suppose f(x) = loga^x and f(4)=2. Find f(16)
Answers
The value of the given function is f(16) = log2(16) = 4.
The problem states that f(x) = loga^x and f(4) = 2, and we need to find f(16).
To solve this problem, we first need to understand the properties of logarithmic functions. One of the key properties of logarithmic functions is that they are the inverse functions of exponential functions. In other words, if y = loga^x, then x = a^y.
Using this property, we can write:
f(4) = loga^4 = 2
4 = a^2
Solving for a, we get:
a = sqrt(4) = 2
Now, we can use the same property to find f(16):
f(16) = loga^16 = log2^16
We can rewrite 16 as a power of 2:
16 = 2^4
Using this, we can simplify log2^16 as follows:
log2^16 = log2^(2^4) = 4*log2^2
We know that log2^2 = 1, since 2^1 = 2. Therefore, we can substitute this into the above equation:
log2^16 = 4 * log2^2 = 4 * 1 = 4
Hence, f(16) = log2^16 = 4.
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Related Questions
Simplify the following expression:
4x-5.2y+6y+7.0x-8x
Answers
Answer:
3x + 0.8y
Step-by-step explanation:
1- Reorder and gather like terms
2- Collect coefficients of like terms
3- Calculate the sum or difference
please help factorise 7ab+a
Answers
Answer:
= a(7b + 1)
Step-by-step explanation:
7ab + a
a(7b + 1).
The 17th term of an Arithmetic sequence is 51. If the commons difference is 7, what is the first term ?
Answers
Answer:
The first term is:
\(a_1=-61\)Step-by-step explanation:
The arithmetic sequence is defined by
\(a_n=a_1+\left(n-1\right)d\)
where
\(a_1\) is the first term
\(d\) is the common difference
as
the 17th term of an arithmetic sequence is 51.
i.e. \(a_{17}=51\)
so
\(a_n=a_1+\left(n-1\right)d\)
\(a_{17}=a_1+\left(17-1\right)d\)
\(51=a_1+\left(17-1\right)7\) ∵ \(n = 17\), \(a_{17}=51\) , \(d=7\)
\(a_1+112=51\) ∵ \(\left(17-1\right)\cdot \:\:7=112\)
\(a_1=-61\)
Therefore, the first term is:
\(a_1=-61\)can someone help meee please
Answers
Answer:
Equation → 5y = 3y + 6
Value of ST = 15
Step-by-step explanation:
From the picture attached,
In right triangles ΔVST and ΔVUT,
Acute angles ∠SVT ≅ ∠UVT [Given]
TV ≅ TV [By reflexive property of congruence]
ΔVST ≅ ΔVUT [Hypotenuse angle congruence of right triangles]
Therefore, corresponding parts of the congruent triangles are congruent.
Therefore, ST ≅ TU
5y = 3y + 6
5y - 3y = 6
2y = 6
y = 3
Therefore, ST = 5y
ST = 5(3)
= 15
The solutions to p(x) = 0 are x = -7 and x = 7. Which quadratic
function could represent p?
Answers
The quadratic equation that represents the solution is F: p(x) = x² - 49.
What is quadratic function?The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.
Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.
Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:
p(x) = (x + 7)(x - 7)
Solving the parentheses we have:
p(x) = x² - 7x + 7x - 49
Cancelling the same terms with opposite sign we have:
p(x) = x² - 49
Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.
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The world population reached 7.53 billion in 2017 and was growing at approximately 1.2% each year. If this growth rate
continues, in what year is the population expected to reach 10 billion people?
2037
2041
2044
2052
Answers
Answer:
2044
Step-by-step explanation:
90,360,000 is each year, and if you multiply that by 10, it is 903,600,000. Do it again to get 1,807,200,000. That would equal the year of 2037, but it isnt enough. Then add 722880000, which would be 2044 and the total would be 7.53 billion + 1807200000 + 722880000 which equals to 10,060,800,000
Pls help I will give brainliest . The answer choices are
x=45, y=90
x=45, y=25
x=57, y=25
x=57, y=90
Answers
Answer:
The answer is B
Step-by-step explanation:
Answer:
C. x = 57, y = 25Step-by-step explanation:
∠LKU = 1/2∠EKU ⇒ ∠LKU = 1/2(90°) = 45°
(x - 12)° = 45°x = 57°∠KCE = 90° as diagonals of a square are perpendicular
(4y - 10)° = 90°4y = 100°y = 100°/4y = 25°Correct option is C. x = 57, y = 25
3 -2 -14
12
543-2
B
Which function could be a stretch of the exponential
decay function shown on the graph?
O f(x) = 2(6)*
O f(x) = -1/-(6)
○ f(x) = 2 [²/2] *
© f(x) = 2 ( 1 )
Answers
The stretch of an exponential decay function is y = 2(1/6)^x
Which is a stretch of an exponential decay function?An exponential function is represented as
y = ab^x
Where
a = initial valueb = growth/decay factorIn this case, the exponential function is a decay function
This means that
The value of b is less than 1
An example of this is, from the list of option is
y = 2(1/6)^x
Hence, the exponential decay function is y = 2(1/6)^x
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which of the following describes a scenario in which a chi-square goodness-of-fit test would be an appropriate procedure to justify the claim? responses a statistician would like to show that one geographical location has a higher proportion of dogs that shed than another geographical location has. the statistician has two independent random samples of dogs from two different geographical locations and has recorded the proportion of dogs that shed in each sample. a statistician would like to show that one geographical location has a higher proportion of dogs that shed than another geographical location has. the statistician has two independent random samples of dogs from two different geographical locations and has recorded the proportion of dogs that shed in each sample. a principal would like to investigate whether more than 50% of the students in a local high school eat in the school cafeteria. the principal has a random sample of individuals within the school and records the proportion of the students who eat lunch in the school cafeteria. a principal would like to investigate whether more than 50% of the students in a local high school eat in the school cafeteria. the principal has a random sample of individuals within the school and records the proportion of the students who eat lunch in the school cafeteria. a campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported. the campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories. a campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported. the campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories. a manager of a water treatment plant would like to investigate whether there is a relat
Answers
a) The campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.
b) A Chi-Square goodness of fit test.
a) A campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported and that's why we know that the campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.
Chi-Square goodness of fit is used to find out how the observed value of a given phenomenon is significantly different from the expected value. In Chi-Square goodness of fit test, the sample data is divided into intervals.
In this case, we have one categorical variable which is the distribution of individuals within several social groups. We want to see if the actual distribution of the variable is significantly different from the distribution within several social groups as claimed(expected) by the newspaper.
Hence, we will use chi-square goodness of fit test for this case.
b) A Chi-Square goodness of fit test.
Here the variable is the distribution of individuals purchasing season pass at an amusement park. The variable has 4 categories based on the age group of the individuals.
A tourist company wants to test the actual distribution of individuals within each age group and wants to check if it is significantly different from the expected distribution i.e the one claimed by the amusement park.
The tourist company randomly sampled 200 individuals entering the park.
The proportion of individuals within each group as claimed by the amusement park is given.
Hence, we will use chi-square goodness of fit test to test if the actual distribution within each group is significantly different or not from the claimed distribution.
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given the following unsorted collection: {-21, 14, 117, -85, 82} what will the collection look like after the third iteration of selection sort (assume we are selecting the minimum element each time)? group of answer choices {82, -85, 117, 14, -21} {-85, -21, 14, 117, 82} {-85, -21, 82, 14, 117} {-85, -21, 117, 14, 82}
Answers
Answer:
Step-by-step explanation:
{-85, -21, 14, 117, 82}
This is a list of five integers: -85, -21, 14, 117, 82. Each integer is separated by a comma. The caret symbols (^) indicate that there is some missing context or information that needs to be explained.
If a ladder is to be placed 3 feet from the side of a house. If top of the ladder rests exactly on the edge of the house when it is placed at an angle of 72 degrees from the ground, how long is the ladder to the nearest foot?
Answers
Answer:
7 feet long
Step-by-step explanation:
This set up will give a right angle triangle where;
Length of the ladder is the hypotenuse = x
The distance of the ladder to the house is the adjacent = 3 feet
Angle of elevation theta = 72 degrees
Using the CAH in trigonometry identity;
cos theta = adjacent/hypotenuse
cos 72 = 3/hyp
hyp = 3/cos72
hyp = 3/0.4258
hyp = 7.05 feet
Hence the ladder is approximately 7 feet long
Please help due ASAP
Answers
Answer:
A.
The scale factor of triangle ABC to DEF is 3.
AC= 1/3 of 15, which is 5.
EF = 3x7, which is 21.
what is (3x – 2)(4x + 1) =
Answers
Answer:
\(12x^{2} -5x -2\)
Step-by-step explanation:
We multiply the first term 3x by 4x and then 3x multiplied by one. We proceed to multiply by -2 by 4x and multiplied by -2 +1. We finally add and get the result.
\(12x^{2} -5x -2\)
if $n$ is a positive integer, then let $f(n)$ be the sum of the digits of $\frac{1}{5^{{}^n}}$ that are to the right of the decimal point. what is the smallest positive integer $n$ such that $f(n) > 10$?
Answers
The smallest positive integer is 1.
What is positive integer?Positive Numbers definition the meaning of positive whole numbers in numerical states that "Numbers that are more noteworthy than zero are positive numbers". Numbers can be grouped into three kinds: negative whole numbers, zero, and positive whole numbers. Normal numbers are extremely normal to people since they come from counting objects like apples or sheep.
If s is integer
S = n (a + l)/2
Normal numbers can be utilized to assess your assets, the amount of you possess. There is no biggest regular number. The following regular number can be found by adding 1 to the ongoing normal number, creating numbers that go on "for eternity". Every one of the numbers we use for counting are positive whole numbers. Positive numbers are entirely of a bigger gathering of numbers called whole numbers. Numbers are the entire numbers, both positive and negative. By entire numbers we mean numbers without divisions or decimals.
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Which of the following are measures of central tendency? Check all that apply.
A.The median
B.A sample statistic
C.The mode
D.The lowest value
E. The mean
Answers
All the measures of central tendency are, The median, The mode, and The mean.
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;
There are some measures,
A. The median
B. A sample statistic
C. The mode
D. The lowest value
E. The mean
We know that;
The four measures of central tendency are mean, median, mode and the midrange.
Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.
Hence, All the measures of central tendency are, The median, The mode, and The mean.
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James and Eron are going on a road trip. Eron drove the first 180 miles of their trip. James drove the next 150 miles of their trip. They decided to drive the same amount of hours each for the rest of the trip. Eron drove at a speed of 60 miles per hour when he drove. James drove at a speed of 55 miles per hour when he drove.Let h represent the number of hours driven by each person.
Answers
Question seems incomplete but some explanation could help
Answer and explanation:
Distance travelled = speed × time
We know the speed for each driver:
Eron drove at 60 miles per hour
James drove at 55 miles per hour
We know they both drove same amount of time = h
Therefore Eron's distance travelled = 60 miles per hour × h = 60h
Jame's distance travelled = 55 miles per hour × h =55h
Total distance travelled for the rest of the trip = 60h + 55h
I need help
Solving this problem
Answers
The required value of x is 22 degrees for the given figure.
Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.
As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:
According to the given figure, it can be written as follows:
2x + 24 + 6x - 20 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176/8
x = 22
Therefore, the required value of x is 22 degrees for the given figure.
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The complete question is as follows:
Find the value of x for the below figure.
Using the given clues find the value of circle plus circle
Answers
Clues have not been provided in the question. However, we can still discuss how to find the value of circle plus circle. Circle plus circle refers to the sum of the areas of two circles.
Therefore, the value of circle plus circle is given by the formula:$$\text {Circle plus Circle} = πr_1^2 + πr_2^2$$ where r1 and r2 are the radii of the two circles respectively. If the values of the radii are provided, then we can substitute them in the above formula to find the value of circle plus circle. To find the value of circle plus circle, we need to add the areas of two circles. As we already know that a circle is a geometric figure having no end. It has many properties. One of its properties is that its area can be measured. When we talk about the area of a circle, we are referring to the region enclosed by it.
The area of a circle is given by the formula: A = πr², where A is the area of the circle and r is its radius. The symbol π represents the constant pi, which is approximately equal to 3.14. Therefore, the area of a circle is proportional to the square of its radius. If we have two circles with radii r1 and r2, then the area of the first circle is given by A1 = πr1², and the area of the second circle is given by A2 = πr2². To find the sum of the areas of the two circles, we simply add their respective areas, i.e., Circle plus Circle = A1 + A2 = πr1² + πr2². This is the formula for finding the value of circle plus circle. If the values of the radii are provided, then we can substitute them in the above formula to find the value of circle plus circle. Therefore, we can say that the value of circle plus circle is given by the formula Circle plus Circle = πr1² + πr2², where r1 and r2 are the radii of the two circles respectively.
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Question 4: Expand -4(3g + 6)
Answers
Answer:
-12g - 24
Step-by-step explanation:
-4(3g + 6)
-12g - 24
For parties of six or more, a restaurant adds a 20% gratuity (or tip). If a
dinner bill for a large party comes to $148.25, find the total dinner bill with
tip. $177.90
Answers
The total dinner bill was $177.90 including a tip of 20%.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Given that, a restaurant adds a 20% gratuity (or tip), a dinner bill for a large party comes to $148.25, we need to find the total dinner bill with tip.
The total bill will be = 148.25 + 20% of 148.25
= 148.25 + 20/100 × 148.25
= 148.25 + 0.2 × 148.25
= 148.25 + 29.65
= 177.90
Hence, the total dinner bill was $177.90 including a tip of 20%.
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Which systems of equations have one or more solutions?
Select all that apply. HELP ASAPPPP
Answers
suppose you have three possible risk scenarios x, y, and z. your initial assessment found that x is twice as likely as z, and y is three times as likely as z. what is p(x), p(y), and p(z)?
Answers
Given,Three possible risk scenarios X, Y and Z. The initial assessment found that X is twice as likely as Z and Y is three times as likely as Z.
Probability of X is p(X) = 2p(Z)
Probability of Y is p(Y) = 3p(Z)
Probability of Z is p(Z)Let the probability of Z be p. So, the probability of X and Y can be written as:
p(X) = 2p(Z)p(Y) = 3p(Z). And, Total probability, p(X) + p(Y) + p(Z) = 1. Given that, p(X) + p(Y) + p(Z) = 12p(Z) + 3p(Z) + p(Z) = 1(6p(Z) = 1)p(Z) = 1/6. Therefore, p(X) = 2p(Z) = 2(1/6) = 1/3p(Y) = 3p(Z) = 3(1/6) = 1/2. Hence, the probability of X, Y, and Z are p(X) = 1/3, p(Y) = 1/2, and p(Z) = 1/6 respectively.
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an $8.5$-by-$11$-inch piece of paper is folded in half repeatedly (never being unfolded), each time shortening what was then the longer side. what is the length of the longest side, in inches, immediately after the second fold? express your answer as a decimal to the nearest tenth.
Answers
The answer is 5.5 inches, expressed as a decimal to the nearest tenth.
The longest side of the paper immediately after the second fold is 5.5 inches. To calculate this, the 8.5-by-11 inch piece of paper was folded in half, repeatedly (never being unfolded), each time shortening the longer side. This results in the longest side of the paper being 4.25 inches after the first fold, and 5.5 inches after the second fold. Therefore, the answer is 5.5 inches, expressed as a decimal to the nearest tenth.
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PLEASR HELP TODAY WHIEVER GIVES ANSWER GWTS BRAINLEST
Answers
The angle measures are given as follows:
m < 5 = 75º.m < 11 = 75º.m < 16 = 65º.How to obtain the angle measures?Angles 5 and 8 form a linear pair, hence they are supplementary, meaning that the mesure of angle 5 is given as follows:
m < 5 + m < 8 = 180º
m < 5 + 105º = 180º
m < 5 = 75º.
Angles 5 and 11 are alternate exterior angles, hence they are congruent and the measure of angle 11 is given as follows:
m < 11 = 75º.
Angles 1 and 13 are corresponding angles, meaning that they are congruent, hence the measure of angle 13 is given as follows:
m < 13 = 115º.
Angles 13 and 16 form a linear pair, hence they are supplementary, meaning that the mesure of angle 16 is given as follows:
m < 13 + m < 16 = 180º
m < 16 = 180º - 115º
m < 16 = 65º.
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PLEASEE ANSWER ASAP PLEASE CAN SOMEONE ANSWER QUESTION A AND B ASAPP
50 POINTTSS
Answers
Answer:
Rotate the shape on the right side 90 degrees.
Step-by-step explanation:
hope this helped!
What is a degree 4 function called?
Answers
Answer:
Quartic function
Step-by-step explanation:
Answer: Quartic function
Step-by-step explanation:
find the slope of the graph
Answers
Answer:
D
Step-by-step explanation:
Using rise over run
:)
WHAT IS THE factor of 28 and 25.
Answers
Answer: 1
Step-by-step explanation:
When you compare the two lists of factors, you can see that the only common factor is 1.
the answer would be 1
when you compare the 2 you can see othe only common factor is 1
Gale owns a car that is worth $9,500 but she still owes $7,400 on the car loan. She has a student loan in the amount of $6,000 and she has a savings account with a balance of $1500. The balance on her credit card is $3200. What is her net worth?
Answers
Answer:
$8000
Step-by-step explanation:
Given: Car worth = $9,500, car loan = $7,400. Student loan = $6,000, savings account = $1500. The balance on her credit card is $3200.
Formula: Total Assets - Total Liabilities - Intangible Assets = Tangible Net Worth.
To find: Gale's net worth
Solution: You can calculate your net worth by subtracting your liabilities (debts) from your assets.
Firstly, calculate the total amount of assets by adding them together;
Total assets = Car worth + car loan + Student loan + savings account + balance on her credit card =
$9,500 + $7,400 + $6,000 + $3200 =$26,100
Secondly, calculate the Liabilities by adding them together;
Car loan + Student loan =
$7,400 + $6,000 = $13,400
Then, calculate the Intangible Assets by adding them together;
Savings account + The balance on her credit card =
$1500 + $3200 = $4700
Finally, subtract the total amounts;
$26,100 - $13,400 - $4700 = $8000
(Note:- If your assets exceed your liabilities, you will have a positive net worth. Conversely, if your liabilities are greater than your assets, you will have a negative net worth.)
first answer = brainliest
Answers
Answer:
120 cubic cm
Step-by-step explanation:
