Which function is a shrink of the exponential growth function shown on the graph?
A.) f(x) = 2(3)x
B.) f(x) = 1/2(3)x
C.) f(x) = 2(1/3)x
D.) f(x) = 1/2(1/3)x
Determine the volume of the pencil
The volume of the pencil is approximately 4.05 cm³.
To determine the volume of the pencil, we need to calculate the volumes of the cylindrical body and the conical tip separately and then add them together.
Volume of the cylindrical body:
The formula for the volume of a cylinder is [tex]V = \pi r^2h[/tex], where r is the radius and h is the height.
[tex]V_{cylinder} = \pi (0.5 cm)^2 * 15 cm[/tex]
Volume of the conical tip:
The formula for the volume of a cone is [tex]V = (1/3)\pi r^2h[/tex], where r is the radius and h is the height.
[tex]V_{cone} = (1/3) * \pi (0.5 cm)^2 * 2 cm[/tex]
Now, we can calculate the volumes:
[tex]V_{cylinder} = \pi * (0.5 cm)^2 * 15 cm = 3.53 cm^3\\\\V_{cone} = (1/3) * \pi * (0.5 cm)^2 * 2 cm = 0.52 cm^3[/tex]
Finally, we can add the volumes of the cylindrical body and the conical tip to get the total volume of the pencil:
[tex]Total\ volume = V_{cylinder} + V_{cone} = 3.53 cm^3 + 0.52 cm^3 = 4.05 cm^3[/tex]
Therefore, the volume of the pencil is approximately 4.05 cubic centimeters ([tex]cm^3[/tex]).
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Solve the system of equations using the linear combination method.
{9x+5y=35
{2x+5y=0
Enter your answers in the boxes.
x =_
y =_
Consider the diagram. What is the length of segment AB?
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
In this problem the line DB is a median of triangle ADC
The line DB is also the altitude of a triangle ADC, because is perpendicular to the side AC
so
AB=BC
we have that
[tex]BC=9\ units[/tex]
therefore
[tex]AB=9\ units[/tex]
the answer is the option
[tex]9[/tex]
Lisa made $286 for 13 hours of work. at the same rate, how many hours would she have to work to make $242 ?
Find the first six terms of the sequence.
a1 = -4, an = an-1 + 7
-4, 3, 10, 17, 24, 31
-4, 7, 14, 21, 28, 35
3, 10, 17, 24, 31, 38
0, 7, 14, 21, 28, 35
Answer: A) -4, 3, 10, 17, 24, 31
Step-by-step explanation: To solve the given problem we need to calculate the first six terms of the sequence (starting with a1):
a1=-4
a2=a1+7
a2=-4+7
a2=3
a3=a2+7
a3=3+7
a3=10
a4=a3+7
a4=10+7
a4=17
a5=a4+7
a5=17+7
a5=24
a6=a5+7
a6=24+7
a6=31.
A test is worth 140 points. Ten percent of those points are from one short-answer question. How many points is the short-answer question worth?
The short-answer question worth of 14 points.
What is unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Total points of test =140
and 10 % of those points are from one short-answer question.
So, the points for short-answer question are
=10 % of 140
=10/100 x 140
=1400/100
=14
Hence, short-answer question worth of 14 points.
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The band is selling wrapping paper for a fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. The band sold a total of 55 rolls and made $950. If a roll of plain wrapping paper cost $14 and a roll of shiny cost $20, how many rolls of each did they sell ?
The roll of plain wrapping paper sold is 25.
The roll of shiny wrapping paper sold is 30.
What are the linear equations that represent the question?a + b = 55 equation 1
14a + 20b = 950 equation 2
Where:
a = roll of plain wrapping paper sold
b = roll of shiny wrapping paper sold
What is the roll of shiny wrapping paper sold?Multiply equation 1 by 14
14a + 14b = 770 equation 3
Subtreact equation 3 from equation 2
6b = 180
Divide both sides by 6
b = 30
What is the roll of plain wrapping paper sold?
Subtract 30 from 55
55 - 33 = 25
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The perimeter of an equilateral triangle with a side of 6 inches is
12 in.
18 in.
36 in.
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation mc022-1.jpg represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
Answer:
7 years
Step-by-step explanation:
An initial investment of $200 is now valued at $350.
The annual interest rate is 8% compounded continuously.
Formula:
[tex]A=Pe^{rt}[/tex]
Where,
A is amount, A=350
P is principle, P=200
R is rate of interest, r=0.08
t is time, t=?
Substitute the value into formula
[tex]350=200e^{0.08\cdot t}[/tex]
[tex]e^{0.8t}=1.75[/tex]
Taking ln both sides
[tex]0.08t = ln(1.75)[/tex]
[tex]t=6.99\approx 7[/tex]
Hence, 7 years ago money was invested.
