Answer:
4.5.
Step-by-step explanation:
f(x) = −6 / x^2
f(1) = -6 / (1)^2 = -6 / 1 = -6.
f(2) = -6 / (2)^2 = -6 / 4 = -3 / 2 = -1.5.
Now, you have two sets of coordinates: (1, -6), and (2, -1.5).
You need to find the slope, which is the average rate of change.
(-1.5 - (-6)) / (2 - 1) = (-1.5 + 6) / 1 = -1.5 + 6 = 4.5
Hope this helps!
The average rate of change of the function from x=1 to x=2 is 4.5
The average rate of change of a function is given by:
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Hence, the average rate of change of the function from x=1 to x=2. f(x)=−6/x² is:
f(2) = -6/2² = -1.5
f(1) = -6/1² = -6
[tex]Average\ rate\ of\ change=\frac{f(2)-f(1)}{2-1}=\frac{-1.5-(-6)}{2-1}=4.5[/tex]
Hence the average rate of change of the function from x=1 to x=2 is 4.5
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WILL MAKE BRAINLIST. - - - If a golden rectangle has a width of 9 cm, what is its length?
Step-by-step explanation:
a = 14.56231 cm
b(width) = 9 cm
a+b = 23.56231 cm
A(area) = 343.1215 cm
Sorry if this doesnt help
Answer:
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
Step-by-step explanation:
In a golden rectangle, the width is a and the length is a + b.
The proportion of the lengths of the sides is:
(a + b)/a = a/b
Here, the width is 9 cm, so we have a = 9 cm.
(9 + b)/9 = 9/b
(9 + b)b = 81
b^2 + 9b - 81 = 0
b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)
b = (-9 +/- sqrt(81 + 324)/2
b = (-9 +/- sqrt(405)/2
b = -9/2 +/- 9sqrt(5)/2
Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2
Length = a + b = 9/2 +/- 9sqrt(5)/2
Since the length of a side of a rectangle cannot be negative, we discard the negative answer.
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
A person stands 15 ft from an elephant. Determine how tall the elephant is in feet, the given diagram.
Answer:
The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
Step-by-step explanation:
It is given that,
Distance between a person and an elephant is 15 ft
The angle of elevation of the elephant is 30 degrees.
We need to find the height of the elephant. For this let us consider that height is h. So,
[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]
So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
Suppose we want to test the claim that the majority of adults are in favor of raising the vote age to 21. Is the hypothesis test left tailed, right tailed or two tailed
Answer:
The hypothesis test is right-tailed.
Step-by-step explanation:
We are given that we want to test the claim that the majority of adults are in favor of raising the voting age to 21.
Let p = proportion of adults who are in favor of raising the voting age to 21
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%
Alternate Hypothesis, [tex]H_A[/tex] : p > 50%
As we know that the majority is there when we have more 50% chance of happening of that event.
Here, the null hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is less or equal to 50%.
On the other hand, the alternate hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is more than 50%.
This shows that our hypothesis test is right-tailed because in the alternate hypothesis, the greater than sign is included.
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
The function A(b) relates the area of a trapezoid with a given height of 10 and
one base length of 7 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 10.57?
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. B(a) = -7
B. B(a) = 9, -5
Answer:
[tex]B(a)=\frac{a}{5} -7[/tex]
Step-by-step explanation:
The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.
y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),
y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )
Now switch the positions of y and b -
b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,
[tex]y+7=\frac{a}{5}[/tex],
[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]
Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7
Find the length of BC
Answer:
The answer is option AStep-by-step explanation:
To find the length of BC we use tan
tan ∅ = opposite / adjacent
From the question
AC is the opposite
BC is the adjacent
So we have
tan 61 = AC / BC
tan 61 = 47/BC
BC = 47/tan 61
BC = 26.05Hope this helps you
The mean rate for cable with Internet from a sample of households was $106.50 per month with a standard deviation of $3.85 per month. Assuming the data set has a normal distribution, estimate the percent of households with rates from $100 to $115.
Answer:
The percent of households with rates from $100 to $115. is [tex]P(100 < x < 115) =[/tex]94.1%
Step-by-step explanation:
From the question we are told that
The mean rate is [tex]\mu =[/tex]$ 106.50 per month
The standard deviation is [tex]\sigma =[/tex]$3.85
Let the lower rate be [tex]a =[/tex]$100
Let the higher rate be [tex]b =[/tex]$ 115
Assumed from the question that the data set is normally
The estimate of the percent of households with rates from $100 to $115. is mathematically represented as
[tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]
here x is a random value rate which lies between the higher rate and the lower rate so
[tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]
[tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]
Where
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where z is the standardized value of x
So
[tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]
[tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]
Now from the z table we obtain that
[tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]
[tex]P(100 < x < 115) = 0.941[/tex]
[tex]P(100 < x < 115) =[/tex]94.1%
The population of a city can be modeled with a linear equation Y equals -80 X +3450 where X is the number of years after 2000 and why is the cities population by the description of the cities population based on equation
Answer:
retype that im not understanding .
