tex] cm
- Second plant after 2 weeks: [tex]\( 4 + 0.75 \cdot 2 = 4 + 1.5 = 5.5 \)[/tex] cm
Since 6 cm (first plant) > 5.5 cm (second plant), the first plant is taller at the end of 2 weeks.
b. Now, let's calculate their heights after 10 weeks:
- First plant after 10 weeks: [tex]\( 5 + 0.5 \cdot 10 = 5 + 5 = 10 \) cm[/tex]
- Second plant after 10 weeks: [tex]\( 4 + 0.75 \cdot 10 = 4 + 7.5 = 11.5 \) cm[/tex]
Since 11.5 cm (second plant) > 10 cm (first plant), the second plant is taller at the end of 10 weeks.
c. The equation given is [tex]\( 5 + 0.5w = 4 + 0.75w \)[/tex]. This equation represents the point in time (number of weeks, w) when both plants will have the same height. Solving for w:
[tex]\[ 5 + 0.5w = 4 + 0.75w \][/tex]
Subtract 0.5w from both sides:
[tex]\[ 5 = 4 + 0.25w \][/tex]
Subtract 4 from both sides:
[tex]\[ 1 = 0.25w \][/tex]
Divide both sides by 0.25:
[tex]\[ w = \frac{1}{0.25} = 4 \][/tex]
Therefore, w = 4 represents the number of weeks after which both plants will have the same height, which is 5 cm.
d. The inequality [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the point in time (number of weeks, w) when the first plant's height (5 cm + 0.5w) exceeds the second plant's height (4 cm + 0.75w). Solving for w:
[tex]\[ 5 + 0.5w > 4 + 0.75w \][/tex]
Subtract 4 from both sides:
[tex]\[ 1 + 0.5w > 0.75w \][/tex]
Subtract 0.5w from both sides:
[tex]\[ 1 > 0.25w \][/tex]
Divide both sides by 0.25:
[tex]\[ w < \frac{1}{0.25} = 4 \][/tex]
Therefore, the solution to [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the number of weeks w when the first plant is taller than the second plant. This happens for ( w < 4 ) weeks.
Justify each step in solving the equation −( + ) = − by writing a reason for each statement.
Answer:
2) -2(3x - 7) = -6x + 14
3) Add 4x to both sides
4) Subtract 14 from both sides
5) Divide both sides by -2
Step-by-step explanation:
24- (12/3 + 8) • (%)
Answer:
12
Step-by-step explanation:
12/3=4
4+8=12
24-12=12
I need help with two questions. I need to write the first five sequences for each problem. Please let me know what they are and how to find them. Thank you much!
Problems:
[tex]a_(1)=-6,a_(n)=4*a_(n)-1\\a_(1)=3,a_(n)=a_(n)-1+9[/tex][tex][/tex]
Answer:
1. -6, -24, -96, -384, -1,536
2. 3, 12, 21, 30, 39
Step-by-step explanation:
1. Given
[tex]a_1=-6\\ \\a_n=4a_{n-1}[/tex]
Find [tex]a_2, \ a_3,\ a_4,\ a_5:[/tex]
[tex]a_2=4a_{2-1}=4a_1=4\cdot (-6)=-24\\ \\a_3=4a_{3-1}=4a_2=4\cdot (-24)=-96\\ \\a_4=4a_{4-1}=4a_3=4\cdot (-96)=-384\\ \\a_5=4a_{5-1}=4a_4=4\cdot (-384)=-1,536[/tex]
2. Given
[tex]a_1=3\\ \\a_n=a_{n-1}+9[/tex]
Find [tex]a_2, \ a_3,\ a_4,\ a_5:[/tex]
[tex]a_2=a_{2-1}+9=a_1+9=3+9=12\\ \\a_3=a_{3-1}+9=a_2+9=12+9=21\\ \\a_4=a_{4-1}+9=a_3+9=21+9=30\\ \\a_5=a_{5-1}+9=a_4+9=30+9=39[/tex]
Complete each geometric sequence.
B. 40, 120, ___, ___
C. 200, 20, 2, ___, 0.02, ___
The missing terms in the geometric sequences are 360 and 1080 for sequence B, and 0.2 and 0.02 for sequence C.
Explanation:In this question, we're working with geometric sequences. A geometric sequence is a sequence in which you multiply by a constant to get from one term to the next.
