The graph of f(x) = a × [tex]b^x[/tex] passes through (2,54) and (5,16).
What is the value of b?
The value of b when the graph of function f(x) = a*bˣ passes through (2,54) and (5,16), is given by, b = 2/3.
Given the function of the graph is,
f(x) = a*bˣ
It is given that the graph of the function passes through the points with coordinates (2, 54) and (5, 16). So this points must satisfy the given function.
Substituting the point (2, 54) in the given function we get,
f(2) = 54
a*b² = 54 ..................... (i)
Substituting the point (5, 16) in the given function we get,
f(5) = 16
a*b⁵ = 16 ..................... (ii)
So dividing equation (ii) by equation (i) we get,
(a*b⁵)/(a*b²) = 16/54
b³ = 8/27
b³ = (2/3)³
b = 2/3
Hence the value of b is 2/3.
To know more about function here
https://brainly.com/question/25638609
#SPJ1
This circle is centered at the origin, and the length of its radius is 5. What is the equation of the circle? A. x2 + y2 = 52 B. x2 + y2 = 5 C. (x - 5)2 + (y - 5)2 = 25 D.
Answer:A
Step-by-step explanation:
Maggie spent $16 on rock climbing. This included a $6 charge for climbing shoes and a $2.50 charge per hour she climbed. If h represents the number of hours she climbed for, write an equation that can be solved to find the number of hours she spent rock climbing.
Answer:
16 = 6+2.5h
Step-by-step explanation:
The total cost is 16 dollars. She spends 6 dollars for shoes and 2.50 per hour.
16 = 6+2.5h
To solve, subtract 6 from each side
16-6 = 6+2.5h-6
10 = 2.5h
Divide each side by 2.5
10/2.5 = 2.5h/2.5
4 =h
She can climb for 4 hours.
A rectangle has length (3x-8) and width (2x-7) cm as shown below... Write down and simplify an expression for the perimeter of the rectangle. (3x-8) (2x-7)
The simplified expression for the perimeter of the rectangle is 10x-30
What is perimeter of a rectangle?The perimeter of a shape is the addition of all the sides of the shape. If l is the length and w is the width, then the perimeter of a rectangle can be expressed as ;
p = 2(l+w)
The length is 3x-8 and the breadth is 2x-7
therefore the perimeter = 2( l+w)
= 2( 3x-8+2x-7)
= 2( 5x-15)
= 10x-30
therefore, the simplified expression for the perimeter of the rectangle is 10x-30
learn more about perimeter of a rectangle from
https://brainly.com/question/19819849
#SPJ1
PQRSTU is plotted on a coordinate plane with vertices p(-1,0) Q(-1,3) R(1,4) S(2,5) T(4,4) and U(4,0) what is the hexagons area
An agency wanted to study annual-sales distribution of 500 cottage industries of the same standard. Since the industries are located in different regions, it will be expensive to collect data from all 500 industries. Thus, the study is to be based on the sales of 75 industries which are selected to represent the whole. a) The agency summarized the collected data in tabular form, displayed it in graph and further found the average annual sales to be 36 thousand birr. What type of statistical technique is used here? b) The average sale of the 500 cottage industries is estimated to be 36 thousand birr based on the sample average. What type of statistical technique is used here?
The type of statistical technique used here is inferential
We are given that;
Annual-sales distribution of cottage industries of the same standard=500
Number of industries=500
Now,
a) The type of statistical technique used here is descriptive statistics, which involves summarizing, organizing, and presenting data in a meaningful way. Descriptive statistics can use tables, graphs, and numerical measures such as mean, median, mode, range, standard deviation, etc. to describe the main features and patterns of a data set.
b) The type of statistical technique used here is inferential statistics, which involves drawing conclusions or making predictions about a population based on a sample. Inferential statistics can use methods such as estimation, hypothesis testing, confidence intervals, regression analysis, etc. to make inferences about the population parameters from the sample statistics.
Therefore, by statistics the answer will be inferential.
Learn more about statistic here:
https://brainly.com/question/1640298
#SPJ1
Apply the repeated nearest neighbor algorithm to the graph above. Starting at which vertex or vertices produces the circuit of lowest cost?
The vertices that produces the circuit of lowest cost is A and D. So, the correct answer is A) and D).
To apply the repeated nearest neighbor algorithm, we need to start at a vertex and repeatedly choose the nearest neighbor until all vertices have been visited. Then, we return to the starting vertex to complete the circuit.