Step-by-step explanation:
Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
Answer:
D.
m = 2 = figures/month
b = 20 = # of action figures
Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 66 times and record the outcomes. They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level. (a) The null and alternative hypotheses are: H0: The die has the uniform distribution. Ha: The die does not have the uniform distribution. (b) χ20=15.091. (c) χ20.05=11.070. (d) What conclusions can be made? Select all that apply. Select all that apply: We should reject H0. We should not reject H0. At the 5% significance level, there is sufficient evidence to conclude that the die is not fair. At the 5% significance level, there is not enough evidence to conclude that the die is not fair.
Answer:
We should reject H0
At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The critical value is 15.091 and test statistic is 11.070. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.
Daniels freezer is set to 0degrees Fahrenheit he places a load of bread that was at a temperature of 78 degrees Fahrenheit in the freezer the bread cooled at a rate of 11 degrees Fahrenheit per hour write and graph an equation that models the temperature t of the bread
Answer:
it took 7 hours for the bread to drop at a constent rate
Step-by-step explanation:
What is the value of x?
Answer:
13=x
Step-by-step explanation:
Since BE is a bisector
ABE = EBC
2x+20 = 4x-6
Subtract 2x from each side
2x+20-2x =4x-6-2x
20 = 2x-6
Add 6 from each side
20+6 = 2x-6+6
26 = 2x
Divide each side by 2
26/2 = 2x/2
13=x
Answer:
x = 13
Step-by-step explanation:
The angle bisector theorem means that m<ABE = m<EBC. Now that we know they are equal, we can set the equations to each other and solve for x.
2x + 20 = 4x - 6
26 = 2x
13 = x
So the value of x is 13.
Cheers.
For each of the following determine a unit rate using the information given. Show the division that leads to your answer. Use appropriate units. All rates will be whole numbers. At a theatre, Mia paid $35 for five tickets
Answer:
Step-by-step explanation:
cool
The prices for a loaf of bread and a gallon of milk for two supermarkets are shown below. Sue needs to buy bread and milk for her church picnic. At Supermarket A, she would pay $137.24. At Supermarket B, she would pay $140.04. Which of the following system of equations represents this situation?
Answer:
B. 3.19b + 4.59m = 137.24
3.49b + 4.39m = $140.04
Step-by-step explanation:
A B
Bread $3.19 $3.49
Milk $4.59 $4.39
Sue paid $137.24 in supermarket A
Sue paid $140.04 in supermarket B
Let
Price of bread A=$3.19
Price of bread B=$3.49
Price of milk A=$4.59
Price of milk B=$4.39
Quantity of Bread=b
Quantity of Milk=m
Pb=price of bread
Pm=price of milk
Qb=Quantity of bread
Qm=Quantity of milk
For each supermarket
Supermarket A Equation
PbQb + PmQm =$137.24
3.19b+ 4.59m = 137.24
Supermarket B Equation
PbQb + PmQm=$140.04
3.49b + 4.39m = $140.04
Combining both equations
3.19b + 4.59m = 137.24
3.49b + 4.39m = $140.04
Maricopa's Success scholarship fund receives a gift of $ 230000. The money is invested in stocks, bonds, and CDs. CDs pay 2.5 % interest, bonds pay 2.2 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 12095 , how much was invested in each account?
Maricopa's Success scholarship fund receives a gift of $ 170000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25 % interest, bonds pay 4.4 % interest, and stocks pay 11.4 % interest. Maricopa Success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 10055 , how much was invested in each account?
--------------------------
Equations:
s + b + C = 170000
11.4s + 4.4b + 3.25C = 1005500
b = C + 25000
-----------------------
Rearrange::
s + b + C = 170000
1140s + 440b + 325C = 100550000
0 + b - C = 25000
--------------------------
Use any method you know to solve the system to get:
stocks = 45000
bonds = 75000
CD's = 50000
----------------
Cheers,
Stan H.
--------------
Maricopa Success invested $
in stocks.
Maricopa Success invested $
in bonds.
Maricopa Success invested $
--------------
Hope this helps!
Brainliest would be great!
--------------
With all care,
07x12!
.19 OF JOE'S SALARY GOES FOR TAXES. WHAT PERCENT OF HIS SALARY DOES THIS REPRESENT?
━━━━━━━☆☆━━━━━━━
▹ Answer
19%
▹ Step-by-Step Explanation
0.19 → hundreth's place.
19/100 (since the denominator is 100, that represents 100% while 19 represents 19%)
Final Answer - 19%
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
This represent 19% of his salary.
Given, Joe's salary goes for tax is 0.19.
We have to represent the value in percent.
Here 0.19 can be written in fraction form as,
[tex]\dfrac{19}{100}[/tex]
It means 19 part from 100 part goes for taxes, means 19% of the Joe's salary goes for taxes.
Hence this represent 19% of his salary.
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https://brainly.com/question/8011401
Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
u = -4 A = 1 0 3
-5 -2 -1 -4
3 3 -3 0
1 -1 3 6
A) In Col A, not in Nul A
B) Not in Col A, not in Nul A
C) In Col A and in NulA
D) Not in Col in Nul A
Answer: d) Not in Col in Nul A
Step-by-step explanation: The definition of Column Space of an m x n matrix A is the set of all possible combinations of the columns of A. It is denoted by col A. To determine if a vector is a column space, solve the matrix equation:
A.x = b or, in this case, [tex]A.x=u[/tex].
To solve, first write the augmented matrix of the system:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\-2&-1&-4&-5\\3&-3&0&3\\-1&3&6&1\end{array}\right][/tex]
Now, find the row-echelon form of matrix A:
1) Multiply 1st row by 2 and add 2nd row;
2) Multiply 1st row by -3 and add 3rd row;
3) MUltiply 1st row by 1 and add 4th row;
4) MUltiply 2nd row by -1;
5) Multiply 2nd row by 3 and add 3rd row;
6) Multiply 2nd row by -3 and add 4th row;
7) Divide 3rd row by -15;
8) Multiply 3rd row by -15 and add 4th row;
The echelon form matrix will be:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\0&1&-2&13\\0&0&1&-\frac{51}{15}\\0&0&0&-13 \end{array}\right][/tex]
Which gives a system with impossible solutions.
But if [tex]A.x=0[/tex], there would be a solution.
Null Space of an m x n matrix is a set of all solutions to [tex]A.x=0[/tex], so vector u is a null space of A, denoted by null (A)
N
5. Use AABC to find the value of sin B.
A 7
B
25
B 24
C
24
А
C7
25
D 24
*see the attachment below for the missing figure
Answer:
[tex] sin B = \frac{24}{25} [/tex]
Step-by-step explanation:
Given a right angled triangle, ∆ABC
AB = 25
BC = 7
AC = 24
<ACB = 90°
Required:
Value of Sin B
Solution:
Using trigonometric ratio formula,
[tex] sin B = \frac{opposite}{hypotenuse} [/tex]
Opposite = AC = 24 (the side opposite to <B)
Hypotenuse = AB = 25 (the longest side facing the right angle)
[tex] sin B = \frac{24}{25} [/tex]
Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.
A. yp(x)=Ax2+Bx+C,
B. yp(x)=Ae2x,
C.yp(x)=Acos2x+Bsin2x,
D. yp(x)=(Ax+B)cos2x+(Cx+D)sin2x
E. yp(x)=Axe2x,
F.yp(x)=e3x(Acos2x+Bsin2x)
1. d2ydx2+4y=x−x220
2. d2ydx2+6dydx+8y=e2x
3. y′′+4y′+20y=−3sin2x
4. y′′−2y′−15y=3xcos2x
Answer and Step-by-step explanation:
1. Data provided
[tex]\frac{d^2y}{dx^2} + 4y = x - x^2 + 20\\\\ \frac{d^2y}{dx^2} + 4y = - x^2 + x + 20[/tex]
Now as a non homogeneous part which is
[tex]- x^2 + x + 20[/tex] let us assume the computation is
[tex]y_p(x) = Ax^2 + Bx + C[/tex]
2. Data provided
[tex]\frac{ d^2y}{dx^2} + \frac{6dy}{dx} + 8y = e^{2x}[/tex]
As a non homogeneous part is [tex]e^2x[/tex] , let us assume the computation is
[tex]y_p(x) = Ae^{2x}[/tex]
3. Data provided
[tex]y'' + 4y' + 20y = -3sin2x[/tex]
As a non homogeneous part −3sin(2x), let us assume the computation is
[tex]y_p(x) = Acos(2x) + Bsin(2x)[/tex]
4. Data provided
[tex]y'' - 2y' - 15y = 3xcos(2x)[/tex]
As a non homogeneous part 3xcos(2x), let us assume the computation is
[tex]y_p(x) = (Ax+B)cos2x+(Cx+D)sin2x[/tex]
Help please and thank you
Answer:
1
Cans 4cans 8 cans 12 cans
Cost $2.25 $4.5 $6.75
2
Ice Cream 180 q 360 q 540 q 720q 900q 1080 q
Hours 2 hours 4 hours 6 hours 8 hours 10 hours 12 hours
***q = quarts
3
Distance 650 miles 1300 miles 1950 miles
Hours 3 hours 6 hours 9 hours
Answer:
Question 1 - 8 cans = $4.50, 12 cans = $10.13
Question 2 - 4 hours = 360 quarts, 6 hours = 540 quarts, 8 hours = 720 quarts, 12 hours = 1,170
Question 3 - 1,950 miles in 9 hours
Hope this helps :)
If the sampled population is finite and at least _____ times larger than the sample size, we treat the population as infinite.
Answer:
The answer is "20".
Step-by-step explanation:
It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.
Its sampling distribution of the "x bar" should also be naturally independent of the random sample, that is usually distributed. We consider the population as endless if the sampling size is at least 20 times greater than the sample size.Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 36 − x2 , y = 0, x = 2, x = 4; about the x-axis
Answer: V = 193.25π
Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:
V = [tex]\pi\int\limits^a_b {[f(x)]^{2}} \, dx[/tex]
f(x) is the area is the function that rotated forms the solid.
For f(x)=y= [tex]\frac{5}{36}-x^{2}[/tex] and solid delimited by x = 2 and x = 4:
V = [tex]\pi\int\limits^4_2 {(\frac{5}{36}-x^{2} )^{2}} \, dx[/tex]
V = [tex]\pi\int\limits^4_2 {(\frac{25}{1296}-\frac{10x^{2}}{36}+x^{4}) } \, dx[/tex]
V = [tex]\pi(\frac{25.4}{1296}-\frac{10.4^{3}}{108}+\frac{4^{5}}{5}-\frac{25.2}{1296}+\frac{10.2^{3}}{108}-\frac{2^{5}}{5} )[/tex]
V = [tex]\pi(\frac{50}{1296}-\frac{560}{1296}+\frac{992}{1296} )[/tex]
V = 193.25π
The volume of a solid formed by y = [tex]\frac{5}{36} - x^{2}[/tex] and delimited by x = 2 and x = 4
is 193.25π cubic units.
pls help me with all 3 questions! correct answer will get brainliest and a kiss...
Answer:
1.union = {20 21 22 23 25 27 29}
2. intersection = {5 14 22}
3.1/3
Step-by-step explanation:
1. union U of sets a nd b ={20 21 22 23 25 27 29}
2. intersection n of sets a nd b = {5 14 22}
3. probability = one item / total
= 1/3
1.
A. {22, 25, 27, 29}
B. {20, 21, 22, 23}
Answer: A∪B = {22, 25, 27, 29, 20, 21, 23}
2.
A. {1, 5, 10, 14, 22}
B. {5, 14, 20, 22, 27}
Answer: A∩B = {5, 14, 22}
3.
A. {1, 5, 10, 14, 22}
B. {5, 14, 20, 22, 27}
Answer: The three items that are intersecting each have a 1/3 chance of being chosen.
20 points! Brainliest will be given!
Answer:
I always factor out the -1 so my leading coefficient is 1
Step-by-step explanation:
-x^2 + 10x -24
I always factor out the -1 so my leading coefficient is 1
-1 ( x^2 -10x +24)
Then what 2 terms multiply to 24 and add to -10
-6*-4 = 24
-6+-4 = -10
-1( x-6)(x-4)
If y ∝ 1∕x and y = –2 when x = 14, find the equation that connects x and y.
Question 11 options:
A)
y = –28x
B)
y = –7∕x
C)
y = –28∕x
D)
y = –7x
C. y= -28/x
y=k/x
cross multiply
k= y×x
k = -2×14
k = -28
y = -28/x [ equation connecting x and y]
The equation that connects x and y si y = –28∕x.
The correct option is (C)
What is proportionality constant?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant. The proportionality constant's value is determined by the proportion between the two specified quantities.
For example, The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
We have given that
y ∝ 1∕x
To remove proportional sign we use proportionality constant
y=k/x
Now, cross multiply
k= y×x
k = -2×14
k = -28
y = -28/x
Hence, the equation is y = -28/x .
Learn more about proportionality here:
https://brainly.com/question/8598338
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Savita was given a set of 250 cherries and Gail was given a set
of 350 cherries. Both were also given a set of small plastic bags.
Savita had to pack 8 cherries in a bag and Gail had to pack 12
cherries in a bag. Explain how you know who will have more
bags of cherries at the end.
Answer:
Savita will have more bags
Step-by-step explanation:
Savita: 250 cherries, 8 cherries per bag
Gail: 350 cherries, 12 cherries per bag
Savita: 250/8 = 31.25 bags
Gail: 350/12 = 29.17 bags
Savita will have more bags since 31.25 > 29.17
Answer:
Savita will have more bags
Step-by-step explanation:
Savita has 250 cherries and 8 cherries per bag
Gail has 350 cherries and 12 cherries per bag
Savita
=250/8 = 31.25 bags
Gail
=350/12 = 29.17 bags
therefore Savita will have more bags since 31.25 is more than Gail with 29.17 bags
A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured.
Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6
Required:
a. Estimate the model: Height = β0 + β1Fertilizer + ε.
b. Does the y-intercept make practical sense?
c. Use the estimated model to predict, after four months, the height of a tomato plant which received 3.0 ounces of fertilizer.
Answer: hello your table is incomplete here is the complete table
Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6
4.0 44.5
3.6 29.7
0.6 21.1
1.6 25.4
2.5 29.6
4.5 27.6
3.6 32.6
2.0 33.5
0.0 22.5
2.5 27.6
3.1 46.4
Answer : a)Height = 18.639 + 5.208 * fertilizer
b) The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
c) 34.263
Step-by-step explanation:
A) Estimating the model
Height = β0 + β1 FERTILIZER + ∈
β0 = 18.639
β1 = 5.208
hence
Height = 18.639 + 5.208 * fertilizer ( using excel )
B) The y- intercept
The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
C ) using the estimated model to predict after four months
the model = 18.639 + 5.208 * fertilizer
fertilizer ounce given = 3
therefore height of tomato plant after 4 months that received 3 ounces of fertilizer = 18.639 + 5.208 * 3 = 34.263
A pyramid shaped building is 311 feet tall and has a square base with sides of 619 ft. The sides of the building are made from reflective glass. what is the surface area of the reflective glass
Answer:
Surface area of the reflective glass is 543234.4 square feet.
Step-by-step explanation:
Given that: height = 311 feet, sides of square base = 619 feet.
To determine the slant height, we have;
[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]
= 96721 + 95790.25
= 192511.25
⇒ l = [tex]\sqrt{192511.25}[/tex]
= 438.761
The slant height, l is 438.8 feet.
Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height
area = [tex]\frac{1}{2}[/tex] × 619 × 438.8
= 135808.6
= 135808.6 square feet
Since the pyramid has four reflective surfaces,
surface area of the reflective glass = 4 × 135808.6
= 543234.4 square feet
An aquarium is to be built to hold 60 m3of volume. The base is to be made of slate and the sides aremade of glass, and it has no top. If stone costs $120/m2and glass costs $30/m2, find the dimensions which willminimize the cost of building the aquarium, and find the minimum cost.
Answer:
Aquarium dimensions:
x = 3,106 m
h = 6,22 m
C(min) = 1277,62 $
Step-by-step explanation: (INCOMPLETE QUESTION)
We have to assume:
The shape of the aquarium (square base)
Let´s call "x" the side of the base, then h ( the heigh)
V(a) = x²*h h = V(a)/x²
Cost of Aquarium C(a) = cost of the base (in stones) + 4* cost of one side (in glass)
C(a) = Area of the base *120 + 4*Area of one side*30
Area of the base is x²
Area of one side is x*h or x*V(a)/x²
Area of one side is V(a)/x
C(x) = 120*x² + 4*30*60/x
C(x) = 120*x² + 7200/x
Taking derivatives on both sides of the equation we get
C´(x) = 2*120*x - 7200/x²
C´(x) = 0 means 240 *x - 7200/x² = 0
240*x³ - 7200 = 0
x³ = 7200/240
x = 3,106 m and h = 60 /x² h = 6,22 m
and C (min) = 120*(3,106)³ - 7200 / 3,106
C(min) = 3595,72 - 2318,1
C(min) = 1277,62
Out of 600 people sampled, 66 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.
Required:
Use a 90% confidence level, and give your answers as decimals, to three places.
Answer:
11% of the Total the entire voting population
Step-by-step explanation:
Let's bear in mind that the total number of sample candidates is equal to 600.
But out of 600 only 66 preffered candidate A.
The proportion of sampled people to that prefer candidate A to the total number of people is 66/600
= 11/100
In percentage
=11/100 *100/1 =1100/100
=11% of the entire voting population