For sequence B, we notice that 120 is three times 40, so we're multiplying by 3 each time. Thus, the next two terms would be 360 (120 * 3) and 1080 (360 * 3).
For sequence C, we're dividing by 10 to get from one term to the next (200 / 10 = 20, 20 / 10 = 2). Thus, the missing terms would be 0.2 (2 / 10) and 0.02 (0.2 / 10).
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Study the following distribution chart.
Number Frequency
1,400 3
1,450 7
1,500 7
1,550 5
1,600 4
1,650 2
1,700 1
What is the mode?
1,500
1,450 and 1,500
1,550
1,525
Answer:
1,450 & 1,500
Step-by-step explanation:
it occured 7 times each
sorry for my hand writing
What is 0.011 divided by 33
Answer:
0.0003333333 is the answer
Answer: 0.00033333333
Step-by-step explanation: U divide, or if ur having trouble with that, use Google.
Hope this helped u :)
what is 6x +3y=12 in slope intercept form
Answer:
y = -2x + 4Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation in a standard form:
[tex]6x+3y=12[/tex]
Convert:
[tex]6x+3y=12[/tex] subtract 6x from both sides
[tex]6x-6x+3y=-6x+12[/tex]
[tex]3y=-6x+12[/tex] divide both sides by 3
[tex]\dfrac{3y}{3}=\dfrac{-6x}{3}+\dfrac{12}{3}[/tex]
[tex]y=-2x+4[/tex]
Simplify to create an equivalent expression.
-5(3p+3)+9(-7+p)
Answer:
-6(p+13)
Step-by-step explanation:
-5(3p+3)+9(-7+p)
-15p-15-63+9p
-15p+9p-15-63
-6p-15-63
-6p-78
simplify
-6(p+13)
Answer:
-6p-78
Step-by-step explanation:
Khan
BTW: Its 100% correct
Sasha research the size of zoos in her State. she found that the zoo in the north part of the state is almost twice as large as the zoo in the South. she also found that the zoo in the South part of the state has 200 fewer than twice the number of animals as the northern Zoo. how many animals per acres does each Zoo have?
acers - number of animals
North : 64 - ?
South : 35 - 3800
Can someone plssss help???
Answer:A
Step-by-step explanation:
The bottles are represented by b. Each bottle costed 2.10, so it's 2.10b. Then he also bought a pizza for 12.99. The total of all of it was 21.39.
Answer:
A. 2.10b+12.99=21.39; 4 bottles
Step-by-step explanation:
Judy wants to buy some cookies for her birthday party. Cookies come in packages of 6. If she is inviting 24 friends to her party, how many packages of cookies does she need to buy so that each of her friends can have one cookie each?
Judy needs to buy 4 packages of cookies for her party, with each package containing 6 cookies to serve her 24 friends.
Explanation:Judy wants to buy some cookies for her birthday party, ensuring each of her 24 friends receives one cookie. Cookies are sold in packages of 6. To calculate the number of packages she needs, divide the total number of friends by the number of cookies in a package.
Calculation: 24 friends ÷ 6 cookies per package = 4 packages
Judy needs to buy 4 packages of cookies to have enough for each friend to have one cookie.
What is the volume of this rectangular prism?
Answer:
B. 30cm³
Step-by-step explanation:
Volume of a prism=length×Breadth×Height(L×B×H)
Where Length(L)=5-cm, Breadth(B)= 2-cm Height(H)=3-cm
∴Volume=5×2×3=30 cm³
Jose wrote the number 36. If his rule is add 6, what is the fourth
number in Jose's pattern? How can you check your answer?
Answer:
60
Step-by-step explanation:
36+6=42
42+6=48
48+6=54
54+6=60
Springfield nuclear energy inc bonds are currently trading at 283.30. The bonds have a face value of $1,000, a coupon rate of 2% with coupons paid annually, and they mature in 20 years. What is the yield to maturity of the bonds?
