Match the pairs of equations that represent concentric circles. Tiles
WORTH 20 POINTS
Which functions are equivalent to f(x)= 4√162? Check all that apply
A)f(x)= 162 x/4
B)f(x)=(3 4√2)x
C)f(x)=9 4√2 x
D)f(x)=162 4/x
E)f(x)=[3 (2 1/4)]x
The options that are equivalent to the given function are;
Option A
Option B
Option E
The correct options are;
A) f(x) = [tex]162^{x/4}[/tex]
B) f(x) = (3∜2[tex])^{x}[/tex]
C) f(x) = [tex]9\sqrt[4]{2^{x} }[/tex]
D) f(x) = [tex]162^{4/x}[/tex]
E) f(x) = [tex](3(2^{1/4}))^{x}[/tex]
We are given the function; f(x) = [tex](\sqrt[4]{162})^{x}[/tex]
Now, when we have something like; [tex]\sqrt[b]{2}^{a}[/tex]
This expression can also be expressed as; [tex]2^{a/b}[/tex]
Therefore our function can also be expressed as; f(x) = [tex]162^{x/4}[/tex]
Option A; This is correct because it is equal to our function gotten
Option B; f(x) = (3∜2[tex])^{x}[/tex]
From earlier, we will have; (3 × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Now, 3 can also be expressed as [tex]81^{1/4}[/tex]
Thus, we now have;
([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Factorizing out the 1/4 exponent gives;
(81 × 2[tex])^{x/4}[/tex]
⇒ = [tex]162^{x/4}[/tex]
This is same with our function and it is correct
Option C; f(x) = (9∜2[tex])^{x}[/tex]
This is similar to our equation in option B which was correct but the difference here is 9 instead of 3 and clearly this option is not correct.
Option D; f(x) = [tex]162^{4/x}[/tex]
This is not the same with our function and so it is wrong
Option E; f(x) = [tex](3(2^{1/4}))^{x}[/tex]
As seen in option B;
3 can also be expressed as [tex]81^{1/4}[/tex]
Thus, we now have;
;([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Factorizing out the 1/4 exponent gives;
(81 × 2[tex])^{x/4}[/tex]
⇒ = [tex]162^{x/4}[/tex]
This is same with our function and it is correct
Read more at; https://brainly.com/question/6504126
Given the expression −10p2q + 7p3q − 5q, do the following as instructed below: A: Write the polynomial in descending order. B: Classify the polynomial by the number of terms. C: State the degree of the polynomial.
PLEASE HELP
Nestor is building a new swimming pool for $11,000. He makes a $1,000 down payment and the builder gives him an add-on loan, charging him an annual interest rate of 7.7%. If he takes a 6-year loan, what will Nestor's monthly payments be?
A 90% confidence interval for a population mean is (65, 77). the population distribution is approximately normal and the population standard deviation is unknown. this confidence interval is based on a simple random sample of 25 observations. calculate the sample mean, the margin of error, and the sample standard deviation.
The sample mean for the given 90% confidence interval (65, 77) is 71. The margin of error is 6. The sample standard deviation cannot be specifically calculated without the t-value, but presuming a common t-value for such datasets (1.96), it approximates to 3.072.
Explanation:The subject at hand pertains to confidence intervals and basic statistics calculations. Given a 90% confidence interval of (65, 77), we can find the sample mean by adding the two limits and dividing by 2. So (65 + 77) / 2 equals 71.
The margin of error for the confidence interval is calculated by subtracting the sample mean from the upper limit. That gives us 77 - 71 equals 6.
Unfortunately, without knowing the value of the t-statistic, we can't calculate the sample standard deviation, as it's calculated via the formula: standard deviation = margin of error / (t-value/sqrt(sample size)). But, usually, for a sample size of 25 observations and a 90% confidence level, the t-value is about 1.96. Using that assumed t-value, the standard deviation calculation gives us 6/(1.96/sqrt(25)) equals approximately 3.072.
Learn more about Confidence Interval Statistics here:
https://brainly.com/question/33193487
#SPJ3
What is the slope-intercept form of this equation?
3x + 9y = 18
A. y = -1/3x + 6
B. y = -1/3x + 2
C. y = 1/3x + 6
D. y = 2/3x + 2
The correct answer is B. y = -1/3x + 2
Sorry if I am wrong, but I believe that this is the correct answer.
one shelf in the greenhouse holds 467 plants how many plants can 6 shelves hold?
Write a unit test for addinventory(). call redsweater.addinventory() with parameter sweatershipment. print the shown error if the subsequent quantity is incorrect. sample output for failed unit test given initial quantity is 10 and sweatershipment is 50: beginning tests. unit test failed: addinventory() tests complete. note: unit test failed is preceded by 3 spaces.
A unit test for the function addInventory() can be written in JavaScript using Jest. The test checks that the quantity of red sweaters increases correctly after calling addInventory(). If the test fails, an error message will be shown.
