Answer:
all real numbers
Algebra Examples
The domain of the expression is all real numbers except where the expression is undefined
Hello!
The domain of an exponential function is the crowd of all real numbers, so: x ∈ ℝ.
Good luck! :)
y is inversely proportional to x when y=9, x=24
Answer:
216
Step-by-step explanation:
y=k÷x
k=xy
k=9×24
k=216
Mr johnson sells erasers for $3 each. He sold 96 erasers last week and he sold 204 erasers this week.
A. $300 B $600 C $100 D $900
I believe your answer is D.) $900
204 + 96 = 300
300 x 3 = 900
I hope this is correct and helps!
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
Use the button on your calculator to complete this
problem.
V=
cm3
Answer:4778.3 cm^3
Step-by-step explanation: The formula for volume of a cone is V=1/3h pi r^2. By plugging in the height and the radius we get our answer.
Answer:
4778.4 :)
Step-by-step explanation:
Last year, Manuel deposited $7000 into an account that paid 11% interest per year and $1000 into an account that paid 5% interest per year. No withdrawals were made from the accounts. Answer the questions below. Do not do any rounding. (a) What was the total interest earned at the end of year? (b) What was the percent interest for the total deposited?
Answer:
The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.
Step-by-step explanation:
Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:
7000 x 0.11 + 1000 x 0.05 = X
770 + 50 = X
820 = X
8000 = 100
820 = X
820 x 100/8000 = X
82,000 / 8,000 = X
10.25 = X
Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.
30 POINTS
Help on Part B pleaseeee
In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:
4x-5
Answer:
Solution given:
B.g(x)=[tex]\frac{x+5}{4}[/tex]
let
g(x)=y
y=[tex]\frac{x+5}{4}[/tex]
Interchanging role of x and y
we get:
x=[tex]\frac{y+5}{4}[/tex]
doing crisscrossed multiplication
4x=y+5
y=4x-5
So
g-¹(x)=4x-5
Given that,
→ g(x) = x+5/4
Then g(x)=y,
→ y = x+5/4
Now we can interchange role of x and y,
→ x = y+5/4
Then use the cross multiplication,
→ 4x = y+5
→ y = 4x-5
Hence, g-¹(x) = 4x-5 is the solution.
from an observer o, the angles of elevation of the bottom and the top of a flagpole are 40° and 45° respectively.find the height of the flagpole?
Answer:
Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.
We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.
Remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus)
So, if we define H as the height of the cliff
X as the distance between the observer and the cliff
and h as the height of the flagopole
we can write:
tan(40°) = H/X
tan(45°) = (H + h)/X
Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.
But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.
We want to find the value of h.
If we take the quotient between both equations, we get:
Tan(45°)/Tan(40°) = (H + h)/H
1.192 = (H + h)/H
1.192*H = H + h
1.192*H - H = h
0.192*H = h
So the height of the flagpole is 0.192 times the height of the cliff.
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-4, -33) (1, 2) (9, 162)
HELP PLZ
9514 1404 393
Answer:
y = x^2 +10x -9
Step-by-step explanation:
Quadratic regression generally requires the use of "technology" to aid in finding the equation of the curve of best fit. Use the technology you've been introduced to.
__
When only a few data points are provided, I prefer to use the Desmos graphing calculator. It shows the equation to be ...
y = x^2 +10x -9
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many students would need to be sampled
Answer:
6546 students would need to be sampled.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The dean randomly selects 200 students and finds that 118 of them are receiving financial aid.
This means that [tex]n = 200, \pi = \frac{118}{200} = 0.59[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many students would need to be sampled?
n students would need to be sampled, and n is found when M = 0.01. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.01 = 1.645\sqrt{\frac{0.59*0.41}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.645\sqrt{0.59*0.41}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.59*0.41}}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.59*0.41}}{0.01})^2[/tex]
[tex]n = 6545.9[/tex]
Rounding up:
6546 students would need to be sampled.
A researcher conducts a repeated-measures design study comparing 2 treatment conditions and obtains 20 scores in EACH treatment condition. How many participants participated in the study
Answer:
20 participants
Step-by-step explanation:
Given
[tex]Conditions = 2[/tex]
[tex]Scores = 20[/tex]
Type: Repeated design
Required
The number of participants (n)
The repeated measure design implies that the test was conducted repeatedly on the same sample size.
Since the score in each test is 20; then:
[tex]n = 20[/tex] --- the number of participants
The volume, V, of a sphere in terms of its radius, r, is given by , V(r)=4/3(pie)r^3. Express r as a function of V, and find the radius of a sphere with volume of 150 cubic feet. Round your answer for the radius to two decimal places.
r(V)=
A sphere with volume 150 cubic feet has radius
_________ feet.
Step-by-step explanation:
If
[tex]V=\dfrac{4\pi}{3}r^3[/tex]
then we can solve for r as
[tex]r = \sqrt[3]{\dfrac{3V}{4\pi}}[/tex]
If the volume of the sphere is 150 ft^3, then the radius is
[tex]r = \sqrt[3]{\dfrac{3(150\:\text{ft}^3)}{4\pi}} = 3.30\:\text{ft}[/tex]
The radius of the given sphere with a volume of 150 cubic feet is 2.29 feet, correct to two decimal places.
