Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest hundredth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank) (4 points)
The proportional relationship between the number of pages (p) and the number of hours (h) is represented by the equation . Write the equation in standard form with a constant of proportionality greater than 1.
Answer:
the answer is p=40h, hope this helps!!!
Step-by-step explanation:
5+25+125+625+3125+15625 rewrite each series using sigma notation
Final answer:
The series 5+25+125+625+3125+15625 can be rewritten in sigma notation as Σ 5*5^(n-1) from n=1 to 6, representing a geometric series with a common ratio of 5 and 6 terms.
Explanation:
To rewrite the series 5+25+125+625+3125+15625 using sigma notation, we first need to identify the pattern of the series. We notice that each term is 5 times the previous term, which is a characteristic of a geometric series. A geometric series can be expressed in sigma notation as Σ a*r^(n-1) from n=1 to N, where a is the first term, r is the common ratio between terms, and N is the number of terms.
In this series, a = 5, and r = 5. The series has 6 terms, so N = 6. Therefore, the series in sigma notation is Σ 5*5^(n-1) from n=1 to 6.
1. Let f(x)=8/1+3e^−0.7x. What is the value of f (−3)?
2. Let f(x)=20/1+9e^3x. What is the y-intercept of the graph of f(x)?
3. Let f(x)=24/1+3e^−1.3x. What are the asymptotes of the graph of f(x)?
4. Let f(x)=15/1+4e^−0.2x. What is the point of maximum growth rate for the logistic function f(x)?
5. Let f(x)=24/1+3e^−1.3x. Over what interval is the growth rate of the function decreasing?
This detailed answer covers evaluating functions at specified values, identifying the y-intercept of a function's graph, determining asymptotes, identifying points of maximum growth rate in logistic functions, and intervals where the function's growth rate is decreasing, all critical concepts in understanding mathematical functions in high school.
Explanation:The questions provided are focused on evaluating specific values of functions, understanding the y-intercept of a graph, determining asymptotes, identifying points of maximum growth rate, and assessing intervals of decreasing growth rate for various exponential and logistic functions. Each of these concepts plays a crucial role in understanding the behaviors and characteristics of different types of mathematical functions, which are fundamental in high school mathematics.
To find f(-3) for the function f(x)=8/(1+3e^{-0.7x}), substitute x=-3 and evaluate.The y-intercept of a graph is found by evaluating the function at x=0.Asymptotes can be determined by evaluating the limits of the function as x approaches infinity or negative infinity.The point of maximum growth rate for a logistic function occurs at the point where the function's second derivative changes sign.The growth rate is decreasing over intervals where the second derivative of the function is negative.
What is the minimum number of weighings on a balance scale need to find a counterfeit coin among 8 coins if the counterfeit coin is either lighter or heavier that the other true coins (which are all the same weight.) describe the algorithm to find the counterfeit coin in this minimum number of weighings?
To find a counterfeit coin among 8 coins with a balance scale, divide the coins and use up to 3 weighings. The algorithm involves grouping and comparing the weights, identifying the counterfeit in the imbalanced group.
Algorithm to Find a Counterfeit Coin among 8 Coins
To find a counterfeit coin among 8 coins with a minimum number of weighings on a balance scale, we need at most 3 weighings. Here is the step-by-step algorithm:
Divide the 8 coins into three groups: two groups of 3 coins each, and one group of 2 coins.Weigh the two groups of 3 coins against each other.If they balance, the counterfeit coin is in the group of 2 coins. Weigh those two coins against each other to find the counterfeit one.If the two groups of 3 coins do not balance, take the lighter or heavier group (depending on whether the counterfeit is known to be lighter or heavier) and divide the 3 coins into three groups of 1 coin each.Weigh one coin against another. If they balance, the third coin is the counterfeit. If they do not balance, the heavier or lighter coin (again, depending on the counterfeit's known weight difference) is the counterfeit.With this algorithm, the maximum number of weighings needed to determine the counterfeit coin is three.
Answer ASAP
Find the area
In this problem, you are asked to find the area of the trapezoid. The formula in finding the area of the trapezoid is:
A = [(a + b)/2] x h
Where a = base 1
b = base 2
h = height
Substituting the given measurements to the formula:
A = [(1.7 m + 6.7 m) / 2] x 5 m
A = (8.4 m / 2) x 5 m
A = 4.2 m x 5 m
A = 21 m^2
Therefore, the area of the trapezoid is 21 square meters.
