The volume of the tree trunk increases 52.64% in one year.
Given,
The height of a tree trunk = 100 inches
The diameter of a tree trunk = 5 inches
Diameter increases 1 inch per year
Height increases 6 inches per year
We have to find the increase in its volume.
Consider the trunk as a circular cylinder.
Volume of circular cylinder = πr²h
Radius, r = 5/2
Height, h = 100
Initial Volume = πr²h
Volume = π × (5/2)² × 100 = π × 6.25 × 100 = 1963.50 cubic inches
After one year
Diameter = 6
Height = 106
Increased Volume = πr²h
Volume = π × (6/2)² × 100 = π × 9 × 106 = 2997.08 cubic inches
The rate of increase in volume = (Increased volume × 100) ÷ Initial volume
= (2997.08 × 100) ÷ 1963.50 = 152.64
That is,
The volume of the tree trunk increases 52.64% in one year.
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please slove this for me-3(x+1)<15
-3(x+1)<15
Divide both-side of the inequality by -3
(x + 1) > -5
subtract 1 from both-side of the inequality
x > -5 - 1
x > -6
Answer:
Step-by-step explanation:
-3(x+1)<15
Divide the inequality by -3, so we need to change the sides of the less than into greater than
x+1 > -5
x > -5 - 1
x > -6
1,857.205 round each number to the place of the underlined digit.0 is the underlined digit
Answer:
1,857.21
Explanation:
In the number: 1,857.205
The digit after 0 is 5.
Since it is a number between 5 and 9, we round up to obtain:
[tex]1,857.205\approx1,857.21\text{ (to the nearest hundredth)}[/tex]
twice a number increased by twenty is at least eighty-five. select all possible value of the number.
31
35
32
30
33
40
20
34
The number when increased by twenty is at least 85, the possible values of the numbers for this are: 35, 33, 40 and 34.
Given, according to the statement in the question, frame the equation:
2x+20 ≥ 85
⇒ 2x + 20 ≥ 85
⇒ 2x ≥ 85 - 20
⇒ 2x ≥ 65
⇒ x ≥ 65/2
⇒ x ≥ 32.5
hence the numbers greater than or equal to 32.5 are 35, 33, 40 and 34.
Hence the possible values of the number are 35, 33, 40 and 34.
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Dog Owners5. A city council wants to know if residents would like a dogpark. They sent a survey to every household in the city.The results of those who responded are shown in the tableat the rightNumbexof Dogs inHouseholdNumber ofHouseholds0513a What is an appropriate first step in finding the experimentalprobability that a household has 2 or more dogs?12182 or more129Find the product of the number of households withone dog and the number with two or more dogs.Find the difference of the number of households with twoor more dogs and the number with no dogs.© Find the sum of the number of households for each category.Find the difference of the number of households with no dogsand the number with one dog or more.b. What is the experimental probability that a householdhas 2 or more dogs?
Given:
A table represents a survey to know if residents would like a dog.
a) What is an appropriate first step in finding the experimental probability that a household has 2 or more dogs?
The first step is to find the total households
So, the answer will be option C
Find the sum of the number of households for each category.
b) What is the experimental probability that a household has 2 or more dogs?
First, the total number of households = 513 + 218 + 129 = 860
And the number of households has 2 or more dogs = 129
So, the probability = 129/860 = 0.15 = 15%
So, the answer will be 15%
Solve the following inequality algebraically. [tex] |x - 1| \leqslant 13[/tex]
lx-1 l ≤ 13
There are 2 solutions:
x-1 ≤ 13
and
x-1 ≥ -13
Solve each one
x-1 ≤ 13
add 1 to both sides of the equation
x-1+1≤ 13+1
x ≤ 14
x-1 ≥ -13
Add 1 to both sides:
x-1+1 ≥-13+1
x ≥ -12
-12 ≤ x ≤ 14
six men can complete a certain work in 20 days .how many men are required to complete the same work in 12 days ?
6 men complete the work in 20 days.
In 1 day it takes:
6 x20 = 120 men
You need to do the same work done in 20 days, in one day. (more manpower)
So, to finish the work in 12 days:
120 men / 12 days = 10 men
You will purchase snacks for the painting class. You have abudget of $40. You want to buy fruit and granola bars. Fruit costs $4 perpound, and the granola bars are $1 each. You need at least 20 granolabars. What combinations of fruit and granola bars can you buy?My variables- f-fruits g-granola
Budget: $40
Fruit: $4/pound
Granola bars: $1 each
At least 20 granolas
Let's call
f: number of pounds of fruit
g: number of granola bars
Therefore
The total cost of fruit is given by: $4 · f
The total cost of granola is given by: $1 · g
The total cost of everything is given by: $4 · f + $1 · g
Since budget: $40 then
$4 · f + $1 · g = $40
4f + g = 40
g > 20 means we have at least 20 granolas
4f + g > 20 means that we have at least 20 granolas, that cost $20, since 4f + g = 40 and 40 > 20
Find the minimum value of
C = 6x + 3y
Subject to the following constraints:
x > 1
y ≥ 1
4x + 2y < 32
2x + 8y < 56
Answer:
9
Step-by-step explanation:
You want the minimum value of objective function C=6x+3y, given the constraints x>1, y≥1, 4x+2y<32, and 2x+8y<56.
MinimumThe objective function has positive coefficients for both x and y, so it will be minimized when x and y are at their minimum values. The constraints tell you these minimum values are x=1 and y=1, so the minimum value of C is ...
C = 6(1) +3(1) = 9
The minimum value of C is 9.
__
Additional comment
The value of x cannot actually be 1, so the value of C cannot actually be 9. However x may be arbitrarily close to 1, so C may be arbitrarily close to 9.
C = 6x +3y ⇒ x = (C -3y)/6
The x-constraint requires ...
x > 1
(C -3y)/6 > 1
C -3y > 6 . . . . . . multiply by 6
C > 6 +3y . . . . . . add 3y
The minimum value of y is exactly 1, so we have ...
C > 6 +3(1)
C > 9
2) The Allen's rectangular backyard has a
perimeter of 144 feet. If the backyard is 40
feet wide, what is the area of their yard?
Answer:
1280 ft²
Step-by-step explanation:
Perimeter is the addition of all sides of the shape added together. Therefore, if the backyard is the rectangular shape you know that two of the sides are 40 feet wide. By adding both sides you get a total of 80 feet. Subtract the total from the perimeter in order to get the total of the unknown sides. 144 minus 80 is equivalent to 64. Now that you have the total of the unknown sides, divide by two in order to get the single unknown length. So, 64 divided by 2 is equal to 32. The area is the multiplication of two sides with quadrilaterals. Therefore, 40 times 32 equals an area of 1280 feet squared.
Last year Collin's salary was $45,000. Because of furlough days, this year his salary was $30,000. Find the percent decrease.Round to the the nearest tenth of a percent
ANSWER:
33.3%
STEP-BY-STEP EXPLANATION:
We can calculate the value of the percentage starting from the following equation:
[tex]45000-x\cdot45000=30000[/tex]We solve for x:
[tex]\begin{gathered} -x\cdot45000=30000-45000 \\ x=\frac{15000}{45000} \\ x=\frac{1}{3}=0.333 \\ \text{ in the percent form:} \\ 0.333=33.3\text{\%} \end{gathered}[/tex]The percentage that decreased was 33.3%
FV - OVSolve for FV in the scientific formula A =Twhere FV and OV are variables.FV =Pls help
FV=OV +TA
1) To solve for a variable means let that variable isolated on one side of the equation.
[tex]A=\frac{FV-OV}{T}[/tex]2) Since we want to solve for FV, let's multiply it crossed like this
[tex]\begin{gathered} TA=FV-OV \\ -FV+TA-TA=-OV-TA \\ -FV=-OV-TA \\ FV=OV\text{ +TA} \end{gathered}[/tex]3) So now we can solve for FV, all that's left are the figures for OV and TA.
A school offers band and chorus classes. The table shows the percents of the 1200 students in the school who are enrolled in band, chorus, or neither class. How many students are enrolled in both classes?