Explanation:Based on the information given, you can create a unit test in many programming languages. Here we are going to illustrate with JavaScript and use the Jest testing framework.
Firstly, let's name the unit test file as redSweater.test.js. In this file, we call the addInventory() of the redSweater object with sweaterShipment as parameter. Note that addInventory() is a method that increases the quantity of red sweaters in inventory by a certain amount provided by sweaterShipment.
Here is a sample unit test for your needs:
const redSweater = require('./redSweater'); // path to your redSweater.js file
test('addInventory() unit test', () => {
let initialQty = 10;
redSweater.qty = initialQty;
let shipmentQty = 50;
redSweater.addInventory(shipmentQty);
expect(redSweater.qty).toBe(initialQty + shipmentQty);
});
This script tests that the quantity of red sweaters increases correctly after calling the addInventory() method. If the quantity is not correct after the method call, the test will fail and show an error message.
Learn more about Unit Testing here:https://brainly.com/question/32106174
#SPJ12
A certain product has a unit price of 9.5 cents per ounce. The product sells in bottles of 14 ounces and is priced at $1.30.
As compared to the unit price, the $1.30 price of the 14-ounce bottle _____.
is too low
is too high
is correct
can't be determined
Answer: the answer is too low i really hope this hepls
Step-by-step explanation:
The graph of a line passes through the points (0, -2) and (6, 0). What is the equation of the line?
Answer:
y = 1/3x - 2
Step-by-step explanation:
Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4?
Answer:
–5 with multiplicity 2 and 0 with multiplicity 4
Step-by-step explanation:
I just got it wrong on edge 2020
Pin Numbers A student loan administrator distributes pin numbers to its debtors. Each pin consists of two letters followed by three numbers. (Assume repetition is allowed, and order is important.) (a) How many different pin numbers are there? (b) What is the probability a pin number selected at random ends in 000? (c) What is the probability a pin number selected at random begins with AA?
Puppies of the Dow Refer to Problems 41 and 43. (a) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability all five will be Puppies of the Dow? (b) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability exactly three will be Puppies of the Dow? (c) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability at least two will be Puppies of the Dow?
40. Hockey There are 15 teams in the Eastern Conference of the National Hockey League for the 2009–2010 season, divided
I will just answer the problem about Pin numbers because the other questions lack other given values.
a. How many different pin numbers are there?
There are 26 letters in total and 10 numbers in total (including zero), therefore the total number of different pin numbers are:
Total possible = 26 * 26 * 10 * 10 * 10
Total possible = 676,000 different pins
b. What is the probability a pin number selected at random ends in 000
The total possible numbers with ending of 0 0 0 is:
Possible numbers = 26 * 26 * 1 * 1 *1
Possible numbers = 676
Therefore the probability is:
Probability = 676 / 676,000
Probability = 0.001 = 0.10%
c. What is the probability a pin number selected at random begins with AA?
The total possible numbers starting with A A is:
Possible numbers = 1 * 1 * 10 * 10 * 10
Possible numbers = 1000
Therefore the probability is:
Probability = 1000 / 676,000
Probability = 1.48 x 10^-3 = 0.148%
A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue)
a.9
b.4/3
c 1/4
d. 3/4
To find the probability of not drawing a blue marble from the bag, one must divide the number of non-blue marbles by the total number of marbles, resulting in a probability of 3/4
The question asks to find the probability of not drawing a blue marble from a bag that contains 8 red marbles, 3 blue marbles, and 1 green marble. The total number of marbles is 8 + 3 + 1 = 12. The probability of not drawing a blue marble (P(not blue)) is the number of marbles that are not blue divided by the total number of marbles. This is (8 red + 1 green) / 12 total marbles. Calculated, the probability is 9/12, which simplifies to 3/4
Find all the real square roots of 0.0625.
-0.25 and 0.25
-0.025 and 0.025
0.25
-0.025
The real square roots of 0.0625 are -0.25 and 0.25, as both of these numbers squared equal 0.0625.
Explanation:The student has asked to find all the real square roots of 0.0625. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for a number which, when squared, equals 0.0625.
To find this, we can recognize that the square root of 0.0625 could be thought of in fraction form as the square root of 625/10000, which simplifies to the square root of 625 divided by the square root of 10000. This reduces to 25/100 because 625 is a perfect square (25 * 25) and 10000 is also a perfect square (100 * 100). Therefore, the principal square root of 0.0625 is 0.25.
However, since every positive number has two square roots, one positive and one negative, and because the square of both -0.25 and 0.25 gives 0.0625, we conclude that the real square roots of 0.0625 are -0.25 and 0.25.
if 8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10, how much does each pen and pencil cost?
Answer with Step-by-step explanation:
Let x be the cost of 1 pen and y be the cost of 1 pencil
8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10
8x+7y= 3.37 -----------------(1)
and 5x+11y= 3.10 -----------------(2)
equation (1)×5-equation(2)×8
5(8x+7y)-8(5x+11y)=3.37×5-3.10×8
40x+35y-40x-88y= -7.95
-53y = -7.95
y= 0.15
Putting y=0.15 in equation (1), we get
8x+7×0.15=3.37
8x+1.05=3.37
8x=2.32
x=0.29
Hence, Cost of 1 pen=$ 0.29
Cost of 1 pencil= $ 0.15
Select all numbers that are irrational.
π
1.33
√196
√20
There are two kinds of real numbers in mathematics, one is rational number and other is irrational number. Out of given options, π and √20 are irrational number. Therefore option A, D are correct option
What is irrational number?Real numbers that can not be written in the form of fraction is called irrational number. Real number that can be written in form of fraction is called rational number.
In option (1) π is an irrational number as it contains infinite decimals when we divide 22 by 7
In option (2) 1.33 is a fixed number so it can be written in fractions so this number is rational number
In option (3) √196, it is square root of 14 so it can be written in fraction so it is rational number.
In option (4) √20 is an irrational number as on finding its square root there will be infinite decimals so it cannot be written in form of fraction
Therefore π and √20 are irrational number. Therefore option A, D are correct option
To know more about irrational number, here:
https://brainly.com/question/4031928
#SPJ5
A university would like to create a circular eating area with picnic tables. the eating area will have small plants that make a path to create individual sections that form sectors. the angle formed by the plants is 0=120 degrees, and the radius is r = 9m. find the area of each sector. a. 3(pi)m(squared) b. 6(pi)m(squared) c. 27(pi)m(squared) d. 54(pi)m(squared)
10-6+(6×8)-8? what would be the answer?
in a certain chemical, the ratio of zinc to copper is 4 of 13. a jar of the chemical contains 338 grams of copper. how many grams of zinc does it contain?
What numbers multiply to -30 and add to -3
Jessie has a piece of wood that is 8 feet long. He needs to cut pieces that are 7/8 of a foot long. How many pieces will he be able to make?
Answer:
9 full pieces.
Step-by-step explanation:
In order to solve this we have to divide the total feets of wood that Jessie has, by the size of the pieces that Jessie needs:
[tex]\frac{8}{\frac{7}{8} }\\\frac{\frac{8}{1} }{\frac{7}{8} }\\\frac{8*8}{7*1}\\\frac{64}{7} =9.14[/tex]
Since Jessie will be able to cut 9.14 pieces of wood, he will have only 9 full pieces, so the total amount of pieces that he would be able to cut will be 9.
Define a method pyramidvolume with double parameters baselength, basewidth, and pyramidheight, that returns as a double the volume of a pyramid with a rectangular base. relevant geometry equations: volume = base area x height x 1/3 base area = base length x base width. (watch out for integer division).
The quotient of-54 and 9, subtracted from 8 times a number, is-18
Please help with 1 & 2
The graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.
Which equation describes g(x)?
g(x)=|x+4|g(x)=|x|−4g(x)=|x−4|g(x)=−4|x|
Answer:
Option D
Step-by-step explanation:
The given function is
[tex]f(x)=4|x|[/tex]
It is given that the graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.
If a figure reflected across x-axis, then the rule of reflection is
[tex](x,y)\rightarrow (x,-y)[/tex]
Using the above rule, if the given function reflected across x-axis, then g(x)=-f(x).
[tex]g(x)=-(4|x|)[/tex]
[tex]g(x)=-4|x|[/tex]
The equation g(x)=-4|x| describes g(x).
Therefore, the correct option is D.
volume of a cube measuring 4 yd on each edge
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. if the fencing costs $16 per linear foot to install and the farmer is not willing to spend more than $8000, find the dimensions for the plot that would enclose the most area.
Inventory for a company is taken hourly from 10 to 4:00. At the start of the day, the warehouse had 65 boxes. Between 10 and 11, 7 boxes were shipped. From 11 to noon, 5 were sent, and another 9 between noon and 1 p.m.
All of the following have the same unit price except _____.
2 for $5.08
5 for $12.70
1/2 for $1.27 2
2 1/2 for $6.25
Answer:
2 1/2 for $6.25
Step-by-step explanation:
Hello
the unit price is the price that you pay for a unit of product, you must find each unit price and compare
the unit price is given by
[tex]Unit\ price = \frac{amount\ paid}{number\ of\ products} \\[/tex]
Step 1
find each unit price
1).2 for $5.08
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 5.08}{2}\\\\Unit\ price =2.54[/tex]
unit price =2.54 $
2).5 for $12.70
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 12.7}{5}\\\\Unit\ price =2.54[/tex]
unit price =2.54 $
3) 1/2 for $1.27 2
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 1.27}{0.5}\\\\Unit\ price =2.54[/tex]
unit price =2.54 $
4) 2 1/2 for $6.25
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 6.25}{2.5}\\\\Unit\ price =2.5[/tex]
unit price =2.5 $
Step 2
define
Now, we can define that the unit price of 2 1/2 for $6.25 is different to the others.
2.5 ≠ 2.54
Have a great day
What is the average speed of an object that travels 50 miles in 2 hours?