Starting at vertex A, we can follow the path A-DE-BE-C-AD-BC-E-A. The total cost of this circuit is 3 + 1 + 13 + 7 + 6 + 5 + 3 = 38. Starting at vertex B, we can follow the path B-E-DE-BC-AD-C-A-B. The total cost of this circuit is 1 + 3 + 7 + 6 + 5 + 15 + 10 = 47.
Starting at vertex C, we can follow the path C-BC-AD-DE-E-B-CA-C. The total cost of this circuit is 5 + 6 + 1 + 13 + 3 + 15 = 43. Starting at vertex D, we can follow the path D-AD-BC-C-E-DE-BD-DA. The total cost of this circuit is 6 + 5 + 7 + 3 + 10 + 11 = 42.
Starting at vertex E, we can follow the path E-DE-BE-C-BC-AD-CA-E. The total cost of this circuit is 1 + 13 + 7 + 5 + 6 + 15 = 47. Therefore, the circuits with the lowest cost are those starting at vertex A and vertex D, both with a total cost of 38 and 42 respectively. So, the correct option is A) and D).
To know more about vertices:
brainly.com/question/14815086
#SPJ1
A metallurgist made two purchases. The first purchase, which cost $1224, included 48 kilograms of an iron alloy and 40 kilograms of a lead alloy. The second purchase, at the same price, cost $507 and included 24 kilograms of the iron alloy and 13 kilograms of the lead alloy. Find the cost per kilogram of the iron and lead alloys. What is the cost of the iron alloy and the lead alloy?
Express all real numbers greater than 2 in interval notation
The interval-notation for "all real-numbers" greater than 2 is (2, ∞).
The "Interval-Notation" is a way of expressing a set of real numbers using brackets to show which numbers are included in the set. In the case of all real numbers greater than 2, we can write this as:
(2, ∞)
The open-bracket "(" indicate that the number 2 is not included in the set, while the symbol "∞" represents all real numbers greater than 2.
This notation is used to express an open interval, meaning that the endpoints (in this case, 2 and infinity) are not included in the set.
Therefore, the required interval-notation is (2, ∞).
Learn more about Interval Notation here
https://brainly.com/question/17249352
#SPJ1
I have part (a) answered, I just need part (b) if anyone could help with that please?
(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.
(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population.
What is range?Range is a statistical measure that refers to the difference between the highest and lowest values in a set of data. In other words, it is the distance between the largest and smallest values in a dataset.
According to given information:(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.
(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population. A biased estimator systematically overestimates or underestimates the population parameter of interest. The fact that the distribution of sample ranges is approximately symmetric and centered around the true population range suggests that the sample range is an unbiased estimator of the population range. However, the variability of the sample range is quite large, which means that a single sample range may not be a very precise estimate of the population range.
to know more about range
brainly.com/question/28135761
#SPJ1
Your antique watch is increasing in value at a rate of 5% each year. If it is worth $500 today, how much will it be worth 3 years from now? Round to the nearest hundredths.
Answer:$578.81
Step-by-step explanation:
✨magic✨
Simplify 5(x+3) -9x+4... Can somebody please help me??
Answer:
-4x+19
Step-by-step explanation:
Otherwise known as option B :D
Which expression is equivalent to 3^4?
Answer: is d
Step-by-step explanation:
well it is just 3 times 3 times 3 times 3
Suppose that the function h is defined as follows.
For the given function h(x) the points can be plotted on,
(-1,-1)(0,0)(1,1)(2,2)The given function h(x) is having four conditions and each condition can be clearly discussed below:
Given that for the first condition, the x-axis is ranging from -1 [tex]\leq[/tex] x < 0, the y-axis point is present exactly at -1. Similarly, for the second condition, the x-axis is ranging from 0 [tex]\leq[/tex] x < 1, and the y-axis point is present at 0. For the third condition, the x-axis is ranging from 1 [tex]\leq[/tex] x < 2, and the y-axis point is at 1.Finally, for the fourth condition, the x-axis is ranging from 2 [tex]\leq[/tex] x < 3, and the y-axis point is at 2.From, the above analysis we plotted the graph and attaching below.
To know more about functions,
https://brainly.com/question/11624077
#SPJ1
Find the perimeter of each figure
Answer: 53 ft
Step-by-step explanation:
The perimeter of a polygon is the sum of all sides. In this example, the sides are 4 ft, 20 ft, 18 ft, and 11 ft, so the perimeter is
4+20+18+11=53 ft
A vehicle use 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can 2 3 the vehicle travel per gallon of gasoline?
If a vehicle uses 2 gallons of gasoline to travel 18¹/₂ miles, at this rate, the vehicle can travel 9¹/₄ miles per gallon of gasoline.
What is the rate?The rate refers to the average speed of the vehicle.
The rate also describes the unit rate or the rate expressed as a percentage or in terms of speed.
The number of gallons of gasoline used to travel 18¹/₂ miles = 2 gallons
The total distance traveled using two gallons of gasoline = 18¹/₂ miles
The average distance traveled per gallon of gasoline = 9¹/₄ miles (18¹/₂ ÷ 2)
Thus, on the average, the vehicle can travel 9¹/₄ miles miles per gallon of gasoline.
Learn more about the average or unit rate at https://brainly.com/question/4895463.
#SPJ1
Correct Question:A vehicle uses 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?
40% of the fish are carp and 60% of the fish are bass. What’s the probability that the next three fish I catch are all carp?
Answer:
0.064 or 6.4%----------------------------
The probability of catching a carp is 40% since 40% of the fish are carp.
We assume the fish is replaced each time so the probability of three carps is:
P = 0.4³ = 0.064 or 6.4%Let u = - 3i + 2j, v = 3i - 3j and w = - 3j
Find the specified scalar or vector.
5u(3v - 4w)
If u = - 3i + 2i, v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.
To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:
3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j
Next, we can perform the scalar multiplication of u and the vector 6i + 14j:
5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)
Expanding the product, we get:
5(-18i² + 36ij + 42ij - 28j²)
Since i² = j² = -1, we can simplify this expression as:
5(18 + 70) = 440
Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.
The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.
To learn more about vectors click on,
brainly.com/question/9201864
#SPJ1
Can someone help me please
Chapter 13/14. The Civil War. Watch the Hari Jones TED talk. Then, answer the following questions in 7-10 sentences. Then, respond to two different classmates' posts by asking a question or challenging their assertions (respectfully). Try to make sure everyone has a response to their post. Finally, respond to the question or assertion your classmate(s) replied to you. Responses are meant to acknowledge what the other student has communicated, and either expand on their ideas, or push back on them, then offer positive feedback. Consider using the following template: "Hi _____. I was interested in ______ about your post because _______. Also/However, ______. I think ______ because _____. Do you think/feel _____/? I feel _____. "
In serving in the military, what contributions did African Americans make to the Union war effort?
What kinds of discrimination did they face? What kind of heroism did they exhibit, and when?
Write a reaction to Dr/ Jones' TED talk. What did you know/not know? What surprised/amazed/angered/made you proud/saddened/made you happy?
Hi Annie. I was interested in engaging you about your post because of my differing view. However, I think I am open to changing my views because I am not dogmatic. Do you think I am too pliable?
How did African Americans contribute?Throughout the Civil War, African Americans assumed crucial roles in the Union war effort. From enlisting as soldiers to acting as laborers and even spies, their contributions left an indelible impact on history.
Despite being subjected to rampant discrimination and racism from both Confederacy and Union forces, these individuals exhibited incredible heroism and bravery.
Excelling in dangerous missions that often led them to become prisoners of war, they persevered as they fought for the freedoms of themselves and others.
Hari Jones' TED talk shines a much-needed light on this overlooked aspect of history, revealing not only the extensive involvement of African American soldiers but also the pivotal role played by women in areas such as nursing, cooking, and espionage.
Read , more about Civil War here:
https://brainly.com/question/24992590
#SPJ1
Evaluate each expression using the values given in the table.
Answer:
a) f(g(1)) = f(0) = 5
b) f(g(2)) = f(-3) = 8
c) g(f(2)) = g(3) = -8
d) g(f(3)) = g(2) = -3
e) g(g(1)) = g(0) = 2
f) f(f(3)) = f(2) = 3
I would be rally thankful if you help
The matrix after the row operation is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
The row operation is given as follows:
Division by 7 = multiplication by 1/7, as the element at the desired position is of 7.
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
We want to have element 1 into row 1 and column 1, that is, the element of 7 at row 1 and column 1 of the matrix must assume a value of -1.
An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
Dividing every element of the first row by 7, the resulting matrix is then given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
More can be learned about operations with matrices at https://brainly.com/question/16901354
#SPJ1
How do you write 9.6 × 103 in standard form?