Class Enrollment
Band 34%
Chorus 28%
Neither 42%
168 students are enrolled in both classes.
This is a problem from set theory. We can solve this problem by following a few steps easily.
First of all, we have to calculate the students present in both classes.
Student present in both classes = the total student - the student not enrolled in both classes.
So the percentage of the students enrolled in both classes or any of one class is ( 100% - 42% ) = 58%.
Now, the students only enrolled in chorus class is ( 58% - 34%) = 24%
So, the students who joined both classes is ( 28%- 24%)= 4%
The total student is 1200, then 4% of the total student is
( 1200 × 14 )/100 = 168 students.
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Write the point slope form of the line satisfying the given conditions. Then use the point slope form of the equation to write the slope intercept form of the equation. Slope=7Passing through (-6,1)
Ok, so
The point slope form of the line is given by the following formula:
[tex](y-y_1)=m(x-x_1)[/tex]Where
[tex](x_1,y_1)[/tex]Is a point of the line, and m is the slope.
If we replace our values:
Slope = 7
Point = (-6, 1)
We obtain that the equation is:
[tex]\begin{gathered} (y-1)=7(x-(-6)) \\ (y-1)=7(x+6) \end{gathered}[/tex]To find the slope intercept form of the equation, we distribute in the brackets:
[tex]\begin{gathered} y-1=7x+42 \\ y=7x+43 \end{gathered}[/tex]And the equation of our line in the slope intercept form will be:
y=7x+43
— 3х + 2 = -4х + 4 need help
Given the following equation:
[tex]-3x+2=-4x+4[/tex]You need to solve for "x" in order to find its value and solve the equation. To do this, you can follow the steps shown below:
1. You need to apply the Subtraction property of equality by subtracting 2 from both sides of the equation:
[tex]\begin{gathered} -3x+2-(2)=-4x+4-(2) \\ -3x=-4x+2 \end{gathered}[/tex]2. Now you can apply the Additio property of equality by adding "4x" to both sides of the equation:
[tex]\begin{gathered} -3x+(4x)=-4x+2+(4x) \\ x=2 \end{gathered}[/tex]Therefore, you get that the solution is:
[tex]x=2[/tex]A textbook store sold a combined total of 217 sociology and history textbooks in a week. The number of history textbooks sold was 77 less than the number of
sociology textbooks sold. How many textbooks of each type were sold?
Answer:
there were 246 chemistry textbooks and 169 psychology textbooks sold
Step-by-step explanation:
Let
c = the number of chemistry textbooks sold
p = the number of psychology textbooks sold
a textbook store sold a combined total 415 chemistry and psychology textbooks in a week
c + p = 415
the number of chemistry textbooks sold was 77 more than the number of psychology textbooks sold
c = 77 + p
by solving the system of equations
c + p = 415
c = 77 + p
we find
c = 246 chemistry textbooks
p = 169 psychology textbooks
There are two box containing only yellow and black pens
SOLUTION; Concept
Step1: Identify the giving information in the question
BOX A contains
[tex]\begin{gathered} 9\text{ yellow pens} \\ 6\text{ Black pens } \end{gathered}[/tex]BOX B contains
[tex]\begin{gathered} 9\text{ yellow pens } \\ 11\text{ black pens} \end{gathered}[/tex]Step2: Find the probability of each event
Event 1: Choosing a green pen from the Box B
[tex]\begin{gathered} \text{ Since there is no gr}een\text{ pen in the box, then probability of choosing a gr}en\text{ box in Box B is 0} \\ \text{then probability of choosing a gr}en\text{ box in Box B is 0} \\ Pr(E1)=0 \end{gathered}[/tex]Event 2: Choosing a black pen from the Box B
[tex]P(E2)=\frac{11}{9+11}=\frac{11}{20}=0.55[/tex]Event 3: Choosing a yellow or black pen from the Box A
Since Box A contains only a yellow or black pen then the probability is
[tex]Pr(E3)=1[/tex]Event 4: Choosing a yellow pen from box A
Since there are 9 yellow pens in box A, the probability of choosing the yellow pen is
[tex]Pr(E4)=\frac{9}{9+6}=\frac{9}{15}=0.6[/tex]Probability describes the likelihood of the event.
Hence From least likely to most likely the occurrence of the event is arranged as follows according to the probability of each event
[tex]\text{Event }1\rightarrow\text{ Event 2}\rightarrow\text{ Event 4}\rightarrow\text{ Event 3}[/tex]
What is the P(A and B) if P(A) = 1/2 and P(B) = 2/7, where A and B are independent events?5/81/71/121/2
EXPLANATION:
To calculate the number of independent events that occur, the product of the probabilities of the individual events occurring must be calculated.
Therefore if A and B are independent events then:
P (A and B) = P (A) • P (B)
The exercise is as follows:
[tex]\begin{gathered} \frac{1}{2}\times\frac{2}{7}=\frac{2}{14};\text{ Now }we\text{ must take }square\text{ r}oot; \\ \frac{2}{14}=\frac{1}{7} \\ \text{ANSWER: }\frac{1}{7} \end{gathered}[/tex]NOTE:
To obtain the product of two fractions, the numerators must be multiplied with each other and the denominators must also be multiplied with each other.
1118 11 + 600-1110
[tex]12 \times (5 + 4)[/tex]
Answer:
111811 + 600 - 1110
111871 - 1110
= 110761
12 × (5+4)
60+4
= 64
Mary’s credit card company charges 16% interest on her outstanding credit card balance each month. Her minimum payment is $20 each month. Mary’s credit card bill is $70 in January. Mary only pays the minimum amount each month, and she does not spend any additional money on her credit card. How long, in months, will it take her to pay off her bill from January?
Answer:
Step-by-step explanation:
ionoknionoinponpoihj
Answer:
Step-by-step explanation:
tipptrptprprprptprtprptpprtprtpprtprptprtprptprtprptr
Solve 5 and 6
for 40 POINTS
Answer:
A= 184.4 yards
Step-by-step explanation:
couldnt figure out b
20 pts, precalc, see attach
If f (x) = 3x2 + 5x − 4, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
The numeric value for the given expression is as follows:
[tex]\frac{j(x + h) - j(x)}{h} = \frac{4^{x - 2}(4^h - 1)}{h}[/tex]
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.
In the context of this problem, the function j(x) is given as follows:
[tex]j(x) = 4^{x - 2}[/tex]
At x = x + h, the numeric value of the function is found replacing the lone instance of x by x + h as follows:
[tex]j(x + h) = 4^{x + h - 2}[/tex]
For the fraction, the subtraction at the numerator is given as follows, applying properties of exponents:
[tex]j(x + h) - j(x) = 4^{x + h - 2} - 4^{x - 2} = 4^{x - 2}(4^h - 1)[/tex]
As the x - 2 term is common to both exponents.
Just dividing by h, the numeric value of the entire expression is given as follows:
[tex]\frac{j(x + h) - j(x)}{h} = \frac{4^{x - 2}(4^h - 1)}{h}[/tex]
Which means that the third option is correct.
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Explain why the volume of these two stacks of quarters are equal? Use Cavaliens principle in your explanation (If you need to)
Given the word problem, we can deduce the following information:
1. Two stacks of 18 pennies each are shown.
To determine if the volumes of the given stacks of quarters are equal, we note that Cavelieri's Principle states:
The volumes of two solids are equal if the areas of the corresponding sections drawn parallel to some given plane are equal.
Since each penny in both stacks has the same base area and has the same number of pennies. Therefore, the volumes of the given stacks are equal.
Find the average rate of change of f(x) = - 2x ^ 2 - x from x = 1 to x = 6 . Simplify your answer as much as possible .
The average rate of change of a function in the interval [a,b] is given by:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]In this case we have that a=1 and b=6; plugging these values in the formula above we have:
[tex]\begin{gathered} \frac{-2(6)^2-6-(-2(1)^2-1)}{6-1}=\frac{-2(36)-6-(-2(1)-1)}{5} \\ =\frac{-72-6-(-2-1)}{5} \\ =\frac{-78-(-3)}{5} \\ =\frac{-78+3}{5} \\ =\frac{-75}{5} \\ =-15 \end{gathered}[/tex]Therefore, the average rate of change in the interval is -15
Help me pretty please I need help
Answer:i have no idea good luck
Step-by-step explanation:
Answer:
4,3 DONT BE MAD IF IM WRONG
On average, Peter goes through three fish hooks in order to catch 7 fish. How many hooks can he expect to use if he needs to catch 189 fish?