Given that
the volume of a sphere = 150 cubic feet.
the radius of the sphere=????
what is a Sphere?a round solid figure, or its surface, with every point on its surface equidistant from its center.
as we know,
the volume of a sphere
[tex]V=\frac{4}{3} *\pi *r^3[/tex]
[tex]r = \sqrt[3]{\frac{3V}{4\pi } }[/tex][tex]r = \sqrt[3]{\frac{3*150}{4\pi } }[/tex][tex]=2.29 feet[/tex]
therefore, the radius of the given sphere is 2.29feet
to get more about sphere refer to the link,
https://brainly.com/question/22807400
rotation 180 degrees about the origin.
Answer:
Take the picture you uploaded.
Click the rotate button twice.
Done
How would you write 8^5 as a multiplication expression?
Answer:
8 * 8 * 8 * 8 * 8
Step-by-step explanation:
8^5 is basically 8 times itself five times.
CHECK MY ANSWERS PLEASE
____
The sequence is geometric:
3, 13, 23, 33,...
True
False***
_____________________
The sequence is geometric:
5, -25, 125, -625,...
True***
False
Answer:
1. False 2. True
Step-by-step explanation:
For a geometric sequence,
[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]
1. The sequence is :
3, 13, 23, 33,...
[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]
It is not geometric. It is false
2. The sequence is :
5, -25, 125, -625
[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]
So, the sequence is geometric as the common ratio is same. It is true.
math help plz
how to solve literal equations, how to understand and step by step with an example provided please
9514 1404 393
Explanation:
Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.
Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.
Simple example
y = mx + b . . . . . . solve for x
In this equation, the operations performed on x are ...
multiplication by maddition of b to the productIn accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.
y -b = mx +b -b ⇒ y -b = mx
Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.
(y -b)(1/m) = (mx)(1/m) ⇒ (y -b)/m = x
Now, we have solved this literal equation for x.
_____
Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.
The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:
x + (-x) = 0
Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.
x · (1/x) = 1
When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:
(x^a)^(1/a) = x^1 = x
arcsin(sin(x)) = x
(√x)^2 = x
10^(log(x)) = x or log(10^x) = x
Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.
When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.
Example:
ax + b = cx +d . . . . . solve for x
ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)
x(a -c) = d -b . . . . . combine x-terms
x = (d -b)/(a -c) . . . . divide by the coefficient of x
Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.
More Complicated Example:
A recent Brainly problem asked for the solution to ...
T = 2π√(L/g) . . . . solve for L
Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:
[tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]
The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.
_____
Key Points
The equal sign is sacred, and its truth must be preserved at every step.Literal equations are solved the same way numerical equations are solved.Inverse operations and functions are used to "undo" operations and functions.The Order of Operations can be helpful when considering what to do first.So for this problem I got the scientific notation however I can not seem to figure out the standard notation. I thought it is the same answer but it is not. Can someone please help me out here please?
Answer:
567000000
Step-by-step explanation:
Standard is the actual number. Multiply 5.67 and 10^8.
the complement of guessing 5 correct answers on a 5 question true or false examination is
Answer:
Guessing at least one incorrect answer
Step-by-step explanation:
The complement of guessing 5 correct answers on a 5-question true/false exam is-
Guessing at least one incorrect answer because, when 1 or more questions are incorrectly guessed, the event of 5 correct answers can not occur.
Here is the general information about the Learn by Doing discussion board exercises (directions, grading, feedback). Prompt
1) Give an example of a research question that involves estimating a characteristic about the population of part-time students at your college.
2) Improve this poorly stated research question: Do students work a lot of hours
Answer:
Step-by-step explanation:
Answer to question 1:
On average do part-time students spend less than 20 hours per work on academic work and assignments ?
Answer to question 2:
On average do students work greater than 50 hours a week ?
will give brainyest (m^2/3 n^-1/3)^6
Step-by-step explanation:
here is the answer to your question
Write an equation that represents the line.
Use exact numbers
The sum of 3 consecutive odd numbers is 183. What is the third number in this sequence?
Answer:
61
Step-by-step explanation:
3x + 6 = 183
3x = 177
x = 59
(x+2) = (59+2) = 61
It is correct on khan academy
Answer:
The third number in this sequence is 63.
Step-by-step explanation:
Let the first odd number be x.
Since our sequence are consecutive odd numbers, the second term must be (x + 2) and the third (x + 4). If we only add one, we will get even numbers.
Their sum is 183. Hence:
[tex]x+(x+2)+(x+4)=183[/tex]
Solve for x. Combine like terms:
[tex]3x+6=183[/tex]
Subtract six from both sides:
[tex]3x=177[/tex]
And divide both sides by three. Hence:
[tex]x=59[/tex]
Therefore, our sequence is 59, 61, and 63.
The third number in this sequence is 63.
Note: If we do not get an odd number or if we get a fraction for x, we can conclude that no three consecutive integers sum to 183.
Suppose that you are headed toward a plateau 37 meters high. If the angle of elevation to the top of the plateau is , how far are you from the base of the plateau?
Answer:
21.36 meters
Step-by-step explanation:
Given
[tex]h = 37m[/tex]
[tex]\theta = 60^o[/tex]
Required
The distance from the base (b)
The question illustrates right-angled triangle (see attachment)
To solve for (b), we make use of tangent formula
[tex]\tan(60)=\frac{h}{b}[/tex]
Make b the subject
[tex]b =\frac{h}{\tan(60)}[/tex]
So:
[tex]b =\frac{37}{\tan(60)}[/tex]
[tex]b =\frac{37}{1.7321}[/tex]
[tex]b =21.36[/tex]
HELP PLEASE!!!!!!!!!!
Answer:
12
Step-by-step explanation:
Simplify the radical expression below square root of 5/64
A square root 5/8
B 5/64
C square root 5/64
D 5/8
Answer:
a
Step-by-step explanation:
square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8
would someone help me out with this question? I got it wrong the first time but I don't understand how.
Answers:
Choice 2) Angle ABC is bisected by ray BD.
Choice 3) BC = 1/2 AC
Choice 5) 2*(angle DBC) = angle ABC
================================================
Explanation:
Since B is the midpoint of AC, this means that AC is cut in half to form the smaller equal pieces AB and BC
We can then say
AB+BC = AC
BC+BC = AC
2BC = AC
BC = (1/2)*AC
which shows why choice 3 is one of the answers
----------------------
Angle ABD is shown to be 90 degrees. Let's say we didn't know angle DBC is also 90. Lets call it x
(angle ABD) + (angle DBC) = 180
90 + x = 180
x = 180 - 90
x = 90
So angle DBC is also 90.
We can see that the 180 degree angle (ABC) is cut in half into two smaller 90 degree angles (ABD and DBC). Therefore, angle ABC has been cut in half and that's why choice 2 is another answer.
------------------------
Using the angle addition postulate, we know that,
(angle ABD) + (angle DBC) = angle ABC
(angle DBC) + (angle DBC) = angle ABC
2*(angle DBC) = angle ABC
Showing why choice 5 is the third answer.
------------------------
Choice 1 isn't true since ray BD helps form angle DBC.
Choice 4 isn't true because there isn't a tickmark on segment BD to indicate it's the same length as BC.
Which choice is equivalent to √3 *√8*√5
A. 2√30
B. 4√30
C. 10√12
D. 24√5
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { A. \:2 \sqrt{30} }}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] = \sqrt{3} \times \sqrt{8} \times \sqrt{5} [/tex]
[tex] = \sqrt{3 \times 2 \times 2 \times 2 \times 5} [/tex]
[tex] = \sqrt{ ({2})^{2} \times 2 \times 3 \times 5} [/tex]
[tex] = 2 \sqrt{2 \times 3\times 5} [/tex]
[tex] = 2 \sqrt{30} [/tex]
Note:[tex] \sqrt{ ({a})^{2} } = a[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Answer:
A. 2√30
Step-by-step explanation:
[tex] \small \sf \: \sqrt{3} \times \sqrt{8} \times \sqrt{5} \\ [/tex]
split √8
[tex] \small \sf \leadsto \sqrt{3 × 2 × 2 × 2 × 5} [/tex]
[tex] \small \sf \leadsto \: 2 \sqrt{2 \times 3 \times 5} [/tex]
[tex] \small \sf \leadsto \: 2 \sqrt{30} [/tex]
True or false: If you are changing a larger unit into a smaller unit, like cm into mm, the decimal is moved to the right because you are multiplying by a power of ten
Answer:true
Step-by-step explanation:
i dont know
Using the quadratic formula, which of the following are the zeros of the quadratic equation below? y=x^2-x-5
Answer:
The roots(Zeros) are
x=2.7913 and -1.7913
A hotel manager believes that 23% of the hotel rooms are booked. If the manager is right, what is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
Answer:
0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A hotel manager believes that 23% of the hotel rooms are booked.
This means that [tex]p = 0.23[/tex]
Sample of 610 rooms
This means that [tex]n = 610[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.23[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{610}} = 0.017[/tex]
What is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%?
p-value of Z when X = 0.23 + 0.03 = 0.26 subtracted by the p-value of Z when X = 0.23 - 0.03 = 0.2. So
X = 0.26
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.26 - 0.23}{0.017}[/tex]
[tex]Z = 1.76[/tex]
[tex]Z = 1.76[/tex] has a p-value of 0.9608
X = 0.2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.2 - 0.23}{0.017}[/tex]
[tex]Z = -1.76[/tex]
[tex]Z = -1.76[/tex] has a p-value of 0.0392
0.9608 - 0.0392 = 0.9216
0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
3. Determine the Area and Perimeter of the
shape below.
13
5
12
Answer:
Perimeter: 30 Area: 30
Step-by-step explanation:
Perimeter of a triangle= Add all sides = 5+12+13 = 30
Area of a triangle= (B*H)/2 = (5*12)/2 = 60/2 = 30
Hope this helps! :)
You are on a 5.6-mile run and have already run 1.98 miles. How many more miles do you need to run?
Answer:
3.62 miles need to be run