Can you help find the first 5 terms and the explicit formula
Which of the following will typically offer the lowest interest rate?
A. Basic savings
B. Certificate of deposit
C. Savings bond
D. Money market savings
@countonme123 @sara17,
Chloe’s 5 ft 4 inches tall. There are 2.54 centimeters in 1 inch . What is Chloe’s height in centimeters ?
Will give Metal! From 1948 to 1994, South Africa existed under a system of apartheid. Under this system, white South Africans- about 18% of the population- controlled all of the instruments of government: the Parliament, the Executive Branch, and the courts. Black and non-white South Africans had few legal rights and could not vote in elections. Voting was limited to white South African citizens. . This passage is describing what type of government? A) autocratic B) democratic C) dictatorship D) oligarchic,
solve for X
This is 10th grade Geometery (USA)
If mike drank more than half the juice inhis glass.what fraction of the juice could mike have drunk.
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.
14ich long 9inch wide half of shape with dotted line
Factorise fully 6m+18
The factorised form of 6m + 18 is given by the equation: 6(m + 3).
Given :
Equation - 6m + 18
Solution :
Factorisation is the method of diminishing the bracket of a quadractic condition, rather than growing the bracket and changing over the condition to a item of variables which cannot be decreased assist.
To factorise the equation 6m + 18 we have to follow some steps:
In first step we have to write 18 = [tex]6\times 3[/tex] so the equation becomes:
[tex]\rm = 6m + (6\times3)[/tex] ----- (1)
In second step we have to take 6 common from equation (1):
[tex]\rm=6(m+3)[/tex]
So the factorised form of 6m + 18 is given by the equation: 6(m + 3)
For more information, refer the link given below
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Samuel paid $720 for a new music system. The list price for the music system was $800. What was his rate of discount?
Answer:
His rate of discount=10%
Step-by-step explanation:
Step 1: Get the discount amount
Discount amount=List price-sale price
where;
List price=$800
Sale price=$720
replacing;
Discount amount=(800-720)=80
Discount amount=$80
Step 2: Calculate discount rate
The discount rate can be calculated as;
discount rate=(discount/List price)×100
where;
discount=$80
List price=$800
replacing;
discount rate=(80/800)×100=10%
discount rate=10%
A system of inequalities is graphed below. The variable x represents the number of cans someone is buying, and y represents the number of bottles. Conditions on the maximum amount of total weight and volume lead to two of the inequalities.
Which descriptions correspond to solutions of this system?
7 cans and 140 bottles
12 cans and 40 bottles
8 cans and 120 bottles
9 cans and 70 bottles
A fishing tackle box is 13 inches long 6inches wide and 2 1/2 inches high. What is the volume of the tackle box?
What is the graph of the function f(x) = the quantity of x plus 4, all over x plus 6?
If 1 inch represents 75 miles on a map, then how many inches will represent 1500 miles? a. 10 c. 12 b. 20 d. 14
Use 3.14 for the radius to estimate the area of a circle the diameter is given round your answer to the nearest hundredth if necessary.
Use substitution to write an equivalent quadratic equation.
(3x + 2)2 + 7(3x + 2) – 8 = 0
On each of 3 days Derrick rode 6.45 km to school 150 meters to the library and then 500 m back home how many km did he ride for the three days all together
Which statement below completes Anastasia's proof?
In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are congruent)
In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are parallel)
In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)
In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are parallel)
are the statments
Great Dish believes that it will need new equipment in 8 years. The equipment will cost $26,000. What lump sum should be invested today at 12%, compounded semiannually, to yield $26,000? a. $20,186.02 c. $16,388.00 b. $16,145.82 d. $10,234.80
Answer:
d. $10,234.80
Step-by-step explanation:
we are given
The equipment will cost $26,000
so, Amount is $26000
A=26000
should be invested today at 12%
r=12%=0.12
It is compounded semiannually
so, n=2
t=8
now, we can use formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
now, we can plug values
[tex]26000=P(1+\frac{0.12}{2})^{2\times 8}[/tex]
now, we can solve for P
[tex]P=10234.80338[/tex]
Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
a) Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain.
b) Write an explicit formula to represent the sequence.
c) Find the value of the computer at the beginning of the 6th year.
We want to answer different things about an exponential decay, the answers are:
a) Geometric.b) [tex]A_n = (0.9)^{n-1}*1250[/tex]c) $738.10.So we know that the original price of the computer is $1250 and the value decays by 10% each year.
So in year 1, the new value of the computer will be:
V = $1250*(1 - 0.1) = $1250*0.9
On year 2, the new value will be:
V = ( $1250*0.9)*0.9 = $1250*(0.9)^2
And so on.
a) This sequence is a geometric sequence because each term is a constant times the previous term, where the constant is 0.9.
[tex]A_1 = 1250\\A_2 = 0.9*1250 = 1125\\A_3 = 0.9^2*1250 = 0.9*1125 = 1012.5 \\...[/tex]
b) The explicit formula for a geometric sequence is:
[tex]A_n = k^{n-1}*A_1[/tex]
where:
k is the constant, in this case, is 0.9
A1 is the first term of the sequence, in this case, is 1250
Then we have:
[tex]A_n = (0.9)^{n-1}*1250[/tex]
c) Here we just need to replace n by 6 in the above formula:
[tex]A_6 = (0.9)^5*1250 = 738.1125[/tex]
This means that the price of the computer in the 6th year is $738.10
If you want to learn more about exponential decays, you can read:
https://brainly.com/question/3966275
An explosion causes debris to rise vertically with an initial velocity of 160 feet per second. What is the speed of debris when the height is 300 feet?
I am using the formula: -16t^2 + vot + h0 because the question is referring to feet.
The speed of the debris is 79.4 ft/s
Calculation of the speed:Since there is an initial velocity of 160 feet per second, height is 300feet
So, we applied the below formula
[tex]v_({final})^2 = v_({initial})^2 + 2ah\\\\ v_({fina})l^2 = (160 ft/s)^2 + 2(-32.15 ft/s^2)(300 ft)\\\\ = 6310 ft^2/s^2\\\\ = (6310 ft^2/s^2)^{1/2}\\\\ = 79.4 ft/s.[/tex]
Therefore, The speed of the debris is 79.4 ft/s
Learn more about speed here: https://brainly.com/question/1825528
the radioisotope cobalt-60 is used in cancer therapy. the half-life isotope is 5.27 years. which is equation determines the percent of an initial isotope remaining after t years?
Answer : The equation determines the percent of an initial isotope remaining after t years is, [tex]\frac{a}{a_o}\times 100=2^{(-\frac{t}{5.27})}[/tex]
Explanation :
Half-life = 5.27 years
Formula used :
[tex]a=\frac{a_o}{2^n}[/tex] ............(1)
where,
a = amount of reactant left after n-half lives
[tex]a_o[/tex] = Initial amount of the reactant
n = number of half lives
And as we know that,
[tex]n=\frac{t}{t_{1/2}}[/tex] ..........(2)
where,
t = time
[tex]t_{1/2}[/tex] = half-life = 5.27 years
Now equating the value of 'n' from (2) to (1), we get:
[tex]a=\frac{a_o}{2^{(\frac{t}{t_{1/2}})}}[/tex] ...........(3)
[tex]a=\frac{a_o}{2^{(\frac{t}{5.27})}}[/tex]
[tex]\frac{a}{a_o}\times 100=2^{(-\frac{t}{5.27})}[/tex]
Therefore, the equation determines the percent of an initial isotope remaining after t years is, [tex]\frac{a}{a_o}\times 100=2^{(-\frac{t}{5.27})}[/tex]
The equation that determines the percent of an initial isotope remaining after t years is: Percent remaining = (100) x (1/2)^(t/h), where t is the number of years and h is the half-life of the isotope.
Explanation:The equation that determines the percent of an initial isotope remaining after t years is: Percent remaining = (100) x (1/2)(t/h), where t is the number of years and h is the half-life of the isotope.
For example, for the radioisotope cobalt-60 with a half-life of 5.27 years, you can use the equation Percent remaining = (100) x (1/2)(t/5.27) to determine the percent remaining after t years.
Let's say you want to find the percent remaining after 10 years, you would substitute t with 10 in the equation, like this: Percent remaining = (100) x (1/2)(10/5.27). Simplify the equation to find the answer.
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Elaine bought a total of 15 shirts and pairs of pants she bought 7 more shirts than the pants how many of each did she buy