A large department store found that it averages 362 customers per hour. Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average. Which statements about this situation are true?
The 99% confidence interval of the population mean is (352.32, 371.68).
To find the 99% confidence interval of the population mean, we need to use the following formula:
CI = x; ± zα/2 * (σ/√n)
where:
x' = sample mean (362)
zα/2 = z-score for 99% confidence level (2.576)
σ = population standard deviation (29.6)
n = sample size (40)
Substituting the values, we get:
CI = 362 ± 2.576 * (29.6/√40)
CI = 362 ± 9.68
This means that if we take many random samples of 40 hours from the population, we can be 99% confident that the true population mean of the number of customers per hour falls between 352.32 and 371.68.
To learn more about sample click on,
https://brainly.com/question/13843114
#SPJ1
Complete question is:
A large department store found that it averages 362 customers per hour. Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average. Find the 99% confidence interval of the population mean.
20x^2-7x-6=0 by factoring
Answer:
x = -2/5
x = 3/4
Step-by-step explanation:
Factoring:
20x²-7x-6=0
20x²+8x - 15x - 6 = 0
4x * (5x + 2) - 3 * (5x + 2) = 0
(5x + 2) * (4x - 3) = 0
Cases:
5x + 2 = 0
4x - 3 = 0
x = -2/5
x = 3/4
Answer:
20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120
Step-by-step explanation:
now,
20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)
5x(4x-3) +2(4x-3)=0
(5x+2) (4x-3)=0
Either 5x=-2
X=-2/5
Or
4x=3
X=3/4
5 years ago i was 5 times older then my son. in 8 years time i will be 3 times older then my son. how old am i today?
Answer:
70 , 18
Step-by-step explanation:
Keeping x as Father and y as son;
5 years ago Person X was 5 times older than Person y , so the equation will be:
x - 5= 5(y-5)
x = 5y - 20
simularily after 8 years , x will be 3 times older than y , so
x + 8 = 3(y + 8.)
I will now try to find y by equating value of x into y:
5y - 20 + 8 = 3y + 24
5y - 3y = 24 + 20 - 8
2y = 44 - 8 = 36
y = 18
so x will be = 5 (18) - 20.
x = 90-20 = 70 years.
therefore father is 70 years , and son is 18 years old.
100 Points! Algebra question. Only looking for an answer to B. Please show as much work as possible. Thank you! Photo attached.
The quotient of functions f(x) and g(x) is given as follows:
(f/g)(x) = (x + 4)/(x - 3).
How to obtain the quotient function?The quotient function of f(x) and g(x) is given by the division of function f(x) by function g(x), as follows:
(f/g)(x) = f(x)/g(x)
The functions for this problem are given as follows:
f(x) = x² + 7x + 12.g(x) = x² - 9.The functions can be factored as follows:
f(x) = (x + 4)(x + 3) -> according to it's roots.f(x) = (x + 3)(x - 3) -> subtraction of perfect squares.The term (x + 3) is common to both numerator and denominator, hence it is simplified and the quotient function is given as follows:
(f/g)(x) = (x + 4)/(x - 3).
More can be learned about quotient functions at https://brainly.com/question/23520000
#SPJ1
Joey wants to buy a $3,000 vehicle with 20 percent down for three years at 12 percent interest. What will his monthly payment be?
Monthly Payment per $1,000 Finance
A. $72.82
B. $89.67
C. $79.70
D. $119.56
Joey’s monthly payment is solved to be
C. $79.70
How to find the monthly payment20% down 600 to calculate the monthly payment on a 3 000 car we would pay 2 400.
the interest rate is 12% per annum which equates to 1% per month the term of the loan is three years which equates to 36 months we can use a formula to calculate the monthly payments
[tex]Monthly salary = (P * r * (1 + r)^n) / ((1 + r)^n - 1) .[/tex]
where
P is the principal (premium),
r is the monthly interest rate, and
n is the number of months.
Plug in the prices and we have:
[tex]Monthly salary = (2400 * 0.01 * (1 + 0.01)^{36} ) / ((1 + 0.01)^{36} - 1)[/tex]
= $79.65 per square foot
So Joey’s monthly payment would be $79.65.
Learn more about percent interest at
https://brainly.com/question/25793394
#SPJ1
what’s the numbers that correspond to the corret number of solutions
The number of solutions for the given system of linear equations is: Infinitely many solutions.