Answer:
Its 7 years
Step-by-step explanation:
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If you wanted to predict the value of the y variable when the x variable is 15, you would be _____ the data.
A.) Correlating
B.) Extrapolating
C.) Interpolating
Answer:
If you wanted to predict the value of the y variable when the x variable is 15, you would be extrapolating the data.
Step-by-step explanation:
If you wanted to predict the value of the y variable when the x variable is 15, you would be Extrapolating the data.
Extrapolation means, estimating the value of a variable beyond its given range.
Rene has a coupon for $3.25 off a package of name brand cookies that normally costs $7.89. The store brand cookies coats $5.58. How much will Rene save if she uses her coupon and buys the name brand cookies instead of the store brand cookies? HELP
Rene will save $0.94 if she uses her coupon and buys the name brand cookies instead of the store brand cookies.
Explanation:To find out how much Rene will save if she uses her coupon and buys the name brand cookies instead of the store brand cookies, we have to first determine how much the name brand cookies will cost after applying the coupon. We subtract the value of the coupon i.e. $3.25 from the original cost of name brand cookies which is $7.89. The result comes out to be $4.64.
To calculate the savings, we now have to subtract the cost of name brand cookies after coupon ($4.64) from the original cost of the store brand cookies ($5.58). Hence, the savings amount to $5.58 - $4.64 which equals $0.94
So, if Rene uses her coupon and buys the name brand cookies instead of the store brand cookies, she will save $0.94.
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“How many times did you ride the Ferris wheel today?” Is the question a statistical question? Explain why or why not.
How do I solve and graph this?
WORTH 20 POINTS!!
The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4). If the coordinates of the 3rd vertex are (1, 0), what are the coordinates of the 4th vertex? (7, -12)
(7, -8)
(-8, -4)
(-4, -12)
Using radicals , write an equivalent expression for the expression 2 1/3
I'm assuming that the 1/3 is an exponent.
If so, then
Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.
The half-life of iodine-123 is about 13 hours. You begin with 52 grams of iodine-123. (a) Write an equation that gives the amount of iodine-123, I , remaining after t hours. Write your answer in the form I ( t ) = a ⋅ b t . Round your answer for b to three decimal places.
Final answer:
The amount of iodine-123 remaining after t hours can be expressed as I(t) = 52 · 0.945^t, where the constant 0.945 is calculated using the half-life of 13 hours.
Explanation:
The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms to decay. For iodine-123, which has a half-life of approximately 13 hours, we can use an exponential decay model to express the amount of iodine-123 remaining after t hours.
The decay formula is generally given by I(t) = I0e-kt, where I0 is the initial amount, k is the decay constant, and t is time. However, the question asks us to express the equation in the form of I(t) = a · bt, which is another common representation for exponential decay.
To find the value of b, we know that after one half-life, b13 = 1/2. Thus, b = (1/2)1/13.
Let's calculate b: b = (0.5)1/13 ≈ 0.945 (rounded to three decimal places).
Since we start with 52 grams of iodine-123, our initial amount (a) is 52. Therefore, the equation for the amount of iodine-123 remaining after t hours is:
I(t) = 52 · 0.945t
The equation to calculate the amount of iodine-123 remaining after t hours is I(t) = a * b^t, where a is the initial amount of iodine-123, b is the decay constant, and t is the time in hours. The decay constant can be calculated using the formula b = 0.693 / t1/2, where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours.
Explanation:The equation that gives the amount of iodine-123 remaining after t hours can be written as:
I(t) = a * b^t
Where:
I(t) is the amount of iodine-123 remaining after t hoursa is the initial amount of iodine-123b is the decay constant, which can be calculated using the half-life formulat is the time in hoursTo calculate the decay constant b, we can use the formula:
b = 0.693 / t1/2
where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours, so:
b = 0.693 / 13 = 0.053
Therefore, the equation becomes:
I(t) = a * 0.053^t
Round the value of b to three decimal places, so b = 0.053.
Which of the following values is closest to the mean for the set of data shown below?
23, 32, 20, 43, 41, 66, 63, 59, 54, 36, 45, 61, 55, 44, 47
A.45.9 B.50 C.58 D.54.3
Which expression can you simplify by combining like terms? Clear Check 6 d 2 +5cd−3dc+8 6d2+5cd-3dc+8 12 c 2 −8 d 2 c+3dc+4 12c2-8d2c+3dc+4 7 d 2 −3 c 2 +6d−c 7d2-3c2+6d-c 16 c 2 +8cd+7c−8d 16c2+8cd+7c-8d
The expression that can be simplified by combining like terms is 16 c^2 + 8cd + 7c - 8d, where 8cd and -3dc are like terms and can be combined to simplify the expression to 16c^2 + 5cd + 7c - 8d.