Answer:
The yield to maturity of the bonds is 11%
Explanation:
Price at which the bonds is currently trading = 283.30$
Face Value = $1000
Coupon rate = 2%
Hence the coupon bond rate = $1000 ×2%
= [tex]1000\times \frac{2}{100}[/tex]
=$20
Years to maturity: 20 years
Formula used:
=[tex]\frac{(C+ (\frac{(F-P)}{n}))}{(\frac{(F+P)}{2})}[/tex]
Where C is the bond coupon rate
F is the face value
P is the price
N is the number of years
=[tex]\frac{(20 +(\frac{(1000-283.30)}{20})}{(\frac{(1000+283.30)}{2})}[/tex]
=11%
The yield to maturity of the bonds is 11%
help is neededdd please
Answer:
○ C. [tex]\displaystyle y = \frac{1}{2}x + 10[/tex]
Step-by-step explanation:
9 = ½[−2] + b
−1
[tex]\displaystyle 10 = b \\ \\ y = \frac{1}{2}x + 10[/tex]
** Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], so −2 becomes ½.
I am joyous to assist you anytime.
The product of -2 and a number minus six is greater than -18
So, its a multiplying question - the product. Also there are multiple answers from x = negative anything to positive 14, so i chose a number.
The product of -2 and a number minus six is greater than -18.
-2 · (x - 6) > -18
-2 · (7 - 6) > -18
-2 · (1) > -18
-2 > -18
x = 7, or anything lower than 15.
On the number line btw, -2 is bigger than -18
write the algebraic expression representing the length and width of marliens house
Answer:
You have to show us the shape for us to write down the expression.
What is the y-intercept of the graph of the linear function?
Answer:Another way to graph a linear function is by using its slope m, and y-intercept. ... The y-intercept is the point on the graph when x =0 x = 0 . The graph crosses the y-axis at (0,1) .
Answer:
Step-by-step explanation:
When you have a linear equation, the y-intercept is the point where the graph of the line crosses the y-axis.
In the year 2007, a person bought a new car for $16000. For each consecutive year after that, the value of the car depreciated by 5%. How much would the car be worth in the year 2011, to the nearest hundred dollars?
The car would be worth $13,000 in the year 2011.
Explanation:To calculate the value of the car in the year 2011, we need to find the depreciated value of the car each year from 2007 to 2011. The value of the car depreciates by 5% each year, which means it retains 95% of its value each year. Here are the calculations:
Year 2007: $16,000Year 2008: $16,000 x 0.95 = $15,200Year 2009: $15,200 x 0.95 = $14,440Year 2010: $14,440 x 0.95 = $13,718Year 2011: $13,718 x 0.95 = $13,032Therefore, in the year 2011, the car would be worth $13,000 to the nearest hundred dollars.
In the gym , there is a scale that measures people weight . The needle is 22 cm long , and it roared 124 when Evelyn stepped on it . How far did needle travel as it rotated.
(From Unit 4 Lesson 1)
5. A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
a. Find a mixture that will make the same shade of green but a smaller amount.
b. Find a mixture that will make the same shade of green but a larger amount.
Findami
Answer:
a. 1 cup of yellow and 1.75 cups of blue
b. 4 cups of yellow and 7 cups of blue
Step-by-step explanation:
a. We can multiply both sides of this ratio by an number of our choice to get an equivalent ratio. 2:3.5 = 1: 1.75. (We are multiplying by 1/2)
b. 2 : 3.5 = 4 : 7 (We are multiplying by 2)
Find the sales tax on a purchase of $18.95 if the tax rate is 6%
Answer: 1.14
Step-by-step explanation:
hate how you gotta pay just to see an answer
The required sales tax on purchases of $18.95 is $1.14.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Amount = $18.95
Sales tax applies is 6% on the amount,
Now,
Sales tax is given as,
tax = amount × tax percentage / 100
tax = 18.95 × 6 / 100
tax = 1.14
Thus, the required sales tax on purchases of $18.95 is $1.14.
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What is a “system of equations”
Answer:
here is the answer
A system of equations is a collection of two or more equations with a same set of unknowns.
Two ships depart from a port at the same time, one heading south and the other east. Seven hours later, they are separated by a distance of 170 miles. If the ship going south travels 70 miles more than the other, how many miles does each vessel travel?
Answer: 80 miles for the first ship, and 150 miles for the other.
Explanation:
First thing we should do is correspond each number with a letter:
Let x be the distance travel by ship heading east
Let y be the distance travel by ship heading south
y = x + 70 -- (1)
sqrt(x^2 + y^2) = 170 -- (2)
Subtract (1) into (2):
sqrt(x^2 + (x + 70)^2) = 170
x^2 + x^2 + 140x + 4900 = 28900
2x^2 + 140x - 24000 = 0
x ^2 + 70x - 12000 = 0
(x - 80)(x + 150) = 0
x = 80 or -150
Since the distance for the first ship can’t be negative, therefore, x = 80 -- (3)
Subtract (3) into (1), therefore, y = 150
Hope this helps! :)
determine the number of solutions for the systems
x+y=2 and 2x+2y=8
Answer:
The number of solutions of the system is zero
Step-by-step explanation:
we have
a) [tex]x+y=2[/tex]
Isolate the variable y
[tex]y=-x+2[/tex] ----> equation A
This is the equation of the line in slope intercept form
where
The slope is m=-1
The y-intercept is b=2
b) [tex]2x+2y=8[/tex]
Isolate the variable y
[tex]2y=-2x+8[/tex]
[tex]y=-x+4[/tex] ----> equation B
This is the equation of the line in slope intercept form
where
The slope is m=-1
The y-intercept is b=4
Remember that
If two lines are parallel, then their slopes are the same
In this problem the lines A and B are parallel lines with different y-intercept
so
The lines don't intersect
therefore
The system has no solution
Amy bakes 250 chocolate chip cookies and sells these in boxes of 9. How many full boxes will she have?
Use long division (see attached image below) to divide 250 over 9. The image shown has a red quotient of 27 and a blue remainder of 7.
This means there will be 27 full boxes with 9 cookies each. That accounts for 27*9 = 243 cookies so far. The remaining 7 won't be able to fill a full box as we're 2 short.
-------
A shortcut is to use a calculator to divide 250/9 = 27.778, then you ignore the decimal portion and focus solely on the whole part 27.
-------
Final Answer: 27Amy will have 27 full boxes of cookies, which is determined by dividing the total number of cookies by the number of cookies per box.
To find out how many full boxes Amy will have when selling 250 chocolate chip cookies in boxes of 9, you can divide the total number of cookies by the number of cookies per box.
Number of full boxes = Total number of cookies / Cookies per box
Number of full boxes = 250 cookies / 9 cookies per box
Using division:
Number of full boxes ≈ 27.777...
Since Amy can't have a fraction of a box, she will have 27 full boxes of cookies.
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If you hike 1/2 mile every 1/5 hour how far do you hike in two hours?
Answer:
5 miles
Step-by-step explanation:
0.5 x 10
= 5
Answer:
5 Miles
Step-by-step explanation:
1/5 of an hour would be 12 minutes. If it is 1/2 mile every 1/5 our, you hike 1 mile for 2/5.
1/5 = 1/2
2/5 = 1
3/5 = 1 1/2
4/5 = 2
5/5 = 2 1/2
So if 1 hour is 2 1/2 miles, you multiply it by 2, or add it withh its same number, which is,
5 miles.
If one inch represents 18 feet, what dimensions would you use to make a scale drawing of a building 630 feet by 450 feet?
Answer:
35 by 25 inches
Step-by-step explanation:
1 inch = 18 feet
each 18 feet in the scale model is one inch, which means that there is one inch per 18 feet, so all you need to do is divide 630 by 18 and 450 by 18.
630/18 = 35
450/18 = 25
so the dimensions of the scale model are 35 by 25 inches
Solve the system of equations:
x - 3y = - 4
2x - 6y= 6
Answer:
No Solution.
Step-by-step explanation:
x-3y=-4
2x-6y=6
-----------
simplify 2x-6y=6 into x-3y=3
-------------
x-3y=-4
x-3y=3
------------
x-3y=-4
-(x-3y)=-1(3)
-----------------
x-3y=-4
-x+3y=-3
---------------
0=-7
no solution
The equations x - 3y = -4 and 2x - 6y = 6 represent a system with parallel lines that do not intersect, therefore there are no solutions to this system of equations.
Explanation:Let's solve the system of equations using the method of substitution or elimination. First, look at the two given equations:
x - 3y = -4 (Equation 1)2x - 6y = 6 (Equation 2)It's clear that Equation 2 is simply Equation 1 multiplied by 2. This implies the two equations are multiples of each other, which could mean the system has an infinite number of solutions or no solutions. Let's simplify Equation 2 to confirm:
Divide Equation 2 by 2:
2x/2 - 6y/2 = 6/2
x - 3y = 3
This new equation contradicts Equation 1 (x - 3y = -4), which indicates that there are no solutions since the two lines are parallel and will never intersect.