Calculating the number of solutionsTo determine the number of solutions for the given system of linear equations:
3x - y = 4
6x - 2y = 8
We can use the algebraic method of solving the system of equations by substitution or elimination.
Let's use the algebraic method to determine the number of solutions:
3x - y = 4 (1)
6x - 2y = 8 (2)
We can simplify equation (2) by dividing both sides by 2:
3x - y = 4 (1)
3x - y = 4 (2')
Equations (1) and (2') are equivalent, which means that they represent the same line.
Therefore, the two equations represent the same line, and we have infinitely many solutions.
Read more about equations at
https://brainly.com/question/148035
#SPJ1
Complete question
What’s the numbers that correspond to the corret number of solutions
0 solution, 1 solution, Many solutions
3x - y = 4
6x - 2y = 8
please help for this question
Translating the shape S by the vector ( -1 , - 3 ) would lead to S ' with vertices of ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).
How to translate the figure ?Given that the translation vector is negative, this means that you would have to subtract the corresponding values of the vector from the x and y coordinates of each vertex.
The vertices of the new shape S' would be :
Vertex 1: (2 , 1 ) + ( -1, -3 ) = ( 2 - 1 , 1 - 3 ) = ( 1, -2 )
Vertex 2: ( 2, 2 ) + ( -1, -3 ) = ( 2 - 1, 2 - 3 ) = ( 1, - 1 )
Vertex 3: ( 4, 1 ) + (-1 , -3 ) = ( 4 - 1 , 1 - 3) = (3 , -2)
Vertex 4: ( 4, 4 ) + (- 1, -3 ) = (4 - 1, 4 - 3 ) = (3 , 1 )
In conclusion, the translated vertices would be ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).
Find out more on translation at https://brainly.com/question/29103332
#SPJ1
I need help, I’m struggling with 3 and 4 can someone help me
Answer:
3 and 4 ==> see work below
[tex]5. \quad\quad f^{-1}(x) = x^{1/7}[/tex]
[tex]6. \quad\quad f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]
Step-by-step explanation:
Definition of inverse functions
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
Or, in other words
If f(g(x)) = (g(f(x)) = x
then f and g are inverse functions
Q3
We have f(x) = x + 4 and g(x) = x - 4
To find f(g(x)), substitute g(x) = x - 4 wherever there is an x term in f(x)
f(g(x)) = g(x) + 4
= x - 4 + 4 = x
g(f(x)) = f(x) - 4
= x + 4 - 4 =x
Hence f(x) and g(x) are inverse functions
Q4
[tex]f(x) = \dfrac{1}{4}x^3\\\\g(x) = (4x)^{1/3}[/tex]
[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\\\\end{aligned}[/tex]
[tex]\begin{aligned}(g(x))^3 &= \left((4x)^{1/3} \right)^3 \\& = (4x)^{\frac{1}{3} \cdot 3}\\& = 4x\end{aligned}[/tex]
Therefore
[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\&= \dfrac{1}{4} \cdot 4x\\&= x\\\end{aligned}[/tex]
[tex]\begin{aligned}g\left(f(x)\right) & = \left(4f(x)\right)^{1/3}\\&= \left(4 \cdot \dfrac{1}{4}x^3\right)^{1/3}\\& = \left(x^3\right)^{1/3}\\& =x& \end{aligned}[/tex]
So f(x) and g(x) are inverse functions
Q5
[tex]\text{Given $f(x) = x^7 $ we are asked to find inverse $f^{-1}(x)$}[/tex]
[tex]\rm{Let \: y = f(x) = x^7}\\[/tex]
Interchange x and y:
[tex]x = y^7[/tex]
Solve for y:
[tex]y = x^{1/7}[/tex]
The right hand side is the inverse function of f(x)
[tex]f^{-1}(x) = x^{1/7}[/tex]
Q6
[tex]\rm{Given \;f(x) = -\dfrac{2}{5}x^3 \:find\:the\:inverse,\;f^{-1}(x)}[/tex]
Using the same procedure as for Q5
[tex]y=-\dfrac{2}{5}x^3\\\\x=-\dfrac{2}{5}y^3\\\\\text{Solve for y}\\[/tex]
[tex]y^3=-\dfrac{5x}{2}[/tex]
[tex]y=-\left(\dfrac{5x}{2}\right)^{1/3}\\\\\\\text{Inverse of $f(x)$ is $f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]
