The process of logarithmic functions in real-worlds problems is given below.
And an example of an application of logarithmic function is given.
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
We know,
logarithmic function and exponential function are inverse of each other.
So, whenever we solve the exponential function,
we use the help of logarithmic functions.
To compute the number with bigger exponents,
we use the logarithms.
Because it reduces the size of the numbers.
Let the bacteria is growing exponentially,
b = 2ⁿ.
We know that the bacteria grows every hour.
We want to find time.
Here, we will use the inverse function to the exponential function.
How long will it take them to get 1000 bacteria?
1000 = 2ⁿ
Taking log on both sides,
log(1000) = n log2
n = log(1000)/log(2)
n = 9.96
n ≈ 10 hours.
Therefore, an application of logarithmic function is given above.
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6 cm
To the nearest cubic centimeter, what is the volume of the regular
hexagonal prism?
17 cm
5.2 cm
The volume of the regular hexagonal prism is about cm3.
Answer:
1,590.02
just round it to the nearest centimeter
Step-by-step explanation:
What Is ''Seven times the sum of x and five is forty-nine'' written with no words?
Answer:
7(x+5)=49
Step-by-step explanation:
7 times means multiplication, so 7 times the sum of x and five is 7(x+5). When they say is 49, that means 7(x+5)=49
A square pryamid have a total surface area of 1,477,500ft² and need to find the slant length. The length is 750ft. Find the slant length.
A.) 610in
B.) 610ft
C.) 3,050ft
D.) 3,050in
Explain why the figure is a parallelogram…. Please I need help ASAP.
Answer:
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Step-by-step explanation:
A concave lear of focal length of 20cm forms an image 1/2 the size of the object .The object distance?
Answer:
60cm
Step-by-step explanation:
given:
focal length (f) = 20cm
image height (v) = ½u
object height (u) = ?
(1÷v) + (1÷u) = (1÷20)
(1÷(½u)) + (1÷u) = (1÷20)
(2÷u) + (1÷u) = (1÷20)
(3÷u) = (1÷20)
u = 20 × 3
u = 60cm
you plan to mark up your taco prices by 15%, of your original prices are 4.50, 2.25, and 3.00 what would be the new prices?
Answer:
Step-by-step explanation:
$4.50 + $4.50(0.15) = $5.18
$2.25 + $2.25(0.15) = $2.59
$3.00 + $3.00(0.15) = $3.45
Select the correct answer from each drop-down menu. A bag contains one green ball, one yellow ball, one red ball, and one blue ball. Jerome picks a ball from the bag, replaces it, and then picks another ball. The sample space for this situation is listed. Fill in the missing values in the list.
G-Y Y-Y R-__ B-Y
G-__Y-R R-R B-R
G-B Y-__ R-B B-B
G-G Y-G R-G B-__
Answer:Y, R, B, G
Step-by-step explanation:
Order matters since the ball is being replaced each time. This is all the possible combinations to take 2 balls with replacement, so you can look at the list and see that RR, RB, and RG are listed. The only other combination when choosing a red first would be to pick a yellow, so RY. This is the same pattern for the others also. Look at the list and see what combinations are already listed.
This is the correct answer;
Please leave a Thanks!
It helps!
The length of a rectangle is 4 feet more than twice the width. The perimeter is 116. Find the dimensions of the rectangle
The dimensions of the rectangle are 40 and 18 units respectively
What is the area and perimeter of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given here: The length of a rectangle is 4 feet more than twice the width.
Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116
3x+4 = 58
3x = 54
x = 18
Hence, the dimensions of the rectangle are 40 and 18 units respectively.
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which of the following best describes the graph below
Option A) In the graph for each value of x there is exactly one value of y
So the function is a One to One function.
What is a function?A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|
A function f is said to be injective if it maps different items in its domain to other elements; for example, f = f implies x1 = x2. Alternatively, every element of the function's codomain is at most one of its domain's elements.
If some function output value corresponds to more than one input value, the function is said to be many-to-one (sometimes written as "many-one"). If the domain of f contains two different values a and b such that f(a)=f, the function f is many-to-one in symbols (b).
In the graph for each value of x there is exactly one value of y
So the function is a One to One function.
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Given that f(x)=√x, describe the function of g(x)
shown on the graph.
The function is represented by the equation
g(x)=√x +
The function g(x) has a domain x²
The function g(x) has a range y ≥
Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.
Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.
And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.
I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.
Step-by-step explanation:
SOMEONE PLEASE HELPPP
The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;
[tex]\bar {x}[/tex] ≈ 13.05
Median = 13.60
What is the mean and median of a dataset?The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.
The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.
The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;
The number of data points = 28
The sum of the data is; (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5
The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05
The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;
2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2
The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;
Median = (12.6 + 14.6)/2 = 13.60
The median is 13.60
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use demoivre's theorem to evaluate the expression (3(cos cos(5pie/6)+isin(5pie/y))))^4 write the answer in rectangular form.
By DeMoivre's theorem,
(3 (cos(5π/6) + i sin(5π/6)))⁴ = 3⁴ (cos(4×5π/6) + i sin(4×5π/6))
… = 81 (cos(20π/6) + i sin(20π/6))
… = 81 (cos(10π/3) + i sin(10π/3))
… = 81 (cos(-2π/3) + i sin(-2π/3))
… = 81 (cos(2π/3) - i sin(2π/3))
… = 81 (-1/2 + √3/2 i )
… = -81/2 + 81√3/2 i
What add up to -3 and multiples to -70
We add (x +7 ) (x - 10) up to -3 and multiply to -70.
What is a quadratic equation?
Any equation in algebra that can be written in the standard form where x denotes an unknown value and a, b, and c denote known numbers, where a 0 is a quadratic equation.
Here,
We illustrate and prove that -9 and 10 multiply to -90 and add up to 1:
7 × -10 = -70
-10 + 7 = -3
We are trying to determine how to factor the following quadratic equation.
x² -3 x - 70 = 0
If so, the solution to factor the quadratic equation above is:
(x +7 ) (x - 10)
To summarize, -10 and 7 multiplied by -70 and add up to -3, you know that the following is true:
x² -3x - 70
= (x +7 ) (x - 10)
Hence, we add (x +7 ) (x - 10) up to -3 and multiply by -70.
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What is the value of 6(2b-4) when b=5?
[tex]6(2b - 4)[/tex]
Expanding the terms,
[tex](6 \times 2b) - (6 \times 4) \\ = 12b - 24[/tex]
Plugging in our value b,
[tex]b = 5 \\ 12b - 24 = 12(5) - 24 = 36[/tex]
So the answer is,
[tex]36[/tex]
Answer:
Given expression: 6(2b - 4)
To find the value of 6(2b - 4) at b= 5, we need to substitute the b=5 in the expression, we get
6(2(5) - 4)
= 6(10 - 4)…[solve parentheses]
= 6(6)
6 * 6 = 36
=> 6(2(5) - 4) = 36
Therefore, the value of 6(2b - 4) is 36, when b=5.
Find the LCM of 7xy and 6y2
Step-by-step explanation:
lcm = hcf × remaining expressions
7xy= 7 × x × y
6y² = 6 × y × y
here only y is common in both. so y is the hcf. now, without hcf, the remaining expressions are : 7x and 6y.
so LCM = hcf × remaining expressions
= y × 7x × 6y
= 42xy²
95 POINTS!!! To increase business, the owner of a shoe store is running a promotion in which a customer's bill can be selected at random to receive a discount. When a customer's bill is printed, a program in the cash register determines randomly whether the customer will receive a discount on the bill. The program was written to generate a discount with a probability of 0.15; that is, 15% of the bills get a discount in the long run. However, the owner is concerned the program is incorrect and is not generating the intended long-run proportion of 0.15.
The owner selects a random sample of bills and finds that only 12% of them received a discount. A confidence interval for p, the proportion of bills that will receive a discount in the long run, is 0.12 ± 0.05, and all conditions for inference are met.
Consider the confidence interval 0.12 ± 0.05.
Part A: Does the confidence interval provide convincing statistical evidence that the program is not working as intended? Justify your answer. (3 points)
Part B: Does the confidence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.15? Justify your answer. (2 points)
Part C: A second random sample of bills is taken that is six times the size of the original sample. In the second sample, 12% of the bills received the discount. Determine the value of the margin of error based on the second sample of bills used to compute an interval for p with the same confidence level as that of the original interval. (2 points)
Part D: Based on the margin of error in part C that was obtained from the second sample, is the program working as intended? Justify your answer.
An area surrounding a measurement that indicates how accurate it is called a confidence interval.
Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.
Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:
p ± Zα/2[√{P(1 –p)/n}] ……(1)
where
Zα/2 is the upper (α/2)% point of N(0, 1),
pcap = sample proportion, and
n = sample size.
One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)
Now to work out the solution,
The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)
for Part (a)
equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.
for Part (b)
equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.
For Part (c)
Margin of error is: Zα/2[√{P(1 –P)/n}]
If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be
[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]
= √(n1/n2)
= 1/√6 [given the second sample size is 6 times the first sample size]
= 0.4082
= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082
= 0.05 x 0.4082
= 0.020.
Thus, the margin of error when the sample size if 6-fold is 0.020.
For Part (d)
The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.
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W is greater than or equal to -2 and less that or equal to 5, write the following as an inequality.
Answer:
Step-by-step explanation:
w≥-2
or -2 ≤w≤5
Can y’all help me on question 19?!
Answer: 178.31
Step-by-step explanation: subtract 574.54 by 396.23
Fractional index
Without using mathematical table simplify the following
(16/81)^-3/4
Answer:
[tex]\frac{27}{8}[/tex]
Step-by-step explanation:
using the rules of exponents/ radicals
• [tex](\frac{a}{b}) ^{-m}[/tex] = [tex](\frac{b}{a}) ^{m}[/tex]
• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{n}[/tex]
then
[tex](\frac{16}{81}) ^{-\frac{3}{4} }[/tex]
= [tex](\frac{81}{16}) ^{\frac{3}{4} }[/tex]
= [tex]\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }[/tex]
= [tex]\frac{3^3}{2^3}[/tex]
= [tex]\frac{27}{8}[/tex]
A random sample of 250 campers at a summer camp were surveyed to see what water activities they were most interested in participating in. The study found that 110 campers were not interested in paddleboarding. The study also showed that 64 of the campers who were interested in paddleboarding were also interested in waterskiing and 90 of the students were not interested in waterskiing. Based on the given information, which of the following relative frequency tables summarizes the data?
The relative frequency table that summarizes the data is given by the image at the end of the answer.
What is Relative frequency?The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.
Given:
The percentage of people interested in waterskiing
= 90/250 x 100
= 36%.
Thus, the percentage of people that was not interested in waterskiing is
=100-36
= 64%
Now, the percentages related to paddle boarding are :
Yes: 72/250 = 28.8%.
No: 18/250 = 7.2%.
Of those not interested in waterskiing, the percentages related to paddle boarding are
Yes: 112/250 = 44.8%.
No: (120 - 72)/250 = 19.2%.
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pls help I have a hundred points for someone who answers
957÷3=319 this divide answer i hope help you
ln cos2y + xy + 5x² = 5, find dy/dx. HELP PLEASE!!!
The circle graph shows how a family budgets its annual income. If the total annual income is $100,000, what amount is budgeted for Clothing?
Answer:
where is the circle graph
NEED HELP 25 POINTS !
A special 8-sided die is marked with the numbers 1 to 8. It is rolled 15 times with the results shown in the table.
Results 3 4 5 2 7 1 3 7 2 6 2 1 7 3 6
The experimental probability of rolling an odd number is
%, which is
% more than the theoretical probability.
Answer:
Step-by-step explanation:
Of the twenty times in this experiment the following are prime (3,5,2,7,3,7,2,2,7,3,3,5) or 12 of the twenty
12/20 = 6/10 = 60%
So 60% is the experimental probabilty.
The theoretical probability given that there are four prime numbers (2,3,5,7) out of 8 on the dice should be 50% because 1/2 of the numbers are prime.
The experimental probability is 10% more than the theoretical probability
60% - 50% = 10%
Answer:
60%, 10%
Step-by-step explanation:
Plato/Edmentum
A normal distribution of scores has a standard deviation of 10. Find the z-scores
corresponding to each of the following values:
Answer:
Yes
Step-by-step explanation:
Which equation is equivalent to 16^2p=32^p+3?
Answer:
C. 2^8p=2^5p+15
:D
1.2/4=x/28 what is the value of x
Answer:
8.4
Step-by-step explanation:
You want to know the value of x that satisfies 1.2/4 = x/28.
One-step equationThe equation ...
x/28 = 1.2/4
can be solved in one step by multiplying by 28.
x = 28(1.2/4) = 8.4
The value of x is 8.4.
__
Additional comment
The fraction involving x can be cleared by multiplying by its denominator, effectively the inverse of the coefficient of x. This is the same way you solve any similar one-step equation.
Often, you are told to "cross-multiply" a proportion. Doing that gives you ...
4·x = 28·1.2
Then you have to divide by 4 (multiply by the inverse of the coefficient of x) to find the value of x:
x = 28·1.2/4 . . . . same as above.
That is, there is no need to multiply by 4, and then divide by 4. You can simply multiply by 28 and be done.
Answer:
8.4
Step-by-step explanation:
[tex]\frac{1.2}{4}[/tex] = [tex]\frac{x}{28}[/tex]
cross multiply to solve for x:
(1.2)(28) = 4x
4x = 33.6
x = 33.6/4 = 8.4
Complete this table so it shows a relation that is not a function.
X
2
-4
-3
y
3
1
7
-5
If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.
what is function ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.
given
Table 1:
x 0 -4 3 -2 9 3
y 5 8 7 8 5 -2
No, Table 1 is not a function.
Since there are two images of element '3'.
i.e. 3 is mapped to 7 and -2.
Table 2:
x 2 -7 5 1 -6 3
y 5 8 -6 8 5 7
Yes, this relation is a function.
Because corresponding to each x there is a single image.
If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.
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An art museum opens at 9 am and closed at 5 pm the function V gives the number of visitors in a museum h hours after it opens explain what this statement tells us about the situation: V(5)=36
Answer:
Five hours after the museum opens, there are 36 visitors.
Step-by-step explanation:
V(5)=36 means that when h is 5, V is 36. Assuming this is a function from what information this gives.
shown below. Which of the triangle congruence theorems could be used to prove the triangles congruent without establishing any additional information? FA 20 20 in 14 m A SSA B SSS CHL D SAS 14 in
The right triangles are congruent by HL theorem.
What are congruent triangles?The triangles having congruent corresponding parts are called congruent triangles.
Given are two right triangles, with equal hypotenuse and one of the bases.
The question is by which theorem do they are congruent,
HL theorem :-
The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Since, we know that, when two right triangles have congruent hypotenuse and one of their legs are also congruent, then both are congruent by HL theorem of congruence.
Here, both the right triangles are following the condition of the HL theorem.
Hence, the correct option is HL.
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