Answer:
Step-by-step explanation:
Part A
If the gardener increases the number of dahlia plants by buying the new bulbs,
Let the equation representing year (x) and number of bulbs purchased (y) is,
y = mx + b
Here, m = Number of plants purchased each year
b = Initial numbers of plants
For x = 0, and y = 6,
6 = m(0) + b
b = 6
For x = 1, y = 56,
56 = m(1) + 6
m = 50
Therefore, equation for this method of increasing the numbers of plants will be,
y = 50x+ 6
Let the equation for the second method of increasing the number of plants is represented by the equation,
y = a(b)ˣ
From the data given in the table,
For x = 0, y = 6
6 = a(b)⁰
a = 6
For x = 1, y = 12
12 = 6(b)¹
b = 2
Therefore, equation representing the second method (By diving the existing bulbs) will be,
y = 6(2)ˣ
Part B
By substituting the value of x = 10 years,
Method - 1
y = 50(10) + 6
y = 506 plants
Method - 2
y = 6(2)¹⁰
y = 6144 plants
Part C
After 5 years number of plants by method - 1,
y = 50(5) + 6
= 256
After 5 years number of plants by method - 2,
y = 6(2)⁵
y = 192
Similarly, After 10 years number of plants by method - 1,
y = 50(10) + 6
= 506
By method - 2,
y = 6(2)¹⁰
y = 6144
Since, number of plants after 5 years are less by the second method as compared to method 1
But after 10 years second method results the number of plants more than method-1,
Therefore, gardener should adopt method 2 for increasing the numbers of plants.
Functions are used to represent tables and equations.
(a) The equation of the functions
The function of "Buy New Bulbs" is a linear function with an initial value of 6, and a rate of 50 (i.e. 56 - 6)
So, the equation is:
[tex]y = 6 + 50x[/tex]
The function of "Divide Existing Bulbs" is an exponential function with an initial value of 6, and a rate of 2 (i.e. 12/6)
So, the equation is:
[tex]y = 6(2)^x[/tex]
Hence, the equations of the functions are [tex]y = 6 + 50x[/tex] and [tex]y = 6(2)^x[/tex]
The expected number of bulbs in 10 years
This means that x = 10.
So, we have:
[tex]y = 6 + 50x =6 + 50*10 = 506[/tex]
[tex]y = 6(2)^x =6 *2^{10} = 6144[/tex]
Hence, the expected number of bulbs in 10 years for both functions are 506 and 6144, respectively
Compare the expected number of bulbs in 5 and 10 years
When x = 5.
We have:
[tex]y = 6 + 50x =6 + 50*5 = 256[/tex]
[tex]y = 6(2)^x =6 *2^5 = 192[/tex]
When x = 15
We have:
[tex]y = 6 + 50x =6 + 50*15 = 756[/tex]
[tex]y = 6(2)^x =6 *2^{15} = 196608[/tex]
By comparison;
In 5 years, the expected number of bulbs for the function of "Buy New Bulbs" is greater than the function of "Divide Existing Bulbs", however the expected number of bulbs for the function of "Buy New Bulbs" is less than the function of "Divide Existing Bulbs" in 15 years
Read more about functions at:
https://brainly.com/question/15602982
Mr. And Mrs. Griffin hope to send their daughter to college in fourteen years. How much money should they invest now at an interest rate of 9.5% per year, compounded continuously, in order to be able to contribute $8,500 to her education?
Answer:
$2,385.75 = P
Step-by-step explanation:
In order to calculate this we need to use the following compound interest formula and solve for the initial investment amount which is P.
A = P (1 + r/n) (nt)
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
If we plug in the values provided in the question which is compounded once per year we would get the following equation which we can solve for P.