Explanation:The expression 16 c2 + 8cd + 7c - 8d can be simplified by combining like terms. Like terms in an algebraic expression are terms that have the same variable raised to the same power. Here, the terms 8cd and -3dc are like terms and can be combined.
Here's the step-by-step simplification:
First, identify like terms in the expression. In 8cd and -3dc, since multiplication is commutative (meaning ab = ba), cd and dc are essentially the same term. So, 8cd and -3dc can be combined.Combine the like terms by adding their coefficients. For 8cd and -3dc, we have 8 - 3 to get 5cd.Now, the simplified expression is 16c2 + 5cd + 7c - 8d.This process of combining like terms helps in simplifying algebraic expressions, making them easier to work with.
After combining like terms, it's important to always check the answer to see if the simplification is reasonable and if there are any other like terms that can be combined.
So, the simplified expressions are:
1. [tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]
2. [tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]
3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]
4. [tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]
Let's simplify each expression by combining like terms:
1. [tex]\(6d^2 + 5cd - 3dc + 8\)[/tex]
Combine like terms:
[tex]\(6d^2 + (5cd - 3dc) + 8\)[/tex]
[tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]
2. [tex]\(12c^2 - 8d^2c + 3dc + 4\)[/tex]
Combine like terms:
[tex]\(12c^2 - (8d^2c - 3dc) + 4\)[/tex]
[tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]
3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]
No like terms to combine.
4. [tex]\(16c^2 + 8cd + 7c - 8d\)[/tex]
Combine like terms:
[tex]\(16c^2 + (8cd + 7c) - 8d\)[/tex]
[tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]
A farmer has a collection of chickens and dogs. all together there are 120 legs and 43 heads. how many of each animal does he have? answer
Number of chicken = 26
And, Number of dogs = 17
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A farmer has a collection of chickens and dogs.
And, all together there are 120 legs and 43 heads.
Hence, Number of chicken = x
And, Number of dogs = y
Thus, We get;
⇒ x + y = 43
⇒ x = 43 - y .. (i)
⇒ 2x + 4y = 120
⇒ x + 2y = 60 .. (ii)
Substitute value of x from (i) to (ii);
⇒ x + 2y = 60
⇒ 43 - y + 2y = 60
⇒ y = 60 - 43
⇒ y = 17
And, From (i);
⇒ x = 43 - y
⇒ x = 43 - 17
⇒ x = 26
Thus, Number of chicken = 26
And, Number of dogs = 17
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Find the volume of this square pyramid, given that its height is 8 m.
A) 24 m3.
B) 72 m3.
C) 216 m3.
D) 648 m3.
Answer:
A) [tex]24\text{ m}^3[/tex].
Step-by-step explanation:
We have been given an image of a square pyramid and we are asked to find the volume of our given pyramid.
[tex]\text{Volume of square pyramid}=\frac{a^2*h}{3}[/tex], where,
a = Base length of square,
h = height of pyramid.
Upon substituting our given values in above formula we will get,
[tex]\text{Volume of square pyramid}=\frac{\text{(3 m)}^2*\text{ 8 m}}{3}[/tex]
[tex]\text{Volume of square pyramid}=\frac{9\text{ m}^2*\text{ 8 m}}{3}[/tex]
[tex]\text{Volume of square pyramid}=\frac{72\text{ m}^3}{3}[/tex]
[tex]\text{Volume of square pyramid}=24\text{ m}^3[/tex]
Therefore, the volume of our given square pyramid is 24 cubic meters and option A is the correct choice.
Answer:
A. 24 m3.
Step-by-step explanation:
what is the approximate distance between the points (1 -2) and (-9 3) on a coordinate grid?
Answer:
11.18
Step-by-step explanation:
The area of a triangle is 1440 cm^2. the base of the triangle is 5 times the height. what is the height of the triangle?
Rico travelled from the United States to the United Kingdom. Once Rico arrived, he converted his American dollars into British pounds (the currency in the U.K.). He gave the bank teller $500 and was given back 295 pounds. At the end of his vacation Rico had 75 pounds left over which he converted back into US dollars. How much money (in US dollars ) did Rico have when he got home? Round the answer to the hundredth.
Five is a solution of (Y < -3)
A.True
B.False
If three tangents to a circle form an equilateral triangle, prove that the tangent points form an equilateral triangle inscribed in the circle
Use k as the constant of proportionality to write the equation expressing the relationship: y varies inversely as x. if y = 10 when x = 5, determine k.
y = k/x
Step-by-step explanation:
Someone please help, with a cherry on top?
View attached graph and find the approx. slope
THANK YOU SOOO MUCH!!!
Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1? 6f – 1 evaluated at f = 9 is 53. 2f + 4f + 2 – 3 evaluated at f = 9 is also 53. 6f – 1 evaluated at f = 3 is 17. what is 2f + 4f + 2 – 3 evaluated at f = 3?
Answer: 17
Step-by-step explanation: