The values of a and b in the exponential function f(x) = [tex]ab^x[/tex] can be found by using the two given points and solving a system of two equation.
To find the values of a and b in the exponential function f(x) = [tex]ab^x[/tex] given that it passes through the points (0, 11) and (3, 1375), we can use the supplied positions where a and b must be solved.
Let's start with the point (0, 11). Plugging x = 0 and y = 11 into the equation, we have:
11 = [tex]a * b^0[/tex]
Since [tex]b^0[/tex] = 1 for any value of b, we have:
11 = a * 1
So a = 11.
Next, let's use the point (3, 1375) to find b. Plugging x = 3 and y = 1375 into the equation, we have:
1375 = [tex]11 * b^3[/tex]
Dividing both sides of the equation by 11, we have:
125 = [tex]b^3[/tex]
By combining the cube roots of the two sides, we obtain:
b = 5
So the values of a and b are a = 11 and b = 5. The exponential function that passes through the points (0, 11) and (3, 1375) is f(x) = [tex]11 * 5^x[/tex].
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The complete question is:
an exponential function f(x) = [tex]ab^x[/tex] passes through the points (0, 11) and (3, 1375). Find the values of a and b?
Please Help Me! I really need this question answered. I am behind in my work!!!!!
Answer:
The flagpole is 15 ft tall.
Step-by-step explanation:
In this problem, we are asked to create a proportion of similar triangles to solve for the height of a flagpole.
1) Setting up the ProportionWe are given an equation with the proportion:
[tex]\dfrac{h}{6\text{ft}}=\dfrac{\square}{\square}[/tex]
We can fill in the blanks as follows:
[tex]\dfrac{h}{6\text{ft}}=\dfrac{25 \text{ft}}{10 \text{ft}}[/tex]
Notice that the heights of the triangles compared are both in the numerator, and the lengths of both triangles are in the denominator.
2) Solving the ProportionThen, to solve for the height of the flagpole, we can isolate the variable h in the proportion.
[tex]\dfrac{h}{6}=\dfrac{25}{10}[/tex]
↓ multiply both sides by 6
[tex]h = \dfrac{150}{10}[/tex]
↓ simplify the fraction
[tex]h = 15 \text{ ft}[/tex]
So, the flagpole is 15 ft tall.
The Son has got his Crown On The pharaoh’s outfitters, ‘Cloaks and Crowns’, sell Cloaks and Crowns in 3 sizes – prince, king and emperor (in increasing size order). He wants to kit out his three sons for the forthcoming festival of Ra. Ahmose chooses a bigger cloak than Kamose, but a smaller crown than Thutmose. Both Thutmose’s cloak and crown are larger than Kamose’s, but the size of Thutmose’s crown matches the size of Kamose’s cloak. Which sizes did the pharaoh’s sons each get?
The only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Let's us consider the sizes of the cloaks by C (prince), B (king), and A (emperor)
The sizes of the crowns by 1 (prince), 2 (king), and 3 (emperor).
Now let us write the following system of inequalities:
B > C
A > B
3 = C (Thutmose's crown matches Kamose's cloak)
2 > C
A > 3
A > 2 (Thutmose's crown is larger than the king size crown)
From the fifth inequality, we know that Thutmose's cloak is the largest of all three cloaks, so A must equal C.
Therefore, we can simplify the system of inequalities to:
B > C, A > B, C = 3, 2 > C, A > 3 and A > 2
Hence, the only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
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A circle has a diameter of 26 feet what is the circumference
Use 3.14 for pie and do not round your answer be sure to include the correct unit in it in your answer
The circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
What is the circumference?
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated as a pole.
The formula for the circumference of a circle is 2 * π * r, where r is the radius of the circle.
To find the circumference, we first need to find the radius of the circle.
The diameter of the circle is 26 feet, so the radius can be calculated by dividing the diameter by 2:
r = 26 feet / 2 = 13 feet
Now that we know the radius, we can find the circumference:
C = 2 * π * r = 2 * 3.14 * 13 = 81.64 feet
Therefore, the circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
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A trail map has a scale of 3 in. : 2 mi. On the map,
a trail is 5 in. long.
How long is the actual trail?
0 1/mi
O2 mi
O O
12
3-mi
O 07 mi
Answer:
Step-by-step explanation:
in: mi
3:2
5:x
3*1.6667=5
2*1.6667=3.3334/
becaus the first answer was rounded up, the last one needs to be rounded down.
so the answer, rounded up to the nearest hundredth is 3.34
(rounded up to the nearest whole number is 3)
Como puedo resolver esto?
- x - y = 4
The points on the graph of the equation represent the solution set to the equation.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the equation as -
- x - y = 4
The given equation is -
- x - y = 4
x + y = 4
The graph of the given equation will represent a straight line. All the points on the line represent the solution set to the equation.
Therefore, the points on the graph of the equation represent the solution set to the equation.
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{Question in english -
How can i solve this?
- x - y = 4}
Your school is going to start offering afterschool clubs they will be nine clubs to choose from to have clubs at least 23 students we will need to sign up for each one what is the least number of students that must sign up to have all nine clubs
At least number of students who must have signed up to have all nine clubs is equal to 207.
Number of clubs school going to start after school = 9 clubs
At least number of students need to sign up in each one of the club is equal to 23 students.
At least number of students need to sign up to have all in nine clubs is equal to :
At least number of student in 1 club > 23
⇒ At least number of student in 9 club > 23 × 9
At least number of student in 9 club > 207
Therefore, at least number of students need to signed up to have in all nine given clubs are 207 students.
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Calculate the volume of this cylinder, giving your answer to 1 decimal point
The volume of the cylinder is approximately 1413.7 cubic centimeters.
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height or length of the cylinder.
Since the base of the cylinder has a diameter of 9cm, the radius is half of that, or r = 4.5cm.
The length of the cylinder is given as 20cm.
Therefore, the volume of the cylinder is:
V = πr²h
= π(4.5)²(20)
= 1413.72 cubic centimeters (rounded to 1 decimal place)
Thus, the volume of the cylinder is approximately 1413.7 cubic centimeters.
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Complete question:
Calculate the volume of this cylinder. give your answer to 1 decimal place. Base is 9cm. Length is 20cm.
1. What is the rule for the following geometric sequence? 64, -32, 16, -8...
an=64(-2)n-1
an = 64(1)-1
an=64(-1)-1
an=64(2)-1
The rule for the given geometric sequence as required to be determined is; a (n) = 64 (-1/2)^(n-1).
Which rule represents the geometric sequence?By observation, the first term of the sequence is; 64.
Also, the common ratio of each successive terms is as follows;
-32 / 64 = 16 / -31, -8 / 16 = -1/2.
On this note, the ratio is; -1/2.
Consequently, it follows that the answer choice which correctly represents the rule for the geometric sequence is; an = 64(-1/2)^n-1.
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David biked 12\frac{7}{8}12
8
7
miles on Tuesday and 5\frac{3}{8}5
8
3
miles on Wednesday.
How much farther did David bike on Tuesday than on Wednesday?
David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.
We are given that David biked [tex]12\frac{7}{8}[/tex] miles on Tuesday and [tex]5\frac{3}{8}[/tex] miles on Wednesday.
In order to find the number of miles David biked farther on Tuesday than on Wednesday, we will subtract the miles biked by him on Wednesday from the miles biked by him on Tuesday as follows -
[tex]12\frac{7}{8} - 5\frac{3}{8}[/tex]
So, first, we will subtract the whole number of parts as follows -
12-5 = 7
Then, we will subtract the fractional parts as follows -
7/8 - 3/8 = 4/8 = 1/2
so we get,
[tex]12\frac{7}{8} - 5\frac{3}{8} = 7\frac{1}{2}[/tex]
Therefore, David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.
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Please help meeh:
Find the first four terms and stated term given the arithmetic sequence, with a, as the 1" term.
an = 25 - 10n, a5
an = 11 + 9n, a6
an = 65 - 35n, a9
The first four terms and the stated term, with an as the first term, are given the arithmetic sequence: 11 + 9n, a6.
What is an arithmetic sequence?The difference between any succeeding term and its preceding term remains constant throughout an arithmetic progression or arithmetic sequence, which is a set of numbers. That arithmetic progression's common difference is the constant difference. A series of numbers in the following format is an arithmetic sequence: a, a + d, a + 2 d, a + 3 d, a + 4 d,... The common difference between the terms in the sequence is d, and number an is the first term. An = a + (n - 1)d gives the nth term of an arithmetic series. A sequence is considered to be arithmetic if there is a constant difference between each subsequent term.To learn more about arithmetic sequence refer to:
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Is 96 the lowest common multiple of 4 and 24?
no
4x6=24
24x1=24
hence 24 is the lowest common multiple , i hope this helped xx
Say you have a 92% in a class and you do 2 assignments and they are both worth 50% of your grade. And you get a 2/5 on one of them and a 5/5 on the other. Whats the resulting grade?
Answer:
70%
Step-by-step explanation:
Somebody please look at this picture and help me pleaseeeeeee
Answer:
I think it's
Step-by-step explanation:
usually involves reading the pattern on the table while keeping in mind that x goes on top and y on
The accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency. a) Which would you expect to be larger: the median or the mean? Explain briefly. b) Which would you report: the median or the mean? Explain briefly.
If Sullivan got 32 pieces of candy, how many did Carter get? Answer
Sullivan received half as many candy as Carter did, or half as many candies as Sullivan received.
What is an amount?aggregate means the complete amount or quantity. attempting to estimate the time required. the amount on hand or being considered. mutable noun How much of something there is, how much you possess, require, or receive, is known as its amount. He is dependent on that sum of money to get by.Therefore, a number only refers to things that we can count. Contrarily, quantity relates to how much of something there is, such as how much liquid, resistance, or stimulation. In actuality, the term "amount" refers to amounts that we can measure but not count individually." Amount is defined as the representation of total quantity of given object."
According to the question,
Number of candies Sullivan got = s
Number of candies Carter got = 2s
Compare the given amount of data we get,
Number of candies Carter got = 2(Number of candies Sullivan got )
This shows Carter got twice number of candies comparison to Sullivan.
or
Number of candies Sullivan got = 1/2 (Number of candies Carter got)
Sullivan got half number of candies compare to Carter.
Hence, we conclude Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.
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find the lower quartile and the upper quartile of the data set
Answer:
Lower Quartile = 13 min; Upper Quartile = 27 min
Step-by-step explanation:
Since we have the median, we now separate the data equally to the left and right of the median.
Thus, on the left (lower) portion we have 10, 11, 13, 18, and 19. We see 13 is the middle term of these 5 values so 13 is the lower quartile (Q1).
Similarly, one the right (upper) portion, we have 22, 25, 27, 30, and 32. We see 27 is the middle term of these 5 values so 27 is the upper quartile (Q3)
cover all material from the lessons but will hopefully remind you of key points. To be prepared,
you must study all packets from Unit 1.
A salesman tracks the number of cars he sells through the model c, where c(m) is number of cars sold
and m is the month for 0 ≤ m ≤ 24.
1. What does c(10) represent?
2. What does
c(16)-c(8)
16-8
represent? 3. What does
represent?
c(7)-c(6.999)
7-6.999
a. It should be noted that c(10) represents the number of cars sold in the 10th month.
b. c(16) - c(8) represents the number of cars sold in the 16th month minus the number of cars sold in the 8th month. This difference could represent the net change in the number of cars sold between those two months.
What is a function about?The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. The process of evaluating a function is typically straightforward when we have the function in the form of a formula.
In this case, c(10) represents the number of cars sold in the 10th month.
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Liz is recording what kinds of shoes people are wearing at the mall. sandals 2 sneakers 12 high heels 6 Considering this data, how many of the next 10 people Liz sees would you expect to be wearing sandals?
10% of the next 10 people Liz sees would be expected to be wearing sandals.
Liz is recording what kinds of shoes people are wearing at the mall. sandals 2 sneakers 12 high heels 6 Considering this data.
We have to determine how many of the next 10 people Liz sees would you expect to be wearing sandals.
Since 12 out of the 20 people Liz has seen were wearing sneakers, and 6 were wearing high heels, then 2 must have been wearing sandals.
Then, Expect to be wearing sandals = Number of people wearing sandals/Total number of records
Expect to be wearing sandals = 2/20 × 100
Expect to be wearing sandals = 1/10 × 100
Expect to be wearing sandals = 10%,
So 10% of the next 10 people Liz sees would be expected to be wearing sandals.
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What is the answer to this equation (5+12i)+(7-5i)
The answer to the equation (5+12i) + (7-5i) is found to be 12-7i.
The provided equation is a simple algebraic relation between two complex numbers.
The given complex numbers are 5+12i and 7-5i.
We have to add these two complex numbers.
We will add the real part of the complex number to the real part and complex part of one complex number to the complex part of the complex number.
Sum of number = (5+12i) + (7-5i)
Sum of number = 12-7i
The sum of the two complex numbers is also complex number that has a real part has 12 and the imaginary or the complex part as -7.
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Lillian needed
2 bottle of glue to make 8 Halloween Decorations. How many can she make
10
with 1 bottle of glue?
What is the solution to 3 (2k + 3) = 6 - (3k - 5)?
Move the correct answer to each box. Not all answers will be used.
k
-8 -2 2
3 8
9
Answer: 22k
Step-by-step explanation:
The solution to the equation is k = 2/9
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
3 ( 2k + 3 ) = 6 - ( 3k - 5 ) be equation (1)
On simplifying , we get
3 ( 2k ) + 9 = 6 - 3k + 5
6k + 9 = 11 - 3k
Adding 3k on both sides , we get
9k + 9 = 11
Subtracting 9 on both sides , we get
9k = 2
Divide by 9 on both sides , we get
k = 2/9
Therefore , the value of k is 2/9
Hence , the solution is k = 2/9
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Shawn's retirement party will cost $6 if he invitês 3 guests. If there are 8 guests, how much
will Shawn's retirement party cost? Assume the relationship is directly proportional.
Step-by-step explanation:
Shawns party will cost $16 if there are 8 guest
Write 60.9% as a decimal.
A.0.0609
B.0.609
C.0.00609
D.6.0900
To convert a percentage to a decimal, divide the percentage by 100, The correct answer is B. 0.609.
What is Decimal number?When the decimal places in the factors are tallied together, they equal the number of decimal places in the product. A decimal number is one with a whole and a fraction part separated by a decimal point.
A base-10 representation of numeric values is used in the decimal numbering system. The system is widely used in daily life to complete routine tasks like grocery shopping, stock trading, keeping track of football scores, or scrolling through cable channels. Decimal numbers include 7, 28, 199, and 532.11.
To convert a percentage to a decimal, divide the percentage by 100.
So, 60.9% as a decimal would be:
60.9 / 100 = 0.609
Therefore, The correct answer is B. 0.609.
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Juan the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Juan trained on Wednesday and Thursday last week. The table below shows the number of Plan A and Plan B clients Juan trained each day and the total time (in hours) he trained.
Wednesday Thursday
Number of
Plan A workouts
Number of
Plan B workouts
Total time
(in hours)
Let be the length (in hours) of each Plan A workout.
Let be the length (in hours) of each Plan B workout.
(a) Write a system of equations that could be used to find the length (in hours) of each type of workout.
(b) How long (in hours) was each type of workout?
A system of equations that could be used to find the length (in hours) of each type of workout
7a + 9b = 12
5a + 3b = 6
Solve this system of equations by multiplying both sides of one of the equation so that when the equations are added or subtracted there will only be one variable.
-I will multiply both sides of the 2nd equation by -3
-3*(5a + 3b) = 6*-3
-15a - 9b = -18
-Now I will get rid of the variable b by adding the two equations together.
7a + 9b = 12
+ -15a - 9b = -18
-8a = -6
a = -6/-8
a= 3/4 (45 minutes)
-Now plug 3/4 into one of the original equations as a to solve for b.
-I will use the 2nd original equation.
5a + 3b = 6
5(3/4) + 3b = 6
15/4 + 3b = 6
3b = 9/4
b = 9/12 = 3/4 (45 minutes)
Both workout plans last the same amount of time.
Plan A lasts 45 minutes.
Plan B lasts 45 minutes.
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The taj Mahal in India is a square about 95.4 on each side.What is the area of the taj mahal?
The area of the Taj Mahal is 9092.16 square meters (97,890.56 square feet).
What is area of a square?The quantity of square units required to completely cover a square is known as the area of a square. The territory that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square meters serving as the standard unit.
The Taj Mahal has an area of 9092.16 square meters (97,890.56 square feet). We utilise the formula for calculating the area of a square, which is length x width. The Taj Mahal's length and width are both 95.4 metres, therefore we just multiply these two values together. 9092.16 square meters = 95.4 × 95.4 square meters (97,890.56 square feet). This is the Taj Mahal's area.
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Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
Answers:
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
A general formula to describe is F = 1.6×d² will be correct answer.
What in math is a proportional?A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.
Finding the general formula we obtain:
F=kd²
40=k×5²
k=1.6
so, F =1.6×d².
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903-814 with solution
Answer:
89
Step-by-step explanation:
903 - 814 =
= (900 + 3) - (800 + 14) =
= 900 + 3 - 800 - 14 = 100 - 11 =
= 89
Help please it's urgent
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
The required formula that describes the given variation is F = 1.6d².
What is the general formula to describe the given variation?The general formula to describe the variation that F is directly proportional to the square of d is F = kd²,
where k is a constant of proportionality.
To determine the value of k, we can use the given information that F = 40 when d = 5:
40 = k(5)²
40 = 25k
k = 40/25
k = 1.6
Substituting this value of k into the general formula, we get:
F = 1.6d²
Therefore, the formula that describes the variation is F = 1.6d².
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in a shipment of 66 vials, only 14 do not have hairline cracks. if you randomly select 4 vials from the shipment, what is the probability that all 4 of the selected vials have hairline cracks?
that the probability of selecting 4 vials with hairline cracks is approximately 0.0375, or 3.75%
We can solve this problem using the hypergeometric distribution, which is used when sampling without replacement from a finite population. In this case, we have a population of 66 vials, out of which 14 are good (do not have hairline cracks) and 52 are bad (have hairline cracks). The probability of selecting all 4 bad vials (with hairline cracks) can be calculated as follows: P(4 bad vials) = (number of ways to choose 4 bad vials) / (total number of ways to choose 4 vials)
The number of ways to choose 4 bad vials from 52 is: C(52,4) = 52! / (4! × (52-4)!) = 270725
The total number of ways to choose 4 vials from 66 is: C(66,4) = 66! / (4! × (66-4)!) = 7219420
Therefore, the probability of selecting all 4 bad vials is: P(4 bad vials) = 270725 / 7219420 = 0.0375
This means that the probability of selecting 4 vials with hairline cracks is approximately 0.0375, or 3.75%
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What is the area of this compound figure?
Answer:
177 mi²
Step-by-step explanation:
are two rectangles, one has sides of 6 and 19 and one has sides of 9 and 7, we find the two areas with the formula A = L x W and add them, all as in the expression:
remember PEMDAS
6 × 19 + 9 × 7 =
114 + 63 =
177 mi²