8500 = P (1 + (0.095/1))^(1*14)
8500 = P (1.095)^(14)
8500 = P (3.56285)
2,385.75 = P
Mr. and Mrs. Griffen need to invest $2,385.75 now for 14 years in order to contribute a total of $8,500
If O is an angle in standard position and its terminal side passes through the point
(3,-1), find the exact value of tan 0 in simplest radical form.
please help !
Answer:
-1/3
Step-by-step explanation:
What is sin 20° cos 4° + cos 20° sin 4º equal to?
Answer:
Sin24
Step-by-step explanation:
Hope you see the given image .
I need to find the value of x
Answer:
9
Step-by-step explanation:
Radius = x
The triangle in the given image is a right angled triangle.
By Pythagoras theorem,
x² + 12² = ( x + 6 )²
x² + 144 = x² + 36 + 12x
x² - x² = 36 - 144 + 12x
0 = - 108 + 12x
12x = 108
x = 108 / 12
x = 9
WILL GIVE BRAINLIEST FOR RIGHT ANSWER 16 POINTS
Answer:
Absolute value means 2 equations so work below.
Step-by-step explanation:
x + 2 = 3
x = -1
x - 2 = 3
x = 5
I hope I didn't just confuse myself it's been YEARS since i've had simple questions like this (i can edit if needed)
A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls the number cube 45 times and the cube lands with a six facing up 12 times. Assuming the conditions for inference have been met, what is the 99% confidence interval for the true proportion of times the number cube would land with a six facing up?
0.27 plus-or-minus 2.58 StartRoot StartFraction 0.27 (1 minus 0.27) Over 45 EndFraction EndRoot
0.73 plus-or-minus 2.33 StartRoot StartFraction 0.73 (1 minus 0.73) Over 45 EndFraction EndRoot
0.27 plus-or-minus 2.33 StartRoot StartFraction 0.27 (1 minus 0.27) Over 45 EndFraction EndRoot
0.73 plus-or-minus 2.58 StartRoot StartFraction 0.73 (1 minus 0.73) Over 45 EndFraction EndRoot
Answer: Option #1
Step-by-step explanation:
99 % confidence level - so it has to be 2.58 not 2.33 ( thats 98% confidence level )
then 12times facing u out of 45 times .... 12/45= .27
Option #1 : 0.27 +/- 2.58 StartRoot StartFraction 0.27 (1 minus 0.27) Over 45 EndFraction EndRoot
The 99% confidence interval for the true proportion of times the number cube would land with a six facing up is 0.27 plus-or-minus 2.58 StartRoot StartFraction 0.27 (1 minus 0.27) Over 45 EndFraction EndRoot.
What is Confidence Interval?This is an operation which is used to measure probability that a parameter will fall between a pair of values around the mean
99 % confidence level is closer to 2.58 and 12 times facing up out of 45 times which is 12/45= .27
Hence the reason why option A was chosen as the most appropriate choice.
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answer: 3/4x - 1/2x -4=12
1/4x - 4 = 12 x = 64
Supposed B is the midpoint of line AC. Use the given information to find the missing measure. AB = 6Y -14, BC = 10-2Y 2Y, what is AC
Given:
B is the midpoint of line AC.
[tex]AB=6Y-14[/tex]
[tex]BC=10-2Y[/tex]
To find:
The length of AC.
Solution:
It is given that B is the midpoint of line AC. So,
[tex]AB=BC[/tex]
[tex]6Y-14=10-2Y[/tex]
[tex]6Y+2Y=10+14[/tex]
[tex]8Y=24[/tex]
Divide both sides by 8.
[tex]Y=\dfrac{24}{8}[/tex]
[tex]Y=3[/tex]
The value of Y is 3.
Now,
[tex]AC=AB+BC[/tex]
[tex]AC=6Y-14+10-2Y[/tex]
[tex]AC=4Y-4[/tex]
Putting [tex]Y=3[/tex], we get
[tex]AC=4(3)-4[/tex]
[tex]AC=12-4[/tex]
[tex]AC=8[/tex]
Therefore, the length of AC is 8 units.
HELPPP PLSSS THIS IS MY THIRD TIME POSTING THIS PLS HELP ME I WOULD MARK YOU BRAINIEST What is the slope of the line below?
(3,5)
(3, 2)
A. positive
B. undefined
C. negative
D. Zero
Answer:
B
Step-by-step explanation:
its undefined because 3/0.
What is the distance between ( 7, -1) and ( 7, -5) and why?
I will give branily to whoever is right
Answer:
The distance is 4
Step-by-step explanation:
Given:
x1 = 7
x2 = 7
y1 = -1
y2 = -5
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(7-7)^2+(-5+1)^2}\\\\d=\sqrt{(0)^2+(-4)^2} \\\\d=\sqrt{0+16} \\\\d=\sqrt{16} \\d=4[/tex]
Answer:
4 units
Step-by-step explanation:
the distance between two points is given by,
[tex]D = \sqrt{{(x_{1}-x_{2})}^{2} + {(y_{1}-y_{2})}^{2} } \\x_{1}=7; x_{2}=7; y_{1}=-1; y_{2}=-5\\D=\sqrt{{([7]-[7])}^{2} + {([-1]-[-5])}^{2} }\\D=\sqrt{{(0)}^{2} + {(4)}^{2} }\\D=\sqrt{0 + 16 }\\D=\sqrt{16}\\D=4[/tex]
Help I will be marking brainliest!! No links please!
A. 42,757.2
B. 4,750.8
C. 128,271.6
D. 256, 543. 2
Show work, if possible. Thanks❤️
Answer:
384130.764(I DIDNT ROUND IT)
Step-by-step explanation:
Hey there, friend!
Here's my answer!
[tex] \colorbox{red}{A{ \colorbox{orange}{N{ \colorbox{yellow}{S{ \colorbox{blue}{W{ \colorbox{royalblue}{E{ \colorbox{cyan} {R{ \colorbox{purple}{S}}}}}}}}}}}}}: [/tex]
[tex] {\bold\green{Answer}} \green\implies\blue{\overbrace{\underbrace{\boxed{\bold\blue{A.\:42,757.2}}}}} [/tex]
B. 4,750.8
C. 128,271.6
D. 256, 543. 2
============================
[tex] \LARGE\bold\blue{\tt{SOLUTIONS}} [/tex]
First, multiply 37 and 42.8
[tex] {\bold\green{37 × 42.8 }} \green\implies\blue{\boxed{\bold\blue{1,583.6 }}} [/tex]
Second, multiply 1,583.6 and 27
[tex] {\bold\green{1,583.6 × 27}} \green\implies\blue{\boxed{\bold\blue{42,757.2}}} [/tex]
[tex] {\bold\green{Final\:answer}} \green\implies\blue{\overbrace{\underbrace{\boxed{\bold\blue{42,757.2}}}}} [/tex]
============================
That's my answer
Keep safe, friend
Aidan makes 12 bracelets on Monday. He makes 8 more bracelets each day from Tuesday through Thursday. How many bracelets does Aidan have in all by the end of the day on Thursday? *
5 points
Answer:
He makes 44 bracelets on Friday.
Brainly me or heart if this helped!
Answer:
36 bracelets
Step-by-step explanation:
12+(3*8)=x
12+24=36
Aidan originally started with 12 bracelets. He makes 8 Tuesday through Thursday, which is three days. 8 * 3 is 24 plus 12 equals 36.
An item is priced at $14.55. If the sales tax is 6%, what does the item cost including sales tax?
Answer:
$15.43
Step-by-step explanation:
$14.55 x 1.06 = $15.423
Work out the value of x.
Answer:
x = 30°
Step-by-step explanation:
4x + 2x = 180° because they are supplemental angles
6x = 180°
divide both sides of the equation by 6:
x = 30°
Which expression is equivalent to 16+ 2 36?
please help ! (4x3x8+9+9)
Answer:
114
Step-by-step explanation:
Plz help
The point of intersection of two function is also called the
A. Center
B. Equation
C. Vertex
D. Solution
Answer:
Step-by-step explanation: Vertex Equatiation Por mxa Plus B = X gtex Lp Cneter to 16u8 Killomtrss to ball
. Es una característica numérica de la población, para su cálculo se emplean formulas y generalmente se indican con letras griegas. A) Estadístico o Valor Estadístico B) Parámetro C) Dato Continuo D) Dato Cuantitativo
Answer:
B) Parameter
Step-by-step explanation:
To find - It is a numerical characteristic of the population, formulas are used for its calculation and are generally indicated with Greek letters. A) Statistical or Statistical Value B) Parameter C) Continuous Data D) Quantitative Data
Answer -
The correct option is - B) Parameter
Reason -
In statistics, A parameter is a numerical characteristic of a population, as distinct from a statistic of a sample.
Find the equation slope and y intercept with these two coordinates (0,-1) and (3,1)
29/1000
The fraction can be written as which decimal?
1,000
A)
0.0029
B)
0.029
0.29
2.9
Please help. Which choice describes the shape of the data?
Answer:
?
Step-by-step explanation:
4x+3(2x-1)-4x
Pls help
Answer:
6x-3
Step-by-step explanation:
4x+6x-3-4x
6x-3
Answer:
6x -3
Step-by-step explanation:
4x + 3(2x - 1) - 4x
4x + 6x - 3 - 4x
Combine same values
6x -3
Marcus ran a 10-Kilometer race in 50 minutes. If Marcus maintains that same pace, how many kilometers can Marcus run in 1 hour?
Answer:
markus could run 12 kilometers in an hour
Step-by-step explanation:
The area of a square floor on a scale drawing is 25 square centimeters, and the scale drawing is
1 centimeter:6 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the
actual area?
The area of the actual floor isſ ] square feet. The ratio of the area in the drawing to the actual
area is 1 square centimeter: square feet
View Example
f Step-by-step
Textbook
Print
Answer:
actual area = 900 square feet
ratio = 1cm2 : 36ft2
Step-by-step explanation:
square room
area = 25cm2
1 side = √ 25
= 5cm
1cm = 6ft
5cm = 5 x 6
= 30ft = 1 side
actual area = 30 x 30 = 900ft
ratio = square cm : square feet
= 25 : 900 ( simplify both ratio )
= 1cm2 : 36ft2
A triangle has vertices A(-2,1), B(2,4), C(4,1).
Find the area of the triangle.
Answer: 6 units squared
Step-by-step explanation: ok here is how you do it so you make the triangle like I did and once you make it. You count the squares about how long it is and how high it is in this case I got for the base 6 and the height 2 so we multiply to get 12 also we divide 12 and 2 to get 6 units squared there you go. hope this helps.
Using the pattern of blocks below, how many blocks does Figure 26 have?
Tanya coasted down the sidewalk on her bike at a constant speed of 15
meters per second for 20 seconds. The distance she traveled was:
a. 0.75 m
b. 1.3 m
c. 35 m
d. 300 m
The faces of a fair 6-sided cube are numbered 1 through 6.
What is the probability that a 2, 3, or 5 will land face-up on
the next roll?
Answer:
1/2
Step-by-step explanation:
2,3,5 are three out of a total of six options
3/6 = 1/2
a little help would be nice here pls
Answer:
11). 3x² -x 12). -5x + 5
Step-by-step explanation:
11). (4x² + x) - (x² + 2x)
4x² + x - x² - 2x
4x² - x² + x - 2x
3x² -x
12). (6x - 3) - (11x -8)
= 6x - 3 - 11x + 8
= 6x - 11x - 3 + 8
= -5x + 5
Which polygons are similar?
1
2
3
4
Triangle 1 and 4 are similar using AAA
number one and four.......