By solving a proportional relation, we conclude that he needs 81 hooks to catch 189 fish.
How many hooks can he expect to use if he needs to catch 189 fish?We assume there is a proportional relationship of the form:
F = k*H
where:
F = number of fish.k = constant of proportionality.H = number of hooks.We know that with 3 hooks he catches 7 fish, then we can replace that:
7= k*3
7/3 = k
So the proportional relation is:
y = (7/3)*x
Then if he wants to get 189 fish we can write:
189 = (7/3)*x
And solve this for x:
189*(3/7) = x =81
He will need 81 hooks.
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HELP PLEASE ASAP!!!!!!!!!!
Answer:
a b
Step-by-step explanation:websites and etc helped.
the variable y varies directly as x. when x =20, y= 12 what is the value of y when x = 15a:7b:9c:18d:25
To direct variations use a rule of three, as follow:
[tex]\begin{gathered} \frac{?}{12}=\frac{15}{20} \\ \\ ?=12*\frac{15}{20} \\ \\ ?=\frac{180}{20} \\ \\ ?=9 \end{gathered}[/tex]Then, when x=15, y is 9Answer: B.9Of the 100 million acres in California,
the federal government owns 45 million
acres. What percent is this?
Step-by-step explanation:
you do know what a percent is ?
1% is the 1/100 part of a whole.
when we have
100,000,000 (one hundred million),
how many 1/100 parts of that are
45,000,000 (45 million)?
well, 45.
45,000,000 is 45/100 of 100,000,000
in other words 45%.
which function is best represented by this graph?A) f(x) = -3x² + 2x + 1 B) f(x) = 3x² + 2x - 4C) f(x) = x² + x - 4D) f(x) = x² + 2x - 3
Answer:
From the graph, the roots of the equation are given below as
[tex]\begin{gathered} x=-3 \\ x=1 \end{gathered}[/tex]These are the points where the curve cuts the x-axis
The y-intercepts of the graph is given below as
[tex](0,-3)[/tex]Concept:
To find the equation of the graph, we will use the formula below
[tex]\begin{gathered} f(x)=a(x+3)(x-1) \\ x=0,y=-3 \\ -3=a(0+3)(0-1) \\ \frac{-3}{-3}=\frac{-3a}{-3} \\ a=1 \end{gathered}[/tex]Hence,
By substituting the values, we will have
[tex]\begin{gathered} f(x)=a(x+3)(x-1) \\ f(x)=1(x+3)(x-1) \\ f(x)=x^2-x+3x-3 \\ f(x)=x^2+2x-3 \end{gathered}[/tex]Hence,
The function of the graph is
[tex]f(x)=x^2+2x-3[/tex]OPTION D is the right answer
Which of the following is equivalent to 1,000,000?
The statement that is equivalent to 1, 0 0 0, 0 0 0 is: C. 10 power of 6.
Determining the equivalent numberGiven digit:
1,0 0 0,0 0 0
Hence,
When something is equivalent to another things it implies or means that both of them are the same or correspond.
We know that 1,000,000 can be re- write as 1 Million and 1000 Thousands.
Now let determine or find the equivalent of 1,000,000 using scientific notation
Scientific notation = 1,000,000
Scientific notation = 10^6
Based on the above 10^6 is equivalent to 1,000,000. We can justified it by pressing 10^6 on our calculator which will in turn gives us 1,000,000.
So,
1,000,000 = 10^6
Therefore we can conclude that the correct option is C based on the fact that 10 raise to power of 6 is the same as 1,0 0 0,0 0 0.
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The complete question is:
Which expression is equivalent to 1,000,000?
A .5 power of 10. B .6 power of 10. C. 10 power of 6. D. 10 power of 5